EXPERIMENTAL INVESTIGATION OF MIXING AND IGNITION OF ... · EXPERIMENTAL INVESTIGATION OF MIXING AND IGNITION OF TRANSVERSE JETS IN SUPERSONIC CROSSFLOWS a dissertation submitted

EXPERIMENTAL INVESTIGATION OF MIXING AND

IGNITION OF TRANSVERSE JETS IN SUPERSONIC

CROSSFLOWS

a dissertation

submitted to the department of mechanical engineering

and the committee on graduate studies

of stanford university

in partial fulfillment of the requirements

for the degree of

doctor of philosophy

Adela Ben-Yakar

December, 2000

c© Copyright 2001 by Adela Ben-Yakar

All Rights Reserved

ii

Abstract

Ignition, flame-holding, and mixing enhancement are fundamental aspects of su-

personic combustion and are critical to the development of hypersonic airbreathing

propulsion engines. High velocities associated with supersonic/hypersonic flight speeds

constrain the performance of propulsion systems because of the limited flow residence

time inside the combustor. A useful hypervelocity propulsion system therefore requires

enhanced mixing of fuel and air, injection with very low drag penalty, and effective

distribution of fuel over the burner cross-section. One of the simplest approaches is

the transverse injection of fuel from wall orifices. The interesting but rather compli-

cated flow-field dynamics of transverse jets injected into a supersonic crossflow has been

studied by many supersonic combustion researchers since 1960’s, but with limited free-

stream flow conditions. Most of the previous research was performed in conventional

wind tunnels by accelerating cold air into supersonic conditions, namely in low velocity

and low total enthalpy flow conditions. However, a real supersonic combustor environ-

ment at flight speeds beyond Mach 8 can only be simulated using impulse facilities due

to the required high total enthalpies. Among various impulse facilities, expansion tubes

are especially useful in providing high total enthalpy flows with the proper chemical

composition, namely the absence of dissociated species.

This research is focused on studying the near-field mixing and ignition properties of

transverse fuel jets injected into realistic supersonic combustor flows. We use advanced

flow visualization techniques, namely planar laser-induced fluorescence (PLIF) imag-

ing of the hydroxyl radical (OH) and ultra-fast-framing-rate schlieren imaging. While

schlieren indicates the location of shock waves, jet penetration and large scale flow

features, OH-PLIF is used to map the regions of ignition.

The first objective of the present work is to characterize the expansion tube facility

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for three operating points, simulating flight Mach 8, 10 and 13 total enthalpy conditions.

The ability of the expansion tube to provide a steady-flow test time of adequate duration

and a core flow of sufficient size for 2 mm diameter jet-in-crossflow studies is verified.

The second objective is to study the flow-field properties of hydrogen and ethylene

jets, owing to their relevance to supersonic combustion. Visual observations of image

data, supported by the results for the convection velocity and jet penetration, reveal

significant differences between the hydrogen and ethylene injection cases with similar

momentum flux ratio. Previously the momentum flux ratio was found to be the main

controlling parameter of the jet penetration but the results here demonstrate the exis-

tence of an additional mechanism which alters the vortical structure, the penetration

and the mixing properties of the jet shear layer. The thickness of the penetration band,

used as the representation of the jet-shear-layer thickness is considerable in the ethy-

lene injection case, due to the “tilting-stretching-tearing” mechanism and also due to

the larger growth rate of the jet shear layer. Furthermore autoignition of an ethylene

transverse jet is achieved at flight Mach 10 conditions despite the relatively long ig-

nition delay times of ethylene (hydrocarbons), a key limitation for hydrocarbon-fueled

scramjets. These results of higher penetration, larger jet shear layer growth rate and

autoignition capability indicate that hydrocarbons might be a useful fuel in scramjets

flying at Mach 10 conditions.

The third objective is to investigate the stability of the jet shear layer at various

speed ratios and density ratios via schlieren. The high shear stresses induced by the

large velocity difference across the jet shear layer have a large effect on the structure of

the layer. For the unstable case, we notice: 1) breakdown of Kelvin-Helmholtz structures

with the tilting-stretching-tearing mechanism; 2) increased growth rates with decreasing

values of jet-to-free-stream velocity ratio; 3) large intrusions of crossflow in between the

eddies, and 4) additional shock waves and distortion of the bow shock around the large

eddies. Stable layers show well-defined Kelvin-Helmholtz spanwise rollers. The results

plotted in a density-effective velocity ratio (s − λ) diagram demonstrate two separate

regions of “stable”and “unstable”jet shear layers with a separation line at a critical

“effective velocity ratio”.

The final objective is to study the ignition and flame-holding capabilities of a hy-

drogen transverse jet injected into flight Mach 8, 10 and 13 total enthalpy conditions.

The results demonstrate self-ignition in the near-field of the hydrogen jet for the high

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total enthalpy conditions (flight Mach 10 and 13). OH-fluorescence is detected along

the jet shear layer periphery in a continuous and very thin filament. For the low total

enthalpy Mach 8 condition, however, the ignition is limited to a small region behind the

bow shock and no OH fluorescence can be observed farther downstream.

It is evident from the results that improved injection schemes for better flame-holding

would be required for practical applications in scramjet engines, especially in the flight

Mach 8 range. During the last few years, cavities have gained the attention of the

scramjet community as a promising flame-holding device, owing to results obtained in

flight tests and to feasibility demonstrations in laboratory scale supersonic combustors.

In this thesis, we summarize the flowfield characteristics of cavities and research efforts

related to cavities employed in low- and high-speed flows. Open questions impacting

the effectiveness of the cavities as flame-holders in supersonic combustors are discussed.

Preliminary studies on cavities with upstream injection are presented indicating self-

ignition inside and around the cavity.

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Contents

Abstract iii

1 Introduction 1

1.1 Background and Motivation . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1.1 Typical Scramjet Burner Entry Conditions . . . . . . . . . . . . 1

1.1.2 Flow-Field Features of Jets in Supersonic Crossflows . . . . . . . 4

1.1.3 Ignition and Flame-Holding Strategies in Supersonic Combustion 8

1.2 Thesis Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2 Experimental Aspects 14

2.1 Critical Parameters in Supersonic Combustion Simulation . . . . . . . . 14

2.2 Experimental Facility . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.2.1 Expansion Tube . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.2.2 Injection System and its Calibration . . . . . . . . . . . . . . . . 20

2.2.3 Cavity/Injection Plate . . . . . . . . . . . . . . . . . . . . . . . . 23

2.3 Test Flow Characterization in the Flight Mach 8 - 13 Range . . . . . . . 23

2.3.1 Flow Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.3.2 Measurement of Flow Properties . . . . . . . . . . . . . . . . . . 27

2.3.3 Boundary Layer Effects on Test Time . . . . . . . . . . . . . . . 32

2.3.4 Core-Flow Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

2.3.5 Flow Establishment Time . . . . . . . . . . . . . . . . . . . . . . 37

2.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3 Flow Visualization Techniques 41

3.1 Ultra-Fast Framing Rate Schlieren . . . . . . . . . . . . . . . . . . . . . 41

vi

3.1.1 Previous and Current High Speed Imaging Efforts . . . . . . . . 43

3.1.2 High-Speed Schlieren Imaging Components . . . . . . . . . . . . 45

3.1.3 Timing and Synchronization . . . . . . . . . . . . . . . . . . . . 47

3.1.4 Resolution Considerations . . . . . . . . . . . . . . . . . . . . . . 49

3.1.5 Image Processing and Analysis . . . . . . . . . . . . . . . . . . . 52

3.2 OH-PLIF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

3.2.1 Excitation and Detection Strategy . . . . . . . . . . . . . . . . . 54

3.2.2 OH-PLIF Laser Source and Tuning . . . . . . . . . . . . . . . . . 54

3.2.3 OH-PLIF Imaging System and Its Spatial Resolution . . . . . . . 55

3.2.4 Interpretation of OH-PLIF . . . . . . . . . . . . . . . . . . . . . 56

3.3 Simultaneous Schlieren and OH-PLIF . . . . . . . . . . . . . . . . . . . 56

4 Time Evolution and Mixing Characteristics of Hydrogen and Ethylene

Transverse Jets 59

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

4.2 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

4.2.1 General Flow-Field Features . . . . . . . . . . . . . . . . . . . . 61

4.2.2 Large Scale Coherent Structures . . . . . . . . . . . . . . . . . . 64

4.2.3 Convection Characteristics . . . . . . . . . . . . . . . . . . . . . 74

4.2.4 Penetration and Shear Layer Properties . . . . . . . . . . . . . . 81

4.2.5 OH-PLIF Results . . . . . . . . . . . . . . . . . . . . . . . . . . 84

4.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

5 The Effect of Velocity and Density Ratio on Transverse Jets 88

5.1 Effect of Jet Molecular Weight . . . . . . . . . . . . . . . . . . . . . . . 89

5.1.1 Flow Visualization Results . . . . . . . . . . . . . . . . . . . . . 89

5.1.2 Penetration and Shear Layer Thickness . . . . . . . . . . . . . . 90

5.1.3 Convection Characteristics . . . . . . . . . . . . . . . . . . . . . 95

5.1.4 Characteristic Large Eddy Frequencies (Possible Transverse Jet

Modes) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

5.1.5 Jet Compressibility Analysis . . . . . . . . . . . . . . . . . . . . 100

5.2 Effect of Density and Velocity Ratios . . . . . . . . . . . . . . . . . . . 104

5.2.1 Flow Visualization Results . . . . . . . . . . . . . . . . . . . . . 104

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5.2.2 Definition of an “Effective Velocity Ratio, λ” . . . . . . . . . . . 106

5.2.3 Discussion on the Effect of the Curvature - Centrifugal Instability

Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

6 Autoignition and Flame-Holding Capability of a Hydrogen Transverse

Jet 114

6.1 Ignition and Flame-Holding Considerations . . . . . . . . . . . . . . . . 114

6.2 Ignition and Flame-Holding Results . . . . . . . . . . . . . . . . . . . . 117

6.2.1 Simultaneous OH-PLIF/Schlieren Results . . . . . . . . . . . . . 117

6.2.2 Top View OH-PLIF Images . . . . . . . . . . . . . . . . . . . . . 117

6.2.3 Comparison of Ignition in Flight Mach 8-13 Total Enthalpy Range 120

6.3 Discussion of the Ignition Process . . . . . . . . . . . . . . . . . . . . . . 123

6.3.1 Ignition Characteristics of Hydrogen . . . . . . . . . . . . . . . . 123

6.3.2 Ignition in Supersonic Combustors . . . . . . . . . . . . . . . . . 126

6.3.3 Ignition of a Hydrogen Transverse Jet . . . . . . . . . . . . . . . 127

6.3.4 Ignition of Ethylene Transverse Jet . . . . . . . . . . . . . . . . . 128

7 Cavity Flame-Holders 132

7.1 Review of Previous Research . . . . . . . . . . . . . . . . . . . . . . . . 132

7.1.1 Cavity Flow-Field Characteristics . . . . . . . . . . . . . . . . . . 132

7.1.2 Cavity in Reacting Flows . . . . . . . . . . . . . . . . . . . . . . 141

7.1.3 Outstanding Questions . . . . . . . . . . . . . . . . . . . . . . . . 148

7.2 Preliminary Cavity Results . . . . . . . . . . . . . . . . . . . . . . . . . 151

7.2.1 Visual Observation of Cavities Using Ultra-Fast Schlieren . . . . 153

7.2.2 Preliminary Ignition Results of Injection/Cavity Schemes . . . . 157

8 Concluding Remarks 161

8.1 Summary of Major Results and Conclusions . . . . . . . . . . . . . . . . 161

8.1.1 Experimental Aspects . . . . . . . . . . . . . . . . . . . . . . . . 161

8.1.2 Flow Visualization Techniques . . . . . . . . . . . . . . . . . . . 163

8.1.3 Characteristics of Hydrogen and Ethylene Transverse Jets . . . . 165

8.1.4 Density and Velocity Ratio Effects . . . . . . . . . . . . . . . . . 166

8.1.5 Ignition and Flame-Holding Capability of a Hydrogen Transverse

Jet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167

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8.1.6 Cavity Flame-Holders . . . . . . . . . . . . . . . . . . . . . . . . 167

8.2 Recommendation For Future Work . . . . . . . . . . . . . . . . . . . . . 169

A Expansion Tube Equations 175

B Maps of Estimated Expansion Tube Test Conditions 178

Bibliography 184

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List of Tables

1.1 Advantages and disadvantages of expansion tubes relative to shock tun-

nels for hypervelocity combustion simulations. . . . . . . . . . . . . . . . 5

2.1 Test gas (free-stream) flow properties simulating the burner entry condi-

tions of three flight Mach numbers. The corresponding values are from

Fig. 1.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.2 Summary of measured, ideal (inviscid 1-D) and predicted (based on

Mirels solution) properties of test gas for Mach 10 and 13 flow condi-

tions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

4.1 Jet exit flow properties. . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

5.1 The general flow exit properties of gaseous jets with different molecular

weights. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

5.2 The specific flow exit properties of gaseous jets used in the study of the

jet molecular weight effect. The free-stream used in these experiments

simulates the flight Mach 10 flow condition. . . . . . . . . . . . . . . . . 90

5.3 Summary of the different conditions used in the study of jet instability

analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

7.1 Summary of cavity oscillation frequencies, fm, for different cavity length

to depth ratios, L/D. The table includes the expected values based on

Rossiter’s formula and the ones measured in our experiments. . . . . . . 153

8.1 Recommended free-stream flow conditions for further ignition studies. . 170

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List of Figures

1.1 Typical scramjet burner entry conditions as a function of flight Mach

number, calculated assuming adiabatic compression. a)The burner en-

try Mach number, M3, for different temperature ratios, T3/T0. b) The

burner entry pressure, p3, and the flight trajectories of constant dynamic

pressure, q0, of 50 and 100 kPa. In our experiments, total enthalpy flows

(Mach number, M3, and static temperature, T3) simulating three nominal

flight conditions (Mach 8, 10 and 13) were generated. . . . . . . . . . . . 2

1.2 Schematic of an underexpanded transverse injection into a supersonic

cross-flow, (a) instantaneous side view at the center-line axis of the jet;

(b) 3-D perspective of the averaged features of the flow-field (Gruber et

al. 1995). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.3 Flow-field schematics of traditional injection/flame-holding schemes for

supersonic combustors. a) underexpanded fuel injection normal to the

crossflow, b) fuel injection at angle, c) injection behind a sudden expan-

sion produced by a step. . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.1 Expansion tube facility (12 m in length and 89 mm inner diameter) and

imaging system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.2 Expansion tube distance-time (x-t) diagram calculated for flight Mach

13 condition. Method of characteristics was used to solve the flow gasdy-

namics properties assuming one-dimensional inviscid theory. Test time

is defined as the time that the test gas has uniform flow quantities and

determined by the time arrival of the contact surface to the tube exit,

and that of the first subsequent rarefaction wave (reflected rarefaction

head in our case of high total enthalpy simulations). . . . . . . . . . . . 19

xi

2.3 Schematic of the test section (27 x 27 cm cross section) where a rake of 4

pitot probes, instrumented with pressure transducers, was located 2.5 cm

downstream of the tube exit. The flow history during the expansion tube

operation was detected via pitot pressure information. Note that the

inner diameter of the tube is 8.9 cm. . . . . . . . . . . . . . . . . . . . . 21

2.4 Optical set-up to measure the test gas velocity, assumed to be equal to

the CS - contact surface velocity. IR emission from 5% CO2 seeded in the

test gas nitrogen is collected by an InSb IR detector at the viewing port

located at 101.6 cm from the end of the tube. The test gas velocity can

then be calculated by considering its time of arrival at the viewing port

and at the pitot rake. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.5 Schematic of a) Injection system, b) cavity/injection plate system. . . . . 23

2.6 Schlieren visualization of an underexpanded gaseous injection into still

air. (a)-(c) hydrogen (d)-(e) ethylene jets. The exposure time of the

images was 3musec. Mach disk height, y1, was measured for different

pressure ratios, Pj/Peb, to calibrate the injection system. . . . . . . . . . 24

2.7 Maps of estimated test gas (nitrogen) conditions (state 5) at the exit of an

expansion tube: a) pressure and temperature, b) total enthalpy and ve-

locity of the test gas are plotted for different initial driven and expansion

section pressures. Calculations are performed using the inviscid 1D equa-

tions for a given driver pressure of P4 = 600 psig (helium). Note that the

effective filling pressure of the driver section is taken as P4,eff = 686 psig,

as its inner diameter (10.2 cm) is larger than that of the driven and ex-

pansion sections (8.9 cm). This area difference is accounted for in the

curves presented above. . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

2.8 Example of IR emission, pitot pressure, wall pressure records and the

Mach number variation based on the pitot-to-static pressure ratios, as

a function of time for the Mach 10 flow condition. t = 0 represents

incident shock arrival at the pitot probe, placed 2.5 cm downstream of

the tube exit, while the wall pressure transducer and IR detector are

positioned 40.6 cm and 101.6 cm upstream of the tube exit, respectively

(see Fig. 2.4). Note that the time scale of the static pressure trace is

shifted by 235µs to match the shock arrival at the pitot probe. . . . . . 29

xii

2.9 Example of IR emission, pitot pressure and wall pressure traces as a

function of time for the Mach 13 flow condition. . . . . . . . . . . . . . . 31

2.10 Example of IR emission, pitot pressure and wall pressure traces as a

function of time for the Mach 8 flow condition. . . . . . . . . . . . . . . 32

2.11 Comparison of the measured contact-surface velocity (test gas velocity)

with the shock-induced gas velocity estimated using the measured shock

speeds in the expansion section. . . . . . . . . . . . . . . . . . . . . . . . 33

2.12 X-t diagrams for the expansion section only. 1-D inviscid calculations

are plotted in straight lines and results applying Mirels’ model to include

the boundary layer effects are plotted in dashed lines. One can see the

improved test time as a result of the contact surface (CS) acceleration

due to the developing boundary layer behind the incident shock in the

low pressure expansion section helium flow. The incident shock velocity

was measured and assumed to be constant along the expansion section. 34

2.13 Useful core-flow size in flight Mach 13, 10 and 8 conditions, (a), (b) and

(c), respectively, determined by measuring the radial variation of pitot

pressure at different distances from the tube exit. . . . . . . . . . . . . . 38

3.1 Schlieren imaging set-up. . . . . . . . . . . . . . . . . . . . . . . . . . . 46

3.2 Examples of schlieren images of jet issuing into quiescent air as obtained

for different positions of the knife edge (razor blade) at the focal point.

We use the set-up demonstrated in (d) where the knife edge cuts the

focused light at an angle to enhance both the vertical and the horizontal

density gradient effects. . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

3.3 Timing diagram of the high-speed rate imaging system and its synchro-

nization with the expansion tube test flow time. . . . . . . . . . . . . . . 48

3.4 Examples of schlieren images with different integration/exposure times:

a) 100 ns exposure time, resolving the instantaneous features of the flow-

field, b) 200 ns exposure time, resulting in blurring of the image, c) 3µs

exposure time, averaging the general features while enhancing the weak

shocks such as upstream separation shock wave and downstream recom-

pression wave. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

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3.5 Timing diagram of the high-speed rate imaging system and its synchro-

nization with the expansion tube test flow time. . . . . . . . . . . . . . . 52

3.6 a)Triggering diagram and timing connections of the imaging, the injec-

tion and the data acquisition systems. b) Timing diagram of simultane-

ous OH-PLIF and schlieren and their synchronization with the expansion

tube test flow time. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

4.1 Examples of hydrogen (a) and ethylene (b) injections into a supersonic

crossflow (nitrogen). Exposure time of each image was 200 ns. The x-axis

is normalized by the jet diameter d. . . . . . . . . . . . . . . . . . . . . 62

4.2 An example of schlieren image with 3µs exposure time for hydrogen

injection case. While the unsteady features (coherent structures) are

averaged to zero, some of the weak shocks such as upstream separation

shock wave and downstream recompression wave are emphasized. . . . . 63

4.3 (a)Bow shock position and its angle at the center-line of the jet as mea-

sured from the long exposure schlieren image shown in Fig. 4.2. (b) The

free-stream velocity behind the bow shock and the flow turning angle

based on the measured bow shock shape. For the calculations a calori-

cally perfect gas has been assumed. . . . . . . . . . . . . . . . . . . . . . 65

4.4 An example of 8 consecutive schlieren images of underexpanded hydrogen

injection (d=2mm) into a supersonic crossflow (nitrogen) obtained by

high-speed-framing camera. Exposure time of each image is 100 ns and

interframing time is 1µs. Free-stream conditions are: U∞=2360m/s,

M∞=3.38, T∞=1290 K, p∞=32.4 kPa; and jet-to-free-stream momentum

ratio is: J=1.4±0.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

4.5 The second example of 4 of 8 consecutive schlieren images of hydrogen

injection into flight Mach 10 condition. Exposure time of each image is

100 ns and interframing time is 1µs. . . . . . . . . . . . . . . . . . . . . 70

4.6 Time evolution of an ethylene jet in a supersonic crossflow (nitrogen)

as observed from 8 consecutive schlieren images. Exposure time of each

image is 100 ns and interframing time is 1.5µs. Free-stream conditions

are: U∞=2360 m/s, M∞=3.38, T∞=1290K, p∞=32.4 kPa; and jet-to-

free-stream momentum ratio is: J=1.4±0.1. . . . . . . . . . . . . . . . . 71

xiv

4.7 The second example of an ethylene transverse jet flow-field in a supersonic

crossflow as observed from 8 time correlated schlieren images. Exposure

time of each image is 200 ns and interframing time is 1.2µs. . . . . . . . 72

4.8 Schematic of the three-dimensional shape (Ω shape) of the unsteady vor-

tical structures formed intermittently (Brizzi et al. 1995). . . . . . . . . 73

4.9 Development of a large-scale ethylene structure (eddy number “-1” in

Fig. 4.7) as it goes through the tilting and stretching processes. Four

different parts of the eddy structure were independently tracked in the

duration of the 8.6µs flow visualization time. . . . . . . . . . . . . . . . 74

4.10 Space-time trajectories of large-scale eddies present in the hydrogen jet

shear layer. The center of the eddies are tracked from the 8 successive

schlieren images shown (a) in Fig. 4.4 and (b) in Fig. 4.5. . . . . . . . . . 75

4.11 Space-time trajectories of ethylene large scale eddies as tracked from 8

time-correlated schlieren images: (a) x-t diagram of the example shown

in Fig. 4.6, (b) x-t diagram of the example shown in Fig. 4.7. . . . . . . 76

4.12 Convection features of coherent large scale structures present in the hy-

drogen jet/free-stream shear layer. The data were subtracted by analyz-

ing the eddy displacement in 8 consecutive schlieren images of 2 exper-

iments (images shown in Figs. 4.4 and 4.5). (a) the convection velocity

of eddies in streamwise and transverse directions, Uc,x and Uc,y, respec-

tively; (b) the convection angle of eddies. . . . . . . . . . . . . . . . . . . 77

4.13 Convection features of eddies present in the ethylene jet/free-stream shear

layer. The data were subtracted by analyzing the eddy displacement in 8

consecutive schlieren images of 2 experiments (images shown in Figs. 4.6

and 4.7). (a) the convection velocity of eddies in streamwise and trans-

verse directions, Uc,x and Uc,y, respectively; (b) the convection angle of

eddies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

4.14 Measured convection velocity of large eddy structures in the hydrogen and

ethylene jet shear layers. The results are compared with the estimated

values of the free-stream velocity immediately behind the bow shock. . . 79

4.15 Schematic showing the low- and high-speed regions of the bow shock-

induced free-stream velocity around the large-scale ethylene eddies. . . . 81

xv

4.16 Transverse penetration data of (a) hydrogen jet and (b) ethylene jet. The

data points were obtained by manually tracking the visually observable

outer edge of the jet from 8 consecutive schlieren images for J = 1.4±0.1.

Both of the figures include analysis of 2 experiments namely 16 images.

For comparison, also shown in the figures is the penetration correlation

given by other studies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

4.17 OH-PLIF results mapping the ignition regions at the jet center-line of:

a) hydrogen injection into air, b) ethylene injection into air, c) ethylene

injection into pure oxygen. . . . . . . . . . . . . . . . . . . . . . . . . . . 86

5.1 Examples of instantaneous schlieren images of jets with different molec-

ular weights. Free-stream conditions are: U∞=2360m/s, M∞=3.38,

T∞=1290K, p∞=32.4 kPa. . . . . . . . . . . . . . . . . . . . . . . . . . 91

5.2 Jet transverse penetration along the axial distance, x/d. Data for four

gases with different molecular weights are presented: a)Mw = 2, J =

1.84, b) Mw = 4, J = 1.72, c) Mw = 8, J = 1.85, d) Mw = 16, J = 1.67.

For comparison, empirical correlations suggested by Gruber et al. (1995)

and Rothstein and Wantuck (1992) are also included for J = 1.75. . . . 93

5.3 Convection velocity of large scale structures in the streamwise (Mc,x)

and transverse (Mc,y) directions as a function of axial distance x/d. The

results for each case (for each molecular weight of jet) are obtained from

4-5 experiments each including 8 consecutive schlieren images. . . . . . . 96

5.4 Formation frequency of the large scale structures and the corresponding

“preferred mode Strouhal number”, Std = fjd/Uj , as a function of the jet

exit velocity. The data were collected from the time evolution observation

of the jet from 8 consecutive schlieren images. Each data point was

obtained by averaging 5-10 experiments with the error bars representing

the deviation from the mean value. . . . . . . . . . . . . . . . . . . . . . 98

5.5 Formation frequency of the large scale structures and the “initial vortex

shedding Strouhal number”, Stθj = fθjθj/Uj , as a function of the jet

Reynolds number. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

5.6 Flow-field schematics used in the jet compressibility analysis. Letters A,

B and C indicate the zones of the jet shear layer. . . . . . . . . . . . . . 101

xvi

5.7 Estimated convective Mach number in zone “A”, MAc , (refer to the

schematic in Fig. 5.6) and the measured visible jet shear layer thickness,

δvis, at x/d≈22 as obtained from penetration width measurements. . . . 102

5.8 Estimated velocity fields for the jet and the free-stream in zones “B” and

“C”. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

5.9 Schlieren images at selected conditions given in Table 5.3. . . . . . . . . 107



5.12 Velocity vector field (U∞, Uj) for a skewed mixing layer and the “effective

velocity ratio”, λ., described in the total velocity vector direction. . . . . 110

5.13 Jet-to-free-stream density ratio vs. velocity ratio. The number near the

data points corresponds to the experimental conditions summarized in

Table 5.3. “Unstable” flow jet is defined when the large structures lose

coherence downstream of the injection port and significant distortions in

the bow shock shape can be observed. . . . . . . . . . . . . . . . . . . . 111

5.14 Jet-to-free-stream density ratio vs. the “effective velocity ratio”, λ. The

number near the data points corresponds to the experimental conditions

summarized in Table 5.3. . . . . . . . . . . . . . . . . . . . . . . . . . . 111

5.15 Schematics illustrating the stability regions based on a) Rayleigh criterion

for centrifugal forces in the curved mixing layers as given in Eq. 5.15 where

cons. = 3 + 2 δvishmax

and b) current experimental results. . . . . . . . . . . 112

6.1 Simultaneous OH-PLIF and schlieren images visualizing hydrogen injec-

tion into supersonic crossflow. Free-stream conditions are M = 3.57,

T = 1300K, P = 0.32 atm, V = 2500m/s. The jet-to-freestream mo-

mentum flux ratio is J = 1.4. a) Schlieren image, b) OH-PLIF image

demonstrating the ignition and combustion regions of jet-in-crossflow at

high enthalpy condition, c) Overlaid OH-PLIF and schlieren images. . . 118

6.2 Instantaneous top-view OH-PLIF images obtained at different height

above the injection plate. Free-stream conditions are M=3.57, T=1300K,

P=0.32atm, V=2500m/s. The jet-to-freestream momentum flux ratio is

J=1.4. a) y/d=3, b) y/d=2.5, c) y/d=2, d) y/d=1 above the injection plate.119

xvii

6.3 Instantaneous OH-PLIF acquired at center-line axis of the hydrogen jet

injected into flight Mach 10 and 13 conditions. The images are obtained

by combination of 2 different instantaneous images: near the exit of the

jet (−5 < x/d < 1) and downstream of the jet (1 < x/d < 10). . . . . . . 121

6.4 Two instantaneous OH-PLIF images acquired at center-line axis of the

hydrogen jet injected into flight Mach 8 conditions. . . . . . . . . . . . . 122

6.5 Explosion limits of a stoichiometric hydrogen-oxygen mixture (after Sung

et al., 1999). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

6.6 Variation of ignition delay times τign of a stoichiometric mixture of H2

and air with temperature and pressure. Calculations are perfomed using

Chemkin and the GRI mechanism. a) τign vs. T , b) pτign vs. T . . . . . 125

6.7 Variation of ignition time with fuel-air equivalence ratio, φ, for cold H2

(Tjet = 300 K) injected into hot air. The values of the ignition delay time

are calculated for different air temperatures, Tair. . . . . . . . . . . . . . 126

6.8 The free-stream temperature and pressure (T2 and P2) behind the bow

shock, measured from schlieren images as discussed in Section 4.2.1 (see

Fig. 4.3). Ignition delay times are calculated for several conditions of air

assuming φ = 0.2. The free-stream flow properties simulate the flight

Mach 10 conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

6.9 Comparison of ignition delay of a stoichiometric mixture of C2H4 (ethy-

lene) and air/oxygen at 1 atm with a stoichiometric mixture of H2 and

air. Two different reaction mechanisms are used to calculate the ignition

delay times of C2H4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

6.10 a)Variation of ignition delay of a stoichiometric mixture of C2H4 (ethy-

lene) and air/oxygen at various pressures. . . . . . . . . . . . . . . . . . 130

xviii

7.1 Flow-field schematics of cavities with different length to depth ratios,

L/D, in a supersonic flow. a) Open cavity flow for L/D < 7 − 10;

shear layer reattaches to the back face while spanning over the cavity.

Small aspect ratio cavities (L/D < 2 − 3) are controlled by transverse

oscillation mechanism while in larger aspect ratio cavities longitudinal

oscillation becomes the dominant mechanism. b)Closed cavity flow for

L/D > 10 − 13; shear layer reattaches to the lower wall. The pressure

increase in the back wall vicinity and the pressure decrease in the front

wall results in large drag losses. . . . . . . . . . . . . . . . . . . . . . . . 134

7.2 Typical longitudinal cavity oscillations are caused by the impingement

of the free shear layer on the rear wall which generates travelling shocks

inside the cavity. The shear layer spanning the cavity becomes unsteady

as a result of these acoustic waves deflecting the shear layer up and down,

and/or by the shock induced vortices generated at the front wall leading

edge of the cavity. As a result unsteady waves emanate from the cavity. 135

7.3 Different concepts can be employed to suppress the cavity oscillations:

a)Cavities with an angled back wall suppress the unsteady nature of the

free shear layer by eliminating the generation of the travelling shocks

inside the cavity due to the free-shear-layer impingement. b) In addition,

small disturbances produced by spoilers or by the secondary jet injection

upstream of the cavity can enhance the free-shear-layer growth rate. The

thickening of the cavity shear layer alters its instability characteristics,

such that its preferred roll-up frequency is shifted outside of the natural

frequency of the cavity, and as a result the oscillations are attenuated. . 137

xix

7.4 Instantaneous schlieren images with 200 ns of exposure time demonstrat-

ing the effect of the back wall angle on the flowfield structure of a cav-

ity exposed to a supersonic flow. The free-stream was generated in an

expansion tube to simulate Mach 10 total enthalpy conditions at the su-

personic combustor entry: M∞ = 3.4, U∞ = 2360m/s, T∞ = 1290K,

p∞ = 32 kPa. The boundary layer thickness at the trailing edge of the

cavity is approximately 1mm. a) Cavity with L/D = 5 shows the un-

steady nature of the shear layer at the reattachment with the trailing

edge of the back wall. b)Cavity with slanted back wall (20o) stabilizes

the shear layer reattachment process. . . . . . . . . . . . . . . . . . . . . 138

7.5 Effect of length-to-depth ratio, L/D on a) magnitude (root-mean-square)

of pressure fluctuations on the bottom of the cavity (at x/D = 0.33),

b) drag of the cavity at Mach 1.5 and 2.5 flows. The values were adapted

from Zhang and Edwards (1990). . . . . . . . . . . . . . . . . . . . . . . 139

7.6 Cavity-actuated supersonic mixing enhancement concepts: (a) Sato et al.

(1999), studied the influence of acoustic waves, emitted from a cavity and

impinging on the initial mixing layer. (b)Yu and Schadow (1994) used

the same concept to enhance the mixing of supersonic reacting jets. . . . 143

7.7 Axisymmetric combustor of the Scramjet engine which was flight-tested

by Russian-CIAM/NASA joint program (1998). In this engine two cav-

ities with angled-rear wall were used for flame-holding purposes. The

dimensions are in mm (McClinton et al. 1996). . . . . . . . . . . . . . . 146

7.8 Position of pressure transducers located at the bottom of the cavity to

measure the history of the flow oscillations inside the cavity. Pressure

transducer located farther downstream at x/D = 1.5 provided a more

accurate oscillation frequency measurements. . . . . . . . . . . . . . . . 151

7.9 Examples of cavity pressure traces in arbitrary units: a)L/D = 3, b)L/D =

5, c) L/D = 5 with upstream hydrogen injection, d)L/D = 7. t = 0

represents incident shock arrival at the cavity. The free-stream (N2) con-

ditions represent Mach 10 total enthalpy at the supersonic combustor

entry: M∞ = 3.4, U∞ = 2360 m/s, T∞ = 1290K, p∞ = 32 kPa. . . . . . 152

xx

7.10 Schlieren images demonstrating the differences in the flow-field structure

of cavities with different length-to-depth ratios and back wall angle. The

depth of the cavities is constant and equal to D = 3mm. The free-

stream was generated to simulate Mach 10 total enthalpy conditions at

the supersonic combustor entry: M∞ = 3.4, U∞ = 2360 m/s, T∞ =

1290K, p∞ = 32 kPa. The boundary layer thickness at the trailing edge

of the cavity is approximately 1mm. . . . . . . . . . . . . . . . . . . . . 155

7.11 Schlieren images demonstrating jet interaction with different cavities.

The hydrogen jet is injected into a non-reacting free-stream 3 mm up-

stream of the cavity from a d = 1mm orifice. The injection is performed

at angle of 30o to the plate. The free-stream, N2, represents the flight

Mach 10 burner entry conditions. . . . . . . . . . . . . . . . . . . . . . . 156

7.12 Instantaneous OH-PLIF images demonstrating the ignition regions of a

hydrogen jet interacting with a L/D = 3 cavity. The images are obtained

from 5 single shots at the same conditions. Hydrogen is injected 3mm

upstream the cavity leading edge at an angle of 30o. The free-stream

(air) properties represent the flight Mach 10 burner entry conditions:

M∞ = 3.4, U∞ = 2360 m/s, T∞ = 1290 K, p∞ = 32 kPa. Note that

a schlieren image is also included to indicate the flow-field properties

around the cavity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

7.13 Instantaneous OH-PLIF images demonstrating the ignition regions of a

hydrogen jet interacting with a cavity with L/D = 3 and 30o back wall.

The images are obtained from 5 single shots at the same conditions.

Hydrogen is injected 3 mm upstream the cavity leading edge at an angle

of 30o. The free-stream (air) properties represent the flight Mach 10

burner entry conditions: M∞ = 3.4, U∞ = 2360 m/s, T∞ = 1290 K,

p∞ = 32 kPa. Note that a schlieren image is also included to indicate the

flow-field properties around the cavity. . . . . . . . . . . . . . . . . . . . 160

8.1 Flow-field schematics demonstrating different concepts of angled jet in-

jection combined with cavity flame-holder. a) upstream injection, b) base

injection , c) cavity injection. . . . . . . . . . . . . . . . . . . . . . . . . 171

8.2 Flow-field schematic of a shock-wave/jet interaction. . . . . . . . . . . . 172

xxi

8.3 Schematic of the 25o wedge to generate a shock wave above the injection

plate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172

8.4 (a)An oblique shock wave impinging the hydrogen jet as visualized us-

ing schlieren imaging. The shock was produced by a 25 o angled wedge

mounted above the injection plate. Flight Mach 13 free-stream condi-

tion. (b)Combined OH-PLIF and schlieren images visualizing the effect

of shock/jet interaction on OH number density. . . . . . . . . . . . . . . 174

B.1 Maps of estimated test gas (nitrogen) conditions at the exit of an expan-

sion tube: a) pressure and temperature, b) total enthalpy and velocity of

the test gas are plotted for different initial driven and expansion section

pressures. Calculations are performed using the inviscid 1D equations for

a given driver pressure of P4 = 300 psig (helium). . . . . . . . . . . . . . 179

B.2 Maps of estimated test gas (Argon) conditions at the exit of an expansion

tube: a) pressure and temperature, b) total enthalpy, velocity and Mach

number of the test gas are plotted for different initial driven and expan-

sion section pressures. Calculations are performed using the inviscid 1D

equations for a given driver pressure of P4 = 300 psig (helium). . . . . . 180

B.3 Maps of estimated test gas (Argon) conditions at the exit of an expansion

tube: a) pressure and temperature, b) total enthalpy, velocity and Mach

number of the test gas are plotted for different initial driven and expan-

sion section pressures. Calculations are performed using the inviscid 1D

equations for a given driver pressure of P4 = 600 psig (helium). . . . . . 181

B.4 Maps of estimated test gas (Helium) conditions at the exit of an expan-

sion tube: a) pressure and temperature, b) total enthalpy, velocity and

Mach number of the test gas are plotted for different initial driven and

expansion section pressures. Calculations are performed using the invis-

cid 1D equations for a given driver pressure of P4 = 300 psig (helium). . 182

B.5 Maps of estimated test gas (Helium) conditions at the exit of an expan-

sion tube: a) pressure and temperature, b) total enthalpy, velocity and

Mach number of the test gas are plotted for different initial driven and

expansion section pressures. Calculations are performed using the invis-

cid 1D equations for a given driver pressure of P4 = 600 psig (helium). . 183

xxii

Chapter 1

Introduction

1.1 Background and Motivation

The success of future hypersonic airbreathing propulsion systems will be largely

dependent on efficient injection, mixing and combustion processes inside the super-

sonic / hypersonic combustion chamber. At flight speeds beyond Mach 6, air entering

the combustor must be supersonic to avoid excessive dissociation of both nitrogen and

oxygen gases. Consequently, the time available for fuel injection, fuel-air mixing and

combustion is very short, of the order of 1 msec, which results in troublesome constraints

on the combustion problem (Ferri 1973; Kumar et al. 1989).

1.1.1 Typical Scramjet Burner Entry Conditions

The combustor entry conditions (Mach number, static temperature and pressure)

of hypersonic airbreathing propulsion systems depend on the flight conditions of the

vehicle. In order to keep the density inside the combustor high for efficient combustion

and the lift at reasonably high values, the flight Mach number, M0, should increase as

the altitude of the vehicle increases.

Residence time is another issue that has to be considered for efficient performance

of a high-speed propulsion system. The air must be compressed in the diffuser in

order to reduce velocities and increase the flow residence time and therefore to allow

a combustor of reasonable length. On the other hand, the reduced velocities at the

combustor entry are restricted by the maximum allowable compression temperature (in

1

CHAPTER 1. INTRODUCTION 2

5 10 15 20 250

1

2

3

4

5

6

7

8

9

10

11

3

2

1

87

T3/T

0=6

Current experiments

1. Mach 8 (3 MJ/kg)

2. Mach 10 (4 MJ/kg)

3. Mach 13 (6 MJ/kg)

M3=1

Burn

er

Entr

yM

ach

Num

ber,

M3

Flight Mach Number, M0

5 10 15 20 25

0

1

2

3

4

5

6

7

8

9

10q

0=50 kPa

q0=100 kPa

p3=1 atm

Burn

er

Entr

yP

ressure

,p

3,atm

Flight Mach Number, M0

20

25

30

35

40

45

Heig

ht,

km

(a) (b)

FIGURE 1.1 Typical scramjet burner entry conditions as a function of flight Mach number, calculated assum-ing adiabatic compression. a) The burner entry Mach number, M3, for different temperatureratios, T3/T0. b) The burner entry pressure, p3, and the flight trajectories of constant dynamicpressure, q0, of 50 and 100 kPa. In our experiments, total enthalpy flows (Mach number, M3,and static temperature, T3) simulating three nominal flight conditions (Mach 8, 10 and 13)were generated.

the range of 1440-1670K (Heiser and Pratt 1994)) to avoid excessive dissociation in

the exhaust flow. These constraints determine the expected values of combustor entry

Mach number and temperature, M3 and T3, respectively.

Considering the above issues, the expected values of flow conditions at the combustor

entrance of an airbreathing propulsion system were estimated and plotted in Fig. 1.1

as a function of flight Mach number, M0. Calculations were performed for different

burner entry temperature to atmosphere temperature ratios (T3/T0) assuming adiabatic

compression (constant total enthalpy) throughout the diffuser according to Eq. 1.1:

T3

T0=

1 + γ0−12 M2

0

1 + γ3−12 M2

0

(1.1)

As shown in Fig. 1.1a, for hypersonic flights beyond Mach 6, (M0 > 6) a supersonic

combustion ramjet (scramjet) where the flow remains supersonic / hypersonic through-

out the engine should be considered.

Furthermore, to keep structural loads on the hypersonic vehicle at acceptable levels,

namely, to keep the dynamic pressure, q0 = 1/2ρ0V20 , in the range of 50-100 kPa, flight

at high speeds is confined to altitudes of 25-40 km. Consequently, the burner entry

pressure, p3 , can be directly evaluated (see Fig. 1.1b) for fixed dynamic pressure, q0 ,


of 50 and 100 kPa, compression efficiency, ηc, of 0.9 and temperature ratio, T3/T0, of 6

using Eq. 1.2 (Heiser and Pratt 1994):

P3

P0=

( T3T0

T3T0

(1− ηc) + ηc

) γcγc−1

(1.2)

where γc is the average specific heat ratio; γc = 1/2(γ0 + γ3). Therefore, at flights

beyond Mach 8, typical pressures at the entrance of supersonic combustors range from

approximately 0.2 to 4 atm depending on the operating parameters for the flight mission,

such as the Mach number and the altitude.

Most supersonic combustion research in the open literature has focused on flight

speeds of Mach 8 and below (Allen et al. 1993; McMillin et al. 1994; Gruber et al.

1995; Parker et al. 1995; Santiago and Dutton 1997), and there are relatively few

works which have been performed for higher flight Mach numbers (Stalker 1989; An-

derson et al. 1990; Bakos et al. 992a; Bakos et al. 992b; Bakos et al. 992c; Erdos

1994; Anderson 1994; Albrechcinski et al. 1995; Wendt and Stalker 1996; Belanger and

Hornung 1996; McIntyre et al. 1997; Erdos 1998; Ben-Yakar and Hanson 002a). Due

to the large total enthalpies (greater than 3 MJ/kg) associated with high flight Mach

numbers, only impulse facilities are capable of providing the required total tempera-

ture and Mach number to replicate a combustor environment. Expansion tubes and

reflected shock tunnels are two possible types of impulse facilities for ground testing.

Of concern for high stagnation enthalpy simulations is the chemical composition of the

test gas. While in reflected shock tunnels significant amounts of dissociated species are

formed, in expansion tubes the amounts of these species are negligible (?). Therefore,

an expansion tube can provide a more correct simulation of the true flight combustion

chemistry including ignition delay and reaction times. In general, however, expansion

tubes have shorter test times than reflected shock tunnels. The principal advantages

and disadvantages of expansion tubes as compared to other hypersonic test facilities,

especially shock tunnels, are summarized in Table 1.1.

In the present study, the Stanford expansion tube facility is used to generate to-

tal enthalpy conditions in the Mach 8-13 flight range. This facility is one of the few

impulse-type facilities which can provide a wide range of total enthalpies. The free-

piston reflected shock tunnel, T5, located at GALCIT (Belanger and Hornung 1996),


Calspan reflected shock tunnel (Albrechcinski et al. 1995) and the HYPULSE expan-

sion tube located at GASL (Bakos et al. 992a; Bakos et al. 992b; Erdos 1994) are

three current examples of larger impulse facilities. In these facilities, generic combustor

models with hydrogen injection have been tested using conventional measurement tech-

niques such as pressure measurements along the combustor and flow visualization with

differential interferometry. While most of the high enthalpy and high speed combustion

flow-field studies in the open literature utilize these methods, modern laser-based diag-

nostics can provide flow-field and species information critical for fundamental research

(Erdos 1994; Erdos 1998; Anderson et al. 1992; Rogers et al. 1992; Ben-Yakar and

Hanson 998b).

1.1.2 Flow-Field Features of Jets in Supersonic Crossflows

Efficient performance of very high-speed combustor systems requires fuel and air

mixing at the molecular level in the near-field of the fuel injection. One of the simplest

approaches is the transverse (normal) injection of fuel from a wall orifice. As the fuel

jet, sonic at the exit, interacts with the supersonic crossflow, an interesting but rather

complicated flow-field is generated. Figure 1.2 illustrates the general flow-features of an

under-expanded transverse jet injected into a cross-flow. As the supersonic crossflow

is displaced by the fuel jet a 3-D bow shock is produced due to the blockage produced

by the flow. The bow shock causes the upstream wall boundary layer to separate,

providing a region where the boundary layer and jet fluids mix subsonically upstream

of the jet exit. This region confined by the separation shock wave formed in front of it,

is important in transverse injection flow-fields owing to its flame-holding capability in

combusting situations, as has been shown in previous publications (Parker et al. 1995;

Ben-Yakar and Hanson 998b).

The recent experimental studies performed by Fric and Roshko (1994) provide a

new insight into the vortical structure of a jet injected into a low speed crossflow. Their

photographs, obtained using the smoke-wire visualization technique, illustrate four types

of coherent structures: (1) the near-field jet-shear layer vortices; (2) the far-field counter

rotating vortex pair (CVP); (3) the horseshoe vortex which wraps around the jet column;

and (4) the downstream wake vortices originating from the horseshoe vortex. Figure 1.2

shows the presumed vortical structures for the jet in supersonic crossflow (which are


TABLE 1.1 Advantages and disadvantages of expansion tubes relative to shock tunnels for hypervelocitycombustion simulations.

Shock Tunnels Expansion Tubes

Significant level of radicals such as ”O”and ”NO” are produced in the test gas af-fecting the combustion chemistry. In the re-flected zone of the shock tube, air dissoci-ates due to high temperatures and recom-bines only partially during the fast expansionprocess.

Negligible amounts of radicals are pro-duced. The working gas never stagnates, thusreduces the extent of dissociation. As a resultthe test gas reaches to the test section withmore accurate chemical composition.

The facility needs to contain the to-tal pressures and temperatures of theflow it generates. As noted by Anderson(1994), at flight Mach numbers above 12, thetotal pressure requirements approaches a mil-lion psi or 68,000 atm, which can be producedonly by expansion tubes.

Higher stagnation pressures and tem-peratures can be achieved in expansiontubes even for the same initial driver pres-sure and sound speed, as velocity is addedto the flow through the unsteady expansionprocess without stagnating it.

Free-stream Mach number is fixed bythe nozzle geometry. Simulation of dif-ferent conditions requires replacement of thenozzle with a new geometry.

Variable Mach numbers and conditionscan be easily obtained by just altering theinitial filling pressures.

Nozzle can be damaged due to the highheat transfer rates at the throat and flyingdiagrams inside the tube.

High heat transfer rates are avoided inthe absence of a sonic throat. However, thetest object is prone to damage from flyingdiagrams arriving at the end of the expansiontube operation.

Boundary layer develops throughoutthe nozzle and can be thick compared to thedimensions of the injection port. It is usuallyrequired to eliminate the boundary layer by,for example, inserting a step before the fuelinjection port (Parker et al. 1995)

A thin boundary layer is developed up-stream of the injection port as the injectionplate is placed in the free-jet exiting the tube.

Test times ≈ 1msecTest times are of the order of 1msec. How-ever, a substantial part of it is wasted dur-ing the nozzle start-up time (of the order of0.5msec), required for the supersonic flow tobe established. Test time decreases with in-creasing stagnation enthalpy.

Test times ≈ 0.2 - 0.5 msecNo nozzle start-up time is required. In addi-tion, the establishment of flow on the studiedmodel begins during the expansion sectiongas flow prior to the test gas arrival. As aresult, less useful test time is consumed dur-ing the flow establishment.

Longer test section because of the longertest time and larger core flow. However, sidewall effects should be taken into account.

Test section dimensions depend on thesize of the core flow at the exit of the tubewhich is diminished by the boundary layergrowth on the tube walls.


known to exist in subsonic jet-in-crossflow) as they were partially observed by numerous

studies (Gruber et al. 1996; Gruber et al. 997a; Ben-Yakar et al. 998a).

The origin of the jet vortical structures was studied by several researchers (Fric and

Roshko 1994; Brizzi et al. 1995; Yuan et al. 1999). Among those studies, Yuan et al.

(1999) performed a large-eddy simulation of transverse jets in subsonic crossflows. Their

results revealed that the majority of the jet vortical structures arose from the Kelvin

Helmholtz (K-H) instability of the jet-shear layer in the near-field. Interestingly, they

do not observe the formation of vortex rings around the periphery of the jet as was

assumed in previous studies. Instead they find two kinds of vortices originating from

the jet exit boundary layer: 1) regularly formed spanwise rollers on the upstream and

downstream edges (large scale jet shear layer vortices), 2) quasi-steady vortices, the so-

called ”hanging vortices” that form in the skewed mixing layers (mixing layers formed

from non-parallel streams) on each lateral edge of the jet leading to the formation of

the CVP.

The near-field mixing of transverse jets is dominated by the so-called ”entrainment-

stretching-mixing process” driven by large scale jet-shear layer vortices. In the region

near the injector exit, the injectant fluid moves with a higher velocity tangent to the

interface than the free-stream fluid. As a result, large vortices are periodically formed

engulfing large quantities of free-stream fluid and drawing it into the jet-shear layer

(macromixing). These large scale vortices also stretch the interface between the un-

mixed fluids. Stretching increases the interfacial area and simultaneously steepens the

local concentration gradients along the entire surface while enhancing the diffusive mi-

cromixing.

Preliminary examinations (Gruber et al. 997a; Ben-Yakar and Hanson 002b) of the

convection characteristics of these large-scale structures, developed in a sonic transverse

jet injection into supersonic crossflows, determined that in the far-field the eddies tend

to travel with velocities that are closer to the free-stream velocity. This indicates that

in high speed free-stream conditions, these large coherent structures, where the fuel and

air are mixed by slow molecular diffusion, will also travel at high speeds. Consequently

the combustion process will be mixing controlled.

High mixing efficiency, however, must be achieved in the near-field of the fuel in-

jection for the success of hypersonic propulsion systems. Therefore, it is important to

understand how these structures and their growth rates evolve as flow and jet conditions


(a)

INJECTANT

(Hydrogen or

Ethylene)

BOW SHOCK

BARREL

SHOCK

RECIRCULATION

ZONE

M¥

>1

RECIRCULATION

ZONE

BOUNDARY LAYER

SEPARATED

REGION

MACH DISK

LARGE-SCALE

STRUCTURES

(b)

3-DBOW SHOCK

M¥

>1

MACH DISK &

BARREL SHOCK

AVERAGE

JET BOUNDARY

COUNTER-ROTATING

VORTEX PAIR (CVP)

HORSESHOE-VORTEX

REGION

FIGURE 1.2 Schematic of an underexpanded transverse injection into a supersonic cross-flow,(a) instantaneous side view at the center-line axis of the jet; (b) 3-D perspective of the av-eraged features of the flow-field (Gruber et al. 1995).


are changed. Two types of fuel are being considered for use in supersonic combustion:

1) hydrogen and 2) hydrocarbon fuels. The large differences in the molecular weights

of these fuels result in a big variation in injection velocities that might lead to a wide

variation in the jet shear layer growth rate and the mixing properties. However, none

of the previous jet penetration studies (Zukoski and Spaid 1964; Schetz and Billig 1966;

Rogers 1971; Rothstein and Wantuck 1992; Papamoschou and Hubbard 1993; Gru-

ber et al. 1995) found any dominant differences between jets with different molecular

weights. Penetration was shown to be dependent primarily on the jet-to-free-stream

momentum flux, J, expressed by:

J =

(ρu2

)jet

(ρu2)∞(1.3)

Most transverse jet-in-crossflow studies were, however, carried out in cold supersonic

flows (namely low velocities) generated in blow-down wind tunnels. The free-stream

temperatures and velocities in these facilities were usually lower than that expected

in a real supersonic combustor environment. Comprehensive studies still need to be

performed to determine the mixing properties of different type of fuels in a relatively

accurate supersonic combustor environment. These observations gave rise for the fol-

lowing question: “is there any other mechanism or controlling parameter which will

alter the large eddy characteristics of the jet shear layer to enhance its near-field mixing

in realistic conditions?”

We were therefore challenged to study the flow features of hydrogen and ethylene

transverse jets exposed to high-speed supersonic free-streams at realistic conditions

leading to high shear levels.

1.1.3 Ignition and Flame-Holding Strategies in Supersonic Combus-

tion

Different injection strategies have been proposed (Billig 1993; Tishkoff et al. 1997;

Abbitt et al. 1993; Hartfield et al. 1994; Riggins et al. 995a; Riggins and Vitt 995b;

Fuller et al. 1998) with particular concern for rapid near-field mixing. These injec-

tion strategies, both flush-mounted injectors and intrusive injectors, typically rely on

the generation of strong streamwise counter-rotating vortices. As a result, mixing is

enhanced both in macro-scale by entrainment of large quantities of air into the fuel


and in micro-scale due to stretching of the fuel-air interface. Stretching increases the

interfacial area and simultaneously steepens the local concentration gradients thereby

enhancing the diffusive micro-mixing. Micro-scale mixing is required for combustion

since chemical reactions occur at the molecular level. However, efficient mixing of fuel

and air does not directly initiate the combustion process.

Ignition and flame-holding in supersonic flows (Huber et al. 1979; Miller 1994; Im

et al. 1998; Sung et al. 1999; Ben-Yakar and Hanson 998b) are two other important

factors that have to be addressed in the design of an injection system. Once the fuel-

air ignition is established, the combustion depends directly on the efficiency of the

mixing. In order for self-ignition (and therefore combustion) to be accomplished in a

flowing combustible mixture, it is necessary that four quantities have suitable values:

static temperature, static pressure, fuel-air mixture, and the residence time at these

conditions. The ignition is considered accomplished when sufficient free radicals are

formed to initiate the reaction system, even though no appreciable heat has yet been

released. When the conditions of spontaneous ignition exist, the distance li at which

it occurs in a medium flowing at a velocity U is: li = Uτi, where τi is the ignition

delay time. As the combustor velocity U becomes larger, the ignition requires longer

distances.

The primary objective of a flame-holder in a supersonic combustion, therefore, is

to reduce the ignition delay time and provide a continuous source of radicals for the

chemical reaction to be established in the shortest distance possible. In general, flame-

holding is achieved by three techniques: 1) organization of a recirculation area where

the fuel and air can be mixed partially at low velocities, 2) interaction of a shock wave

with partially or fully mixed fuel and oxidizer, and 3) formation of coherent structures

containing unmixed fuel and air, wherein a diffusion flame occurs as the gases are

convected downstream.

These three stabilization techniques can be applied in a supersonic combustor in

different ways. One of the simplest approaches is the transverse (normal) injection of

fuel from a wall orifice (see Fig. 1.3a). As the fuel jet interacts with the supersonic

crossflow a bow shock is produced. As a result, the upstream wall boundary layer

separates, providing a region where the boundary layer and jet fluids mix subsonically

upstream of the jet exit. This region is important in transverse injection flowfields owing

to its flame-holding capability in combusting situations, as has been shown in previous


Fuel

Bow Shock

MM¥

>1>1

Fuel

Bigger

Recirculation Region

Weaker Bow Shock

(~ Mach Wave)

Fuel

Smaller

Recirculation Region

Autoignition

Zones

Combined Bow and

Step-Induced Shock

(a)

(b)

(c)

FIGURE 1.3 Flow-field schematics of traditional injection/flame-holding schemes for supersonic combustors.a) underexpanded fuel injection normal to the crossflow, b) fuel injection at angle, c) injectionbehind a sudden expansion produced by a step.

publications (Huber et al. 1979; Ben-Yakar and Hanson 998b; Ben-Yakar and Hanson

999a). However, this injection configuration has stagnation pressure losses due to the

strong 3-D bow-shock formed by the normal jet penetration, particularly at high flight

velocities.

Another way of achieving flame stabilization is by means of a step, followed by

transverse injection (see Fig. 1.3c). The step creates a larger recirculation area with the

hot gases serving as a continuous ignition source. This approach can provide sustained

combustion but, like the previously described method, has the disadvantage of stagna-

tion pressure losses and increase in drag due to the low flow pressure base behind the

step.

On the other hand, it is possible to reduce the pressure losses associated with the


injection process by performing angled injection (e.g., 60o or 30o rather than 90o) so that

the resulting bow shock is weaker (see Fig. 1.3b). In this approach, jet axial momentum

can also contribute to the net engine thrust. Riggins et al. (995a) studied the thrust

potential of a supersonic combustor at Mach 13.5 and Mach 17 flight conditions with

30o flush wall injection of hydrogen and concluded that the major component of thrust

potential gain is due to the jet momentum. In our previous work (Ben-Yakar and

Hanson 998b; Ben-Yakar and Hanson 999a), autoignition of a hydrogen jet transversely

injected into Mach 10-13 flight enthalpy flow conditions was observed in the upstream

recirculation region of the jet and behind the bow shock. However, different experiments

(McMillin et al. 1994) performed for similar geometry but at much lower total-enthalpy

flow conditions showed that ignition occurred only far downstream of the jet. Based

on those observations, angled injection is likely to reduce or eliminate these forms of

autoignition and stabilization especially at flight speeds lower than Mach 10. Therefore,

it is likely that a new technique will be required to obtain autoignition and downstream

combustion stabilization.

In recent years, cavity flame-holders, an integrated fuel injection/flame-holding ap-

proach, have been proposed as a new concept for flame-holding and stabilization in

supersonic combustors (Tishkoff et al. 1997). Cavity flame-holders, designed by CIAM

(Central Institution of Aviation Motors) in Moscow, were used for the first time in a

joint Russian/French dual-mode scramjet flight-test (hydrogen fueled) (Roudakov et al.

1993). Further experiments (Vinagradov et al. 1995; Ortweth et al. 1996; Owens et al.

1998) showed that the use of a cavity after the ramp injector significantly improved

the hydrocarbon combustion efficiency in a supersonic flow. Similar flame stabilization

zones, investigated by Ben-Yakar et al. (998a), have been employed within a solid-fuel

supersonic combustor, demonstrating self-ignition and sustained combustion of PMMA

(Plexiglas) under supersonic flow conditions.

In November 1994, NASA contracted CIAM (Roudakov et al. 1996; McClinton

et al. 1996) to continue exploring the scramjet operating envelope from dual-mode

operation below Mach 6 to the full supersonic combustion mode at Mach 6.5. The

proposed combustor design also included two cavity flame-holders (20 mm in depth by

40mm in axial length and 30mm by 53 mm). The performance predictions obtained by

analytical solutions indicated that these cavities would be quite effective as autoignition

and flame-holding devices. Indeed, the recent flight test of this combustor has been


successfully completed, encouraging further investigation of cavity flame-holders.

It is worth noting that, although there is recent interest in cavity flame-holders for

supersonic combustors, their application in subsonic combustors goes back to the 1950’s.

Probably, the first published investigation of cavity flame-holders is due to Huellmantel

et al. (1957), who studied various shapes of cavities to sustain combustion in low speed

propane-air flames. The main purpose of this thesis is to summarize relevant known

characteristics of cavities in supersonic flows and research efforts related particularly to

cavities employed in low- and high-speed combustors.

1.2 Thesis Objectives

The ultimate objective of this dissertation is to investigate near-field mixing and

flame-holding characteristics of different gaseous fuels such as hydrogen and ethylene

injected normally from a single orifice into a realistic supersonic combustor environ-

ment. We apply advanced non-intrusive flow diagnostic techniques such as Planar

Laser-Induced Fluorescence of OH radicals (OH-PLIF) and schlieren imaging using an

ultra-fast-framing rate digital camera. These techniques and the simulation of high

speed and high temperature free-stream conditions enable unique observations that

were not available in the previous studies. The thesis includes four primary elements:

1. The experimental approach: The goal is to generate a relatively accurate

supersonic burner entry condition, namely a radical-free, high total enthalpy air

flow. An expansion tube is used to generate three nominal free-stream conditions

for flight Mach 8, 10 and 13 regimes. The experimental approach is discussed in

Chapter 2 which includes descriptions of the critical parameters that have to be

considered in the simulation of a supersonic combustor environment, the facility

itself and the measurement techniques. The characterization of the test flow is

then presented summarizing determination of the useful test time, core-flow size

and boundary layer effects, issues that have to be addressed to fully characterize

the flow generated in an expansion tube. The flow visualization techniques are

discussed in detail in Chapter 3.

2. Mixing: In Chapter 4, we study the flow features of hydrogen and ethylene trans-

verse jets exposed to high-speed supersonic free-streams at realistic conditions


leading to high levels of shear. Guided by the observations of these experiments,

we continue in Chapter 5 with a more fundamental study looking into the origin

of the observed phenomena. The outstanding questions that we investigate are:

How do the jet shear layer vortices develop and which parameters control their

stability and coherence? What is the contribution of the jet shear layer vortices

to the near-field mixing? Does the penetration mechanism only depend on jet-to-

crossflow momentum ratio as has been proposed for the last 40 years or is there

any other mechanism leading to higher penetration and better mixing properties?

3. Ignition and flame-holding: The ignition and the flame-holding capabilities of

a hydrogen jet in high total enthalpy flow conditions are presented in Chapter 6.

We study the self-ignition regions in the near-field of the jet in flight Mach 8, 10

and 13 flow conditions using OH-PLIF flow visualization. We also compare the

near-field ignition results of a hydrogen transverse jet with an ethylene transverse

jet at flight Mach 10 conditions.

4. Cavity flame-holders: In Chapter 7, an extensive overview of cavities, which

are considered as a promising flame-holding devices for supersonic combustion, is

presented. Open questions impacting the effectiveness of the cavities as flame-

holders in supersonic combustors are then discussed. Preliminary experimental

results are also summarized. The goal is to study the ignition capability of a jet-

cavity configuration and to observe the differences in the shock wave structures

around cavities as the length-to-depth ratio and the geometry of the cavity back

wall are changed.

Chapter 2

Experimental Aspects

Our experimental approach includes the use of an expansion tube to provide a wide

range of variability in the freestream conditions with relatively accurate chemical compo-

sition. The latter is critical for supersonic combustion studies in the high total enthalpy

flows associated with hypersonic air-breathing propulsion systems.

Efforts are focused on achieving three operating points, simulating flight Mach 8, 10

and 13 total enthalpy conditions at the entrance of a supersonic combustor. The ability

of the expansion tube to provide a steady-flow test time of adequate duration and a

core-flow of sufficient size for 2 mm jet-in-crossflow studies is verified.

In the following sections, the important parameters that must be considered in the

design of a supersonic combustion experiment are discussed and the facility and the test

flow characterization techniques are then summarized. Additional test conditions are

characterized for fundamental fluid mechanical studies and are presented in Chapter 5.

2.1 Critical Parameters in Supersonic Combustion Simu-

lation

An experimental simulation of a supersonic reacting flow requires the replication of

5 parameters (Heiser and Pratt 1994). These simulation parameters including pressure

(p), temperature (T ), velocity (u), characteristic length of the model (L) and gas com-

position (νi) must be manipulated to provide the flight values of certain non-dimensional

parameters such as:

14

CHAPTER 2. EXPERIMENTAL ASPECTS 15

Mach number:

M ∼ u√T

(2.1)

Reynolds number:

Re ∼ ρ√T∼ pL

u

T 3/2(2.2)

Damkohler number:

Da ∼ L

uτc(2.3)

Damkohler number represents the ratio of flow residence time, L/u, through the com-

bustor to chemical time, τc, and must be larger than 1 to achieve flame-holding and

a complete combustion process. For flame-holding considerations ignition delay time,

τi, replaces the chemical time in Damkohler number, τc = τi. For a hydrogen-air com-

bustion process, the ignition delay time, varies inversely with pressure because of the

two-body reactions and depends exponentially on temperature. As a result, Damkohler

number can be related to basic parameters in the following form:

Da ∼ pL

u · exp(θ/T )(2.4)

where θ is a characteristic temperature for the ignition time.

Consequently, in order to preserve the values of these three non-dimensional param-

eters it is required to simulate all 5 basic parameters, including temperature, pressure,

velocity, model length and the gas chemical composition. However, it is worth noting

the following point: If the chemical composition of the flow, its velocity and temper-

ature were to be duplicated, then a constant value of the product pL would satisfy

the requirements for simulation of the three non-dimensional parameters. Therefore,

from the standpoint of mixing and flame-holding studies a correct simulation of only 4

parameters is essential: chemical composition, temperature, velocity and the product

pL.

In our experimental approach, we replicate 3 of these 4 parameters: the required

burner entry velocity and burner entry static temperature, u3 and T3, respectively,

according to the values of burner entry Mach number, M3, estimated in Fig. 1.1a. The

use of an expansion tube enables acceleration of the air to total enthalpy conditions


(3-6MJ/kgair) corresponding to the Mach 8-13 flight range, without exposing it to

high stagnation temperatures (3000-6000 K). Therefore, the free-stream contains only

negligible amounts of radicals, produced only by the incident shock wave. The test gas,

first shocked to its maximum temperature (1700-2150 K), is then accelerated and cooled

to the required static temperature (1250-1400 K). Through this unsteady expansion

process, the test gas gains in total temperature and total pressure.

Although in our experiments the free-stream flow composition, Mach number and

static temperature correspond to typical scramjet combustor entrance values, its static

pressure is somewhat below that of actual systems. Table 2.1 summarizes the three

nominal test flow conditions, Mach 8, Mach 10 and Mach 13, achieved in the Stanford

expansion tube facility. Furthermore, since the characteristic length scale in our exper-

iments is small, about 2mm (the diameter of the injection orifice), the parameter pL

is not sufficiently high to replicate a real combustor environment. This might result

in chemical kinetic limitations on the H2 - air ignition and combustion process. On the

other hand, this limitation can be circumvented if an elevated concentration of oxygen

is used in the test gas to increase the collision rates as suggested by Bakos et al. (992b).

Finally, in the current study we have shown that in high-enthalpy flows, ignition of

hydrogen, injected transversely into a free-stream of air, can be achieved in the near-

vicinity of the injector, even at low pL values. Therefore, the ignition will be guaranteed

at higher pressures as the Damkohler and Reynolds numbers increase linearly with pL

in realistic systems.

In conclusion, the most important parameters that have to be replicated for su-

personic combustion studies are chemical composition, temperature and velocity of the

free-stream, and the less important parameter is the product pL. Variation in pressure

affects the ignition time linearly, while variation in temperature has an exponential ef-

fect through the activation energy (and hence characteristic temperature ignition time,

θ) in chemical kinetics.


TABLE 2.1 Test gas (free-stream) flow properties simulating the burner entry conditions of three flightMach numbers. The corresponding values are from Fig. 1.1.

Flight Simulation Mach 8 Mach 10 Mach 13

(1) (2) (3)Initial filling pressuresDriven section, He, psig 300 600 600

(2.17MPa) (4.24 MPa) (4.24MPa)Driven section, 95% N2 +5% CO2, psia 0.45 0.5 0.15

(3.10 kPa) (3.45 kPa) (1.04 kPa)Expansion section, He, torr 70 20 2

(9.13 kPa) (2.67 kPa) (0.27 kPa)Free-stream conditionsTotal enthalpy, MJ/kg 2.9± 0.05 3.9± 0.1 6.2± 0.15Mach number 2.40± 0.03 3.38± 0.04 4.66± 0.07Static temperature, K 1400 1290 1250Static pressure, atm 0.65 0.32 0.04

(65.9 kPa) (32.4 kPa) (4 kPa)Velocity, m/sec (measured) 1800± 20 2360± 25 3200± 50Test time, µsec (measured) 170± 10 270± 10 400± 10Test “slug length”, m (velocity× test time) 0.31 0.64 1.28Establishment length for laminar boundarylayer at L1 = 50 mm, m

0.15 0.15 0.15

Maximum measured recirculation regionlength, L2, (djet = 2mm)

∼ 1.5 djet ∼ 2 djet ∼ 4 djet

Establishment time for the jet upstream re-circulation region, m based on (30−70)×L2

0.09 - 0.21 0.12 - 0.28 0.24 - 0.56

Free-stream Reynolds number at the injec-tion port, Rex = 50mm

29,000 22,000 3,800

Boundary layer thickness upstream of theinjection port, mm

0.65 0.75 1.80

Shock speeds in the expansion section, m/s(measured)

2468 3175 3650

Shock Mach number in the expansion sec-tion

2.44 3.14 3.61

Maximum temperature that the test gas isexposed to, T2, K

1690 1750 2140


Driver S

ection

Driven S

ection

Expansion Sectio

n

Dump Tank

Amplifiers &

Interval Counters

ICCD Camerafor OH-PLIF Imaging

578 x 384 Array

DoubleDiaphragm

8 Channel D

ata

Acquisition

System

KnifeEdge

YM 1200 Nd:YAG Laser

HD 500 Dye Laser

HT 1000

Frequency

Doubler

Long durationXenon Arc

Light Source

DichroicMirror

IMACON 468Ultrafast Framing Camera

for Schlieren Imaging(inc. 8 ICCD modules,

each 576 x 384)

Image A

cquisition

Computers

Driven/ExpansionDiaphragm

Mirror 2

Mirror 1

FocusingMirror

FIGURE 2.1 Expansion tube facility (12m in length and 89 mm inner diameter) and imaging system.

2.2 Experimental Facility

2.2.1 Expansion Tube

The expansion tube facility with its dedicated lasers and optical arrangement is

schematically illustrated in Fig. 2.1. The tube is 12 m in length (including dump tank)

with an inner diameter of 89 mm, and includes three sections: driver, driven and ex-

pansion. The driver section is filled with high pressure helium gas and is separated

by double diaphragms from the lower pressure driven section, which is filled with the

desired test gas. Mylar film (6.35µm thick) is used as the diaphragm material at the

driven/expansion interface to separate the test gas from low pressure helium gas in the

expansion section.


-1 0 1 2 3 4 5 6 7 80.000

0.001

0.002

0.003

0.004

0.005

0.006

0.007

IR detector

Test

Section

1

1

4 10

10

520

23

4

contact surface

1 Quiescent Test Gas

2 Test Gas Behind Incident Shock

3 Expanded Driver Gas

4 Driver Gas

5 Expanded Test Gas

10 Expansion Gas

20 Expansion Gas

Behind Incident Shock

Expansion

Section

(He)

Driven

Section

(CO2/N

2/O

2)

Driver

Section

(He)

first disturbance arrival

rarefaction tail

rarefaction head

reflected rarefaction head

incident shock, s1

test time

tim

e,sec

x-distance, m

FIGURE 2.2 Expansion tube distance-time (x-t) diagram calculated for flight Mach 13 condition. Methodof characteristics was used to solve the flow gasdynamics properties assuming one-dimensionalinviscid theory. Test time is defined as the time that the test gas has uniform flow quantitiesand determined by the time arrival of the contact surface to the tube exit, and that of thefirst subsequent rarefaction wave (reflected rarefaction head in our case of high total enthalpysimulations).

The operating sequence of an expansion tube is best represented by the distance-time

(x-t) diagram shown in Fig. 2.2. A run is initiated by bursting the double diaphragms,

which generates a shock wave propagating into the test gas and producing flow of

intermediate velocity with an increased pressure and temperature. The shocked test

gas is then accelerated by an unsteady and constant area expansion process from the

driven section into the lower pressure expansion section, while gaining total temperature


and total pressure. The test gas emerging from the downstream end of the expansion

thus has both a higher stagnation enthalpy and higher effective stagnation pressure than

the shock tube flow from which it originated. Further detail on the operating cycle of

an expansion tube can be found in the review papers of Erdos (1994) and Anderson

(1994).

A square viewing chamber of 27×27 cm cross section is mounted at the exit of the

expansion tube (see Fig. 2.3). A rake of pitot tubes or an instrumented model with the

injection system, is positioned in this test section, which is equipped with an opposed

pair of square (13×13 cm) quartz windows for observation and a fused silica slot on top

of the chamber for admission of the vertical laser sheet.

Six piezo-electric pressure transducers are mounted along the driven and expansion

sections for shock speed and wall pressure measurements. An additional transducer,

mounted 20.3 cm downstream of the driven/expansion diaphragms, is used to monitor

the unsteady expansion process at that location.

The expansion section is also equipped with sapphire viewing ports for optical mea-

surements during flow characterization experiments. In those tests, an InSb IR detector

(Judson J-10 InSb equipped by a Perry model 720 amplifier) is mounted at a viewing

port (see Fig. 2.4) to detect the arrival of the test gas (at the viewing port) through

the emission of IR light by small amount of CO2 (5%) seeded into the test gas (nitro-

gen). Also, for flow characterization tests, the injection system is replaced with a pitot

rake consisting of four pressure transducers across the diameter of the tube as shown

in Fig. 2.3. The test gas velocity can then be calculated by considering its arrival time

at the viewing port and at the pitot rake. Data from these sensors are recorded at

1Msample/sec on a PC-based, 8-channel (12-bit) computer-scope. The flow imaging

techniques include Planar Laser-Induced Fluorescence of OH radicals (OH-PLIF) and

schlieren imaging using an ultra-high-speed framing digital camera. Detailed descrip-

tion of these systems and their synchronization with the expansion tube operation are

provided in Chapter 3.

2.2.2 Injection System and its Calibration

The injection system is positioned right at the exit of the expansion tube inside

the test section (Fig. 2.5a). The system consists of a flat plate with an attached high


FIGURE 2.3 Schematic of the test section (27 x 27 cm cross section) where a rake of 4 pitot probes, instru-mented with pressure transducers, was located 2.5 cm downstream of the tube exit. The flowhistory during the expansion tube operation was detected via pitot pressure information. Notethat the inner diameter of the tube is 8.9 cm.

speed solenoid valve (less than 1 msec response time, General Valve Series 9, Iota One

controller) which allows near-constant injection flow rates during the expansion tube

test time period. For the results presented here, an under-expanded transverse jet

of hydrogen with a 2 mm port diameter has been used. The jet port is located at a

distance 30 mm downstream of the tube exit and about 50mm downstream of the flat

plate leading edge. At this location, the boundary layer thickness, developing on the flat

plate, is approximately 0.75 mm for the conditions presented in this paper. Table 4.1

summarizes the jet flow exit properties.

Calibration of the injected system was performed to determine the stagnation pres-

sure losses through it. This was accomplished by comparing the Mach disk height of an

underexpanded jet into still air with a well-known empirical correlation. Schlieren flow

visualization (Fig. 2.6) was used to measure the Mach disk height for different pres-

sure ratios. The expected jet Mach disk position, based on the correlation suggested


Wall PressureTransducer

Globar

Focusing Lens

Band-Pass Filter

4.263 - 4.303 mmInSb IRDetector

D @x 104 cm

SapphireOptical Port

Test Gas5%CO / N

2 2

Acceleration GasHe

PitotProbe

CS

40.6 cm 2.5 cm

FIGURE 2.4 Optical set-up to measure the test gas velocity, assumed to be equal to the CS - contact surfacevelocity. IR emission from 5%CO2 seeded in the test gas nitrogen is collected by an InSb IRdetector at the viewing port located at 101.6 cm from the end of the tube. The test gas velocitycan then be calculated by considering its time of arrival at the viewing port and at the pitotrake.

by Ashkenas and Sherman (1966) as a function of jet stagnation pressure (Ptot,jet) to

effective back pressure (Peb) ratio, is given by:

y1

djet= 0.67 ·

(Ptot,jet

Peb

)1/2

(2.5)

On the basis of this correlation, measurements indicated a stagnation pressure loss

of 48% for hydrogen injection and 41% for ethylene injection during valve operation

(note that the fuels were supplied from flow lines of different length).

In addition, the valve actuation time and the tube firing have to be synchronized

such that the jet is fully developed by the time the steady test flow conditions are

obtained. Within that constraint, the time interval between the valve actuation and

the test gas arrival should be short enough to avoid significant changes in the expansion

section initial pressure. To determine the jet development time, schlieren imaging was

used to observe the temporal development of the jet. This combined with the traces

obtained using a fast response pressure transducer located at the jet exit, allowed the

determination of the optimum valve actuation time ( 1.5 msec before start of test time).


(a) (b)

FIGURE 2.5 Schematic of a) Injection system, b) cavity/injection plate system.

2.2.3 Cavity/Injection Plate

The cavity/injection system (Fig. 2.5b) is designed with different cavity and jet

inserts to systematically study the following configurations: 1) 90o and 30o flush wall

gaseous fuel (hydrogen, ethylene) injection, 2) cavities with length-to-depth ratio of

L/D=3,5,7 with 90o, 60o and 30o rear-walls, 3) cavities with 30o upstream fuel injection.

In addition, a miniature pressure transducer (PCB dynamic piezo transducer, model

1105B12) was installed inside the cavity to measure the pressure oscillations and to

monitor the flow establishment time.

2.3 Test Flow Characterization in the Flight Mach 8 - 13

Range

There are several issues that have to be addressed to fully characterize the properties

of a supersonic flow generated in an impulse facility. Of particular concern are the

determination and characterization of flow conditions, the steady-flow test time, the


(a) (b) (c)

(d) (e)

JetBoundary

BarrelShock

Mach Disk

Pj, M =1j

y1

FIGURE 2.6 Schlieren visualization of an underexpanded gaseous injection into still air. (a)-(c) hydrogen(d)-(e) ethylene jets. The exposure time of the images was 3 musec. Mach disk height, y1,was measured for different pressure ratios, Pj/Peb, to calibrate the injection system.

core-flow size and the boundary layer effects on the flow properties.

2.3.1 Flow Conditions

A variety of flow conditions can be easily achieved using an expansion tube by simply

changing the initial filling pressures and the speed of sound of the gases at different

sections of the expansion tube. In our facility, helium gas was used in the expansion

and driver sections with a maximum filling pressure of 4.24 MPa (600 psig) in the driver

section.

The selection of correct initial pressures to achieve the required flow conditions,

however, is not straight-forward as the expansion tube combines two shock tubes in

tandem. We have, therefore, calculated the flow conditions that can be achieved in an


expansion tube as a function of initial filling pressures. Figure 2.7 presents maps of these

flow conditions estimated using simple one-dimensional inviscid theory (see Appendix A

for a given driver filling pressure of 4.24MPa (600 psig). These maps provide guidelines

in the selection of the initial pressures for different conditions of interest.

Note the blank (forbidden) regions in the maps of Fig. 2.7. These are the regions

where the shocked test gas cannot expand into the expansion section as the pressure in

the expansion section is higher than the pressure of the shocked test gas.

In a conventional shock tube, for a given driver initial pressure, one must decrease

the driven section pressure to generate flows with higher velocities, temperatures and

Mach numbers. As the driven section initial filling pressure decreases the shock-induced

static pressure decreases as well. In expansion tubes, on the other hand, the flow velocity

and static pressure do not vary significantly as the driven initial pressure is changed for

a given driver and expansion section pressures. As shown in Fig. 2.7, different velocities

can be achieved primarily by manipulating the expansion section initial pressure. For

lower expansion section pressures, the flow accelerates to higher velocities and expands

to lower pressures.

In our experiments, we have used the maps in Fig. 2.7 to simulate the required

burner entry conditions of flight Mach 8, 10 and 13 based on the estimated values

from Fig. 1.1. Simulation of our flight Mach 10 condition, for example, corresponds to

4MJ/kg of total enthalpy and a Mach number of about 3.5. Therefore, according to

the maps in Fig. 2.7, initial filling pressures of the expansion and driven sections were

determined to be 2.67 kPa (20 torr) and 3.45 kPa (0.50 psia), respectively, to simulate

flight Mach 10 total enthalpy condition at the selected driver initial pressure of 4.24 MPa

(600 psig). Initial pressures required to simulate flight Mach 8 and 13 were chosen in a

similar manner and are marked on the maps of Fig. 2.7.

As discussed in the previous section, our experimental approach includes correct

replication of the velocity and temperature of the air entering the combustor. The

static pressure in our experiments, on the other hand, is lower than the expected values

in a supersonic combustor at those flight conditions. However, the correct replication of

pressure is not as crucial as the simulation of the required total temperature and burner

entry Mach number, in the basic study of ignition and flame-holding processes of differ-

ent injection schemes. Pressure dependence of the ignition process can be extrapolated


(a)

0.1

2

3

4

5

6

7

89

1

2

3

4

5

Dri

ven

Gas (

Nit

rog

en

) In

itia

l P

ressu

re, P

1

(ps

ia)

12 3 4 5 6 7 8 9

102 3 4 5 6 7 8 9

1002

Expansion Gas (Helium) Initial Pressure, P10 (torr)

2400 K

2200 K

1800 K

1400 K

1000 K

600 K

400 K

300 K

1 a

tm

0.8

atm

0.6

atm

0.4

atm

0.3

atm

0.2

atm

0.1

atm

0.0

5 a

tm

Mach 13

Mach 10

Mach 8

1.4

atm

(b)

0.1

2

3

4

5

6

7

89

1

2

3

4

5

Dri

ven

Gas (

Nit

rog

en

) In

itia

l P

ressu

re, P

1 (p

sia

)

12 3 4 5 6 7 8 9

102 3 4 5 6 7 8 9

1002


6

2.5

34

00

m/s

32

00

m/s

30

00

m/s

28

00

m/s

26

00

m/s

24

00

m/s

22

00

m/s

20

00

m/s

18

00

m/s

7 6 MJ/kg

3.5

3 MJ/kg

5.5

4 MJ/kg 4.5

5 MJ/kg

6.5

Mach 13

Mach 10

Mach 8

FIGURE 2.7 Maps of estimated test gas (nitrogen) conditions (state 5) at the exit of an expansion tube:a) pressure and temperature, b) total enthalpy and velocity of the test gas are plotted fordifferent initial driven and expansion section pressures. Calculations are performed using theinviscid 1D equations for a given driver pressure of P4 = 600 psig (helium). Note that theeffective filling pressure of the driver section is taken as P4,eff = 686 psig, as its inner diameter(10.2 cm) is larger than that of the driven and expansion sections (8.9 cm). This area differenceis accounted for in the curves presented above.


to higher pressures since the Damkohler number is approximately proportional to pres-

sure in hydrogen-air combustion systems. Furthermore, the oxygen concentration can

be increased in the test gas if the combustion process is rate-limited due to low static

pressure.

Table 2.1 summarizes the initial filling pressures of the three test conditions charac-

terized in the Stanford expansion tube. Other factors, such as the maximum available

injector pressure, were taken into account in determining these test flow conditions.

The initial driver pressure for the Mach 8 condition, for example, was chosen to be

2.17MPa (300 psig) instead of 4.24MPa (600 psig) to provide reasonable penetration of

the fuel jet. Penetration of fuels injected transversely into supersonic flows is known to

be strongly correlated with the jet-to-free-stream momentum flux ratio (J) defined as

J =

(ρu2

)jet

(ρu2)∞=

(γpM2

)jet

(γpM2)∞(2.6)

where the subscript “jet” corresponds to the jet exit conditions and ∞ corresponds to

free-stream conditions ahead of a bow shock. In our experiments, the jet-to-free-stream

momentum flux ratio was typically J = 1.5 − 2.

2.3.2 Measurement of Flow Properties

The test flow conditions (pressure, temperature, velocity, Mach number and test

time), presented in Table 2.1, were determined using the combined data of wall pressure,

pitot pressure, and IR emission. Briefly, the test flow characterization was performed

in the following stages:

1. the shock speeds at the driven and expansion sections were measured using six

piezo-electric pressure transducers mounted in the tube,

2. gasdynamic conditions of the post-shock test gas in the driven and expansion

sections were obtained from the measured shock speeds by a 1-D frozen-chemistry

code using standard thermochemical data,

3. the test gas temperature and sound speed at the exit of the tube were then

calculated assuming isentropic expansion of the shocked test gas in the driven

section to the expected value of the post-shock static pressure of the acceleration

gas in the expansion section,


4. the velocity of the contact surface was deduced by measuring the time interval

between its arrival at the IR detector port and the pitot probe located at the exit

of the tube,

5. test gas flow velocity was then estimated by equating the contact surface ve-

locity with that of the test gas immediately after it.

An example of IR emission from CO2 seeded in the test gas, together with pitot and

static pressure traces measured in flight Mach 10 flow simulation is given in Fig. 2.8.

Note that in characterization experiments, instead of air, a mixture of 95% N2+5% CO2

was used as a test gas, which provides an effective molecular weight (28.8 gr/mole)

equivalent to that value of the air. Based on the time history of the pitot pressure

at the tube exit, it is possible to identify the arrival of the shock wave, the period

of expansion section helium flow, the helium/test gas contact surface, and the steady

flow test time. It is evident that the contact surface is not a perfectly sharp boundary

between helium and test gas. Instead test gas concentration seems to increase over a

period of time.

A similar trend can be observed in IR emission which can be detected with the

arrival of the helium/test gas contact surface (CS) to the viewing port. The intensity

of IR emission increases through the CS passage as the CO2 concentration in the CS

increases. At the end of the steady test gas the emission intensity decreases as the

test gas cools down with the arrival of the expansion waves (reflected rarefaction tail).

During the steady flow test time, we observe that the IR emission is, however, not as

constant as the traces of the pitot and static pressures. Instead, an initial peak followed

by a monotonic increase are observed in the Mach 10 flow characterization (see Fig. 2.8).

In general, the intensity of IR emission increases with the volume of emitting gas, its

temperature and concentration. Since the IR emission is the integrated emission across

the tube including the wall boundary layer, it does not reflect the properties of the

core-flow only. The monotonic increase of the intensity (subsequent to the drop from

its initial peak value) can be explained as due to an increase in the volume of the hotter

CO2 in the growing boundary layer, while the initial peak signal can be attributed to

the small hot region formed by the reflected shock during the break of the helium/test

gas diaphragm.


-0.2 0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.5

1.0

1.5

2.0

2.5

3.0

Test Time

~270 msec

CS Velocity:

2360±25 m/s440±5 msec

Dx=104 cm

Rarefaction

Wave

Test Gas

CS

Shock Wave

Arrival HeliumFlow Time

~455 msec

Norm

alize

dP

itotP

ressure

-0.2 0.0 0.2 0.4 0.6 0.8 1.0

CS

Arrival

IRE

mis

sio

n

-0.2 0.0 0.2 0.4 0.6 0.8 1.00.0

0.5

1.0

1.5

2.0

CS Test Gas

Rarefaction

Wave

Shock Wave

Arrival

Norm

alize

d

Sta

tic

Pre

ssure

-0.2 0.0 0.2 0.4 0.6 0.8 1.00.0

0.5

1.0

1.5

2.0

time, msec

Test Gas

Rarefaction

Wave

Shock Wave

Arrival

Norm

alize

d

Mach

num

ber

FIGURE 2.8 Example of IR emission, pitot pressure, wall pressure records and the Mach number variationbased on the pitot-to-static pressure ratios, as a function of time for the Mach 10 flow condition.t = 0 represents incident shock arrival at the pitot probe, placed 2.5 cm downstream of the tubeexit, while the wall pressure transducer and IR detector are positioned 40.6 cm and 101.6 cmupstream of the tube exit, respectively (see Fig. 2.4). Note that the time scale of the staticpressure trace is shifted by 235 µs to match the shock arrival at the pitot probe.


The steady test period was taken to be the time over which the pitot pressure

changed by no more than ± 5% from the average value. Accordingly the measured test

time was approximately 270µs. The steady test period is always limited by the arrival

of waves, either the unsteady expansion waves (rarefaction tail) or the reflected waves

(reflected rarefaction head) from the intersection of the driver gas interface with the

unsteady expansion waves. In any case, the arrival of waves is clearly identifiable as

the test gas pressure rises sharply and the IR emission from cooling test gas begins to

decrease.

An average value of 2360m/s for the test gas flow velocity was measured over the

104 cm length between the IR emission port and pitot rake (see stages 4 and 5 described

above). The test gas velocity was also estimated from measured shock speeds in the

expansion section using inviscid 1-D theory, resulting in 2130 m/s. The measured ve-

locity (2360m/s) therefore exceeds the estimated inviscid value based on shock speed

by approximately 10%, as may be explained by the acceleration of the flow due to the

growing boundary layer on the tube walls.

The Mach number of the test gas was calculated using the measured contact surface

velocity and calculated sound speed as described in stage 3. The results indicated an

exit Mach number of 3.38±0.04 for the flight Mach 10 condition. Mach number variation

in the test gas can also be obtained from the pitot to static pressure ratio as shown in

Fig. 2.8. It is worth noting that while the static pressure of the test gas rose sharply

after the arrival of the reflected rarefaction wave, the Mach number of the flow varied

little over the following 400 - 500µs.

Figure 2.9 presents an example of flight Mach 13 flow characterization traces which

have features similar to those of flight Mach 10 traces. The characterization results

show a relatively long test time of 400µs in the case of flight Mach 13 simulation; this

is much larger than the ideal values (180µs). The test gas velocity was measured to be

3200m/s, about 23% faster than the shock-induced ideal flow velocity. This acceleration

of the test gas is again believed to be a result of the boundary layer developed on the

tube walls.

Shorter test times (∼170µs) are observed for low total-enthalpy conditions as shown

in Fig. 2.10 presenting an example of flight Mach 8 flow characterization traces. Note

that the static pressure stays constant for a longer period of time although the pitot

pressure increases significantly by the arrival of the first disturbances.


-0.2 0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.5

1.0

1.5

2.0

2.5

3.0

~180 msec

CS Velocity:

3200±50 m/s325±5 msec

Dx=104 mm

Rarefaction

Wave

Test Time

~400 msec

CS

Shock Wave

Arrival

Helium

Flow Time

Norm

alize

dP

itotP

ressure

-0.2 0.0 0.2 0.4 0.6 0.8 1.0

CS Test Gas

IRE

mis

sio

n

-0.2 0.0 0.2 0.4 0.6 0.8 1.00.0

0.5

1.0

1.5

2.0

CS

time, msec

Test Gas

Rarefraction

Wave

Shock Wave

Arrival

Norm

alize

d

Sta

tic

Pre

ssure

FIGURE 2.9 Example of IR emission, pitot pressure and wall pressure traces as a function of time for theMach 13 flow condition.

In Fig. 2.11, we compare the measured values of the free-stream velocity with the ex-

pected values estimated using the measured shock speeds in the expansion section. The

results indicate that the measured velocities are always larger than the expected ideal

values. In addition, as the flight Mach number increases and therefore the static pres-

sure decreases the measured velocity approaches the shock velocity. These observations

suggest that boundary layer effects are significant, causing the flow to be non-uniform.

As a result of the viscous effects, the shock slows down and the contact surface (test

gas) accelerates. At the limit of a sufficiently long expansion section, boundary layer

effects would cause the shock and the contact surface to equilibrate to a constant veloc-

ity. Accordingly, an additional calculation, taking into account the viscous effects based

on Mirels’ solution (Mirels 1963; Mirels 1966) for post-shock boundary layers, has been


-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2

0.0

0.5

1.0

1.5

2.0

2.5

3.0

CS

Test Time

~170 msec

Velocity: 1800±20 m/s

578±5 msec, Dx=104 cm

Rarefaction

Wave

Test Gas

Shock Wave

Arrival

HeliumFlow Time

~725 msec

Norm

alize

dP

itotP

ressure

-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2

CS

Arrival

IRE

mis

sio

n

-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.20.0

0.5

1.0

1.5

2.0

CS

time, msec

Test Gas

Rarefaction

Wave

Shock Wave

Arrival

Norm

alize

d

Sta

tic

Pre

ssure

FIGURE 2.10 Example of IR emission, pitot pressure and wall pressure traces as a function of time for theMach 8 flow condition.

performed, and will be discussed in the following section.

2.3.3 Boundary Layer Effects on Test Time

The uniform flow time of test gas at the expansion tube exit is defined as the test

time; this period begins with the arrival of the driven/expansion contact surface at the

tube exit, and ends with arrival of the first rarefaction wave (in our case, the rarefaction

head reflected from driver/driven contact surface as shown in the x-t diagram in Figs. 2.2

and 2.11.

Under ideal conditions, where no wall effects exist, the shock wave and the contact


4000

3500

3000

2500

2000

1500

1000

Velo

city, m

/s

3.63.43.23.02.82.62.4

Expansion Section Shock Mach Number, Ms,2

Mach 13P=0.04atm

Mach 10P=0.32atm

Mach 8P=0.65atm

Measured contact-surface velocity

Estimated shock-induced velocity Measured shock velocity

FIGURE 2.11 Comparison of the measured contact-surface velocity (test gas velocity) with the shock-induced gas velocity estimated using the measured shock speeds in the expansion section.

surface would move with constant velocities and the flow between them would be uni-

form. However, in a real shock tube, the flow becomes non-uniform as the boundary

layer develops at the tube walls. The presence of a wall boundary layer causes the

incident shock to decelerate and the contact surface to accelerate. Consequently, the

time duration of the flow between the shock and the contact surface (expansion section

helium flow time) is reduced. In conventional shock tubes, therefore, the test time is

reduced as a result of the boundary layer growth.

In expansion tubes, on the other hand, the effect of the boundary layer in accelerating

the contact surface can actually lead to an increase in test time as observed in our

experiments. We have measured 400µsec of steady test time at the Mach 13 condition,

while only 180µsec of test time is expected based on 1-D inviscid calculations (see x-t

diagram in Fig. 2.12a).

To study the boundary layer effects on the test time, we have performed an improved

calculation taking into account the viscous effects based on Mirels’ boundary layer

solution. The predicted contact surface velocity from this solution was implemented in x-

t diagram calculations and the results are plotted together with 1-D inviscid calculations

in Fig. 2.12a. The calculations (dashed lines in Fig. 2.12a) resulted in a test time of


3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0

0.0018

0.0021

0.0024

0.0027

0.0030

0.0033

0.0036Inviscid Solution

Mirels' Model

inc. boundary layer

rare

facti

onta

il

rare

fact

ion

head

reflected rarefactio

n head

Inviscid

CS

Incident Shock (Measured)

(measured test time = ~ 400 msec)

CS withBoundary Layer

ideal test time

180 msec

450 msec

tim

e,sec

x-distance, m

(a) Mach 13 condition

3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.00.0018

0.0021

0.0024

0.0027

0.0030

0.0033

0.0036

0.0039

0.0042

Inviscid

Mirels' Model

inc. boundary layer

Invisc

idCS

Incident Shock (Measured)

(measured test time = ~ 270 msec)

CS withBoundary

Layer

ideal test time

140 msec

380 msec

tim

e,sec

x-distance, m

(b) Mach 10 condition

FIGURE 2.12 X-t diagrams for the expansion section only. 1-D inviscid calculations are plotted in straightlines and results applying Mirels’ model to include the boundary layer effects are plotted indashed lines. One can see the improved test time as a result of the contact surface (CS)acceleration due to the developing boundary layer behind the incident shock in the low pressureexpansion section helium flow. The incident shock velocity was measured and assumed to beconstant along the expansion section.


450µsec, agreeing well with the measured value of 400µsec. This effect can be explained

by the fact that the contact surface, accelerated by viscous effects, arrives at the test

section earlier than if viscous affects were negligible. Therefore, the test time duration

is increased as the time of arrival of the first flow disturbance is delayed relative to the

contact surface arrival.

An additional interesting result can be observed from the x-t diagrams: the length

of the current expansion section is seen to be optimum to achieve a maximum test time

duration for flight Mach 13 simulation as the arrival of both the rarefaction wave and

the reflected rarefaction head overlap at the end of the tube (see the dashed lines in

Fig. 2.12a.) Any variation in the length of the expansion section will cause the test

time to decrease. By contrast, the x-t diagram calculated for the Mach 10 condition

(Fig. 2.12b) demonstrates that the expansion section length is longer than its optimum

value. A 30% longer test time could have been achieved if the expansion section was

1.8m shorter than its current length.

The calculation based on Mirels’ solution also gives an improved estimation of the

expansion section helium flow time of 170µsec, which compares well with that inferred

from the pitot pressure trace, 180µsec (within 5.5% accuracy). The test gas velocity

obtained from this calculation, 3300m/s, shows improved agreement with the measured

value of 3200 (within 3%). These results, summarized in Table 2.2, confirm the impor-

tance of boundary layer effects and demonstrates that the viscous calculations based on

Mirels’ model provide good estimates of the test time and the test gas velocity at the

low pressure flight Mach 13 condition.

Mirels’ solution, performed for the flight Mach 10 condition (see Fig. 2.12b), results

in a less accurate prediction of flow properties. As summarized in Table 2.2, the cal-

culated test time based on Mirels’ solution overpredicts (by 41%) the actual test time.

The reason for the overprediction is that the initial filling pressure in the expansion

section is relatively high (20 torr), and therefore the wall boundary layer behind the

shock wave is not fully developed as assumed in Mirels’ solution. In addition, we have

assumed that the boundary layer properties of the test gas were similar to the properties

of the expansion section helium gas, which can be significantly different as the pressure

increases.

We have shown that the flow test time is affected by the boundary layer development

in the expansion section tube walls in such a way that the steady test time duration is


TABLE 2.2 Summary of measured, ideal (inviscid 1-D) and predicted (based on Mirels solution) propertiesof test gas for Mach 10 and 13 flow conditions.

Test Time Test Gas Helium FlowVelocity Time

µsec m/s µsecMeasured 270± 10 2360± 25 455± 2

Mach 10 Ideal 140 2130 660Mirels 380 2510 520

Measured 400± 10 3200± 50 180± 2Mach 13 Ideal 180 2440 520

Mirels 450 3300 170

increased. Longer test times are important in supersonic flow experiments as the length

of the test period determines the maximum model length for which steady flow can be

fully established.

2.3.4 Core-Flow Size

The other parameter which limits the maximum model length is the radius of the

axially uniform flow called the useful core-flow. While the test time increases as the

boundary layer on the tube walls develops, the useful core-flow size, on the other hand,

becomes smaller. The thickness of the boundary layer developed in the acceleration

section can be large in comparison to the tube radius because of the low filling pressures

of the expansion section.

In our experiments, we characterized the useful core-flow size by measuring the pitot

pressure at different radial and axial locations. The results, plotted in Fig. 2.13, show

that at 12.7 mm (0.5”) away from the tube exit, pitot pressure varied only ±5% within

a 25 mm core-flow diameter for the three conditions that we have studied. As we moved

the pitot probe downstream of the tube exit, the core-flow size at the Mach 13 condition

did not change significantly. On the other hand, the flight Mach 10 and 8 conditions

resulted in a deceased core-flow size as we moved away from the tube exit. At the

Mach 8 condition, the pitot pressure at the center line of the tube decreased by 15%


at 63.5 mm (2.5”) downstream of the tube exit. This is expected for the flight Mach 8

condition, since the Mach number of the free-stream is only about 2.4, corresponding

to a steeper Mach wave angle.

In conclusion, the results indicate the existence of a 25 mm core-flow diameter that

is suitable for near-field studies of transverse fuel jets injected from a 2mm diameter

orifice. The injection plate is positioned as close as possible to the tube exit and 6.4 mm

(1/4”) below the centerline to allow a maximum field of study of the jet.

2.3.5 Flow Establishment Time

Undesirably, part of the steady test time is consumed during the flow establishment

process for the model under investigation. Correlations are available in the literature

(Rogers and Weidner 1993; Jacobs et al. 1992; Davies and Bernstein 1969; Holden 1971)

for predicting the flow establishment times for different flow features of the model. In

general, the test “slug length”, defined as the distance traveled by the volume of test

gas during the period of steady test time, must be larger than the characteristic length

of the flow device or process by some multiple. The criterion for the establishment of

flow over a flat plate requires that the test “slug length”, i.e., the product of test time

and gas velocity, t · u, satisfies (Davies and Bernstein 1969).

t · u =

2 · L1, for turbulent boundary layer

3 · L1, for laminar boundary layer(2.7)

where L1 is the distance from the edge of the plate. The flow establishment criterion

for separated flows, on the other hand, is required to be tens of times larger than the

characteristic recirculation region length L2, as given by (Holden 1971) for the wake of

sphere

t · u =

for separated flows

30 · L2, based on pressure measurements

70 · L2, based on heat transfer measurements

(2.8)

Note that L2 is the length of the recirculation region and therefore smaller than the

characteristic distance L1 by more than an order of magnitude, resulting in similar flow

establishment times.


(a)

1.0

0.8

0.6

0.4

0.2

0.0

Norm

aliz

ed p

itot pre

ssure

403020100-10-20

Free-stream flow radius, mm

Distance from the tube exit 12.7mm (0.5") 38.1mm (1.5") 63.5mm (2.5")

Flight Mach 13 condition

useful core flow~ 25 mm

(b)

1.0

0.8

0.6

0.4

0.2

0.0

No

rma

lize

d p

ito

t p

ressu

re

403020100-10-20




(c)

1.0

0.8

0.6

0.4

0.2

0.0

Norm

aliz

ed p

itot pre

ssure

403020100-10-20




FIGURE 2.13 Useful core-flow size in flight Mach 13, 10 and 8 conditions, (a), (b) and (c), respectively,determined by measuring the radial variation of pitot pressure at different distances from thetube exit.


Based on these correlations, we have estimated two flow establishment times in our

experiments and summarized the conclusions in Table 2.2. First, the boundary layer

flow establishment time was calculated by assuming laminar flow, as the local Reynolds

numbers at the injection port were relatively small. Second, the establishment time of

the recirculation region upstream of the injection port was estimated. In general, the

bow shock around the jet interacts with the approaching boundary layer and causes its

separation. This recirculation region length confined with the separation shock wave

was measured from schlieren images and used as the characteristic length, L2, of the

separation zone.

The estimated flow establishment values indicated that the “test slug” (1.28m) for

the flight Mach 13 condition is fairly long as compared to the predicted flow estab-

lishment times (0.15m for boundary layer and 0.56m for the recirculation region heat

transfer establishment time =0.71 m in total). Therefore, about 0.60 m of a “test slug”

or 235µs of test time is still available for measurements. By contrast, at the flight

Mach 8 condition, flow establishment seems to consume most of the steady test time.

However, it is worth noting that the expansion section helium flow prior to the test gas

arrival contributes to the establishment of jet flow even though it is not considered as a

part of the test time. Furthermore, the useful test time in our experiments is determined

using the pitot probe after the flow is established around it. Therefore, the estimated

flow establishment times given in Table 2.2 are expected to be larger than the actual

flow establishment times, so that even at the flight Mach 8 condition, part of the slug

length is useful for measurements after the flow-field is established.

To summarize, as the flight Mach number in our facility increases, a longer test

“slug length” becomes available for measurements. This is a result of the long test

times achieved with high-total enthalpy, low-pressure conditions and the fact that higher

speed implies faster flow establishment.

2.4 Summary

We used the Stanford expansion tube to generate high total enthalpy flow conditions

in the Mach 8-13 flight range. A variety of supersonic flow conditions are also simulated

in the facility for fundamental mixing studies of transverse jets. These conditions are

summarized in Chapter 5. See also Appendix B for maps of ideal flow conditions that


can be achieved using an expansion tube. The maps are calculated for different free-

stream gas (Nitrogen, Helium and Argon) and for two different initial driver pressures

(P4 = 300 and 600 psig).

Chapter 3

Flow Visualization Techniques

Much of our basic understanding of the behavior of flows has come from flow visu-

alization. One of the best examples of this is the work of Brown and Roshko (1974),

which shows the existence of large scale structures in a two-dimensional shear layer using

shadowgraphs. A clear visualization of axisymmetric shear layers, as the one present in

the periphery of transverse jets in crossflows, is more difficult to achieve due to three

dimensional effects, especially when the jet characteristic length is as small as d=2mm.

The flow visualization of transverse jets in supersonic crossflow studied in this work

was obtained using an ultra-high-framing-rate schlieren system and Planar Laser In-

duced Fluorescence (PLIF) of the hydroxyl radical (OH). The ability to image the flow

with good temporal and spatial resolution is particularly important, because of the high

velocities of the flows and also because it provides a means of examining the instanta-

neous turbulent structures that control the mixing and combustion processes.

3.1 Ultra-Fast Framing Rate Schlieren

The ability to capture the time evolution of unsteady supersonic flows is critical to

their understanding. Non-intrusive visualization techniques, such as schlieren and laser-

based planar flow imaging, are powerful and commonly used optical methods. However,

tracking the structural evolution of high-speed flows requires acquisition of images at

fast (typically MHz) repetition rates. In addition, very short exposure times (20-200 ns)

are required to resolve instantaneous features. As the spatial resolution is increased to

41

CHAPTER 3. FLOW VISUALIZATION TECHNIQUES 42

avoid the blurring of turbulent structures, the exposure time must be reduced and the

repetition rate increased. It is challenging to fulfill the temporal resolution requirements

of high-speed imaging while maintaining meaningful spatial resolution for supersonic

flows.

Before we introduce previous and current efforts towards the development of super-

sonic flow visualization at ultra-fast-framing rates, it is useful to present the motivation

behind such efforts. Of great interest is the study of shear layers formed at the interface

of two parallel or skewed fluid streams. Since Brown and Roshko (1974) demonstrated

that large-scale coherent structures are dominant in subsonic shear layers and that their

structure and evolution control the mixing process, many researchers have concentrated

their efforts on measuring large-scale convection characteristics of shear layers in super-

sonic flows. However these studies were limited to double-pulse visualization techniques,

such as double-pulse schlieren by Papamoschou (1991), double-pulse Mie/Rayleigh scat-

tering by Elliott et al. (1995), double-exposure planar laser-induced fluorescence (PLIF)

of acetone by Papamoschou and Bunyajitradulya (1997) and Fourguette et al. (1991)

and double-pulse imaging using simultaneous aceton/OH-PLIF by Seitzmann et al.

(1994). Those studies focused on measuring the convective velocity (Uc) of large-scale

structures by capturing a maximum of two images that are temporally correlated.

Of particular interest to our research is the shear layer formed when a gaseous jet

interacts with a supersonic crossflow stream, an example of skewed shear layers. This

is also a common fuel injection scheme in practical systems, such as a scramjet, and

therefore fundamental study of its mixing process is important. Although there have

been numerous studies of the shear layer properties of two parallel streams, there have

been relatively few works on jets in supersonic crossflow. Among those studies only

Gruber et al. (997a) studied the large-eddy convection characteristics of jets in su-

personic crossflow, again by capturing two consecutive Rayleigh/Mie scattering images.

Their results revealed the convection characteristics of helium and air jets injected into

a Mach 2 crossflow. The highly compressible helium jet exhibited larger convection

velocities in the near-field of the injection than the air jet of low compressibility. How-

ever, the accuracy of the velocity measurement was only about ±10%, as the minimum

separation between the laser pulses was limited to 1µsec.

It is crucial to characterize the full life cycle of the flow-field. For example, the large-

scale eddies, formed periodically at the early stages of shear layer development, undergo


structural evolution as they convect downstream while entraining, pairing, engulfing,

stretching and tearing. Therefore, measurement of the formation frequency of these

eddies and their evolution should aid understanding of the origin and formation of the

jet vortical structure and, hopefully, provide tools in controlling its mixing properties.

Such studies require application of an ultra-high-speed imaging system.

In our experiments, we therefore selected a new fast-framing imaging system capable

of recording 8 consecutive high-resolution schlieren images at rates up to 100 MHz. Our

goal is to study the time evolution and convection properties of large-scale structures

present in the shear layer of the jet/free-stream interface. It is important to understand

how these structures and growth rate vary as flow conditions and fuel types are changed.

Moreover, most of the earlier jet studies were carried out in blow-down wind tunnels

where the free-stream conditions were usually of low temperature and therefore with

relatively low speeds. Free-stream velocity in the experiments of (Gruber et al. 997a),

for example, was about 515m/s. In our experiments we employ an impulse facility which

can generate realistic conditions of a typical supersonic combustor with high velocities

(1800-3300m/s) and high static temperatures (1300K) (Ben-Yakar and Hanson 2000).

However, these facilities have short test times (∼0.2 - 2ms) during which there is only a

brief opportunity to perform a flow-diagnostic measurement. As a result, application of

MHz imaging in impulse facilities becomes almost necessary as we can obtain multiple

images that are also time-correlated. In our facility, the amount of data obtained per

experiment is, therefore, increased by at least 8 times by the new ultra-high-speed

imaging system.

In the following sections, we present the components of the ultra-fast schlieren

imaging system and discuss issues of resolution, timing, synchronization and image-

processing techniques.

3.1.1 Previous and Current High Speed Imaging Efforts

High-speed imaging requires two components: a camera which can acquire at high

framing rates and a light source with either long duration time or high pulsing rate.

Early flow visualization at high-speed framing rates was performed using a rotating

mirror camera. Mahadevan and Loth (1994), for example, utilized a rotating mirror

camera to temporally resolve compressible mixing layer structures at approximately


350 kHz using schlieren and Mie scattering. A Xenon flash system with square pulse

durations up to 200µs was used as a continuous light source. The quality of images was

poor because of the low resolution and blurring of the images due to the convection of

the flow structures.

Patrie et al. (1993, 1994), on the other hand, performed 3-D snapshots of instanta-

neous flow structures using Mie scattering and laser-induced fluorescence of flames and

turbulent jets. Their camera system included a high-speed image converter coupled by

fiber optics to a CCD camera. Up to 20 sequential planar images were collected at the

rate of 10 MHz. The output of the system was a single digital image with 400× 700

pixels, containing the sequence of 20 images, namely, each image was approximately

160× 140 pixels for a 10 image set. This imaging system required post-processing al-

gorithms to correct the spatial distortion of the images caused by electrodynamic in-

teraction of the photoelectric currents within the camera. Island et al. (1996) used

the same imaging system to study the three-dimensionality of supersonic mixing layers.

The planar illumination for a 3-D scan was provided from a 2µs pulse duration of a

flashlamp-pumped dye laser with a pulse energy of 3 J at 590 nm. The laser output

was reflected from a high-rpm rotating mirror. The pixel resolution was approximately

1mm resolving only the largest scales of mixing.

Recently, several researchers including Huntley et al. (2000), Thurow et al. (2000)

and Wu et al. (000b) reported their efforts toward MHz-rate digital planar flow visualiza-

tion using a prototype CCD camera manufactured by Princeton Scientific Instruments,

Inc. (PSI) with pixel format of 180× 90 or 180× 180. This camera has a 32 image stor-

age buffer built onto the image sensor chip itself, and can frame at rates up to 1 MHz.

The drawback of the PSI camera is the low pixel resolution of images (the pixel size is

50µm× 50µm) and the low fill factor of the light sensitive area which is about 14%.

Princeton Scientific Instruments, Inc has attempted to develop this unique high-speed

framing CCD camera under a government SBIR contract. However, further develop-

ment of this prototype camera is currently not possible because of the manufacturing

difficulties of the chip.

The PSI camera is typically paired with a laser working in a pulse “burst” concept

(Wu et al. 000b). The “burst”train of 30-40 pulses was formed by applying a high-speed

Pockel Cell “slicer”to the long duration output (200µs) from a continuous wave (CW)

Nd:YAG ring laser. The energy of each of the individual pulses comprising the train was


0.5 - 1mJ, with minimum separations of 1ms (1MHz). With this energy level of pulses

the researchers succeeded in performing CO2-enhanced Filtered Rayleigh Scattering

measurements in supersonic flows.

As summarized above, since the early 90’s, several research groups attempted to

perform high speed imaging of supersonic flows. Their results showed the excellent

potential of high speed 2-D and 3-D measurements. However, their imaging systems

were usually of low resolution and low light sensitivity.

In the following sections, we present initial results with a new commercial imaging

system that can capture images (free of distortions) at rates up to 100 MHz. The system

includes a fast framing rate camera (IMACON 468) combined with a long duration, high

intensity light source (Xenon flashlamp) to acquire 8 consecutive schlieren images of

supersonic flows with 578× 384 pixel resolution. In this system, resolution and blurring

of the images can be controlled by adjusting the image exposure time which can be as

small as 10 ns.

A similar fast framing camera system with a maximum repetition rate of 1 MHz

is also being used by Kaminski et al. (1999) to study turbulent reacting flames. The

system performance was demonstrated at 8 kHz repetition rate using a custom-built

unit (BMI) of four double-pulsed Nd:YAG lasers with an accompanying dye laser. This

laser system allowed variable inter-framing times of 25 to 145µsec.

3.1.2 High-Speed Schlieren Imaging Components

The ultra-fast-framing schlieren system illustrated in Fig. 3.1 comprised three com-

ponents: 1) a high-speed framing camera, (Imacon 468, manufactured by Hadland Pho-

tonics), 2) a long duration light source, (Xenon flash-lamp), and 3)mirrors and knife

edge in a standard Z-arrangement.

The Imacon 468 consists of 8 independent intensified CCD cameras for high-speed

framing that can capture 8 consecutive images with variable exposure and interframing

times down to 10 ns. The single optical input is divided uniformly and distortion-free by

a special beam splitter into 8 different intensified CCD modules, each with a 576× 384

array of 22× 22µm size pixels.

The light source is a high intensity Xenon flash discharge unit (Hadland Photonics

model 20-50 flash system with an extension to 200µs duration). The unit has three


Xenon FlashLight Source

Mirror 1

Test Section

Mirror 2

KnifeEdge

FocusingLens

Camera

Fiber Optic Link

Control Computer &Image Monitor

Input Trigger

Power Supply

IMACON 468

FIGURE 3.1 Schlieren imaging set-up.

ranges providing 20µs, 50µs and 200µs durations of the light source with intensity

levels of each being 125 J, 375 J and 700 J per pulse, respectively.

In the optical set-up, two f/10, 200 cm focal length concave mirrors are used to

collimate the light through the test section, and then refocus it onto a knife edge (razor

blade). This knife edge (KE) at the focal point of the second schlieren mirror is used to

partially cut off the deflected rays for observing the schlieren effect (visualization of the

density gradients). Blocking more of the light by moving the KE transverse to the optical

axis makes the system more sensitive, showing more features of the jet (Merzkirch 1965).

The KE, oriented horizontal or vertical with respect to the focused light, will emphasize

the density gradients in the horizontal or vertical directions respectively. In Fig. 3.2,

examples of schlieren images with different KE orientations are presented. These are

the images of an underexpanded hydrogen jet issuing into quiescent air. Significant


(a) (b) (c) (d)

Knife edge

Razor blade

Light source

at the focal point

FIGURE 3.2 Examples of schlieren images of jet issuing into quiescent air as obtained for different positionsof the knife edge (razor blade) at the focal point. We use the set-up demonstrated in (d) wherethe knife edge cuts the focused light at an angle to enhance both the vertical and the horizontaldensity gradient effects.

differences in the details of the flow-field can be observed just by positioning the KE

at different orientations. In our experiments, the KE is positioned at 45o to emphasize

both the vertical and horizontal gradients.

The test object is then imaged with a single constant focal length lens onto the

intensified CCD camera. Two different focal length lenses (an f/12.5, 100 cm focal

length lens and an f/6, 49 cm focal length lens) were used to capture different sizes of

the field of interest. For the images presented in this paper, de-magnification of 0.44

was required and obtained using a 100 cm focal length (f/12.5) lens.

3.1.3 Timing and Synchronization

Flow establishment, timing and synchronization are important issues that have to

be addressed very carefully in preparation of an experiment in an impulse facility. The

imaging system must be synchronized with the facility operation and the delay times

must be set to allow the data to be acquired during the short steady test time. There-

fore, test flow arrival and its steady duration are first studied through characterization

experiments (see Chapter 2) to determine the required delay times. The general ap-

proach is to replace the injection plate with a pitot probe and to trace the flow history at


1 2

Injection Valve

P8 trig in

Valve opens

P2 trig in

Trigger pulse

to the imaging systemPulse Generator

Pitot Pressure

83 4 5 6 7

Ultra-Fast Framing Camera

Hadland Imacon 468

Xenon Flashlamp

Light Source

Driver Section Driven Section Expansion Section

P8P9P10 P1P2P3Pressure Transducers:

1.1-1.2 ms ~ 1.1 ms

Shock wave

arrival

Test time = 270 sm

20, 50 or 200 sm

Free-stream

flow is established

Exposure time

typ. 100-200 ns

Interframing time

typ. 0.5-3 sm

FIGURE 3.3 Timing diagram of the high-speed rate imaging system and its synchronization with the expan-sion tube test flow time.

the injection location by analyzing the pitot pressure. An example of the pitot pressure

trace is given in the timing and synchronization diagram described in Fig. 3.3. Based on

the time history of this pitot pressure, it is possible to identify the arrival of the shock

wave, the time period of expansion section flow, the pressure rise as the contact surface

between the test gas and expansion section gas arrives, and finally the steady flow test

time. The images can be acquired during the last ∼100µsec of the 270µsec window of

the steady flow test time, after the free-stream flow around the jet is established.

As described in Fig. 3.3, the imaging system and the injection plate are synchronized

by the instantaneous pressure rise of one of the piezoelectric transducers located on the

tube walls as the incident shock travels through. The injection system is triggered

early enough to allow the injector valve to actuate and the underexpanded jet to be


fully developed by the time the steady test flow conditions are obtained. Within that

constraint, the time interval between the valve actuation and the test gas arrival should

be short enough to avoid significant changes in the expansion section initial pressure.

The delay times for the imaging system are then set to sample during the actual test

time when both the free-stream (expansion tube flow) and the flow around the jet are

established.

The high-speed camera, IMACON 468, and the long-duration light source receive

the delayed trigger pulse simultaneously. The gating/exposure times of the 8 intensifiers

and their interframing times are then controlled by the image acquisition computer. The

first ICCD is set to acquire after the build-up time of the light source as the uniform

light intensity is achieved.

3.1.4 Resolution Considerations

Each intensified CCD detector in the ultra-fast framing camera has an 8-bit dynamic

resolution (0 - 255 gray scale) 576× 384 array with 22× 22µm pixel size. For the results

presented in Chapter 4, the field of view is about 28× 18mm (de-magnification of 0.44),

corresponding to a minimum spatial resolution of 50× 50µm.

Visualization without blurring from the flow velocity requires careful consideration

of the gating/exposure time. First the characteristic length scales and velocities of the

flow-field need to be known. In the experiments presented in Chapter 4, we study the

time evolution of jets issuing from a 2 mm sonic orifice into a high speed (2360m/s)

free-stream. Of particular interest is the convection characteristics of the jet-shear layer

large eddies with dimensions ranging between 1-2 jet diameters (2 - 4mm). We expect

these structures to travel at speeds between that of the jet at the injector exit and

the free-stream flow, namely between 1205 - 2360 m/s (∼1.2 - 2.4 mm/ns) in the case of

hydrogen injection. Therefore, to achieve 1 pixel spatial resolution (50× 50 µm), the

exposure time must be in the range of 42 - 21 ns.

Exposure time of schlieren images are determined by optimizing the following com-

peting factors: 1) schlieren sensitivity, 2) spatial resolution, 3) dynamic range, and 4) signal

to noise ratio. The sensitivity to detect the smallest density gradients in the flow, is con-

trolled by the KE position when the light source intensity and the optical components

are fixed. As the KE cuts off more deflected rays, schlieren sensitivity increases while


less light reaches into the camera. For short exposure times, however, a high intensity

light source is required to cover the full dynamic range (256 gray levels). Therefore,

we performed an optimization between these counteracting effects to achieve the best

performance available from the system. We chose an exposure time of 100 ns to visualize

the flow-field of 28× 18mm, even though shorter gating times as low as 10 ns are avail-

able in our ultra-fast-framing camera. During 100 ns, the large scale structures translate

120 - 240 mm which is about 2 - 10 % of their thickness (2 - 4 mm). This corresponds to

blurring of images by 2 - 5 pixels. In addition, the ICCD modules were set to intensify

30 - 40% of their maximum potential. We found that larger gain results in noise levels

that confuse the details of the flow features.

Figure 3.4 represents 3 examples of schlieren images captured with different exposure

times, 100 ns, 200 ns and 3µs. Schlieren images with a 100 ns exposure time (Fig. 3.4a)

provide the instantaneous features of the flow-field with an optimized spatial resolution

(2 - 5 pixels). Increase of the exposure time to 200 ns (Fig. 3.4b) results in a significant

blurring of the features, as the flow structures translate larger distances (4 - 10 pixels).

Instantaneous flow features are eventually diminished with further increase of the inte-

gration time to the order of microseconds (Fig. 3.4c). While, the instantaneous features

of the flow are wiped out due to the integration during the long exposure time, these

images, on the other hand, provide information on the average features of the flow-field.

Note that the noise level in the long exposure image is very low as the intensifier is set

to its minimum value. Average features with laser-based diagnostic techniques can be

achieved only by capturing a large number of images as the integration time is fixed

with the laser pulse width or the fluorescence time. As noted in the introduction it is

very difficult to achieve multiple images in an impulse facility because of the short test

times. Observations obtained from the schlieren images of Fig. 3.4 will be discussed in

Chapter 4.

Temporal resolution, or the interframing time, was chosen so that we could capture

events occurring on very short time scales, less than or equal to the convection time of

the flow through the region of interest. For the jet diameter (2 mm) and free-stream ve-

locities up to 4000m/s, studied in our investigation, framing rates of 2MHz to 200 KHz

(interframing times between 0.5 - 5µsec) are needed to resolve and to follow the devel-

opment of the flow structures (convection of large eddies, fluctuation of shock waves

around the jet.)


(a)

(b)

(c)

FIGURE 3.4 Examples of schlieren images with different integration/exposure times: a) 100 ns exposuretime, resolving the instantaneous features of the flow-field, b) 200 ns exposure time, resultingin blurring of the image, c) 3 µs exposure time, averaging the general features while enhancingthe weak shocks such as upstream separation shock wave and downstream recompression wave.


( )tD

Dt

yyU;

Dt

xxU 12

cy12

cx

-=

-=

÷÷ø

öççè

æ

--

=12

12

xx

yyarctanF

F

FIGURE 3.5 Timing diagram of the high-speed rate imaging system and its synchronization with the expan-sion tube test flow time.

3.1.5 Image Processing and Analysis

Post image processing of the images was performed using several image processing

software packages (IPLab, Matlab, Adobe Photoshop and Premiere). Background im-

ages were acquired just prior to each test and subtracted from the schlieren image to

eliminate speckle from the imperfections in the test section windows. Normalization of

the intensity levels and the “gamma-factor” were changed to improve the contrast of

the images. “Gamma-factor” is a factor applied to intensity distribution of images to

enhance the perception of the human eye which has a non-linear sensitivity.

To compute the convection characteristics of the large-scale eddies each individual

structure was tracked with the cross-correlation method using the fast Fourier transform

(FFT). In this tracking procedure, we measured the displacement of a particular feature

in the streamwise and transverse directions. Guidelines for a fully automated classical

cross-correlation method can be found in Smith and Dutton (1999). We utilized an

FFT in our cross-correlation method to decrease the image-processing time.


The cross-correlation is calculated (see Fig. 3.5) from the complex conjugate multi-

plication of their Fourier transforms:

Rfg(∆x,∆y, ∆t) ⇔ F (∆x,∆y, ∆t + ∆t) ·G∗(∆x,∆y, ∆t) (3.1)

The size of the interrogation window (128× 128 pixels for the results presented in this

paper) is selected to be large enough to include the eddy and its later location while

maintaining the maximum resolution. Figure 3.5 describes the cross-correlation proce-

dure and presents a representative cross-correlation field of the two images shown in

the same figure. The highest cross-correlation magnitude corresponds to the convection

distance of the large-scale structure. Therefore, the correlation peak was detected by

simply scanning the correlation plane Rfg for the maximum correlation value R(i, j)

and storing its integer coordinates (i, j) with uncertainty of a ±1/2 pixel. A subpixel

accurate displacement estimate could be achieved for example by applying three point

interpolation (Raffel et al. 1998). However, the largest uncertainty in our measurements

originates in the determination of the interrogation region. In summary, displacement

measurement accuracy in our technique is ±1 pixel which corresponds to a velocity

uncertainty of ±50m/s (∼2% of the free-stream velocity) when the interframing time

is 1 µs.

Once the displacement from image to image is known, the large-scale convection

velocity and the convection angle are determined using

Uc,x =x2 − x1

∆t, Uc,y =

y2 − y1

∆t(3.2)

Φ = arctan(

x2 − x1

y2 − y1

)(3.3)

where ∆t is the interframing time between images. An interframing time of ∆t = 1µs

was chosen based on the residence time of the eddies in the field-of-view. It takes the

coherent structures about 8µs to travel 6 jet diameters near the injector port. For

interframing times larger than 3µs, it becomes difficult to track the structures as they

travel large distances.

3.2 OH-PLIF

PLIF imaging of reactive flows relied on OH, a naturally occurring combustion

radical, as the fluorescent tracer. OH is an indicator of ignition and reaction zones. For


the purpose of this thesis, OH visualization provides information on whether ignition is

occurring at all, and if so, in which regions it does occur.

3.2.1 Excitation and Detection Strategy

The OH-PLIF measurements are obtained by excitation of the A2 ∑+ ← X2Π(1, 0)

band of OH, near 283 nm combined with detection of the strong (1,1) band near 315 nm

(ranged from ∼308 - 325 nm). This excitation strategy, which can be performed using a

frequency-doubled dye laser, was chosen to avoid fluorescence trapping, the absorption

of the emitted OH fluorescence by other OH molecules (Seitzmann and Hanson 1993).

In addition, the limited pulse energies (∼1-30mJ) available from the frequency-doubled

dye laser sources provide a linear fluorescence measurement regime.

The isolated Q1(7) transition at 283.266 nm is selected to minimize signal dependence

on temperature (i.e., ground state population). For J”=7.5, the population term is only

weakly sensitive to temperature over a wide range of temperatures (i.e., 1500-3000K).

The relative uncertainty in number density for a nearly constant pressure region is

approximately ±10% due to Boltzmann temperature variations (Parker et al. 1995).

3.2.2 OH-PLIF Laser Source and Tuning

The UV laser radiation for excitation of the OH molecule is provided by the frequency-

doubled output of a dye laser pumped by a pulsed Nd:YAG laser (Lumonics models

YM-1200, HD-500, HT-1000). The 532 nm output of the Nd:YAG laser (400-450 mJ)

pumps the grating-tuned dye laser which provides approximately 60 - 70mJ/pulse at a

wavelength of 566 nm using Rhodamine 590 dye. The dye laser beam formed as a 0.5 cm

wide sheet is frequency doubled using a KT*P crystal in a temperature controlled hous-

ing, which is angled-tuned with a stepper-motor system to provide maximum energy

(8 - 10mJ/pulse at 283 nm).

At the exit of the frequency doubler, a Pellin-Broca prism is used to separate the

UV beam from the fundamental. The beam is raised and turned toward the test section

using four UV-enhanced turning mirrors and it expands to almost 35mm near the test

section. The beam is then focused into a 300 - 400µm thick× 35mm wide sheet using

a f = 50 cm spherical lens. The top test section window, through which the laser sheet

reaches the injection plate, is made of fused-silica to provide a low UV-beam reflection.


The laser tuning is performed using a fluorescence measurement in an atmospheric

methane/air flame. The actual laser calibration (the dial offset) is determined by mea-

suring the OH-fluorescence across multiple excitations in the wavelength range 280 -

285 nm and comparing the results to the estimated spectra using the programs LINES

and SPECTRA (Seitzmann 1991). The fluorescence is collected using a Hamamatsu

photomultiplier tube (PMT) fitted with Schott UG11 and WG-305 filters, and the re-

sulting PMT signal is integrated using a boxcar averager. The laser wavelength dial

offset did not drift significantly from day to day and, therefore, it was not necessary to

perform this tuning procedure before each experiment.

The laser linewidth in the current experiments is broader than the absorption

linewidth by almost an order of magnitude. The absorption linewidth for OH is around

0.04 cm−1 for the temperature and the number densities present in the current work,

and the laser linewidth is approximately 0.3 cm−1. The assumption of broad excitation

is then valid, minimizing the potential errors due to laser tuning and lineshape effects.

A real-time laser sheet correction is performed using a beam splitter/dye-cell/CCD

camera arrangement (McMillin, Seitzmann, and Hanson 1994). The laser sheet energy

distribution is measured by imaging the visible fluorescence of a dye-cell containing

a Rhodamine 6G dye/methanol mixture which is excited by the partial reflection of

the laser sheet. A Cohu 4810 CCD camera with an f/1.8 Nikon (50 mm) lens is used to

detect the visible fluorescence from the dye cell. Post-image processing, performed using

commercially available software, includes remapping of the 1-D laser intensity profile

into 2-D sheet and normalization of the OH-PLIF image by this 2-D intensity profile.

3.2.3 OH-PLIF Imaging System and Its Spatial Resolution

The fluorescence is collected onto the 578× 384 pixel array of an ICCD (Princeton

Instruments) camera using a UV lens system (Nikon 50mm, f/4.5). UG-5 and WG-305

Schott glass filters (2 mm thick) are used to block elastic laser scattering and background

emission which was minimal in the current experiments.

For the jet-in-crossflow and the cavity experiments performed in this thesis, the

imaged region was 20× 30mm. The minimum flow feature that can be resolved with

an ideal detection system is ∼51µm corresponding to 51× 51µm per pixel (based on

384× 578 array with 23µm pixels, magnification=0.45). In a real system, however,


the minimum spatial resolution is actually limited to about 3 - 4 pixels (McMillin 1993)

because of the imperfections in the imaging system (focusing errors, limited spatial

resolution of the intensifier). Thus, the gating time of the camera intensifier is set to

collect photons for a maximum duration of 100 ns to prevent further resolution reduction

by flow motion. In conclusion, the resulting resolution of the PLIF imaging system is

∼200 - 250µm (4 - 5 pixels).

3.2.4 Interpretation of OH-PLIF

The relationship between the fluorescence signal and number density or mole fraction

has been described by Hanson et al. (1990). Briefly, the fluorescence is proportional to

the laser energy, the fluorescence yield, the species number density, and the Boltzmann

population fraction for the absorbing transition. Effective combustion visualization with

OH PLIF requires that the variation in OH mole fraction in the region of interest affect

the fluorescence signal more than changes in the other parameters described above. The

most critical issue, typically, is the temperature dependence of the Boltzmann fraction

of the absorbing state. At the combustion pressures in this work, the fluorescence signal

can be modeled as (Hanson et al. 1990):

Sf = χOH

[fJ”√

T

](3.4)

where χOH is the OH mole fraction, and fJ” is the Boltzmann fraction of OH molecules

in the absorbing state. For the absorption transition considered here - the Q1(7) tran-

sition of the A2 ∑+ ← X2Π(1, 0) band of OH, located at 283.31 nm - such effects play

a relatively minor role in interpreting the signal in the regions observed to contain OH,

and the fluorescence intensity can be qualitatively linked to OH mole fraction.

3.3 Simultaneous Schlieren and OH-PLIF

Two intensified CCD cameras are used simultaneously to collect both schlieren and

OH-PLIF images. The fluorescence signal is collected through the same exit window as

that of the schlieren system. To separate both light signals, we mount a 5 cm diame-

ter dichroic mirror at 45 o to the optical axis perpendicular to the exit window. The

dichroic, designed for larger than 99% reflectivity between 300 and 320 nm, reflects the

OH fluorescence but is transparent to the schlieren beam.


Figure 3.6 shows the triggering and timing diagrams of the simultaneous schlieren

and OH-PLIF imaging. A homemade firing box and two delay generators are used to

synchronize the laser/Xenon-lamp/cameras with the expansion tube operation. Because

of the long rise time of the Xenon flash lamp and also because of its emission in UV,

OH-PLIF was performed approximately 2µs before schlieren to avoid background noise

in OH fluorescence. The firing box is designed to keep the laser operating (i.e, pulsing

at 10 Hz) until the initiation of the expansion tube operation to minimize shot-to-shot

pump laser energy fluctuations. The laser pulsing is stopped when a firing pulse is sent

to double diaphragms to initiate the test, and then, the laser is pulsed once more to

acquire the OH-PLIF image during the useful test time. Operating the pump laser in

this fashion prevented laser misfires.


(a)

Driver SectionDriven SectionExpansion Section

P8 P9 P10P1 P2 P3

P2 trig in

BNC pulse

generator

Firing box

(home-made)

PLIF camera

Gage-Scope

Data acq sys

Set image

delay time

Laser System

for PLIFTo YAG laser

flashlamps

From Q-switch

Set

delay time

ICCD-1

Injection

Valve

Controller

Pressure

Transducers

Sclieren camera

ICCD-2

Schlieren

light source

P8 trig in P10 trig in

(b)

Injection Valve

P8 trig in

Valve opens

P2 trig in

Trigger pulse

to the imaging systemPulse Generator

Pitot Pressure at the test section

OH-PLIF Imaging

Schlieren Imaging

1.1-1.2 ms ~ 1.1 ms

Shock wave

arrival

Test time = 270 sm

~2 sm

Flow established

Laser pulse

typ. 10 ns OH-PLIF camera

exp. time typ. 150 ns

Schlieren camera

exp. time typ. 100-200 ns

Xenon Flashlamp~3 sm

FIGURE 3.6 a)Triggering diagram and timing connections of the imaging, the injection and the data acqui-sition systems. b) Timing diagram of simultaneous OH-PLIF and schlieren and their synchro-nization with the expansion tube test flow time.

Chapter 4

Time Evolution and Mixing

Characteristics of Hydrogen and

Ethylene Transverse Jets

In this part of the investigation, flow-field properties of hydrogen and ethylene jets

injected into a supersonic flow are reported. The free-stream flow replicates a repre-

sentative supersonic combustor environment associated with a hypersonic airbreathing

engine flying at Mach 10. The structural evolution, the penetration and the convection

characteristics of both jets are analyzed.

4.1 Introduction

Early studies suggested that the jet-to-free-stream momentum flux ratio, J , is the

dominant parameter which controls the transverse jet penetration while the mechanism

for mixing is controlled mainly by the counter-rotating vortex pair. However, large scale

coherent structures are dominant in the jet shear layer and their structural evolution

might have a big influence on the jet near-field mixing process. In the studies of mixing

layers of two parallel streams (Brown and Roshko 1974) the mixing process was found to

be controlled by large scale vortical structures. It is therefore important to understand

how these structures and their growth rates evolve with time in the case of transverse

jets as the crossflow and jet conditions are changed.

59

CHAPTER 4. EVOLUTION OF HYDROGEN AND ETHYLENE JETS 60

TABLE 4.1 Jet exit flow properties.

Jet exit conditions Hydrogen EthyleneMjet 1 1Ujet, m/s 1205 315Tjet, K 246 263pjet, MPa 0.49 0.55J 1.4±0.1 1.4±0.1Mw,jet, g/gmole 2 28γjet 1.42 1.27djet, mm 2 2νjet 0.16×10−6 1.32×10−6

Redjet=Ujet djet/νjet 150,000 477,000

4.2 Results and Discussion

We have studied the flow-field properties of both hydrogen and ethylene transverse

jets using non-intrusive diagnostic techniques. Time-correlated schlieren images pro-

vides information on the structural evolution and convection characteristics of the jet,

and OH-PLIF maps the regions of ignition where the fuel and the crossflow (air or

oxygen) are mixed and burn at the molecular level.

The jet exit flow properties for both fuels are presented in Table 4.1. Note that

the exit velocities of hydrogen and ethylene sonic jets are quite different because of

the substantial difference in their molecular weights. Also included in Table 4.1 is the

jet-to-free-stream momentum flux ratio (J) that is chosen to be identical (J = 1.4) for

both cases and expected to result in similar penetration heights for each case, as was

suggested in previous studies. In this chapter, we will present results obtained from only

one value of J . It is worth noting that experiments with different values of J provide

similar results.

In the following sections, we will first present the global flow-field properties of a

transverse injection into a supersonic crossflow. Then the characteristics of the large

scale eddies, their convection and mixing properties, the jet penetration and finally the

OH-PLIF results will be discussed.


4.2.1 General Flow-Field Features

Schlieren imaging provides a visual observation of both instantaneous and average

characteristics of the flow-field depending on the exposure time of the image. While a

short duration schlieren image (100 - 200 ns exposure time) reveals some of the instanta-

neous vortex and shock structure of the flow-field, a long duration schlieren image (3µs

exposure time) provides information on the average and more steady properties.

Two instantaneous schlieren images related to hydrogen and ethylene injection cases

are shown in Fig. 4.1. Free-stream fluid (nitrogen) flows from left to right, and the fuel jet

(hydrogen or ethylene) enters from the bottom at x/d = 0. Several interesting features,

such as the large-scale structures at the jet periphery and the bow shock are very

apparent in those images. The large-scale eddies are periodically generated in the early

stages of the jet/free-stream interaction. While those eddies exist in both cases, they

demonstrate significant differences in their development as they convect downstream.

In the hydrogen case, these structures preserve their coherence with distance while in

the ethylene case they disappear beyond about 12 jet diameters downstream. This

result is not a schlieren contrast issue, rather it might be related to the enhanced

mixing characteristics of the flow-field. As will be discussed in the following section

the schlieren contrast for ethylene injection is expected to be 3 to 4 times larger than

the hydrogen case in the absence of mixing (hot nitrogen vs. cold ethylene). Since

the molecular weight of ethylene is nearly similar to nitrogen, the schlieren contrast

will diminish when the hot free-stream fluid begins to mix with the cold ethylene jet

while creating a region of reduced density gradient. The ethylene structures are bigger

and penetrate deeper into the crossflow. Besides the bow shock, additional weak shock

waves are formed around the ethylene eddies indicating their subsonic motion relative

to the free-stream. A detailed examination of these large scale structures is performed

using high speed schlieren movies and will be discussed in the following sections.

Figure 4.1 also demonstrates that the bow-shock is almost merged with the jet close

to the injection location with a very small stand-off distance and curves sharply down-

stream. Its local shape appears to depend strongly on the large scale shear layer struc-

tures, especially close to the jet exit where the free-stream behind the steep bow shock

is subsonic. As a result the bow-shock reveals local fluctuations in position, small in the

hydrogen case but significant in the ethylene case. Figure 4.2 shows an example for the


(a)

(b)

FIGURE 4.1 Examples of hydrogen (a) and ethylene (b) injections into a supersonic crossflow (nitrogen).Exposure time of each image was 200 ns. The x-axis is normalized by the jet diameter d.

hydrogen flow-field, visualized with a longer exposure time (3µs). Additional features

are emphasized and become visually observable: such as the upstream separation shock

wave and the downstream reattachment shock. The small instantaneous fluctuations of

the bow shock are observed to average into a smoother and slightly thicker one.

The barrel shock and the Mach disk are, however, not very clear even in the long

exposure schlieren images, most probably due to the unsteadiness of the shear layer


FIGURE 4.2 An example of schlieren image with 3 µs exposure time for hydrogen injection case. While theunsteady features (coherent structures) are averaged to zero, some of the weak shocks such asupstream separation shock wave and downstream recompression wave are emphasized.

vortical structures. Only the Prandtl-Meyer expansion fan of the underexpanded jet is

observable (the white region at the jet core) indicating that the jet is indeed underex-

panded. We have therefore attempted to estimate the displacement of the first Mach

disk for our experiments by substituting an “effective back pressure” term in the Ashke-

nas and Sherman correlation given in Eq. 2.5. The effective back pressure introduced

in earlier works is a notion which permits an analogy between the very complicated

flow-field of an underexpanded jet emerging into a supersonic crossflow and that for the

simpler and well-understood case of a jet exhausting into a quiescent medium. Among

those previous studies, Schetz and Billig (1966) suggested Peb = 0.8P ′∞, where P ′∞ is

the free-stream pressure behind a normal shock wave. Later on, Billig et al. (1971)

developed a correlation to predict the height of the Mach disk, y1, assuming that the

effective back pressure is equal to two thirds of the free-stream stagnation pressure

behind a normal shock: Peb = 2/3P ′tot,∞. More recently Everett et al. (1998) mea-

sured the pressure distribution around a sonic jet injected transversely into a Mach 1.6

free-stream using a pressure-sensitive-paint technique. Their averaged surface pressure

resulted in Peb∼= 0.35P ′∞ (for J<1.5) which differs greatly from the earlier works. This

discrepancy was attributed to the larger jet-to-momentum flux ratios (J) used in the


earlier works. We have adopted the back pressure values of Everett (Peb∼= 0.35P ′∞),

as the value of J in our experiments is small. Using Eq. 2.5, the Mach disk height for

the current experiments was estimated to be around y1 ≈ 1.7 · djet which compares well

with the jet bending location (see discussion below).

The free-stream conditions behind the hydrogen bow shock could be estimated by

measuring the average bow shock position. Figure 4.3 presents two plots; the first shows

the measured bow shock position and its angle (β), while the second plot exhibits the

bow shock-induced free-stream velocity (U2) and its turning angle (θ). Calculations are

performed assuming a calorically perfect gas. In the region of 10 jet diameters studied in

this work, the bow shock starts almost at 90o and weakens downstream as it angle decays

continuously down to 20o-25o. Further downstream, the bow shock is expected to reach

its minimum strength or a Mach wave with an angle of 17.2o (M∞=3.38). The induced

velocity of the free-stream behind the bow shock is subsonic upstream to the location of

the critical bow shock angle (βcr ∼ 67.6o), defined as the minimum angle for an oblique

shock to be attached to the wedge. It is interesting to see that the bow shock reaches this

angle around 1.8-1.9 jet diameters above the wall at the expected height of the upper

side of the Mach disk. Since the Mach disk occurs at a rather high Mach number on the

jet centerline, the jet loses most of its momentum and the subsequent trajectory of the

jet turns nearly parallel to the free-stream direction. Consequently, beyond the critical

angle, the bow shock curves sharply downstream and the shock-induced free-stream

velocity becomes supersonic varying between approximately 1050m/s to 2260m/s at

9.5 jet diameters downstream (note that the free-stream velocity is U∞ = 2360m/s).

In the following sections, this estimated free-stream velocity behind the bow shock will

be compared to the measured convection velocity of the large-scale structures. Before

that we will first discuss the temporal evolution of these structures.

4.2.2 Large Scale Coherent Structures

The most interesting observations are related to the coherent structures easily iden-

tified in instantaneous schlieren images. The large scale jet-shear layer vortices are con-

sidered important because of their role in the near-field mixing. These intermittently

formed eddies tend to enlarge and engulf free-stream fluid as they travel downstream

with the flow. We therefore studied the temporal evolution of large eddies and their


(a)

-1 0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

6

7

8

9

b

y/d

y/d

x/d

20

30

40

50

60

70

80

90

critical bow

shock angle:

bcr~67.6°

Bow

Shock

Angle

,b

(deg)

(b)

-1 0 1 2 3 4 5 6 7 8 9 10

600

800

1000

1200

1400

1600

1800

2000

2200

2400

qmax

=38.8°

q

U2

Fre

e-s

tream

Velo

city,U

2(m

/s)

x/d

0

10

20

30

40

50

supersonicsubsonic

Bow

Shock

Angle

,b

(deg)

FIGURE 4.3 (a) Bow shock position and its angle at the center-line of the jet as measured from the longexposure schlieren image shown in Fig. 4.2. (b) The free-stream velocity behind the bow shockand the flow turning angle based on the measured bow shock shape. For the calculations acalorically perfect gas has been assumed.


properties for both hydrogen and ethylene jets utilizing the high-speed-framing rate

camera. Examples of instantaneous schlieren images are presented in Figs. 4.4 and 4.5

for hydrogen injection and in Figs. 4.6 and 4.7 for the ethylene case. While large-

scale eddies are visible in the early stages of the jet/free-stream interaction, there are

significant differences in their development for hydrogen and ethylene injection.

Hydrogen large scale coherent structures survive long distances. Coherence of these

shear layer eddies can be seen in Figs. 4.4 and 4.5, which constitute consecutive schlieren

images from two different experiments. Close to the jet exit, the spanwise rollers rise

periodically creating gaps in between the eddies. The evolution of these eddies occurs

primarily through engulfment of the cross-flow fluid into the jet but also through merg-

ing/pairing of smaller eddies in the beginning of the shear layer (see eddy number 3

in Fig. 4.4). Beyond 3-4 jet diameters downstream, the separation between the eddies

becomes constant and no further merging is visible. The energetic structures elongate

in the transverse direction while the crossflow fluid fills the braid regions in between the

eddies.

Interesting features in the evolution of ethylene large-scale structures are demon-

strated in Figs. 4.6 and 4.7 through two examples of 8 consecutive schlieren images.

Larger structures appear in the near-field of the ethylene jet and persist until the jet

bends with the crossflow. In the bending region, the large scale structures begin to tilt

in the streamwise direction. Simultaneously, the shear between the accelerating cross-

flow and the jet increases, leading to the stretching of the large-scale structures. In the

case of ethylene injection the jet exit velocity (315m/s) is four times smaller than in the

hydrogen case (1205 m/s). Therefore, for ethylene injection the eddies are exposed to

very large velocity gradients across the shear layer. As a result, these large-scale eddies

lose their coherence as they turn in the streamwise direction and break up into smaller

eddies through a “tilting-stretching-tearing” mechanism. Further downstream, beyond

6-8 jet diameters, the jet shear layer is not visually observable by schlieren imaging

anymore, as the vortical structures tear down into smaller scale turbulence.

The flow visualization of large scale structures using schlieren is based on the prin-

ciple of refraction of light. The contrast in schlieren imaging, defined as the relative

change in the illumination, is expressed in terms of the optical index of refraction (n)


and parameters related to schlieren system (Saad 1985):

∆I

I=

fL

ny1

dn

dy(4.1)

where f is the focal length of the focusing lens, L is the width of the test section and

y1 is the size of the image of the light source (where the knife edge is positioned to

cut the deflected beam). For a given schlieren system, the parameters f , L and y1 are

constant. The contrast is, therefore, directly proportional to the gradient of the index

of refraction in the flow:∆I

I∝ dn

dy(4.2)

The index of refraction of a gas is expressed as a function of density (ρ) and a constant

characteristic of the gas (β), :

n = 1 + βρ

ρs(4.3)

where ρs is the density at standard conditions (273 K and atmospheric pressure). The

density ratio for a specific gas is equal to:

ρ

ρs=

PTs

PsT(4.4)

Substituting from Eqs. 4.4 and 4.3 gives:

∆I

I∝ d

dy(β

ρ

ρs) ∝ d

dy(β

PTs

PsT) (4.5)

Consequently, the flow visualization of large scale structures based on schlieren is

a result of the differences in the pressure, the temperature and the characteristic β

constant of the free-stream fluid and the jet fluid. As the jet turns in the streamwise

direction the static pressure between the hot free-stream (∼ 1300K) and the cold jet

(∼ 300K) approaches to equilibrium. The schlieren contrast between unmixed jet and

free-stream fluids can therefore be expressed in terms of:

∆I

I∝ (β

Ts

T)∞ − (β

Ts

T)jet (4.6)

By substituting the values of β and T in Eq. 4.6 we found that the schlieren contrast

between the ethylene jet and the free-stream nitrogen (or air) should be 3 to 4 times

larger than the hydrogen jet case. The loss of the visibility of the ethylene jet shear layer

structures can, therefore, be attributed to the loss of the coherence of the vortical struc-

tures and also to enhanced molecular-mixing. When the ethylene large structures burst


into smaller scale turbulent structures due to stretching, molecular mixing between the

crossflow and the ethylene jet might be enhanced. As a result, the observable schlieren

contrast degrades as the difference between β/T across the shear layer decreases.

Although the large scale eddies seem to be two-dimensional, recall that they are

part of the unsteady Kelvin-Helmholtz spanwise rollers wrapping around the jet. They

are only the traces of three-dimensional transverse vortex tubes whose cores coiled up

around the jet with their legs connected downstream of the jet exit. The schematic in

Fig. 4.8 shows a diagram of the three-dimensional unsteady structures as adapted from

Brizzi et al. (1995). Similar flow-field features were also observed by Fureby and Ben-

Yakar (2000), where a similar geometry and conditions are being studied by large eddy

simulation. In the simulation results for the hydrogen injection case, large Ω-shaped

vortices develop that grow as they convect downstream. We suggest that the vortex

tubes on the sides of the Ω-vortices are stretched by increased shear stresses in the

regions of steep velocity gradient.

Time evolution of the tearing mechanism of ethylene eddies can be easily followed

in the sequence of schlieren images. For example, the temporal development of eddy

number “0” in Fig. 4.6 is captured during the 10.6µs of visualization time. This eddy,

generated by merging of two individual smaller eddies, is an energetic structure which

penetrates deep into the free-stream. The initially almost round eddy stretches in the

transverse direction due to the increasing velocity gradients across the layer while it is

tilting in the clockwise direction. In the 8th image the eddy numbered “0” has almost

entirely dispersed into smaller eddies as the side arms of the vortex tube cannot continue

to sustain the large shear stresses. Eddy number “-1” in Fig. 4.7 is another example

for the “tilting-stretching-tearing” mechanism. We have plotted the evolution of this

eddy in a y-x diagram shown in Fig. 4.9, by tracking different parts of its structure

across the shear layer. While the bottom part of the eddy travels at the slower jet

velocity, the upper part of it is exposed to higher crossflow velocities. The shear stress

steepens further downstream as the crossflow behind the weaker bow shock accelerates.

Consequently, the eddies begin to stretch in the transverse direction while continuously

tilting towards the fast crossflow stream.


1) t = 0.1 µs 5) t = 4.1 µs

2) t = 1.1 µs 6) t = 5.1 µs

3) t = 2.1 µs 7) t = 6.1 µs

4) t = 3.1 µs 8) t = 7.1 µs

FIGURE 4.4 An example of 8 consecutive schlieren images of underexpanded hydrogen injection (d=2mm)into a supersonic crossflow (nitrogen) obtained by high-speed-framing camera. Exposure time ofeach image is 100 ns and interframing time is 1 µs. Free-stream conditions are: U∞=2360m/s,M∞=3.38, T∞=1290 K, p∞=32.4 kPa; and jet-to-free-stream momentum ratio is: J=1.4±0.1.


a) (Image 1) t = 0.1 µs

b) (Image 3) t = 2.1 µs

c) (Image 5) t = 2.1 µs

d) (Image 7) t = 3.1 µs

FIGURE 4.5 The second example of 4 of 8 consecutive schlieren images of hydrogen injection into flightMach 10 condition. Exposure time of each image is 100 ns and interframing time is 1 µs.


1) t = 0.1 µs 5) t = 4.1 µs

2) t = 1.1 µs 6) t = 5.1 µs

3) t = 2.1 µs 7) t = 6.1 µs

4) t = 3.1 µs 8) t = 7.1 µs

FIGURE 4.6 Time evolution of an ethylene jet in a supersonic crossflow (nitrogen) as observed from 8consecutive schlieren images. Exposure time of each image is 100 ns and interframing time is1.5 µs. Free-stream conditions are: U∞=2360m/s, M∞=3.38, T∞=1290K, p∞=32.4 kPa;and jet-to-free-stream momentum ratio is: J=1.4±0.1.


1) t = 0.2 µs 5) t = 5.0 µs

2) t = 1.4 µs 6) t = 6.2 µs

3) t = 2.6 µs 7) t = 7.4 µs

4) t = 3.8 µs 8) t = 8.6 µs

FIGURE 4.7 The second example of an ethylene transverse jet flow-field in a supersonic crossflow as observedfrom 8 time correlated schlieren images. Exposure time of each image is 200 ns and interframingtime is 1.2 µs.


FIGURE 4.8 Schematic of the three-dimensional shape (Ω shape) of the unsteady vortical structures formedintermittently (Brizzi et al. 1995).

Space-time trajectories of large structures:

Following the sequential high-speed-framing rate schlieren images, space-time trajec-

tories (x-t diagram) of the identifiable coherent structures have been traced. Figure 4.10

presents two x-t diagrams of hydrogen eddies as analyzed from the schlieren images of

Figs. 4.4 and 4.5. The spacing between the core of the eddies varies with distance,

eventually reaching an average value of almost 3 jet diameters. Occasionally, big gaps

of the order of 4 to 5 jet diameters in dimension (see Fig. 4.10b) are created as the

smaller eddies are amalgamated into the larger ones.

Two x-t diagrams showing the trajectories of the identifiable ethylene eddies are

plotted in Fig. 4.11. None of the coherent large scale eddies could be traced beyond

6-8 jet diameters downstream. The spacing between the initial eddies is larger than the

ones in the hydrogen case because of the large amounts of the crossflow intrusion in

between the eddies, and also because of the larger size of the eddies formed near the jet

exit. Information on the eddy formation frequency can also be obtained from the x-t


-1 0 1 2 3 4 5 6 7 8 9 101

2

3

4

5

6

7

frame

number:8

7

65

43

21

y/d

x/d

tilting

stretching

FIGURE 4.9 Development of a large-scale ethylene structure (eddy number “-1” in Fig. 4.7) as it goesthrough the tilting and stretching processes. Four different parts of the eddy structure wereindependently tracked in the duration of the 8.6 µs flow visualization time.

diagrams. Only 2 eddies are formed during the 10.6µs time evolution of the ethylene

jet, while in the hydrogen case 4 eddies are formed in even a shorter time period of

7.1µs. Experiments with different sonic jets (see Chapter 5) revealed that the eddy

formation frequency scales linearly with the jet exit velocity.

4.2.3 Convection Characteristics

Once the centers of the large scale eddy structures are identified (as shown in the

x-t diagrams), their convection velocity and the angle of inclination may be computed.

For that purpose, each individual structure was tracked from image to image using

cross-correlation techniques, as explained in Chapter 3.

The resulting large-scale convection characteristics are summarized in Figs. 4.12

and 4.13, for hydrogen and ethylene cases respectively. Data for each case were collected

from 16 images (two experiments per case). Included also in the figures are the reference

lines for the jet exit velocity and for the free-stream velocity. The uncertainty in the

determination of the eddy displacement is ±1 pixel (±45 m/s) in the hydrogen case


(a)

-1 0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

6

7

8

9

Uc,x

=Dx/Dt

Dt

Dx

Fra

me

Num

ber

x/d

0

1

2

3

4

5

6

7

8

Tim

e,ms

ec

eddy 4

eddy 3

eddy 1

eddy 2

(b)

-1 0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

6

7

8

9

Fra

me

Num

ber

x/d

0

1

2

3

4

5

6

7

8Tim

e,msec

eddy 4

eddy 3

eddy 1

eddy 2

FIGURE 4.10 Space-time trajectories of large-scale eddies present in the hydrogen jet shear layer. The centerof the eddies are tracked from the 8 successive schlieren images shown (a) in Fig. 4.4 and (b) inFig. 4.5.


(a)

-1 0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

6

7

8

9

Uc,x

=Dx/DtDt

Dx

Fra

me

Num

ber

x/d

0

2

4

6

8

10

12

eddy 0

Tim

e,ms

ec

eddy 1

eddy 2

(b)

-1 0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

6

7

8

9

bottompart middle part

upper part

Fra

me

Num

ber

x/d

0

2

4

6

8

eddy -1eddy 0

Tim

e,msec

eddy 1

eddy 2

FIGURE 4.11 Space-time trajectories of ethylene large scale eddies as tracked from 8 time-correlatedschlieren images: (a) x-t diagram of the example shown in Fig. 4.6, (b) x-t diagram of theexample shown in Fig. 4.7.


-1 0 1 2 3 4 5 6 7 8 9 10

0

500

1000

1500

2000

2500

Ujet

=1205 m/s

U¥=2360 m/s

Uc,x

Uc,y

Convective

Velo

city,

m/s

x/d

-1 0 1 2 3 4 5 6 7 8 9 10-10

0

10

20

30

40

50

60

70

Convection

Angle

,F

(deg)

x/d

(a)

(b)

FIGURE 4.12 Convection features of coherent large scale structures present in the hydrogen jet/free-streamshear layer. The data were subtracted by analyzing the eddy displacement in 8 consecutiveschlieren images of 2 experiments (images shown in Figs. 4.4 and 4.5). (a) the convectionvelocity of eddies in streamwise and transverse directions, Uc,x and Uc,y, respectively; (b) theconvection angle of eddies.


-1 0 1 2 3 4 5 6 7 8 9 10-20

-10

0

10

20

30

40

50

60

70

80

90

Convection

Angle

,F

(degre

es)

x/d

-1 0 1 2 3 4 5 6 7 8 9 10

0

500

1000

1500

2000

2500

Ujet

=315 m/s

U¥=2360 m/s

Uc,x

Uc,y

Convection

Velo

city,

m/s

x/d

(a)

(b)

FIGURE 4.13 Convection features of eddies present in the ethylene jet/free-stream shear layer. The datawere subtracted by analyzing the eddy displacement in 8 consecutive schlieren images of 2experiments (images shown in Figs. 4.6 and 4.7). (a) the convection velocity of eddies instreamwise and transverse directions, Uc,x and Uc,y, respectively; (b) the convection angle ofeddies.


-1 0 1 2 3 4 5 6 7 8 9 100

500

1000

1500

2000

2500

measured, Uc

measured free-stream velocity

behind the average bow shock, U2

U¥=2360 m/s

Convection

Velo

city,U

c(m

/s)

x/d

(a) hydrogen injection

-1 0 1 2 3 4 5 6 7 8 9 100

500

1000

1500

2000

2500

U2

Ujet

=315 m/s

U¥=2360 m/s

Convection

Velo

city,U

c(m

/s)

x/d

(b) ethylene injection

FIGURE 4.14 Measured convection velocity of large eddy structures in the hydrogen and ethylene jet shearlayers. The results are compared with the estimated values of the free-stream velocity imme-diately behind the bow shock.


and ±2 pixels (±62-71m/s) in the ethylene case. It is important to note that some of

the eddy positions were tracked manually, especially near the injector exit where the

cross-correlation method was not able to identify the initial small eddies at the vicinity

of the bow shock.

According to the results of Fig. 4.12, the hydrogen eddies initially travel fast in

the transverse direction with velocities close to the jet exit velocity. As the jet bends

downstream, the eddies start to accelerate monotonically in the streamwise direction

and achieve almost 90% of the free-stream velocity 9 jet diameters downstream. At this

location, the jet moves at shallower angles to the crossflow direction (around 0o-10o)

with reduced transverse convection velocities (between 0-400m/s). This reveals that

beyond 9 jet diameters the jet shear layer eddies are convected almost parallel to the

free-stream while the transverse penetration of the jet is just slightly increasing.

Convection properties of the ethylene eddies (Fig. 4.13) are somewhat different from

those in the hydrogen case. A large scattering of the velocity both in the transverse

and streamwise directions is visible. The convection characteristics were measured not

only by following the coherent large structures but also by tracking parts of the eddies

that had began to lose their coherence. We observe that the upper part of the eddies

tend to travel at higher velocities in both streamwise and transverse directions than the

lower part of the eddies (see also Fig. 4.9). The transverse velocity (y-component) of

some eddies is higher than the jet exit velocity. As the eddies stretch due to the large

velocity gradient across the jet shear layer, the transverse velocities, specially at the

upper part of the eddy, becomes as high as 700 m/s. The convection velocity in the

streamwise direction is, on the other hand, much lower than the free-stream velocity. A

result that can be attributed to the stronger (steeper) bow shock present for ethylene

injection as the eddies rise up higher into the crossflow. The convection angle of the

ethylene eddies, shown in Fig. 4.13b, are larger than the hydrogen ones, again a result

of the higher penetration of the energetic ethylene eddies in the transverse direction as

will be discussed in the following section.

The free-stream velocity behind the bow shock, U2, is computed based on the average

bow shock position measurements as explained in section 4.2.1. The results for the

hydrogen injection are plotted in Fig. 4.14a together with the measured total convective

velocities. We observe that the convection velocities of the low density hydrogen eddies

are mainly influenced by the free-stream, as most of the eddies follow the shock-induced


low U2

low U2

high U2

free-streamentrainment

DU2

bow shock

large-scaleeddies

ethylene

nitrogen

FIGURE 4.15 Schematic showing the low- and high-speed regions of the bow shock-induced free-streamvelocity around the large-scale ethylene eddies.

free-stream velocity. For the ethylene case, it is not possible to compute an average

shock-induced free-stream velocity because of the bow shock fluctuations. Instead, we

have measured two instantaneous bow shock positions and plotted the corresponding

shock-induced free-stream velocities in Fig. 4.14b together with the total convective

velocity across the ethylene shear layer. We observe large fluctuations in the values

of U2 varying in a wide range, between 1400m/s to 2300m/s around a single eddy.

Figure 4.15 illustrates the low- and high-speed regions of U2. Large velocity variation

in the values of U2 around the ethylene eddies, as opposed to monotonic increase in

the hydrogen case, might be contributing to the tilting and stretching of eddies while

contributing to the mixing process. Also, the reduced convective velocity of ethylene

eddies provides longer flow residence time, crucial for the completion of the mixing

process in shorter distances.

4.2.4 Penetration and Shear Layer Properties

The upper boundary of the jet is defined by the maximum penetration of its shear

layer vortices while the penetration bandwidth can be related to the visible thickness


of the jet shear layer. By measuring the visually observable upper edge of the jet

in schlieren images, jet maximum penetration and bandwidth data became available.

Brown and Roshko (1974), in their mixing layer studies, have shown that the “visi-

ble”shear layer width, as would be measured in a schlieren image, corresponds to about

1% concentration of molecularly mixed fluid. The results are presented in Fig. 4.16 to

quantify the penetration properties and to compare it to previous studies.

We observe significant differences in the penetration data and its width between

hydrogen and ethylene injection. While the hydrogen jet penetrates 5.5 jet diameters

into the free-stream at about 10 jet diameters downstream of the injection port, the

ethylene jet penetrates as much as 8 jet diameters at the same location. This result is

not surprising after studying the jet large-scale structure development in the previous

sections. It is very surprising, however, when it is compared to previous studies (Schetz

and Billig 1966; Rogers 1971; Papamoschou and Hubbard 1993; Gruber et al. 1995).

These earlier studies showed that the jet transverse penetration into the crossflow is

mainly controlled by the jet-to-free-stream momentum flux ratio (J). Therefore, both

jets studied here should have comparable transverse penetration into the crossflow as

the two cases have essentially the same momentum flux ratio. However, it is very clear

from the results that the transverse penetration height of ethylene jet is higher than the

hydrogen jet case.

A power law fit to the penetration data has been proposed by various authors (Mc-

Daniel and Graves 1988; Rothstein and Wantuck 1992; Gruber et al. 1995) who found

that the upstream boundary layer properties, that is laminar/turbulent and the bound-

ary layer thickness play an important role in the penetration of the jet. The most

comprehensive and recent study was performed by Gruber et al. (1995), who suggest a

power law fit of the form of:y

dJ= c

(x

dJ

)1/3

(4.7)

where the constant c has the value of 1.23 for circular injection. Their measurement

technique relies on Mie scattering from ice particles in the free-stream, and defines the jet

penetration as the trajectory where the jet concentration is about 10%. The thickness

of the approaching boundary layer (δ/d=1) and the range of the jet-to-momentum ratio

(J = 1 − 3) of their experiments were similar to the ones in our experiments, so that

a comparison can be made. Therefore, the above correlation is plotted for J = 1.4


-1 0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

6

7

8

Rothstein & WantuckMcDaniel & GravesGruber et al.present work

d @6d

y/d

x/d

-1 0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

6Rothstein & WantuckMcDaniel & GravesGruber et al.present work d@3d

y/d

x/d

(a) hydrogen injection

(b) ethylene injection

FIGURE 4.16 Transverse penetration data of (a) hydrogen jet and (b) ethylene jet. The data points wereobtained by manually tracking the visually observable outer edge of the jet from 8 consecutiveschlieren images for J = 1.4±0.1. Both of the figures include analysis of 2 experiments namely16 images. For comparison, also shown in the figures is the penetration correlation given byother studies.


in Fig. 4.16 together with our results measured for J = 1.4 ± 0.1. Two additional

empirical correlations suggested by McDaniel and Graves (1988) and Rothstein and

Wantuck (1992) are also included in Fig. 4.16 for further comparison.

The penetration band in our experiments lies on top of the expected 10% penetra-

tion trajectory based on Gruber’s correlation. The measurement of the “visible” jet’s

penetration as measured in schlieren images corresponds to 1% of the jet concentration,

while Gruber’s results correspond to 10%. Therefore, it is reasonable that the pene-

tration measurements based on schlieren are somewhat lower than the ones based on

10% concentration measurements. A better agreement is achieved with the correlation

of Rothstein and Wantuck (1992) who used OH fluorescence to visualize the jet pene-

tration. Their experimental conditions (hydrogen jet injected into a high temperature

air crossflow) are similar to our hydrogen injection case.

In summary, the penetration data for the hydrogen case agrees relatively well with

the previous studies. The differences in the observed penetration between hydrogen and

ethylene data are most probably due to the tearing mechanism explained above. The

thickness of the ethylene shear layer (the penetration width) grows to 6 jet diameters,

twice as much as the hydrogen case at the end of the field of view. The practical

impact of this result is significant as it indicates a mechanism for enhanced fuel (jet)

distribution. It might eventually be possible to enhance and control the fuel penetration

based on the flow properties.

It seems that there is an additional mechanism which controls the jet penetration

besides the jet-to-free-stream momentum flux ratio. This mechanism is expected to be

associated with the jet shear layer properties which control its growth rate and therefore

the near-field mixing of the transverse jet. Jet-to-free-stream density and velocity ratios

are the two main parameters which might influence the large scale vortical structure

development of the jet. In the next chapter (Chapter 5), we discuss the effects of these

two parameters on the penetration and the development of the jet.

4.2.5 OH-PLIF Results

To gain further insight into the coherence and the mixing properties of the injection

flow-field we have examined the ignition characteristics of hydrogen and ethylene jets


using Planar Laser Induced Fluorescence of OH radicals. The presence of OH, a natu-

rally occurring combustion product, indicates that the fuel and the oxidizer are mixed

at the molecular level and the conditions for ignition to occur are met. As the total

enthalpy of the free-stream in our experiments is high (∼4MJ/kg), namely the total

temperature is about 4000 K, autoignition of a transverse fuel jet is achieved.

Figure 4.17 contains three instantaneous side-view images of OH-PLIF captured at

the center-line of hydrogen and ethylene transverse jets injected into a reacting crossflow.

OH-PLIF is a two-dimensional visualization technique which maps the auto-ignition

locations illuminated by a roughly 0.4 mm thick laser sheet. The first image (Fig. 4.17a),

related to a hydrogen jet injected into air, demonstrates a continuous and a very thin

filament along the jet shear layer periphery. The side-view 2-D visualization clearly

shows the presence of the large scale shear layer vortices. Since a relatively cold hydrogen

jet is injected into hot air, there will be a significant variation of temperature with

equivalence ratio through the mixing layer around the jet. The ignition time is a strong

function of the mixture temperature, which will be higher at low equivalence ratios (fuel

lean). The self-ignition point is therefore on the lean side of the mixing layer around

the jet. Namely, ignition is likely to occur as soon as a fuel particle meets with the high

temperature oxidizer. Since OH appears only quite near the hydrogen jet we suspect

that the mixing is only occurring in the finite-thickness interfacial diffusion region that

separates the unmixed fluids.

Figures 4.17b and 4.17c are related to an ethylene jet injected into air and pure

oxygen crossflows, respectively. Due to longer ignition delay times associated with

ethylene, self-ignition could only be achieved when a higher concentration of oxygen was

used in the crossflow. In contrast to hydrogen, OH radicals in the ethylene case could

be detected in a wide region distributed across the jet. This is most likely a result of the

enhanced molecular-mixing related to “stretching-tilting-tearing” mechanism discussed

above. An additional interesting observation is related to the intense OH signals taking

place in the vicinity of the Mach disk. This is the region where ethylene is self-igniting

even when it is injected into air (see Fig. 4.17b). At this location, the ethylene jet

becomes subsonic behind the Mach disk and begins to lose its transverse momentum

letting the high temperature crossflow intrude deep inside the jet. Santiago and Dutton

(1997), have also shown that the regions of high turbulent kinetic energy (TKE) exist

in the jet shear layer near the Mach disk leading to better mixing properties.


(a)

x/d

(b)

x/d

(c)

x/d

FIGURE 4.17 OH-PLIF results mapping the ignition regions at the jet center-line of: a) hydrogen injectioninto air, b) ethylene injection into air, c) ethylene injection into pure oxygen.


In conclusion, OH-PLIF results demonstrated that significant differences exist in

the near-field ignition properties for ethylene and hydrogen injection. These results

support the tearing mechanism suggested to enhance the near-field mixing properties

of the ethylene jet.

4.3 Summary

In this part of the thesis, we have summarized results that are related to hydrogen

and ethylene fuel jets because of their relevance to supersonic combustion. Significant

differences related to the development of large-scale coherent structures were found to

be present in the jet shear layer. The results demonstrate features not observed in

previous studies where the free-stream conditions were limited to low velocities and low

temperatures. In the current effort, the use of an impulse facility made it feasible to

achieve high temperature and high velocity conditions relevant to a realistic supersonic

combustor environment. The application of supersonic flow visualization at ultra-fast-

framing rates enabled a detailed study of the temporal evolution of the fuel jets.

Further investigations of the experimental results are presented in the next chapter,

which examines the dominant influences of different parameters on the stability and

structural characteristics of the shear-layer formed in the jet periphery.

Chapter 5

The Effect of Velocity and

Density Ratio on Transverse Jets

In the previous chapter, we studied the temporal evolution of the shear layer struc-

tures of ethylene and hydrogen jets because of their relevance to supersonic combus-

tion. The large difference in the molecular weights of these two gases revealed two

important observations: 1) a “tilting-stretching-tearing”mechanism which caused the

ethylene large-scale structures to lose their coherence and to burst into smaller eddies

and 2) higher transverse penetration of the ethylene jet for a similar momentum flux

ratio, J , as the hydrogen jet due to highly energetic ethylene eddies which penetrate

deep into the free-stream.

In the current chapter, we report our study of the fundamental origin of these phe-

nomena. The parameters expected to be influential in the stability, and the structural

characteristics, of the jet shear layer are the jet-to-crossflow density and velocity ratios.

These two parameters are, however, coupled through the molecular weight of the jet.

An increase in the jet’s molecular weight reduces the exit velocity and increases the

density. Therefore, to understand the role of each parameter on the instability of the

large-scale eddies, we must decouple the two parameters and study them independently.

The first part of this chapter discusses the effect of systematically changing the

jet molecular weight. The second part presents the independent influence of the jet-

to-crossflow density and velocity ratios on the flow features. To decouple these two

parameters, a variety of free-stream conditions are used. Also we discuss possible flow

88

CHAPTER 5. VELOCITY AND DENSITY RATIO EFFECTS 89

instabilities, such as centrifugal instabilities associated with curved shear layers which

could potentially cause the spanwise rollers to lose their coherence.

5.1 Effect of Jet Molecular Weight

Gaseous jets with five different molecular weights (Mw,jet =2, 4, 8, 16 and 28 g/mole)

are studied. Tables 5.1 and 5.2 summarize the composition and the properties of these

jets. The experiments are designed for similar jet-to-crossflow momentum flux ratio in

the range J = 1.67 − 1.85. Note the high Reynolds numbers associated with the jet

exit properties. Also included in Table 5.2 are the jet-to-free-stream velocity ratio (r),

the density ratio (s) and a convective Mach number parameter (MAc , see section 5.1.5)

defined to estimate the compressibility level of the jet shear layer for the cases studied

here.

r =Ujet

U∞(5.1)

s =ρjet

ρ∞=

(Mw/T )jet

(Mw/T )∞(5.2)

5.1.1 Flow Visualization Results

Examples of instantaneous schlieren images obtained using the ultra-fast framing

camera are presented in Fig. 5.1 for visual observations of the flow-field. A systematic

increase in the jet molecular weight gradually changes the structural characteristics of

the jet shear layer. Large-scale structures, which dominate the jet shear layer in all cases,

become larger with the increase of the molecular weight. The heavier jets penetrate

deeper into the free-stream. Consequently, the shape of the bow shock changes as it

wraps around the large eddies. This process starts to be visible for Mw=16 and becomes

very pronounced for Mw=28.

The coherent structures occur less frequently with increasing Mw, which results in a

larger spacing between the eddies. This is followed by large intrusions of the crossflow

between the eddies. In the case of Mw=28, the fast crossflow stream sweeps the jet as the

eddies lose their coherence. In the case of N2 injection shown in Fig. 5.1e (Mw=28) the

large-scale structures are not visible beyond x/d ∼ 8− 10. In Chapter 4 we postulated

that the reason the large-scale structures lose their coherence is related to the “tilting-

stretching-tearing” mechanism which is due to the large velocity differences between


TABLE 5.1 The general flow exit properties of gaseous jets with different molecular weights.

Jet Gas Mw,jet γe Te Ue = ae µe

g/mole K m/s Pa·s(T=Te)

1) H2 - Hydrogen 2 1.42 246 1205 7.76× 10−5

2) 85.7% H2 +14.3% CH4 4 1.40 248 850 8.28× 10−6

3) 57.2% H2 +42.8% CH4 8 1.37 252 600 9.30× 10−6

4) CH4 - Methane 16 1.32 257 420 1.14× 10−5

5) N2 - Nitrogen 28 1.40 248 320 1.54× 10−5

TABLE 5.2 The specific flow exit properties of gaseous jets used in the study of the jet molecular weighteffect. The free-stream used in these experiments simulates the flight Mach 10 flow condition.

Jet Mw,jet pe,eff J ν = µ/ρ Red r s MAc

g/mole atm m2/s(T=250K)

1) 2 6.3 1.84± 0.1 1.24× 10−5 194,000 0.51 0.37 0.52

2) 4 5.9 1.72± 0.1 7.14× 10−6 238,000 0.36 0.74 0.43

3) 8 6.5 1.85± 0.1 3.69× 10−6 324,000 0.25 1.46 0.35

4) 16 6.1 1.67± 0.1 2.46× 10−6 342,000 0.18 2.87 0.27

5) 28 6.1 1.76± 0.1 1.84× 10−6 349,000 0.14 5.20 0.22

the jet and the crossflow. We will provide more evidence supporting this hypothesis in

section 5.2.

5.1.2 Penetration and Shear Layer Thickness

Figure 5.2 includes plots of the transverse penetration height and the penetration

width of jets with different molecular weights but with almost identical jet-to-momentum

flux ratios (J =1.67-1.84). The data are obtained by identifying the visually observable

upper edge of the jet shear layer in the instantaneous schlieren images. The penetration

profiles clearly demonstrate an increasing improvement in the penetration height for

increasing values of the jet molecular weight. The same trend can also be observed

for the growth rate of the jet shear layer. In Chapter 4 we suggested a relationship


a) Mw = 2 g/mole b) Mw = 4 g/mole

c) Mw = 8 g/mole d) Mw = 16 g/mole

e) Mw = 28 g/mole

FIGURE 5.1 Examples of instantaneous schlieren images of jets with different molecular weights. Free-stream conditions are: U∞=2360m/s, M∞=3.38, T∞=1290K, p∞=32.4 kPa.


between the jet shear layer thickness and the width of the maximum jet penetration.

Accordingly, the visible jet shear layer thickness, δvis, ranges between 4d-7d at ∼22

jet diameters downstream where the thicker shear layer is associated with the larger

Mw. The peak transverse penetration in the low Mw (2 g/mole) case is about y/d=6.5

while in the high Mw (16 g/mole) case is about y/d=10. The penetration height and

therefore its width are expected to increase further downstream especially for the higher

Mw cases.

These observations are not in agreement with other studies which state that identical

penetration heights should be observed independent of the jet molecular weight. During

the last 30-40 years of studies, the jet penetration height was believed to scale with the

momentum flux ratio J . For comparison with previous results two empirical correlations

proposed by Gruber et al. (1995) and Rothstein and Wantuck (1992) are also plotted

in Figs. 5.2a- 5.2d for J = 1.75. Gruber et al. measured the penetration of hydrogen

and air jets injected into a cold free-stream flow based on 10 % of the jet concentration.

Rothstein and Wantuck, on the other hand, used OH fluorescence imaging to detect

the hydrogen penetration injected into a high temperature reacting crossflow. The

penetration measurements obtained in this work are higher than those observed in

previous studies for all cases except the hydrogen case (Mw=2g/mole) which agrees

reasonably well with Rothstein’s correlation. Also, note that penetration profiles of

Rothstein and Wantuck are almost 20 % higher than those reported by Gruber et al. The

variation between these works are likely due to differences in experimental conditions

and measurement techniques as we will discuss next.

We may explain the agreement between our hydrogen injection results and the

measurements of Rothstein and Wantuck through similarities in our experimental ap-

proaches. The free-stream velocity and temperature in both works are high (r < 1 in

both experiments) and the measurement techniques are quite similar. In our reacting

experiments (see Chapter 6), we demonstrated that OH radicals lie on the periphery of

the hydrogen jet shear layer observed through a simultaneous OH/PLIF and schlieren

imaging. Therefore, measurements based on OH emission and schlieren imaging should

provide similar penetration profiles.

Experimental procedure may also explain the discrepancy between the results of

Gruber et al. and Rothstein and Wantuck. The free-stream velocity and temperature

in the experiments of Gruber et al. are lower (r > 1, s < 1) than those in the work of


-2 0 2 4 6 8 10 12 14 16 18 20 220

2

4

6

8

10 Rothstein 1992

Gruber et al. 1995a) Mw=2

dvis

@4dy/d

x/d

-2 0 2 4 6 8 10 12 14 16 18 20 220

2

4

6

8

10b) M

w=4

dvis

@5d

y/d

x/d

-2 0 2 4 6 8 10 12 14 16 18 20 220

2

4

6

8

10c) M

w=8

dvis

@6d

y/d

x/d

-2 0 2 4 6 8 10 12 14 16 18 20 220

2

4

6

8

10d) M

w=16

dvis

@7d

y/d

x/d

FIGURE 5.2 Jet transverse penetration along the axial distance, x/d. Data for four gases with differentmolecular weights are presented: a) Mw = 2, J = 1.84, b) Mw = 4, J = 1.72, c) Mw = 8,J = 1.85, d) Mw = 16, J = 1.67. For comparison, empirical correlations suggested by Gruberet al. (1995) and Rothstein and Wantuck (1992) are also included for J = 1.75.


Rothstein and Wantuck.

As will be argued in the second part of this chapter, the velocity ratio, r, is an im-

portant factor in the development and growth rate of the jet shear layer structures and,

therefore, directly affects the penetration of the jet. An increase in the jet molecular

weight decreases the jet exit velocity and hence the velocity ratio, r. In our experi-

ments, higher penetration is observed for lower values of r. The penetration results

of Lee et al. (1995) are an example which supports our findings. They measured jet

penetration using PLIF (Planar Laser-Induced Fluorescence) measurements of NO of a

non-reacting injectant (N2) and OH of a reacting injectant (H2) in a high temperature

supersonic flow. The penetration height indicated by NO fluorescence was significantly

larger than that indicated by OH fluorescence for the same J . Their reasoning for this

phenomena, however, was not complete. They related the differences between N2 and

H2 injections to the frictional losses in the H2 injector and to the consumption of H2

near the stoichiometric ratio. First, the frictional losses can only drop the penetration

height by 5% at most. Second, combustion between the cold hydrogen and the hot

oxygen takes place in the lean region of the mixture where the mixture temperature

is high and not near the stoichiometric value, as Lee et al. suggested. We propose,

therefore, that the velocity ratio differences between the two cases (r = 1.1 for H2 vs.

r = 0.3 for N2) cause the different penetrations observed by Lee et al. (1995). Namely,

the smaller the r, the better the penetration.

Another noteworthy observation was recently recorded by Mathur et al. (1999) in a

high temperature (850 K), high velocity (1750 m/s) free-stream flow. Flame spreading

angles of ethylene gas (Mw=28) injected from a flush wall injector were measured and

found to be twice as large as the predicted spreading. Mathur et al. concluded that some

other mechanism, in addition to the transverse momentum of the fuel, must cause the

rapid spreading of the flame around the ethylene jet. Indeed, their jet-to-free-stream

velocity ratio was r = 0.18, similar to the case with Mw=16 g/mole studied in our

investigation.

Here we suggest that variables other than the jet-to-free-stream momentum flux ra-

tio, J , influences the penetration trajectory. We can achieve higher penetration heights

as the molecular weight of the jet is increased systematically. Increase in the jet’s molec-

ular weight decreases the jet exit velocities, namely the r. Our findings are also consis-

tent with previous investigations where similar experimental conditions were studied.


We can provide an improved explanation for their observations and for the discrepancies

shown in the previous works by taking into account the velocity ratio, r, in addition to

the momentum flux ratio, J .

5.1.3 Convection Characteristics

Figures 5.3a - 5.3b summarize the convection velocity of large scale eddies in the

transverse and streamwise directions. Also included in the figures are the velocity of

the jets at the exit of the injector and the velocity of the free-stream. The convection

characteristic of nitrogen eddies (Mw=28 g/mole) could not be measured beyond x/d=8,

as they lose their coherence through the bursting mechanism explained in the previous

chapter.

From consideration of the y-momentum equation, the pressure rise behind the Mach

disk implies that the jet fluid loses its momentum in the y-direction. As the jet loses

its y-momentum, the shear layer eddies accelerate in the free-stream direction because

of the crossflow which applies drag forces on the jet. Further downstream, the eddies

eventually convect with velocities that are closer to the free-stream velocity independent

of the jet’s molecular weight. The only difference between the cases is the distance where

the eddies achieve their maximum velocity. Low density eddies (low Mw) could follow

the free-stream velocity earlier than the denser ones with larger Mw. For example in the

case of Mw=2, the maximum convection velocity was achieved around x/d=7, while in

the case of Mw=16 the plateau was reached just after x/d=16. This result is consistent

with the fact that drag forces are the main cause of the convection of the eddies in the

streamwise direction. For the same drag force, acceleration of heavier eddies is slower

than the acceleration of lighter eddies.

5.1.4 Characteristic Large Eddy Frequencies (Possible Transverse Jet

Modes)

Since coherent structures include concentrated regions of vorticity which are the

main mechanisms for the entrainment of the crossflow into the jet shear layer, under-

standing the origin of vorticity is essential for understanding the structures. We have,

therefore, measured the characteristic formation frequency of the large scale eddies in

the jet shear layer using the ultra-fast-framing schlieren system. Before presenting


0 5 10 15 20

0

500

1000

1500

2000

2500

~2100 m/s

a) Mw=2 U

c,xU

c,y

Ujet

=1205 m/s

U¥=2360 m/s

Convection

Velo

city,

m/s

x/d

0 5 10 15 20

0

500

1000

1500

2000

2500

~2000 m/s

b) Mw=4 U

c,xU

c,y

Ujet

=850 m/s

U¥=2360 m/s

Convection

Velo

city,

m/s

x/d

0 5 10 15 20

0

500

1000

1500

2000

2500

~1950 m/s

c) Mw=8 U

c,xU

c,y

Ujet

=600 m/s

U¥=2360 m/s

Convection

Velo

city,

m/s

x/d

0 5 10 15 20

0

500

1000

1500

2000

2500

~2050 m/s

d) Mw=16 U

c,xU

c,y

Ujet

=420 m/s

U¥=2360 m/s

Convection

Velo

city,

m/s

x/d

FIGURE 5.3 Convection velocity of large scale structures in the streamwise (Mc,x) and transverse (Mc,y)directions as a function of axial distance x/d. The results for each case (for each molecularweight of jet) are obtained from 4-5 experiments each including 8 consecutive schlieren images.


the results, we first summarize the possible instability modes of free-jets and jets-in-

crossflows.

Free-jets generally have two dominant instability frequencies associated with differ-

ent sizes of vortices. The first is originated by the instability of the shear layer at the jet

orifice. The initial vortex shedding frequency, also called the most amplified frequency,

fθj , scales with the initial shear layer momentum thickness, θj , and jet exit velocity, Uj .

The corresponding “initial vortex shedding Strouhal number”,

Stθj =fθjθj

Uj(5.3)

is found to be scattered from 0.01 to 0.018 (Gutmark and Ho 1983). The second

dominant jet instability mode is related to larger scale structures present downstream

of the jet potential core. The characteristic frequency of this mode is referred to as

the “preferred mode frequency, fj”of the jet. The initial vortices of the shear layer

grow by merging and entrainment as they convect downstream. At the end of the jet

potential core the dominant frequency is governed by the jet column instability (Crowe

and Champagne 1971). The preferred mode frequency, fj , scales with the jet exit

diameter and velocity, d and Uj to yield the “preferred mode Strouhal number”

Std =fjd

Uj(5.4)

While many researchers confirmed the existence of a preferred mode, their experi-

mental results surveyed by Gutmark and Ho (1983) revealed that the value of Stj varies

widely between 0.24 to 0.64. These discrepancies were attributed to the various initial

conditions of different facilities.

To determine the origin of the large scale structures of sonic jets in crossflows, an

analogy between this and the case of a free-jet has been presented. Using the concept

of “the preferred mode frequency”, we obtain a dominant “preferred Strouhal number”

for the transverse injection case.

Figure 5.4 represents the measured dominant frequency of the eddy formation in the

beginning of the jet shear layer and the corresponding Strouhal number as measured for

different jet exit velocities. The measurements are obtained by analyzing 5-10 different

experiments for each case. Each experiment includes 8 time correlated schlieren images.

The appropriate interframing time between the images allows us to identify the newborn


200 400 600 800 1000 1200

0.8

1.0

1.2

St j

200 400 600 800 1000 12000

100

200

300

400

500

600

700

f j,kH

z

Ujet

, m/s

FIGURE 5.4 Formation frequency of the large scale structures and the corresponding “preferred modeStrouhal number”, Std = fjd/Uj , as a function of the jet exit velocity. The data werecollected from the time evolution observation of the jet from 8 consecutive schlieren images.Each data point was obtained by averaging 5-10 experiments with the error bars representingthe deviation from the mean value.

eddies during the flow visualization time (ranging between 10-30µs). The results show

that the characteristic frequency of the eddy formation is scaled linearly with the jet

exit velocity. This suggests that the shear layer eddies are associated with the preferred

instability mode of the jet. The corresponding “preferred mode Strouhal number” can

therefore be calculated based on Eq. 5.4. The results indicate that this “preferred mode”

corresponds to a Strouhal number of about Std = 1 for all the cases studied in this work.

A comparison with previously published results is not possible due to the lack of

such measurements in supersonic crossflows. The only comparison that can be made

is with the results of Fric (1990) performed in subsonic flows. From his measurements,

the preferred mode frequency of the subsonic transverse jet was found to decrease with

distance along the jet. Merging of the eddies was the main reason for the decrease in the

frequency, changing the Strouhal number from Std ≈ 1− 2 down to 0.2 around x/d∼5.


1.5x105

2.0x105

2.5x105

3.0x105

3.5x105

4.0x105

1.0

1.2

1.4

1.6

1.8

St q

j/S

t qj,

min

1.5x105

2.0x105

2.5x105

3.0x105

3.5x105

4.0x105

0

100

200

300

400

500

600

700

f j,kH

z

Rejet

FIGURE 5.5 Formation frequency of the large scale structures and the “initial vortex shedding Strouhalnumber”, Stθj = fθj θj/Uj , as a function of the jet Reynolds number.

Std ≈ 0.2 is smaller than the values quoted for free jets. In our experiments, the number

of eddies are counted just before the bending of the jet as they become identifiable.

Further downstream, the vortex merging does not happen very often. Std ≈ 1 can

therefore be presented as the “preferred mode Strouhal number” for the transverse jets

in supersonic crossflows for the geometry examined in this work. This Strouhal number

is larger than those quoted for free-jets. It is also larger than the ones measured for

transverse jets in subsonic flows.

We can also calculate the Strouhal number based on the initial shear layer mo-

mentum thickness, θj . However, the appropriate data are not available to estimate

the momentum thickness of the jet shear layer exiting the injector port. We therefore

normalized the Stθjwith its minimum value assuming that θj =

√Rejet. Figure 5.5

summarizes the findings showing that the formation frequency is not associated with

the initial vortex shedding frequency. Stθj appears to increase with increasing Rejet.


These results suggest that the shear layer eddies are independent of the exit shear layer

instability characteristics, because the characteristic length scale of the mode has been

shown to be the jet diameter and not the thickness of the exit shear layer. The most

amplified frequency of the jet column instability is the origin of its large-scale structures.

5.1.5 Jet Compressibility Analysis

In studies of mixing layers of two parallel streams, it has been shown that compress-

ibility levels control the growth rate of the mixing layer which decreases with increasing

compressibility. We have therefore attempted to analyze the effect of compressibility on

transverse jets.

Convective Mach number, Mc, is a key compressibility parameter which is based on

the velocity of the large scale structures relative to either free-streams. Papamoschou

and Roshko (1988) defined a convective Mach number for each stream:

Mc1 =U1 − Uc

a1; Mc2 =

Uc − U2

a2(5.5)

where U1 and U2 are the high and low speed streams, respectively (refer to Fig. 5.6).

Assuming that entrained fluid stagnates isentropically in the frame of the structures,

the pressure-matching condition at the stagnation point yields:

Mc1 =√

γ2

γ1Mc2 (5.6)

Uc

U1=

1 + r√

s

1 +√

s(5.7)

assuming γ1 = γ2

Mc1 = Mc2 = Mc =U1 − U2

a1 + a2(5.8)

At low compressibilities (Mc < 0.5) the structure of a non-reacting shear layer is

two-dimensional and the large eddies travel with the average convective Mach number,

Mc. As the compressibility increases, this theory seems to fail as the central mode

stabilizes and a transition from a two- to three-dimensionality occurs. Beyond Mc=0.5,

experimental results by Papamoschou (1991 and 1997) and by Dimotakis (1991) showed

that convective velocities follow the “stream selection rule” which is based on the exis-

tence of “fast” and “slow” modes. If one stream is supersonic and the other subsonic,

the convective velocity of structures will be closer to that of the fast stream (fast mode),


(a) (b)

JetBoundary

y1

P =?eb

P M=1j, j

x1

1

1'

2M >1

Bow Shock InducedFree-Stream

A

B

C

M >11

M >11 '

U2

U1

Uc

U -U2 c

U -Uc 1

Stationary Frame

Convective Frame

FIGURE 5.6 Flow-field schematics used in the jet compressibility analysis. Letters A, B and C indicate thezones of the jet shear layer.

and when both streams are supersonic the convective velocity will favor the slow speed

stream (slow mode).

One could basically adapt the convective Mach number concept to scale the com-

pressibility of transverse jets. However, because of the three-dimensional complexity of

the flow-field and lack of the velocity field information, there is an additional difficulty

in predicting the convective Mach number of transverse jets in supersonic crossflows.

Neither crossflow nor jet-flow properties are uniform. The underexpanded jet acceler-

ates inside the barrel shock and eventually gets compressed through the Mach disk,

while the crossflow changes its properties continuously behind the curved bow shock.

We, therefore, suggest separating the jet flow-field into three different zones to ana-

lyze the compressibility effects. The schematic of the proposed regions are illustrated in

Fig. 5.6 and indicated with letters A, B and C. Zone A is close to the jet exit where the

y-component of the free-stream velocity is negligible. The convective Mach number in

zone A (MAc ) can therefore be calculated using the equation 5.8 and by assuming that

U1 = Ujet and U2 = 0. Figure 5.7 shows the estimated values of MAc together with the

visible thickness of the jet shear layer, (δvis) at x/d≈22 as obtained from penetration


200 400 600 800 1000 1200

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0.55

Convective

Mach

Num

ber,

MC

A

Uj

(m/s)

4.0

4.5

5.0

5.5

6.0

6.5

7.0

7.5

8.0

dvis

Mc

A

Shear

Layer

Thic

kness,d

vis/d

FIGURE 5.7 Estimated convective Mach number in zone “A”, MAc , (refer to the schematic in Fig. 5.6) and

the measured visible jet shear layer thickness, δvis, at x/d≈22 as obtained from penetrationwidth measurements.

width measurements (see Section 5.1.2). A decrease in δvis is observed for increasing

values of MAc , indicating that the compressibility properties in the initial region of the

jet shear layer affect its growth rate.

For zone B, the convective Mach number model, given by Gruber et al. (997b),

guided our calculations. Gruber et al. suggested quantifying the compressibility level

of transverse jets at a single point in the jet shear layer near the Mach disk (zone B

in our case). For this calculation, the jet velocity just upstream of the Mach disk (U1)

is estimated. Figure 5.8a presents the estimated values of U1 with error bars obtained

for a range of assumed pressure ratios (P ′1/P∞). Also included in this plot is the range

of the free-stream velocity downstream of the bow shock, which is determined using

the oblique shock relations for a range of shock angles (45o < β < 65o) measured

in section 4.2.1). Evident in Fig. 5.8 is that the free-stream velocity behind the bow

shock is faster than the heavy jets (Mw = 28 and 16) and slower than the light jets

(Mw = 2 and 4). In the experiments of Gruber et al. the free-stream velocity was

slower than both the heavy and the light jets and therefore a comparative convective

Mach number could be identified to quantify the compressibility level of jets. In the


200 400 600 800 1000 12000

500

1000

1500

2000

2500

U¥

behind the bow shock

U¥=2360 m/s

(a) B-zone

Maxim

um

JetV

elo

city,U

1(m

/s)

Uj

(m/s)

200 400 600 800 1000 12000

500

1000

1500

2000

2500

U¥

behind the bow shock

U¥=2360 m/s

(b) C-zone

JetV

elo

city

Behin

dth

eM

ach

dis

k

U1'

(m/s

)

Uj

(m/s)

FIGURE 5.8 Estimated velocity fields for the jet and the free-stream in zones “B” and “C”.

current experiments, however, it is difficult to find a clear dependence of δvis on MBc .

We, therefore, suggest the use of the convective Mach number in zone A (MAc ) as an

indicator for the jet compressibility level.

Figure 5.8b presents an estimate for the expected velocities in zone C. The value of jet

velocity U ′1, immediately after the Mach disk, is calculated using the normal shock and

isentropic relations. The free-stream velocity behind the bow shock is again estimated

using the measured bow shock angle as described above. The plot indicates that the

supersonic free-stream is significantly faster than the jet which becomes subsonic behind

the Mach disk. It is possible that in this region the “stream selection rule” mentioned

above applies. According to this rule the convective velocity of structures will be closer

to that of the fast stream (fast mode) as one stream is supersonic and the other subsonic.

In the previous section, the jet shear layer eddies in zone C and beyond are indeed

demonstrated to convect with velocities close to the fast free-stream values.

In summary, we propose the convective Mach number in zone “A” as an indicator

of the jet compressibility level. The growth rate of the shear layer scales with MAc .

The convective velocity of the eddies, on the other hand, seems to follow the “stream

selection rule” as observed in the shear layers of two parallel streams.


5.2 Effect of Density and Velocity Ratios

In this part of the investigation, we pursue the decomposition of the molecular weight

effect into its constituent parameters, velocity and density. For a given pressure and

temperature of the jet:

Uj ∝√

γ

Mw,jand ρ ∝ Mw,j (5.9)

Therefore, by changing the jet molecular weight, its density and velocity are also

changed. By using different free-stream conditions we can control the jet-to-free-stream

velocity and density ratios independent of each other. For that purpose, 24 different

experimental conditions, summarized in Table 5.3, are studied. The stability of the jet

shear layer eddies are analyzed by the aid of the flow visualization.

5.2.1 Flow Visualization Results

Having examined the effect of jet molecular weight, we showed that the coherence

of the large scale eddies is significantly affected by the increase of the jet molecular

weight. The eddies “burst” into smaller structures by the “tilting-stretching-tearing”

mechanism discussed in the previous chapter. This “bursting” mechanism will hence-

forth be referred as the “instability” of the eddies. We observed the stability of the

eddies by visual observations based on schlieren imaging. In such work, the eddies are

identified as “unstable” when the structures lose coherence and significant distortions

in the bow shock shape can be observed.

Examples of schlieren images for selected experiments are shown in Figs. 5.9, 5.10

and 5.11. The first set of experiments numbered as 1 to 5 in Table 5.3, is performed in

the flight Mach 10 condition. These experiments are already discussed in detail in the

studies of jet molecular weight effect (see Section 5.1). Here we will discuss the rest of

the experiments, numbered from 6 to 24.

The first goal is to eliminate the density ratio effect by simulating conditions with

a similar velocity to the Mach 10 case, but with much lower static temperature so that

the density ratio varies minimally when the jet molecular weight is changed. Therefore,

the free-stream conditions (600/9/6) for the second set of experiments (experiments no.

6-8) have static temperature of only 243K. Results of these experiments show that the

jet becomes unstable again as the velocity ratio is decreased to below 0.17 (see Figs. 5.9b


TABLE 5.3 Summary of the different conditions used in the study of jet instability analysis.

No Free-stream Mw,∞ γ∞ U∞ p∞ T∞ M∞ Mw,j r sCondition m/s atm K Uj/U∞ ρj/ρ∞

1 600a/0.5b/20c 28 1.32 2360 0.32 1290 3.38 2 0.51 0.372 (flight 4 0.36 0.743 Mach 10) 8 0.25 1.464 16 0.18 2.875 28 0.14 5.206 600/9/6 28 1.4 2420 0.083 243 7.75 2 0.50 0.077 16 0.17 0.548 28 0.13 0.989 600/4/6 28 1.4 2572 0.1 392 6.48 2 0.47 0.1110 16 0.16 0.8711 600/0.3/60 28 1.29 2037 0.72 1840 2.46 2 0.59 0.5312 16 0.21 4.0913 28 0.1 7.4214 300/0.45/70 28 1.32 1760 0.61 1410 2.37 2 0.69 0.4115 (flight 16 0.24 3.1416 Mach 8) 28 0.18 5.6917 600/4/20 28 1.38 2212 0.29 516 4.89 2 0.55 0.1518 300/10/15 40 1.667 1686 0.124 207 6.46 16 0.25 0.3219 28 0.19 0.5820 300/10/15 4 1.667 2560 0.26 220 3.04 28 0.13 6.2121 80a/5b 28 1.38 520 1.9 550 1.1 2 2.32 0.1622 28 0.62 2.2223 100/0.5 28 1.33 1058 0.585 1077 1.62 2 1.14 0.3124 28 0.30 4.34

The free-stream conditions are represented by the expansion tube initial filling pressureswith nomenclature referring to Fig. 2.2. a. P4, psig, b. P1, psia, c. P10, torr.

and c) even though the density ratio stays at low values at which the Mach 10 condition

showed stable flow structures. The bow shock which stays smooth in the hydrogen

injection case (Fig. 5.9a) is distorted in the case of methane and nitrogen injections.

Additional shock waves are generated around shear layer structures as the velocity of

the free-stream becomes supersonic relative to the convection of the eddies. Tilting of

the eddies is visible in the region close to the wall. Note also the shock waves generated

from leading edge of the plate. These are actually weak Mach waves which are clearly

visible owing to the high sensitivity of the schlieren system. The same flow features


are obtained in the third set of experiments (experiments no. 9 an 10) presented in

Figs. 5.9d and e, as the flow conditions (600/4/6) are similar to the second set.

The second goal is to eliminate the velocity ratio effect by generating conditions of

high density ratio while keeping the free-stream velocity low. For that purpose we run

the facility in a shock tube mode, namely without the second diaphragm between the

expansion and driven sections (experiments no. 21 to 24). As shown in Figs. 5.11b and

5.11d, the jet eddies stay coherent for high values of s (experiments no. 22 and 24) at

which jet eddies in the Mach 10 condition lose their stability. The eddies stay coherent

without large intrusions of air into the jet. It is worth noting that these span the range

of velocity conditions at which most of the previous studies were performed. Therefore,

not many significant differences in the flow field could be observed in those studies.

Finally, note the shock waves emitting from the injection location (see Figs. 5.11a and

c). In these experiments the jet exit velocity is larger than the free-stream velocity,

r > 1. Note also the large stand-off distance of the bow shock because of the low Mach

numbers.

The results are presented in a density versus velocity ratio (s-r) diagram shown in

Fig. 5.13. Separate regions of stable and unstable flows can clearly be identified. The

plot indicates that the density ratio, s, has a little effect on the instability of the jet

shear layer structures while the velocity ratio, r, is the main controlling parameter. We

therefore propose to use an “effective velocity ratio”, λ, which will be presented in the

following section.

5.2.2 Definition of an “Effective Velocity Ratio, λ”

We propose to define an “effective velocity ratio”, λ, as a measure of the magnitude

of the velocity difference across the jet shear layer. We assume that near the jet exit

port, the jet issues in the y-direction at velocity Uj and the free-stream flows in the

x-direction at velocity U∞. This configuration, shown schematically in Fig. 5.12, is a

special case of skewed mixing layers with a skewing angle of 90 o between high- and low-

speed streams. The jet fluid is expected to convect in the direction of the total velocity

vector. Therefore, the effective shear will be proportional to the velocity difference in

that direction. The components of Uj and U∞ in the direction of the total velocity


a) H2 injection in 600/9/6 (No.6) d)H2 injection in 600/4/6 (No.9)

b) CH4 injection in 600/9/6 (No.7) e) CH4 injection in 600/4/6 (No.10)

c)N2 injection in 600/9/6 (No.8)

FIGURE 5.9 Schlieren images at selected conditions given in Table 5.3.


a) H2 injection in 600/0.3/60 (No.11) d) CH4 injection in 300/10(Ar)/15 (No.18)

b) CH4 injection in 600/0.3/60 (No.12) e) N2 injection in 300/10(Ar)/15 (No.19)

c)N2 injection in 600/0.3/60 (No.13) f) N2 injection in 300/10(He)/15 (No.20)



a) H2 injection in 80/0.5 (No.21) c) H2 injection in 100/0.5 (No.23)

b)N2 injection in 80/0.5 (No.22) d) N2 injection in 100/0.5 (No.24)



D

U

jU

a

¥U

¥U cos( )a

jU sin( )a

jU = U sin( ) -a ¥U cos( )a

DU

FIGURE 5.12 Velocity vector field (U∞, Uj) for a skewed mixing layer and the “effective velocity ratio”, λ.,described in the total velocity vector direction.

vector are:

Uj‖ = Uj sin(α) and U∞‖ = U∞ cos(α) (5.10)

The velocity difference ∆U is therefore equal to:

∆U

U∞=

Uj sin(α)− U∞ cos(α)U∞

(5.11)

by substituting tan(α) = Uj/U∞, the effective velocity ratio, λ, can then be calculated

as the ratio of the velocity difference ∆U to the free-stream velocity U∞

λ =∆U

U∞=

1− r2

√1 + r2

(5.12)

Therefore, when λ = 0, there is no shear, and when λ ∼= 1, the shear is a maximum as

the free-stream velocity is much higher than the jet velocity.

Figure 5.14 presents the experimental results in a new “velocity-density” diagram

where the effective velocity ratio λ is used instead of r. Again two distinct regions

of stable and unstable flows are identifiable. Clearly, a critical value for the effective

velocity ratio exists in the vicinity of λcr ≈ 0.94 beyond which the jet flow becomes

unstable as the “tilting-stretching and tearing” mechanism becomes important.

5.2.3 Discussion on the Effect of the Curvature - Centrifugal Instabil-

ity Analysis

Certain configurations possessing curvature are prone to centrifugal instabilities.

Curvature introduces centrifugal forces which tend to produce streamwise vortical struc-

tures of the Taylor-Gortler type. Rayleigh (1880) showed that the stability condition


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

0

1

2

3

4

5

6

7

8

9

12

3

69

11

2

14

15

1718

22

24

4

13

16

19

20

5

7

8 10

Stable

Unstable

¥r

r

=j

s

¥

=

U

Ur

j

StableUnstable

1

FIGURE 5.13 Jet-to-free-stream density ratio vs. velocity ratio. The number near the data points corre-sponds to the experimental conditions summarized in Table 5.3. “Unstable” flow jet is definedwhen the large structures lose coherence downstream of the injection port and significant dis-tortions in the bow shock shape can be observed.

2

2

r1

r1

U

U

+

÷øöç

èæ -

=D

=l¥

¥r

r=

js

0.4 0.5 0.6 0.7 0.8 0.9 1

0

1

2

3

4

5

6

7

8

9

12

3

6 9

11

12

14

15

1718

22

24

4

13

16

19

20

5

7

810

Stable

Unstable

crl

Stable Unstable

FIGURE 5.14 Jet-to-free-stream density ratio vs. the “effective velocity ratio”, λ. The number near thedata points corresponds to the experimental conditions summarized in Table 5.3.


s stable

unstable

s

rr

Experimental resultsRayleigh-Synge criterion forcentrifugal stability:

.consr2s <+

¥r

r=

js

¥

=

U

Ur

j

(a) (b)

unstable

stable

FIGURE 5.15 Schematics illustrating the stability regions based on a) Rayleigh criterion for centrifugal forcesin the curved mixing layers as given in Eq. 5.15 where cons. = 3 + 2 δvis

hmaxand b) current

experimental results.

for an inviscid flow depends on the gradient of angular momentum. Synge (1933)

gave a stability criterion taking into account that a density difference may also pro-

duce an unstable layer. The associated instability mechanism is therefore known as the

Rayleigh-Synge criterion and is given in the form of:

d

dr

(ρU2r2

)> 0 (5.13)

for dr > 0, this criterion can be written as follows:

dρ

ρ+ 2

dU

U+ 2

dr

r> 0 (5.14)

by substituting dρ = ρ∞ − ρj , dU = U∞ − Uj and dr/r = δvis/hmax we obtain:

ρj

ρ∞+ 2

Uj

U∞< 3 + 2

δvis

hmax(5.15)

where the curvature radius is assumed to be the maximum jet penetration height, hmax.

Eq. 5.15 (s + 2r < const), therefore, provides a criterion for the stability of the curved

jet shear layer in case the centrifugal forces play an important role on the stability.

However, comparison of Equation 5.15 with the results presented in Fig. 5.13 indicates

the opposite trends. As shown in Fig. 5.15, the regions where a curved jet shear layer


is stable are actually the regions of the unstable jet shear layer as observed in our

experiments. Therefore, we can conclude that instabilities associated with curved shear

layers do not contribute to the instabilities in the case of a normal injection into a

crossflow.

Chapter 6

Autoignition and Flame-Holding

Capability of a Hydrogen

Transverse Jet

This chapter describes the experimental efforts in characterizing the ignition and the

flame-holding capabilities of a transverse jet injected into high total enthalpy supersonic

crossflows. The use of an expansion tube provides a correct simulation of true flight

combustion chemistry, including ignition delay and reaction times. The experiments are

designed to map the hydroxyl radical (OH) in the near-field of an underexpanded hy-

drogen jet injected into flight Mach number 8, 10 and 13 total enthalpy flow conditions.

6.1 Ignition and Flame-Holding Considerations

The stabilization of flames in supersonic flow is a difficult issue for two primary rea-

sons: First since flow times are short, ignition delays can result in significant travel of the

jet plume through the combustor. Second, strain rates tend to be high in compressible

flows which can suppress combustion.

Transverse injection is a commonly used flame stabilization scheme in supersonic

combustors. It provides flame stabilization: 1) by organization of an upstream recir-

culation zone, 2) by formation of coherent structures containing unmixed fuel and air,

where a diffusion flame occurs as the gases are convected downstream, provided the

114

CHAPTER 6. IGNITION OF HYDROGEN JET 115

strain rates are not too high.

Transverse injection schemes have two main points where the ignition is likely to

occur: the region behind the jet bow shock where high temperatures and pressures are

obtained, and the recirculation regions ahead of and behind the base of the jet where

long residence times and high temperatures exist. The residence time of the hydrogen-

air mixture in the bow shock region is short, since the mixture expands around the

jet flow-field immediately after compression in the bow shock. For the higher Mach

number flows, however, ignition may still be initiated in the bow shock region due to

the relatively high static temperature, though a more likely place for ignition to occur is

in the recirculation region upstream the jet exit as will be shown in the results section.

In scramjet combustors, where relatively cold hydrogen is injected into hot air, there

is a significant variation of temperature with equivalence ratio (φ) through the mixing

layer around the jet. Since the temperature of the mixture will be higher at low equiv-

alence ratios, and since ignition time is a strong function of the mixture temperature,

it is expected that the self-ignition point will be on the lean side of the mixing layer

around the jet (φ ∼= 0.2 (Huber et al. 1979)). The ignition delay times associated with

hydrogen-air mixtures will be discussed in Section 6.3.2.

In order for self-ignition (and therefore combustion) to be accomplished in a flowing

combustible mixture, it is necessary that four quantities have suitable values: static

temperature, static pressure, fuel-air ratio, and the residence time at these conditions.

In a reacting system, ignition is considered accomplished when sufficient free radicals are

formed to initiate the reaction, even though no appreciable heat has yet been released.

When the conditions of spontaneous ignition exist, the distance li at which it occurs in

a medium flowing at a velocity u is:

li = u · τi (6.1)

Since the ignition delay time τi varies inversely with pressure (because of the two body

reactions involved in the ignition chemistry of hydrogen and air) the product τip is

effectively constant for a given temperature and fuel-air equivalence ratio. This allows

the use of the binary scaling law for the ignition of hydrogen-air mixtures in the following

form,pliu≈ constant (6.2)


This means that for a given combustor entry temperature (typically in the range of

1440-1670K, Heiser and Pratt 1994), the ignition lengths are directly proportional to

flight velocity, V0, by

li ∼ u

p∼ 1

V 30

(hyrogen fuel) (6.3)

Remember that supersonic burner entry pressures and velocities are scaled with the

flight velocity according to: p3 ∼ 1/V 20 and u3 ∼ 1/V0 (see Chapter1). Equation 6.3

indicates that the ignition lengths in a hydrogen-fueled scramjet become very large

at high flight speeds. The ignition lengths are even larger if hydrocarbon fuels are

employed. Because of the larger dependence of the ignition delay time on pressure, the

ignition length in a hydrocarbon-fueled scramjet has a larger dependence on 1/V0 as:

li ∼ u

pn∼ 1

V 2n+10

(ethylene fuel) (6.4)

where n > 1. This is one of the reasons why hydrocarbon fuels are not likely to be used

for high-flight Mach numbers.

In the supersonic combustion area, a general consensus is: storable JP-type hydro-

carbon fuels can be used up to Mach 6-8. Liquid methane could be used to somewhat

higher Mach numbers, but speeds in excess of about Mach 10 requires liquid hydrogen.

Mainly because hydrogen fuel is characterized by fast reaction rates and high heat re-

lease per kilogram of fuel (120 MJ/kgfuel). On the other hand, hydrocarbon fuels have

significant shortcomings in supersonic combustion when compared to hydrogen. The

hydrocarbon fuels have relatively long ignition delays and limited cooling capability.

Furthermore, at low speed flight conditions (flight Mach below 8), the total tempera-

ture of the free-stream is lower introducing difficulties on flame stabilization inside the

supersonic combustor. These considerations will require some innovative thinking (see

Chapter 7) especially when the fuel of choice is a heavy hydrocarbon (JP-7, decane,

etc.)

The main objective of this study is therefore to investigate the combustion char-

acteristics of a hydrogen transverse jet in order to obtain a picture of its near-field

autoignition and flame-holding capability. The second objective is to compare the hy-

drogen jet autoignition capability with that of the ethylene jet.


6.2 Ignition and Flame-Holding Results

6.2.1 Simultaneous OH-PLIF/Schlieren Results

Figure 6.1 demonstrates an example of simultaneous schlieren and a side view OH-

PLIF image overlaid in a single image (Fig. 6.1c). These images are obtained at the

flow conditions simulating flight Mach 10. Apparent in the images are the regions

containing OH molecules, indicating the location of the reaction zone. The structural

evolution of the reaction zone is in good agreement with the jet position determined by

the schlieren imaging although there is a small shift between their position due to the

fact that schlieren image was taken ∼ 2µs after the PLIF image. A significant and fairly

uniform level of OH along the outer edge of the jet plume attached to the recirculation

area upstream of the injector is visible. However, farther downstream a decrease of OH

fluorescence is obtained as the mixture expands around the jet flow-field. As explained

in Section 3.2.4, the fluorescence signal in this case is essentially proportional to the

OH mole fraction. Therefore the decrease in signal level observed in the sheet corrected

PLIF images is a direct indication of the decrease in OH mole fraction.

6.2.2 Top View OH-PLIF Images

In order to achieve a more complete picture of the combustion, we have also obtained

top PLIF views of the jet. A set of 4 instantaneous top view images collected at 4

different heights above the jet exit is shown in Fig. 6.2 (the white dots in the images

indicate the center of the jet exit.) The results show OH around the jet while the center

of the plume has no OH-formation. The bottom image at 1-jet diameter above the

plate shows two main features: 1) the jet spreads very quickly in the lateral direction

(up to about 8-jet diameters) assuming that the flame is around the jet-air interface, and

2) the OH concentration downstream of the jet remains nearly constant. By contrast,

the other three images obtained at 2, 2.5 and 3-jet diameters height demonstrate the

same tendency of the side views, namely that the OH signal level decreases as the jet

moves downstream.


Region Illuminated by

PLIF Sheet

0 2 4 6 8

0 2 4 6 8 10 12

x/d

14

0 2 4 6 8 10 12 14

Air

(a) (b)

(c)

FIGURE 6.1 Simultaneous OH-PLIF and schlieren images visualizing hydrogen injection into supersoniccrossflow. Free-stream conditions are M = 3.57, T = 1300 K, P = 0.32 atm, V = 2500 m/s.The jet-to-freestream momentum flux ratio is J = 1.4. a) Schlieren image, b)OH-PLIF im-age demonstrating the ignition and combustion regions of jet-in-crossflow at high enthalpycondition, c) Overlaid OH-PLIF and schlieren images.


(a) y/d=3

(b) y/d=2.5

(c) y/d=2

(d) y/d=1

FIGURE 6.2 Instantaneous top-view OH-PLIF images obtained at different height above the injectionplate. Free-stream conditions are M=3.57, T=1300K, P=0.32atm, V=2500m/s. The jet-to-freestream momentum flux ratio is J=1.4. a) y/d=3, b) y/d=2.5, c) y/d=2, d) y/d=1 abovethe injection plate.


6.2.3 Comparison of Ignition in Flight Mach 8-13 Total Enthalpy Range

Figure 6.3 compares examples of OH-PLIF imaging conducted at the center-line of

the hydrogen jet injected in flight Mach 10 and 13 conditions. Each image includes 2

separate subimages from different tests: the first has been acquired near the jet exit

while the second has been acquired farther downstream.

Apparent in the images is the isolated thin filament along the outer edge of the

plume. The center of the plume itself has no OH-signals indicating poor mixing of the

air with the core of the hydrogen jet. The OH radicals are primarily produced in the

hot separation region upstream of the jet exit and behind the bow shock and convected

downstream with the shear-layer vortices.

Ignition in our experiments is likely due to the hot and radical-rich separation region

upstream of the jet exit where the boundary layer and jet fluids mix subsonically. Al-

though these recirculation kernels in general are small in volume, in high enthalpy flows

the temperature of these zones can be as high as the stagnation temperature of the bulk

flow. In Mach 10 condition, a low signal level of OH in the recirculation zone/boundary

layer upstream of the injector is visible. In Mach 13 condition, on the other hand, a

fairly uniform and intense OH signal level is observed even when air is used as the free-

stream gas. The high concentration of OH radicals in the upstream recirculation region

can be attributed to high recovery temperatures associated with high total enthalpy

flows. The ignition process will initiate instantaneously in the upstream recirculation

region as the delay times effectively approach zero (∼ 1−5µs) at the Mach 13 condition.

Figure 6.4 presents two instantaneous OH-PLIF images obtained at the center-line of

the hydrogen jet injected at Mach 8 flight conditions. Limited amounts of OH are visible

on the leading edge of the jet, mainly behind the steep regions of the bow shock. The

ignition is quenched farther downstream. It is evident from these results that improved

injection schemes for better flame-holding would be required for practical applications

in scramjet engines flying at low Mach numbers (below 10).


b) Mach 13

Oxygen

M¥= 4.7

V¥= 3200 m/s

P¥= 0.04 atm

T¥= 1250 K

H2 , J=5

x/d

a) Mach 10

Air

M¥= 3.4

V¥= 2360 m/s

P¥= 0.32 atm

T¥= 1290 K

x/d

H2 , J=1.4

FIGURE 6.3 Instantaneous OH-PLIF acquired at center-line axis of the hydrogen jet injected into flight Mach10 and 13 conditions. The images are obtained by combination of 2 different instantaneousimages: near the exit of the jet (−5 < x/d < 1) and downstream of the jet (1 < x/d < 10).


Mach 8

Air

M¥= 2.4

V¥= 1800 m/s

P¥= 0.65 atm

T¥= 1400 K

Ht,¥= 2.9 MJ/kg

x/d

H2

x/d

H2 J=2.3

FIGURE 6.4 Two instantaneous OH-PLIF images acquired at center-line axis of the hydrogen jet injectedinto flight Mach 8 conditions.


6.3 Discussion of the Ignition Process

6.3.1 Ignition Characteristics of Hydrogen

Ignition of hydrogen and air in high-temperature turbulent flow fields associated

with supersonic combustors can be characterized purely by radical runaway as opposed

to thermal runaway (Im et al. 1994; Im et al. 1998; Sung et al. 1999). Thus, the heat

release of combustion is not essential for the propagation of the ignition/combustion

process.

The well-known explosion limits of a hydrogen-oxygen system are plotted in Fig. 6.5

(after Sung et al. 1999). Nishioka and Law (1997) have shown that the state of the

second explosion limit is an important boundary in the ignition response of a hydrogen-

air laminar mixing layer. The crossover temperature, Tc, for the second explosion limit

is defined as the temperature at which the rate of the main chain-terminating reaction

H + O2 + M −→ HO2 + M (R1)

equals that of the rate-controlling branching reaction

H + O2 −→ OH + O (R2)

Reaction (R2) is a two-body, temperature-sensitive branching reaction with an activa-

tion energy of 68.8 kJ/mole (16.44 kcal/mole), while (R1) is a three-body, temperature

insensitive terminating reaction because HO2 is relatively inactive. Thus increasing

temperature promotes (R2) and hence the overall ignitability. When the mixture tem-

perature in the flow, Tmix, is larger than Tc, the system response is controlled by (R2).

The chain-branching ignition in coflow mixing layers leads to a continuous growth

of the radical pool. If the temperature is sufficiently above crossover, then the effect of

three body recombination reactions, responsible for most of the heat release in H2-O2

combustion, is negligible, and the two streams mix and react initially without signifi-

cant chemical heating. This gives rise to a thermally frozen branched-chain explosion

(Sanchez et al. 1997).

As a point of reference, we first calculated the ignition delay times, τign, for hydrogen-

air mixtures. The chemical kinetics software package Chemkin, developed by (Kee et al.

1980), was used for the delay time calculations. The reaction mechanism was taken

from GRI-Mech 2.12 (Bowman et al.). The ignition times based on the time when

[OH]= 1/2 [OH]max are plotted in Fig. 6.6. If the pressure and fuel-air mixture are

held constant, the effect of temperature on ignition time can be readily shown in this


FIGURE 6.5 Explosion limits of a stoichiometric hydrogen-oxygen mixture (after Sung et al., 1999).

figure. Note that the ignition time has a strong exponential dependence on temperature.

Over the range 1000 K to 1700 K, τi varies by about a factor of 100. At temperatures

between 800-1000 K (depending on pressure) the ignition time approaches infinity and

self-ignition cannot occur.

We have earlier discussed that at temperatures above the crossover temperature, Tc,

the hydrogen-air system response is controlled by the two-body reaction (R2). Thus the

product pτi forms a single curve in Fig. 6.6b for all the pressures at high temperatures.

We however observe a deviation from the binary scaling law at a critical temperature

depending on pressure. This critical temperature is lower for low pressures consistent

with the second explosion limit discussed above.


0.6 0.7 0.8 0.9 1.0 1.1 1.210

0

101

102

103

104

4atm2atm

1atm

p=0.3atm

H2-air for f=1

Ignitio

nTim

e(m

sec)

1000/T(K)

(a)

0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2

101

102

103

0.3atm

1atm2atm

4atmH

2-air for f=1

pt ig

n(a

tm-m

sec)

1000/T(K)

(b)

FIGURE 6.6 Variation of ignition delay times τign of a stoichiometric mixture of H2 and air with temperatureand pressure. Calculations are perfomed using Chemkin and the GRI mechanism. a) τign vs.T , b) pτign vs. T


0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

1

10

100

1000

Tmix

=1265KTmix

=1120

K Tmix

=1527K

Tair=3200K

Tair=2400K

Tair=1800K

T air=1

500K

T air=1

300K

Tmix=10

10K

Tmix

=1425K

Tmix

=1650K

Tmix

=1720K

Ignitio

nTim

e(m

sec)

Equivalence Ratio, f

FIGURE 6.7 Variation of ignition time with fuel-air equivalence ratio, φ, for cold H2 (Tjet = 300 K) injectedinto hot air. The values of the ignition delay time are calculated for different air temperatures,Tair.

6.3.2 Ignition in Supersonic Combustors

In scramjet combustors, auto-ignition is achieved by injecting a relatively cold fuel

into hot air. Therefore there is a significant variation of temperature and equivalence

ratio, φ, inside a supersonic combustor. In order to approximate the variation of temper-

ature with φ, a simplified one-dimensional enthalpy balance between the cold hydrogen

and the hot air is used. The gases are assumed to be nonreacting, thermally and calor-

ically perfect and ideally mixed without compressibility effects. Based on this model,

the enthalpy balance between the two streams can be written as

nairCp,air(Tair − Tmix) = nH2Cp,H2(Tmix − TH2) (6.5)

where n is the number of moles which is related to the equivalence ratio φ; Cp is the

specific heat at the mixed mean temperature. The mixture temperature, Tmix, can then


-1 0 1 2 3 4 5 6 7 8 9 10

1600

2000

2400

2800

3200

3600

tign

=43 ms

tign

=10 ms

tign

=5 ms

tign

=2 ms

tign

=1 ms

T2

Fre

e-s

tream

Tem

pera

ture

,T

2(K

)

x/d

0

1

2

3

4

5

P2 F

ree-s

tream

Pre

ssure

,P

2(a

tm)

FIGURE 6.8 The free-stream temperature and pressure (T2 and P2) behind the bow shock, measured fromschlieren images as discussed in Section 4.2.1 (see Fig. 4.3). Ignition delay times are calculatedfor several conditions of air assuming φ = 0.2. The free-stream flow properties simulate theflight Mach 10 conditions.

be calculated by rearranging Eq. 6.5 as

Tmix =Tair + αTH2

1 + α(6.6)

where α = nH2Cp,H2

nairCp,air.

Representative ignition delay times are plotted in Fig. 6.7 as a function of φ for

various values of Tair. The results indicate that OH is likely to be formed in the hot,

lean regions of the mixing layer (φ ∼= 0.2) where the temperatures are the highest. For

air temperatures below 1800 K the ignition delay times are much larger than 10µs, which

exceeds the residence time of the hydrogen within the imaged region studied here (based

on the hydrogen large-scale convection velocities of 2 mm/µs and 10 jet diameters).

6.3.3 Ignition of a Hydrogen Transverse Jet

The transverse jet interacts strongly with the crossflow, producing a bow shock and

localized highly three-dimensional flow-field around it. Therefore, it is very difficult


to formulate the ignition characteristics of this field. We can however try to estimate

characteristic time scales of the ignition process in an attempt to explain the OH-PLIF

results.

The OH-PLIF images shown in Figs. 6.3 and 6.4 are taken at the center-line of the

jet. At this location, the average free-stream flow properties behind the bow shock were

estimated using schlieren images (see Section 4.2.1 for more details). Figure 6.8 shows

these estimated values of static temperatures and pressures of free-stream behind the

bow shock, T2 and p2 respectively, at the flight Mach 10 condition.

Considering the values of T2 and p2 and using the Eq. 6.6 we calculated the ignition

delay times at several locations along the x-axis of the jet. We assumed that the cold

hydrogen (TH2 = 300 K) interacts with hot air at the lean side of the jet shear layer

where φ=0.2. The results shown in Fig. 6.8 indicate that an instantaneous autoignition

can be achieved close to the jet exit as the ignition delay times are of the order of

1-2µs. Further downstream beyond x/d ≈ 6, the ignition delay times become larger

(τign > 10µs) exceeding the maximum flow residence time of the imaged region. As the

air temperature behind the weaker bow shock begins to decrease below 1800 K (Tmix <

1120K for φ = 0.2) OH radicals can only be formed downstream of the imaged region,

beyond x/d = 10. This might be the reason for the reduced OH mole fractions observed

downstream the injection location at the flight Mach 10 condition (see Fig. 6.3a). OH

radicals generated near the jet exit are convected downstream with the shear-layer

vortices. However, since new radicals are not formed instantaneously downstream of

the injector the OH concentration dilutes and therefore the OH-PLIF signal is reduced.

6.3.4 Ignition of Ethylene Transverse Jet

In scramjet engines the hydrocarbon fuel may be partially cracked to C1-C3 species

through its use as a coolant before reaching the combustor. It is anticipated that this

partially reacted fuel will burn as well as ethylene, namely with combustion properties

(such as ignition delay) approaching that of ethylene. We therefore studied the near-

field ignition characteristics of ethylene jet as it is a good simulant for hydrocarbons in

scramjets and the OH-PLIF results were summarized previously in Section 4.2.5.

Here, we calculated the ignition delay times for ethylene-air mixtures using two

different chemical reaction systems. Due to the large number of elementary reactions


800 1000 1200 1400 1600 1800 2000

101

102

103

104

p=1atm, f=1

H2-air

C2H

4-air using GRI-mechanism

C2H

4-air using LLNL-mechanism

C2H

4-O

2using LLNL-mechanism

Ignitio

nTim

e(m

sec)

T(K)

FIGURE 6.9 Comparison of ignition delay of a stoichiometric mixture of C2H4 (ethylene) and air/oxygenat 1 atm with a stoichiometric mixture of H2 and air. Two different reaction mechanisms areused to calculate the ignition delay times of C2H4.

involved in the ignition process of ethylene, a large number of data for reaction rates is

required. This makes the ignition delay times of ethylene fuel difficult to calculate. The

most comprehensive data is available in the GRI Mechanism 3.0 (Smith et al.). The

latest version of GRI-Mech was recently updated by Marinov et al. (1998) at LLNL

(Lawrence Livermore National Labs.). The calculated ignition delay times are plotted

in Fig. 6.9. Note that the LLNL chemical mechanism which is optimized for ignition

processes estimates longer ignition delay times than the GRI mechanism.

As shown in Fig. 6.9, longer ignition delay times are associated with the ethylene-air

mixtures compared to the values of hydrogen-air. Indeed, when we performed react-

ing experiments where ethylene fuel was injected into air simulating flight Mach 10

conditions, no ignition could be observed in the near-field of the transverse jet (see

Fig. 4.2.5b).


1000 1200 1400 1600 1800 200010

1

102

103

104

C2H

4- air

C2H

4- O

2

C2H

4- air for f=1

p=1 atm

p=2 atm

p=0.3 atm

Ignitio

nTim

e(m

sec)

T(K)

FIGURE 6.10 a) Variation of ignition delay of a stoichiometric mixture of C2H4 (ethylene) and air/oxygenat various pressures.

Although, in our experiments the air composition, Mach number and static tem-

perature corresponds to typical scramjet combustor entrance values, its static pressure

(0.32 atm) is somewhat below that of the actual systems (1.3 - 2.6 atm). This limitation

can be circumvented partially by using higher concentration of oxygen in the test gas. As

plotted in Fig. 6.10, the ignition delay times of a stoichiometric ethylene-oxygen mixture

at p = 0.3 atm are smaller than those for an ethylene-air mixture at similar conditions.

Indeed, in our experiments when ethylene was injected into pure oxygen crossflow (see

Fig. 4.2.5c), autoignition in the near-field of ethylene transverse jet could be achieved.

Eventough ethylene-oxygen delay times are smaller than the ones for ethylene-air, still

they are almost an order of magnitude larger than these for hydrogen-air. The reason

for ethylene autoignition in our experiments can be attributed to the longer residence

time of ethylene large-scale eddies which have slower convective velocities than the hy-

drogen ones. OH-radicals could be observed across the jet shear layer as opposed to


thin-filament observed around the hydrogen jet. The improved mixing properties of

high molecular weight transverse jets might be the primary reason for these results (see

more explanation in Chapters 4 and 5.

Note that ethylene has higher temperature or activation energies for ignition than

hydrogen. Hydrocarbons have effective activation energy for ignition in excess of 150-

200 kJ/mole compared with about 60 kJ/mole for hydrogen. While autoignition of ethy-

lene fuel seems to require higher temperatures and pressures, hydrogen fuel combustion

is more challenging because of the lower reaction rates. From experiments presented in

this thesis, we therefore learned that autoignition of an ethylene transverse jet could be

achieved at flight Mach 10 conditions. This result indicates that hydrocarbons might

be a useful fuel in scramjets flying at Mach 10 conditions. This is an important result

as the long ignition delay time of ethylene (hydrocarbons) relative to hydrogen is a key

limitation for hydrocarbon-fueled scramjets. However, once ignition in hydrocarbon fu-

els is achieved, the combustion process would be completed faster than the hydrogen

fueled scramjet.

Chapter 7

Cavity Flame-Holders

This chapter describes ongoing research efforts in the scramjet community, in gen-

eral, as well as our preliminary study on cavity flame-holders, a concept for flame-holding

and stabilization in supersonic combustors.

During the last few years, cavities have gained the attention of the scramjet commu-

nity as a promising flame-holding device, owing to results obtained in flight tests and

to feasibility demonstrations in laboratory scale supersonic combustors. However, com-

prehensive studies are needed to determine the optimal configuration which will yield

the most effective flame-holding capability with minimum losses. In this chapter, we

summarize the flowfield characteristics of cavities and research efforts related to cavities

employed in low- and high-speed flows. Open questions impacting the effectiveness of

the cavities as flame-holders in supersonic combustors are discussed (Ben-Yakar and

Hanson 2001).

7.1 Review of Previous Research

7.1.1 Cavity Flow-Field Characteristics

Supersonic flow over cavities has been extensively studied (McMillin et al. 1994;

Roudakov et al. 1993; Vinagradov et al. 1995; Ortweth et al. 1996; Owens et al.

1998; Ben-Yakar et al. 998a; Angus et al. 1993; Roudakov et al. 1996; McClinton

et al. 1996; Huellmantel et al. 1957) for many years because of their relevance to

aerodynamic configurations. A cavity, exposed to a flow, experiences self-sustained

132

CHAPTER 7. CAVITY FLAME-HOLDERS 133

oscillations which can induce fluctuating pressures, densities and velocities in and around

the cavity, resulting in drag penalties. This problem motivated many experimental and

computational studies which have been directed toward improving the understanding

of the physics of cavity flows and the means to control their nature.

Cavity flow regimes: In general, cavities can be categorized into two basic flow

regimes depending primarily upon the length-to-depth ratio, L/D (see Fig. 7.1). In all

cases, a shear layer separates from the upstream lip and reattaches downstream. For

L/D < 7 − 10 the cavity is termed “open” as the upper shear layer reattaches to the

back face. The high pressure at the rear face as a result of the shear layer impingement,

increases the drag of the cavity. For L/D > 10−13 the cavity is termed “closed” as the

free shear layer reattaches to the lower wall resulting in significantly increased drag (see

Fig. 7.1b). The critical length-to-depth ratio, at which a transition between different

cavity flow regimes occurs, depends also on the boundary layer thickness at the leading

edge of the cavity, the flow Mach number and the cavity width.

Cavity oscillations: The cavity pressure fluctuations consist of both “broadband”

small amplitude pressure fluctuations typical of turbulent shear layers, as well as discrete

resonances whose frequency, amplitude, and harmonic properties depend upon the cavity

geometry and external flow conditions.

Experimental results reviewed by Zhang and Edwards (1990) found open cavities

to be dominated either by longitudinal or transverse pressure oscillations (Fig. 7.1a)

depending on L/D ratio and the Mach number (M∞). In the short cavity filled by a

single large vortex, the oscillation is controlled by a transverse mechanism, while in the

long cavity filled by vortices, the oscillation is controlled by a longitudinal mechanism.

The transition from transverse oscillation to longitudinal oscillation has been found to

occur near L/D = 2 at Mach 1.5 and between L/D =2 to 3 at Mach 2.5.

There are currently two primary models used to explain the longitudinal cavity

oscillation process (Fig. 7.2). The unsteady motion of the shear layer above the cavity

is the paramount mechanism for cavity oscillations and results in mass addition and

removal at the cavity trailing edge (rear wall). The shear layer impinging on the rear wall

causes free-stream flow to enter the cavity. As a result of the impingement, the cavity

pressure increases and creates an acoustic wave (compression wave) which propagates

upstream at the local sound speed and impacts the front wall. The first model proposes

that this acoustic wave induces small vortices at the leading edge of the front wall which


Transverse

MechanismLongitudinal

Mechanism

OPEN CAVITY FLOW (L/D < 7-10)

CLOSED CAVITY FLOW (L/D > 10-13)

transition at

L/D ~ 2-3

Cp 0

Cp 0

D

L

(b)

(a)

FIGURE 7.1 Flow-field schematics of cavities with different length to depth ratios, L/D, in a supersonicflow. a) Open cavity flow for L/D < 7 − 10; shear layer reattaches to the back face whilespanning over the cavity. Small aspect ratio cavities (L/D < 2−3) are controlled by transverseoscillation mechanism while in larger aspect ratio cavities longitudinal oscillation becomes thedominant mechanism. b) Closed cavity flow for L/D > 10− 13; shear layer reattaches to thelower wall. The pressure increase in the back wall vicinity and the pressure decrease in thefront wall results in large drag losses.

grow as they are convected downstream. Due to instabilities, the shear layer deflects

upwards and downwards resulting in a shock/impingement event on the rear wall of the

cavity. The second model, on the other hand, assumes that the acoustic wave reflection

from the front wall, rather than the shedding vortices, is the cause of the shear layer

deflection and therefore the impingement event on the rear wall. The oscillation loop

is closed when the instability (caused either by vortex shedding or a reflected acoustic

wave) propagates downstream and the mass added in the beginning of the loop is ejected

at the trailing edge again.

Typically, the frequency of the longitudinal oscillations is expressed in terms of the


Shear layer impingement

at the rear wall

Shedding vortices and

reflected acoustic waves

FIGURE 7.2 Typical longitudinal cavity oscillations are caused by the impingement of the free shear layeron the rear wall which generates travelling shocks inside the cavity. The shear layer spanningthe cavity becomes unsteady as a result of these acoustic waves deflecting the shear layer upand down, and/or by the shock induced vortices generated at the front wall leading edge ofthe cavity. As a result unsteady waves emanate from the cavity.

Strouhal number based on the cavity length (impingement length, L).

SL =fmL

U∞(7.1)

Multiple peaks of comparable strength in unsteady pressure spectra were observed in

compressible flow-induced cavity oscillations. These resonant frequencies can be pre-

dicted using the Rossiter’s semi-empirical formula (Rossiter 1964), developed based on

the coupling between the acoustic radiation and the vortex shedding (model 1),

fm =m− α

M∞ + 1k

· U∞L

(7.2)

M∞ and U∞ are the free-stream Mach number and flow speed, respectively; fm is the

resonant frequency corresponding to the mth mode, and a and k are empirical constants.

While k represents the ratio of the speed of the convection of the shear layer vortices

to the free-stream flow speed (U∞), α is the phase shift between the acoustic waves

and the shear layer instability. This equation is modified by Heller and Bliss (1975) for


compressible flows by taking into account the effect of the higher sound speed within the

cavity, which is approximately equal to the free-stream stagnation sound speed. Their

model assumes that the pressure fluctuations are a result of the interaction of the shear

layer with the reflected acoustic waves (model 2),

fm =m− α

M∞√1+ γ∞−1

2M2∞

+ 1k

· U∞L

(7.3)

where γ∞ is the ratio of specific heats. Heller and Delfs (1996) determined from their

experiments that a = 0.25, k = 0.57 for cavities with L/D ratio of 4 or more and

estimated the difference between the formula and experiments as ±10%.

Therefore, the oscillatory frequency of a particular mode in a shallow cavity decreases

with increasing length or L/D ratio of the cavity. However, the dominant oscillatory

mode (the mode with the largest amplitude) jumps from a lower mode to a higher mode

as the L/D ratio increases.

Stabilization techniques for cavity oscillations: Several passive (Perng and

Dolling 1998; Zhang et al. 1998) and active (Sarno and Franke 1994; Vakili and Gauthier

1994; Lamp and Chokani 1997) control methods have been proposed and developed to

suppress the cavity oscillations (Fig. 7.3). Since the shear layer interaction with the

rear cavity wall is the main factor for fluctuations as discussed above, the stabilization

or control of the shear layer can ultimately suppress the cavity oscillations. Passive

control methods, which are usually inexpensive and simple, utilize mounted devices

such as vortex generators and spoilers upstream of the cavity or a slanted trailing edge

that modifies the shear layer so that the reattachment process does not reflect pressure

waves into the cavity. These methods are found to be very effective in suppressing the

cavity oscillations. However, since those are permanent devices, the performance of a

cavity at different conditions may actually be worse than the performance of a cavity

without passive control.

A visual observation of a cavity flow-field stabilized by an oblique rear wall is shown

in Fig. 7.4. This figure contains two instantaneous schlieren images from our recent

experimental efforts demonstrating the stabilizing effect of a slanted back wall upon

the shear-layer reattachment with the back wall. While the cavity with a 90o back

wall (Fig. 7.4a) emits shock waves at the trailing edge as the pressure increases due to

shear layer impingement and recompression of the flow, the angled back wall shown in


Reduced

Cavity Oscillations

Injection

Small Upstream

DisturbancesEnhanced

Shear Layer Growth

Angled Back Wall

(No Reflected Acoustic Waves)

q

q

(b)

(a)

FIGURE 7.3 Different concepts can be employed to suppress the cavity oscillations: a) Cavities with anangled back wall suppress the unsteady nature of the free shear layer by eliminating the gener-ation of the travelling shocks inside the cavity due to the free-shear-layer impingement. b) Inaddition, small disturbances produced by spoilers or by the secondary jet injection upstream ofthe cavity can enhance the free-shear-layer growth rate. The thickening of the cavity shear layeralters its instability characteristics, such that its preferred roll-up frequency is shifted outsideof the natural frequency of the cavity, and as a result the oscillations are attenuated.

Fig. 7.4b leads to a steady shear-layer reattachment process.

Active control methods, on the other hand, can continuously change to adapt to

different flow conditions. Forcing of the shear layer can be accomplished by various

mechanical, acoustical or fluid injection methods. The use of steady or pulsating mass

injection upstream or at the leading edge of the cavity is one of the most commonly

studied techniques. Various researchers (Sarno and Franke 1994; Vakili and Gauthier

1994; Lamp and Chokani 1997) have examined the feasibility of this technique. Vakili

and Gauthier (1994) observed significant attenuation of cavity oscillations with up-

stream mass injection. This was attributed to the thickening of the cavity shear layer,

which altered its instability characteristics, such that its preferred roll-up frequency was

shifted outside of the natural frequencies of the cavity.

Cavity Drag: Two components produce pressure drag in the cavity. First, the

pressure in the backward facing step may be lower than the free stream pressure. This


(b)

(a)

Shear Layer

Recirculation Zone

Oblique Shock Wave

M=3.5M>1

D=3mm

L = 15 mm

Reflected Acoustic Waves

Cp

0

D=3mm

9 mm

L = 17.2 mm

FloorFrontWall

BackWall

Cp

0Floor

FrontWall

BackWall

20°

Trailing Edge Vortex

FIGURE 7.4 Instantaneous schlieren images with 200 ns of exposure time demonstrating the effect of theback wall angle on the flowfield structure of a cavity exposed to a supersonic flow. The free-stream was generated in an expansion tube to simulate Mach 10 total enthalpy conditions atthe supersonic combustor entry: M∞ = 3.4, U∞ = 2360 m/s, T∞ = 1290 K, p∞ = 32 kPa.The boundary layer thickness at the trailing edge of the cavity is approximately 1mm. a) Cavitywith L/D = 5 shows the unsteady nature of the shear layer at the reattachment with thetrailing edge of the back wall. b) Cavity with slanted back wall (20o) stabilizes the shear layerreattachment process.

results in a net force in the positive x-direction (drag force) acting on the base area

(base pressure higher than freestream would result in a thrust force). Second, the

reattachment of the shear layer at the back wall produces a region of high pressure that

imparts a force in the positive x-direction acting on the forward facing area.

In Fig. 7.5, the magnitude of pressure fluctuations on the floor of the cavity and

the drag coefficient for different L/D are given, as adapted from Zhang and Edwards

(1990). Their experimental results demonstrate a sharp rise of the oscillatory level and

the drag when the oscillatory mode inside the cavity changes from a transverse mode

to a longitudinal one. The magnitude of the fluctuations decreases gradually with the


0 1 2 3 4 5 6 7 8 9 100.00

0.04

0.08

0.12

0.16

0.20

M=1.5

M=2.5

Cavity

Dra

g

L/D

0 1 2 3 4 5 6 7 8 9 100.00

0.02

0.04

0.06

0.08

0.10

M=1.5

M=2.5

Prm

s/(r

U2 /2

)

L/D

Longitudinal

Mode

Transverse

Mode

(b)

(a)

FIGURE 7.5 Effect of length-to-depth ratio, L/D on a)magnitude (root-mean-square) of pressure fluctua-tions on the bottom of the cavity (at x/D = 0.33), b) drag of the cavity at Mach 1.5 and 2.5flows. The values were adapted from Zhang and Edwards (1990).

increasing L/D of the cavity, while the average drag coefficient, however, rises signifi-

cantly. As the L/D of the cavity increases, the shear layer thickens at the reattachment

point damping the oscillations and simultaneously increasing the pressure on the back

wall of the cavity. Subsequently, the time-mean pressure on the upstream wall of the

cavity drops as a result of the momentum diffusion across the shear layer. These com-

bined effects of increasing pressure in the back wall of the cavity and decreasing pressure

in the upstream wall of the cavity, increase the drag of the cavity. The drag penalties

become larger as the cavity L/D ratio reaches a critical value at which the closed cavity

flowfield is established.

The drag coefficient of an open cavity is affected greatly by the cavity back wall


geometry. Gruber et al. (999a) studied the drag penalties of open cavities with θ = 16o

and 30o angled back wall, where θ is defined as the angle relative to the horizontal wall

(see Fig. 7.3). They concluded that the drag coefficient increases for shallower back wall

angles. First, the small back wall angles lead to the formation of an expansion wave

(rather than a compression wave) at the cavity leading edge that reduces the pressure

on the backward facing step adding drag. Second, the shear layer deflects farther into

the cavity which results in a larger area of recompression on the angled back wall, again

increasing the drag.

In contrast to Gruber et al. (999a) findings, numerical calculations of Zhang et al.

(1998) resulted in a reduced average drag coefficient as the back wall angle is decreased

from θ = 90o to θ = 67.5o and 45o. The observations from these two references agree,

however, that the pressure on the upstream face of the cavity decreases with decreasing

back wall angle. It is possible that in the 67.5o and 45o cases studied by Zhang et al.

(1998), the compressive nature of the separation wave at the upstream corner of the

cavity actually keeps the shear layer from deflecting into the cavity and could result in

lower levels of pressure drag than the 16o case that Gruber et al. (999a) studied. In

a different study, Samimy et al. (1986) used a cavity with a 20o of back wall angle to

create an undisturbed free shear layer. This geometry was chosen such that the wall

pressure across the cavity would stay unchanged, thereby minimizing the drag losses

associated with the shear layer deflection inside the cavity. These observations suggest

that there might be a critical back wall angle (between θ = 45o to 16o) at which the

drag penalties of a cavity are minimal.

A qualitative description of the pressure distribution along the back wall surface of

cavities with and without an angled wall is plotted in Fig. 7.4. In a rectangular cavity,

below the shear layer reattachment point, the trailing edge vortex accelerates the flow

and causes a pressure decrease in the middle of the back wall. On the other hand, in

the cavity with the angled wall, the high pressure at the corner of the cavity disappears

and a monotonic increase of pressure takes place behind the reattachment point. The

drag coefficient depends strongly on the back wall pressure distribution as it is altered

by the cavity geometry. Further comprehensive studies are required to complete our

understanding of cavity geometry, particularly the effect of the back wall angle on the

drag penalty.

Cavity Residence Time: Residence time, τ , of the flow inside a cavity is a direct


function of the mass exchange rate in and out of the cavity. In the open cavities, mass

and momentum transfer mechanism are controlled by the longitudinal oscillations and

the vortex structure inside the cavity. Computational visualizations of Gruber et al.

(999a) demonstrate the existence of one large vortex stationed near the trailing edge of

the cavity and a secondary vortex near the upstream wall. The mass exchange of the

cavity is controlled by the large trailing vortex which interacts with the unstable shear

layer. The mass exchange between the vortices inside the cavity, on the other hand,

is relatively small, and therefore as the trailing edge vortex occupies larger volume

inside the cavity, the mass exchange increases and flow residence time inside the cavity

decreases. Consequently, the steady-state numerical calculations showed that the flow

residence time in a large cavity (L/D = 5) is smaller than the value in a small cavity

(L/D = 3), in contrast with expectation. Although the volume of the cavity increases

(increases τ) with increasing length, the mass exchange rate, on the other hand, increases

even more (decreases τ), resulting in a decreased residence time. However, it is not yet

clear how the flow residence time inside a cavity is affected by the unsteady nature of the

cavity. The steady state computations (Gruber et al. 999a) mentioned above, estimated

that 1 msec is the order of magnitude of residence time in an L/D = 5 cavity with 9

mm depth size in a Mach 3 cold flow. This value decreases for slanted wall cavities.

As summarized above, the cavity is a basic fluid dynamic configuration which gen-

erates both fundamental and practical interest. A cavity is often characterized by a

strong oscillation inside the cavity driven by the instability of the shear layer. Hence,

these oscillations may be controlled and suppressed by the stabilization of the shear

layer.

7.1.2 Cavity in Reacting Flows

In the past few years, the use of cavities has been considered as a means of perfor-

mance improvement in a supersonic combustor. Basically there are two main directions

in which several research groups have focused their efforts: 1) cavity-actuated mixing

enhancement, 2) trapping a vortex within the cavity for flame-holding and stabilization

of supersonic combustion. Some recently performed studies, investigating the above

concepts are summarized in the following sections.


Cavity-Actuated Supersonic Mixing Enhancement

It is known that the normalized growth rate of the mixing layer between supersonic

air and gaseous fuel in a scramjet combustor decreases as the convective Mach number

increases due to compressibility effects (Papamoschou and Roshko 1988). Researchers

suggested that cavity flow oscillations can actually be used to provide enhanced mix-

ing in supersonic shear layers. A shear layer develops instability waves in its initial

region. This long wavelength Kelvin-Helmholtz instability which leads to large “rollers”

are suppressed at high convective Mach numbers. As a method to enhance the K-H

instability, Kumar et al. (1989) suggested using oblique oscillating shock waves of high

frequency, and Yu and Schadow (1994) concluded that for the required frequency exci-

tation, transverse acoustic waves emanating from cavities are powerful enough to affect

mixing in a significant manner.

Yu and Schadow (1994), therefore, suggested use of cavities to enhance the mixing

of supersonic non-reacting and reacting jets, where the cavity was attached at the exit

of the jet circular nozzle, Fig. 7.6b. When the cavity was tuned for certain frequencies,

large scale highly coherent structures were produced in the shear layer substantially

increasing the growth rate. The spreading rate of the initial shear layer with convective

Mach number Mc = 0.85 increased by a factor of three, and for jets with Mc = 1.4

by 50%. Finally, when the cavity-actuated forcing was applied to reacting supersonic

jets, 20 − 30% reduction in the afterburning flame length with modified intensity was

observed.

Sato et al. (1999) also studied the effect of an acoustic wave, emitted from a cavity

and impinging on the initial mixing layer, Fig. 7.6a. Their results revealed that the

mixing was enhanced by the acoustic disturbance and the rate of the enhancement was

controlled by the cavity shape while the total pressure losses were negligibly small.

This novel use of cavity-induced oscillations in turbulent compressible shear layers to

control the mixing rate, which have been demonstrated in the experiments mentioned

above, encourages the use of unstable cavities in high speed propulsion applications.

However, before implementing such techniques, one must consider and evaluate the

potential thrust loss and noise generation associated with the technique.


CAVITY

supersonic jet

cavity actuated

mixing layer

initial mixing layerSUPERSONIC

NOZZLE

CAVITY

acoustic wave

mixing layer

M>1

fuel injection

(b)

(a)

FIGURE 7.6 Cavity-actuated supersonic mixing enhancement concepts: (a) Sato et al. (1999), studied theinfluence of acoustic waves, emitted from a cavity and impinging on the initial mixing layer.(b) Yu and Schadow (1994) used the same concept to enhance the mixing of supersonic reactingjets.

Cavity as a Flame-Holder

While an unstable cavity can provide enhancement in the turbulent mixing and com-

bustion as discussed above, a stable cavity can be used for flame-holding applications.

In an effort to reduce the combustor length required for efficient high speed combustion,

during the past few years, the scramjet community has proposed the use of wall cavities

to stabilize and enhance supersonic combustion. The main idea is to create a recircula-

tion region inside the cavity with a hot pool of radicals which will reduce the induction

time, such that autoignition of the fuel/air mixture can be obtained. However, for a

stable combustion process, the cavity recirculation region has to be sufficiently stable

to provide a continuous ignition source (pilot flame). As discussed above, it is possible

to control the self-sustained oscillations occurring in cavities either by proper design of


the cavity or by a passive/active control system.

In the following sections, we will first discuss the literature for low-speed and then

the recent advances in high-speed combustors which utilize cavity flame-holders.

Cavity TV - “Trapped Vortex” concept in low-speed flows: Recently, cavities

have been employed in low-speed flows to stabilize combustion utilizing the so-called

“trapped-vortex” concept (Hsu et al. 1998). In this concept, a stationary vortex is

established or “trapped” inside the cavity by optimal design of the dimensions, namely,

by optimal cavity length to depth ratio (L/D). It is known that a vortex will be trapped

in the cavity when the stagnation point is located at the downstream end of the cavity

which also corresponds to the minimum drag configuration (Heller et al. 1970). Based

on this evidence, Hsu et al. (1998) designed an experimental cavity to investigate the

low-speed flame stability characteristics of a trapped-vortex combustor, while Katta

and Roquemore (998a, 998b) performed numerical calculations for this geometry. Their

results showed that a vortex is locked in a short cavity (L/D < 1).

However, when a vortex is trapped in the cavity, very little fluid is entrained into the

cavity, resulting in very little exchange of the main flow and cavity fluid. When flame

stabilization is a consideration, a continuous exchange of mass and heat between the

cavity and the main flow is required. To overcome this problem, it has been suggested

to directly inject both fuel and air into the cavity in a manner that reinforces the vortex

and increases mass transfer of the reactive gases with the freestream.

The main conclusions revealed from low-speed cavity flame-holder studies can be

summarized as follows:

1. In non-reacting flows, a stable cavity flow was observed at an optimal dimension

(L/D = 0.6) that produces minimum drag, namely, minimum pressure drop. This

was also the optimal cavity length which provided the most stable flame.

2. A sufficient amount of fuel and air must be injected directly into the cavity to

obtain good performance characteristics of a combustor with a trapped-vortex

cavity.

3. The fluid injection inside the cavity had a strong impact on the stability of the

vortex inside the cavity. When jets were injected in such a way that they reinforced

the vortex, the flame stabilization capability of the cavity was enhanced.


4. The optimum size (L/D) for steady flow should be larger in the case of cavities

with fluid injection than for cavities with no injection.

Cavity flame-holders in high-speed flows: In the scramjet community, there

is a growing interest in the use of cavity flame-holders. In a 1997 Air Force/NASA

workshop (Tishkoff et al. 1997), an integrated fuel injector/cavity flame-holder was

mentioned as one of the new concepts that may provide potential performance gain in

a scramjet engine. It was indeed very encouraging to see this new concept employed

and flight-tested in the scramjet engine by the Central Institute of Aviation Motors

in Moscow (Roudakov et al. 1993; Vinagradov et al. 1995; Ortweth et al. 1996;

Owens et al. 1998; Roudakov et al. 1996; McClinton et al. 1996). The combustor of

the axisymmetric scramjet engine, illustrated in Fig. 7.7, included three fuel injection

stages, two with cavity flame-holders (D = 20 mm by L = 40 mm and D = 30mm by

L = 53 mm) and one with a step flame-holder (D = 17 mm). The injection of the fuel

(hydrogen) was performed within the cavity flame-holders from the front-facing wall at

30o to the engine axis and just upstream of the step at 45o. With this integrated injec-

tion/cavity flame-holder approach, numerical studies (McClinton et al. 1996) showed

that autoignition and flame-holding within the cavity could be obtained at Mach 6.5

flight, even without the spark ignition plugs. Their analysis also revealed that without

the cavity, the ignition is unlikely due to the small injector dimension (dj = 1.25−2mm)

and low combustor operation pressure (p ≈ 0.4 atm) as estimated previously by Huber

et al. (1979). Finally, the joint Russian / U.S. effort demonstrated in the flight test

performed on February 12, 1998 that a positive thrust from the scramjet engine could

be successfully achieved.

One can find several recent studies investigating cavities for flame stabilization of a

supersonic combustor. Some of these works, performed for different kinds of fuels (solid,

liquid and gaseous fuels), are summarized as follows.

The combustion of kerosene in a scramjet requires additional ignition and flame-

holding elements because of the long ignition times and reduced reaction rates as com-

pared to hydrogen. Owens et al. (1998) tried to determine the flame stability of kerosene

injected upstream of a cavity flame-holder with Mach 1.8 free-stream conditions. Due

to the low stagnation temperatures of 1000K, ignition was provided by pilot hydrogen

fuel injected into the cavity. Flame-holding could be achieved only when large flow rates


71 175 248 274

30 68Cavity 120 x 40

Cavity 230 x 53

Injector30°

Injector30°

InjectorStep

FIGURE 7.7 Axisymmetric combustor of the Scramjet engine which was flight-tested by Russian-CIAM/NASA joint program (1998). In this engine two cavities with angled-rear wall wereused for flame-holding purposes. The dimensions are in mm (McClinton et al. 1996).

of hydrogen were used. In this case the enlargement of the recirculation region led to

entrainment of additional quantities of fresh air contributing to the flame stability. An

additional investigation of scramjet combustors operating on kerosene was performed by

CIAM (Vinagradov et al. 1995). In their configuration, the combustion was sustained

by a row of hydrogen fuel injectors placed in front of a cavity.

The use of cavities as flame-holders in solid fuel supersonic combustors has been also

studied (Ben-Yakar et al. 998a; Angus et al. 1993). In the experiments of Ben-Yakar

et al. (998a), self-ignition and sustained combustion of PMMA (Plexiglas) solid fuel with

no external aid (such as reactive gas injection or a pilot flame) was demonstrated under

supersonic hot-air flow conditions. This was accomplished by a recirculation region

formed inside a cavity which was positioned at the entrance of the combustor. Typically,

in a subsonic solid fuel ramjet, a step is used for flame-holding purposes, and it is

known that larger step heights (leading to bigger recirculation zones) can provide better

flame stabilization. However, in supersonic flows where a large step is required, the

free-stream flow velocity would increase as well by the sudden expansion, deteriorating

the flame-holding capability. Under those considerations, a cavity consisting of a step

followed by an angled wall was chosen as a flame-holder in the supersonic solid fuel

experiments mentioned above. The results revealed that both the cavity length (L) and

the step height (D) have significant effect in sustaining the combustion. While short L

caused flameout even for relatively large D, the inverse, namely small D, did not permit

sustained combustion even though L was quite long. Ultimately, cavity length-to-depth

ratio between 1.7 < L/D < 2 showed a regime of sustained combustion.

Besides the use of cavities in liquid and solid fueled supersonic combustors, there are


other research groups (Yu et al. 1998; Yu et al. 1999; Niioka et al. 1995; Mathur et al.

1999; Davis and Bowersox 997a; Davis and Bowersox 997b) concentrating on character-

ization of cavity flame-holders in gaseous supersonic combustors. Initial experimental

efforts were performed by Yu et al. (1998, 1999). They analyzed flow stability and

flame-holding characteristics of several wall cavities with various sizes and aspect ratios

(L/D = 0.5, 1, 2, 3 and inclined cavity) in a Mach 2 air-stream. Pressure oscillations,

observed in cold flow experiments, were diminished in reacting flow, when the thin shear

layer above the cavity disappeared by three fuel jets injected at 45o upstream of the

cavity. Typically, small aspect ratio (1 < L/D < 3) cavities appeared to be good flame-

holders, which is consistent with the “trapped vortex” concept discussed above. The

narrow cavities (L/D = 0.5) provided very steady flame-holding, however they had rela-

tively little effect on the downstream emission characteristics. With the inclined cavity,

which was also the longest cavity tested (L/D = 5), no flame-holding was observed.

Additional experiments were conducted by Niioka et al. 1995 in Mach 1.5 airflow. They

achieved flame stabilization using two struts and by injecting hydrogen gas in the in-

terval between the two parts. They showed that flame stability could be controlled by

the cavity length which controls the competition between the mass transfer rate and

the chemical reaction rate, i.e., the Damkohler number.

Wright-Patterson Air Force Research Laboratories have also initiated a program

(Mathur et al. 1999; Davis and Bowersox 997a; Davis and Bowersox 997b) to examine

the effectiveness of cavities in supersonic flows. Experiments on a cavity with upstream

ethylene fuel injection were performed in the supersonic combustor facility operating at

conditions that simulate flight Mach numbers between 4 and 6. Initial results demon-

strate flame-holding and large flame spreading in the cavity vicinity. In parallel, Mach 3

cold flow research is also in-progress to study the fundamental aspects of cavities. The

results showed that:

1. The cavity geometry had an effect on mass entrainment rate and residence times.

A decrease in cavity residence time was observed in cavities with longer length

and slanted walls.

2. In general, the length of the cavity determined the mass entrainment, while the

cavity depth determined the cavity residence time.


3. Larger cavities (L/D = 7) had significantly higher drag coefficients than the

smaller cavities (L/D = 3). Reduction of the back wall angle below 90o resulted

in additional drag penalties.

4. Cavities with offset ratios larger than 1 (upstream wall height is larger than the

back wall height) caused the cavity base to experience lower pressures and there-

fore larger drag penalties.

In addition, Davis and Bowersox (997a, 997b) used a combined CFD/perfectly

stirred reactor methodology as a design guide for sizing of the cavity. He recom-

mends that initial cavity size can be estimated based on the minimum residence time

required to obtain ignition by assuming a perfectly stirred reactor cavity flow. Similar

to Gruber et al. (999a), he concluded that cavity depth, D, which mainly controls

the residence time, can be estimated using their numerically obtained empirical equa-

tion: D = τr · U/40, where τr is the required residence time for ignition and U is the

free-stream velocity.

7.1.3 Outstanding Questions

As discussed above, during the last few years, cavities have gained attention as

promising flame-holding devices. However, comprehensive studies still need to be per-

formed to determine optimal configurations which yield the most effective flame-holding

capability with minimum losses.

We can pose the following questions concerning the effectiveness of the cavities as

stable flame-holders in supersonic combustors:

1. Can the TV concept be used in supersonic combustors? Several investiga-

tors have recognized the aerodynamic advantages of trapping vortices inside small

aspect ratio cavities (L/D < 1) both as a means of reducing the drag penalties of

cavities and also obtaining stable flame-holding in a low-speed combustor. Stable

small aspect ratio cavities may possibly be adapted to provide sustained combus-

tion in supersonic flows. However, the cavity flow residence time associated with

high-speed flows will be smaller than in low-speed flows and might eliminate its

flame-holding capability. Therefore, stable cavities may possibly be adapted to


provide sustained combustion in supersonic flows as long as the Damkohler num-

ber is larger than unity (namely, the residence time inside the cavity is sufficient

to initiate the ignition process). For example in the flight tested scramjet engine,

designed by CIAM and NASA, fuel was injected within the cavity flame-holder

to provide autoignition and flame-holding (McClinton et al. 1996). Otherwise,

autoignition was unlikely due to the low total enthalpies of the Mach 6 flight

condition, and small injector dimensions and the low combustor pressures of the

design point.

2. What are the cavity dimensions and its geometry? Open cavities with

L/D < 7− 10 are good candidates for flame-holding owing to their reduced drag

coefficients relative to the closed cavities. The dimensions of an open cavity have

to be derived from ignition and flame-holding considerations. The cavity depth

can be determined according to the required residence time to initiate ignition.

The cavity length, on the other hand, has to be chosen to provide sufficient volume

of radicals to sustain the combustion further downstream.

3. Can an unstable cavity be used to establish flame-holding? While a

stable cavity is preferable to sustain continuous and stable combustion, an unstable

cavity can be used to enhance mixing and ignition by the shock waves emitted as

a result of strong cavity oscillations. However, unstable cavities are unlikely to

provide a continuous flame-holding region inside the cavity as will also be shown

in our preliminary ignition experiments (see Section 7.2).

4. How does fuel injection affect the cavity flow-field? Jet injection upstream

or inside the cavity can alter the shear layer specifications (its thickness and sta-

bility) directly, and therefore, the cavity performance. Raman et al. (1999), for

example, have found that jet interaction with a cavity can produce different oscil-

lation frequencies.

5. How does the cavity flow-field affect a fuel jet injected upstream? Shock

waves emanating from a cavity can enhance the mixing of fuel jets injected up-

stream of the cavity. As shown by several researchers, the acoustic waves of an

unstable cavity can be used to enhance mixing. On the other hand, a stable cav-

ity can also enhance mixing. As the jet reaches to the back wall it interacts with


the strong trailing edge shock wave of the cavity. It is known that an oblique-

shock-wave-jet interaction enhances the molecular mixing between supersonic air

and gaseous fuel by the vorticity generated due to the baroclinic torque. This

might have immediate significance to the spreading rate of the jet and mixing

enhancement of the fuel-air, resulting in enhanced combustion efficiency.

6. Is local wall heating inside the cavity a problem? High total temperatures

of air stagnating inside the cavity can result in excessive heat transfer to the walls.

However, the transpiration technique of mass addition from a porous surface can

be used as a way to cool the cavity surfaces. This method can, furthermore,

decrease the skin friction losses on the cavity floor surface and reduce the drag

losses associated with the shock wave structure of the cavity (Castiglone et al.

1997). Fuel mass bleeding inside the cavity can alter the shear layer bending

towards the cavity by increasing the cavity pressure distribution. In this way,

the strong trailing edge reattachment shock wave can be eliminated or reduced

in strength. Therefore, an optimized transpiration cooled cavity may also be

designed to improve the pressure losses and the drag penalties.

7. At which flight conditions can a cavity flame-holder be effective? At

high flight Mach numbers, beyond Mach 8, the velocity and the total enthalpy of

air entering the combustor is high. In this hypersonic flight regime, hydrogen fuel

is preferred owing to its reduced combustion characteristic times. Ignition of the

hydrogen-air system can be purely characterized by radical runaway without the

need for thermal feedback (substantiated by direct numerical analysis of Im et al.

(1998)). Therefore, for a hydrogen-air system, a cavity flame-holder, in which

the high-stagnation temperatures will initiate ignition by radical runaway, can be

designed even though no appreciable heat has yet been released. As we move into

lower flight speeds, below Mach 8, application of a flame-holder becomes crucial.

In this supersonic flight regime, the selection of a cavity flame-holder is required

to achieve longer flow residence times inside the cavity because of the reduced

total enthalpies and longer ignition delay times associated with hydrocarbon fuels,

which are the candidate fuels for supersonic flight below Mach 8. Consequently,

cavities can be utilized in a wide range of flow conditions, in both supersonic and

hypersonic airbreathing propulsion systems.


L/D=3

L/D=5

x/D=1.5

P P

x/D=0.5

cavity pressuretransducers

FIGURE 7.8 Position of pressure transducers located at the bottom of the cavity to measure the historyof the flow oscillations inside the cavity. Pressure transducer located farther downstream atx/D = 1.5 provided a more accurate oscillation frequency measurements.

7.2 Preliminary Cavity Results

Here, we will summarize our preliminary results, where the primary objective is to

demonstrate the feasibility of the experimental set-up to provide information for cavity

flame-holder studies. These appear to be the first cavity experiments performed in such

high total enthalpy flows.

The pressure is measured within the cavity to monitor the time dependent acoustic

field. The fast response pressure measurements are performed at 1.5D downstream the

forward face of the cavity as illustrated in Fig. 7.8. Established cavity oscillations are

observed and a sequence of oscillation cycles could be captured during the limited test

time (∼ 300µs) of the flow facility.

Figure 7.9 shows examples of the cavity pressure development at x/D = 1.5 during a

typical expansion tube run. These pressure traces are obtained for 4 different geometries:

a)L/D = 3, b)L/D = 5, c)L/D = 5 with hydrogen injection upstream of the cavity

and d) L/D = 7. After the arrival of incident shock wave, different flow regimes exist

including: a time during which helium is flowing; a period during which the contact

region is passing; and a window in which there is a steady flow of test gas before the

arrival of rarefaction waves. These flow periods can clearly be visualized in cavity

pressure measurements where the pressure rises by the arrival of contact surface. After


0 200 400 600 800 1000-0.5

0.0

0.5

1.0

~53ms

Test GasL/D = 7

Pcavi

ty,A

U

t, msec

0 200 400 600 800 1000-0.5

0.0

0.5

1.0

~18ms

Test GasL/D = 3

Pcavi

ty,A

U

t, msec

0 200 400 600 800 1000-0.5

0.0

0.5

1.0

~38ms

Test Gas

L/D = 5

Pcavi

ty,A

U

t, msec

0 200 400 600 800 1000-0.5

0.0

0.5

1.0

~38ms

Test GasL/D = 5 with

30o

injection

Pcavi

ty,A

U

t, msec

(d)

(a)

(b)

(c)

FIGURE 7.9 Examples of cavity pressure traces in arbitrary units: a) L/D = 3, b) L/D = 5, c) L/D = 5with upstream hydrogen injection, d) L/D = 7. t = 0 represents incident shock arrival at thecavity. The free-stream (N2) conditions represent Mach 10 total enthalpy at the supersoniccombustor entry: M∞ = 3.4, U∞ = 2360 m/s, T∞ = 1290 K, p∞ = 32 kPa.


TABLE 7.1 Summary of cavity oscillation frequencies, fm, for different cavity length to depth ratios, L/D.The table includes the expected values based on Rossiter’s formula and the ones measured inour experiments.

L/D Rossiter’s formula Present data Differencefm, kHz Tm,µs Tm, µs %

3 52.2 19.2 18± 1 -6.3± 55 31.3 31.9 37± 1 16.0± 47 22.4 44.7 53± 2 18.6± 2

a period of flow establishment time (about 200µs), several cycles of distinct pressure

oscillations are observed during the steady flow test time.

The measured frequencies, averaged from several experiments, together with the

expected frequencies estimated from Rossiter’s empirical formula are summarized in

Table 7.1. A good agreement within 6% could be achieved for the frequency measure-

ment of L/D = 3. For larger L/D ratios, the agreement is weaker and the difference

between the measured and the expected frequencies reaches up to 20%. This difference

might be due to the difference in total temperature (∼ 4000K) of the flow tested in

our experiments. Note that the formula of Rossiter’s contains two empirical parameters

derived from cold flow experiments. However, before any conclusion can be made, we

have to analyze the flow-field dynamics of different cavity geometries in more detail.

These results show that 2-D cavities with the geometry chosen here (D = 3 mm,

L/D =3, 5, 7) can be studied in an expansion tube facility despite the limited test time.

However, a longer test time is required to achieve accurate values of the acoustic field

frequencies inside/around the cavity.

7.2.1 Visual Observation of Cavities Using Ultra-Fast Schlieren

Flows around two-dimensional cavities are investigated to show the effects of vari-

ations in length-to-depth ratio (L/D) of the cavity. For this purpose cavities with

L/D =3, 5 and 7 are tested. In addition, a 30 degrees angled rear wall was tested for

the cavities with L/D =3 and 5. All the cavities have the same depth of 3 mm. The

different length-to-depth ratios are formed by removable back wall inserts.

Figure 7.10 summarizes examples of instantaneous schlieren images (200 ns exposure


time) obtained for cavities with L/D = 3, 5, and 7 that we have tested. In all cases,

the boundary layer separates from the upstream lip and reattaches downstream.

As the boundary layer separates from the leading edge of the cavity, a free shear layer

forms. Depending upon the pressure inside the cavity the shear layer deflects upwards

or downwards producing a compression or an expansion wave consequently. For the

cavity with L/D = 3 (Fig. 7.10a) a compression wave appears at the leading edge of

the cavity. As the cavity length is increased to L/D = 5 (Fig. 7.10b) this compression

wave weakens. Eventually, for the cavity with L/D = 7 (Fig. 7.10c), it diminishes and

an expansion wave at the leading edge takes place instead of the compression wave.

The strongest shock wave appears from the trailing edge of the cavities which is con-

sistent with the numerical observations of Zhang et al. (1998). The shear layer deflects

downward near the trailing edge of the cavity and creates a high pressure stagnation

point on the downstream face (the dark regions as can be seen in schlieren images in

Figs. 7.10a and 7.10b). While this strong shock wave seems to be attached to the trail-

ing edge of the cavities with L/D = 3 and 5, it moves upstream off the back wall for

the cavity with L/D = 7.

There are generally two basic flow regimes that a cavity can yield depending upon

the length-to-depth ratio, L/D (see Fig. 7.1). A cavity is termed “open” if the shear

layer reattaches to the back face while the drag of the cavity is small (Fig. 7.1a). Beyond

some critical L/D ratio, the cavity is termed “closed” as the free shear layer reattaches

to the lower wall resulting in significantly increased drag. Based upon this description,

in our experiments cavities with L/D = 3 and 5 demonstrate “open” cavity flow-field

features, while a cavity with L/D = 7 seems to be in the transition regime between

“open” and “closed” cavity.

These results are also consistent with the numerical calculations of Baurle and Gru-

ber (1998). Their results showed that larger cavities (L/D = 7) have significantly higher

drag coefficients than the smaller cavities (L/D = 3).

Figures 7.10d and 7.10e demonstrate instantaneous flow-field structure of cavities

with a back wall angled at 30 degrees. These schlieren images reveal that the leading

edge compression waves observed for the cavities with L/D = 3 and 5 do not exist with

an angled aft wall cavity. However, the strong trailing edge shock wave still exits as the

shear layer reattaches at the angled back wall.

Additional experiments are performed in order to study the influence of upstream


(a) L/D = 3 (d)L/D = 3 with 30o angled back wall

(b) L/D = 5 (e) L/D = 5 with 30o angled back wall

(c)L/D = 7

FIGURE 7.10 Schlieren images demonstrating the differences in the flow-field structure of cavities withdifferent length-to-depth ratios and back wall angle. The depth of the cavities is constantand equal to D = 3 mm. The free-stream was generated to simulate Mach 10 total enthalpyconditions at the supersonic combustor entry: M∞ = 3.4, U∞ = 2360 m/s, T∞ = 1290 K,p∞ = 32 kPa. The boundary layer thickness at the trailing edge of the cavity is approximately1mm.


(a) L/D = 3

(b) L/D = 3 with 30o back wall and upstream injection

(c)L/D = 5 with upstream injection

FIGURE 7.11 Schlieren images demonstrating jet interaction with different cavities. The hydrogen jet isinjected into a non-reacting free-stream 3mm upstream of the cavity from a d = 1 mm orifice.The injection is performed at angle of 30o to the plate. The free-stream, N2, represents theflight Mach 10 burner entry conditions.


fuel injection onto the cavity flow field. The results shown in Fig. 7.11 include 30 degrees

hydrogen injection from a 1 mm diameter orifice positioned at 3mm upstream of the

cavity leading edge. Those schlieren observations present no significant differences in the

cavity flow field structure due to the upstream injection. On the other hand, some cavity

influence on the jet can be observed. The jet seems to be disturbed as it propagates

over the cavity for the case of L/D =3 and 5 by the compression waves at the leading

edge. As this leading edge shock wave diminishes for the cavities with an angled wall

the jet is not disturbed as it spans over the cavity until it reaches to the trailing edge.

As the jet reaches to the back wall it interacts with the strong trailing edge shock

wave emitting from the cavity. This shock wave - jet interaction at the trailing edge of

the cavity might have an important role in reacting cases. It is known that an oblique

shock wave - jet interaction enhances the molecular mixing between supersonic air and

gaseous fuel. The vorticity generated when a shock wave interacts with a shear layer

(due to the baroclinic torque) has immediate significance to the mixing enhancement in

supersonic flows resulting in enhanced combustion efficiency.

Furthermore, the trailing edge shock is expected to direct the fuel jet towards the

airflow, increasing the fuel penetration, the static pressure, the static temperature, and

therefore the reaction rates.

Since the fuel jet penetration is expected to decrease as the angle of injection de-

creases, an improved transverse penetration and lateral spreading of the fuel might be

achieved by interaction of the jet with the cavity leading edge shock wave.

7.2.2 Preliminary Ignition Results of Injection/Cavity Schemes

The ignition of a hydrogen jet interacting with a cavity is studied using OH-PLIF.

Several instantaneous OH-PLIF images obtained at the center-line of the jet are pre-

sented in Fig. 7.12 for cavity with L/D = 3 and in Fig. 7.13 for cavity with a 30o angled

back wall. Hydrogen is injected 3 mm upstream the cavity leading edge at an angle

of 30o and the free-stream (air) properties represent the flight Mach 10 burner entry

conditions: M∞ = 3.4, U∞ = 2360m/s, T∞ = 1290 K, p∞ = 32 kPa.

For a cavity with L/D = 3, five images (see Fig. 7.12) are obtained from different

experiments. The unsteady nature of the jet/cavity interaction is apparent as the in-

tensity level of OH radicals change from experiment to experiment. Figure 7.12a shows


an ignition along the jet/cavity shear layer with a little OH fluorescence signal inside

the cavity. As the jet interacts with the hot cavity air an auto-ignition can be achieved

at the interface. The jet/cavity shear layer impinging on the back wall causes jet and

free-stream flows to enter the cavity. Figures 7.12b-e show significant levels of OH con-

centration inside the cavity. The intensity differences between the images might be a

result of the breathing motion of the cavity. However, quenching of OH is observed

downstream of the cavity for all of the five experiments, indicating that this cavity

configuration can not provide flame-holding.

The OH-signal levels from shot to shot are more uniform inside the cavity with an

angled back wall as the cavity oscillations are suppressed (see Fig. 7.13). This cavity

configuration provides a continuous ignition downstream of the cavity. Also visible in

Fig. 7.13a is the ignition on the upper side of the jet, most likely induced by the shock

wave attached to the cavity back wall.

In summary, the few OH-PLIF images indicate no ignition around the jet even in

the high total enthalpy conditions of flight Mach 10 due to the shallow injection angle.

Addition of a cavity downstream the injection port does provide ignition in the near-

field. However, the flame-holding capability of these cavities need to be examined in

more detail.


(a)

(b) (c)

(d) (e)

FIGURE 7.12 Instantaneous OH-PLIF images demonstrating the ignition regions of a hydrogen jet interact-ing with a L/D = 3 cavity. The images are obtained from 5 single shots at the same condi-tions. Hydrogen is injected 3 mm upstream the cavity leading edge at an angle of 30o. Thefree-stream (air) properties represent the flight Mach 10 burner entry conditions: M∞ = 3.4,U∞ = 2360 m/s, T∞ = 1290 K, p∞ = 32 kPa. Note that a schlieren image is also included toindicate the flow-field properties around the cavity.


(a)

(b) (c)

FIGURE 7.13 Instantaneous OH-PLIF images demonstrating the ignition regions of a hydrogen jet interact-ing with a cavity with L/D = 3 and 30o back wall. The images are obtained from 5 singleshots at the same conditions. Hydrogen is injected 3mm upstream the cavity leading edge atan angle of 30o. The free-stream (air) properties represent the flight Mach 10 burner entryconditions: M∞ = 3.4, U∞ = 2360 m/s, T∞ = 1290 K, p∞ = 32 kPa. Note that a schlierenimage is also included to indicate the flow-field properties around the cavity.

Chapter 8

Concluding Remarks

8.1 Summary of Major Results and Conclusions

8.1.1 Experimental Aspects

• We have demonstrated the feasibility of using an expansion tube to generate clean

(radical-free), high-total enthalpy supersonic flows of air associated with hyperve-

locity combustors.

• Characterization experiments with test gas mixtures of 95%N2 + 5%CO2 were

performed to study the facility’s performance such as the free-stream flow proper-

ties, the useful test time and the core-flow size available for mixing and combustion

studies of a 2mm jet in crossflow. Our experimental approach included simulation

of the required total enthalpy (3-6MJ/kgair) of flight Mach 8, 10 and 13 condi-

tions by simulating the required burner entry Mach number, burner entry static

temperature, and consequently the burner entry velocity. As the burner entry

static temperatures were chosen to be in the range of 1250-1400 K, velocities of

1800, 2360 and 3200 m/s were generated for the flight Mach 8, 10 and 13 condi-

tions, respectively. On the other hand, simulated static pressures were below the

desired values because of the limited maximum pressures available in the current

driver section and the limited maximum pressures at which the jet injector valve

could operate with sufficient speed.

• The steady test time duration and the core-flow size of the expansion tube flow

161

CHAPTER 8. CONCLUDING REMARKS 162

were characterized. These are important parameters which define the model di-

mensions where a fully established flow can be achieved. In addition, primary

effects of the boundary layer on expansion tube flow were observed. In particu-

lar, test times ranging between 170 - 400µs, higher than the ideal values, were

observed. In contrast with shock tunnels, the expansion tube allows an increased

duration of useful test times, as the corresponding flight Mach number of the test

flow increases. The boundary layer developed on the tube walls increases the con-

tact surface velocity and therefore delays the arrival of the first disturbance wave.

However, in our experiments the static pressure of the free-stream was low for

high enthalpy flows, causing the boundary layer effects to increase the test time.

Simulation with higher pressures might result in shorter test times, and therefore

shorter useful test “slug lengths” would be available.

• We have demonstrated that Mirels’ solution for boundary layer effect implemented

in x-t diagrams is a useful tool for prediction of test time and for optimizing the

expansion section length to achieve the maximum test duration.

• Pitot pressure surveys at the exit of the expansion tube have identified an inviscid

test core of approximately 25 mm diameter over which the pitot pressure is con-

stant to within ±5%. While the core-flow size in Mach 10 and 13 conditions did

not diminish significantly at 6.35 cm downstream of the tube exit, the core-flow

size for the Mach 8 condition dropped by half. Since the Mach wave angle is

steeper for small free-stream Mach numbers, the boundary layer information at

the tube exit reaches to the centerline in a smaller distance at the flight Mach 8

condition.

• Finally, compared to large facilities that can average a limited number of experi-

ments per day, many experiments per day in this facility can be performed with

the effort of just one student. Therefore, this facility provides a useful tool for

basic study of near-field features of different fuel injection configurations that have

potential for future application in scramjet engines.


8.1.2 Flow Visualization Techniques

We used two non-intrusive flow diagnostic techniques: Planar Laser-Induced Fluores-

cence of OH radicals (OH-PLIF) and schlieren imaging with an ultra-fast-framing-rate

digital camera. While schlieren showed the location of shock waves and jet penetration,

OH-PLIF mapped the regions of combustion.

Ultra-Fast Framing Rate Schlieren

• We have presented the first demonstration of an ultra-fast flow visualization sys-

tem (at framing rates up to 100 MHz) based on schlieren imaging. High-temporal

and high-spatial resolutions allowed both qualitative and quantitative study of

supersonic flows. The system included a fast-framing camera (IMACON 468),

capable of acquiring 8 full resolution images in a 576× 384 pixel format with in-

terframing times and exposure times down to 10 ns and a Xenon flashlamp system

capable of providing up to 200µs duration of a uniform light source. Supersonic

movies were obtained by assembling the consecutive images. These movies ba-

sically slow the flow motion by one million times, elucidating the instantaneous

unsteady features. For example, the pulsating nature of periodically formed eddies

causing the bow shock to fluctuate is very apparent and can be easily followed.

• Qualitative flow observations as well as quantitative measurements such as veloc-

ity, propagation angle and formation frequency of large-eddy structures, jet pen-

etration and the width of the jet shear layer were obtained. A cross-correlation

technique using fast Fourier transforms has been employed to analyze the 8 con-

secutive images. Among those measurements, the spatial-temporal development

(x-t diagram) of unsteady structures and their frequency of formation were part

of the unique measurements available only by analysis of time correlated multi-

ple images. For example, due to pairing and stretching, the spatial gap between

eddies is not necessarily a measure of the eddy formation frequency. Therefore,

only high-speed framing rate imaging could provide such information, necessary

for understanding the origin of the jet shear layer vortical structures, which are

the dominant mechanism in the near-field mixing of jets.


• We have shown optimum exposure and inter-framing times which require the op-

timization of four main factors including the schlieren sensitivity, the spatial res-

olution, the dynamic range and the signal-to-noise ratio. The image area was

28× 18mm and the exposure time was 100 ns. In other words, the spatial res-

olution was 100× 100µm in the near-field (x/d < 2) and 250× 250µm in the

far field (x/d > 8) depending on the large-scale structure movement during the

exposure time. The corresponding resolving power was 2-5 pixels, achieved by

the optimization of the four factors discussed above. Resolution considerations

became important with increasing velocities and decreasing region of interest. In

our experiments, we could achieve very high quality schlieren images even though

light deflections were minimum since the jet diameter was only 2mm. The inten-

sified CCD cameras and the high intensity light source allowed us to control the

sensitivity of the imaging system and achieve the required quality for quantitative

data analyses.

• The application of a high-speed-framing rate imaging system became even more

important as it was combined with an impulse facility operation. The unique

free-stream conditions with high-speed and high-temperatures studied in this in-

vestigation could only be generated for very short times. Therefore, the use of

the ultra-fast schlieren system was crucial because it increased significantly the

amount of data available from a single experiment.

OH-PLIF and Simultaneous Measurements

• The OH-PLIF measurements were obtained by excitation of the A2 ∑+ ← X2Π(1, 0)

band of OH, near 283 nm, and by the detection of the (1,1) band near 315 nm. A

broader excitation assumption was valid as the linewidth of the laser beam, pro-

vided from a frequency-doubled dye laser source, was broader than the absorption

linewidth. The isolated Q1(7) transition at 283.266 nm was selected to minimize

signal dependence on temperature. Therefore, the fluorescence intensity could be

related directly to OH mole fraction.

• Simultaneous OH-PLIF and schlieren imaging could be implemented using two

intensified CCD cameras and a dichroic mirror to separate the OH fluorescence

from the schlieren beam.


8.1.3 Characteristics of Hydrogen and Ethylene Transverse Jets

We studied the flow-field properties of hydrogen and ethylene jets injected into flight

Mach 10 conditions at similar jet-to-free-stream momentum flux ratio. The results reveal

significant differences in the development of large-scale coherent structures present in

the jet shear layer. Previously, the momentum flux ratio was found to be the main

controlling parameter of the jet penetration; the results here demonstrated the existence

of an additional mechanism which altered the vortical structure, the penetration and

the mixing properties of the jet shear layer. These new observations became possible

by the simulation of high velocity and high temperature free-stream conditions which

could not have been achieved in the facilities that have been widely used in previous

studies. The details of the main results can be summarized in the following points:

• Visual observations, supported by the qualitative measurements of the convec-

tion velocity and jet penetration, reveal large differences between the hydrogen

and ethylene injection cases. Special attention was given to the large scale co-

herent structures present at the jet/free-stream interface. Instantaneous images

provided a well-resolved representation of the coherent structures at the jet pe-

riphery. While the hydrogen eddies persisted for long downstream distances, in

the ethylene case the eddies dissipated quickly. It is conjectured that increasing

stresses due to the steep velocity gradient across the shear layer are responsible

for this change. The large variation in the molecular weight between hydrogen

and ethylene leads to significantly different exit velocities at the sonic orifice. Be-

cause of the low jet exit velocity of ethylene (315 m/s), the shear layer vortical

structures tilt and stretch in the direction of the fast crossflow (2360 m/s). The

large structures eventually became unstable and were torn apart by the stretching

of the vortical structures.

• The above observations were supported by PLIF imaging of OH radicals which

maps the regions of auto-ignition. These ignition regions can be related to homoge-

nously mixed regions since molecular mixing is required before the fuel and the

oxidizer react. Ethylene injection demonstrated high concentration of OH radicals

across the jet while in the hydrogen case only a thin flamelet could be observed

around the large eddy structures. Clearly, molecular mixing of the ethylene jet


was dramatically altered during or after the onset of the tilting-stretching-tearing

process.

• Eddy convection characteristics and jet transverse penetration were also differ-

ent between the two cases. Hydrogen structures tended to travel with velocities

(∼2200m/s) that were closer to the free-stream velocity as they align with the

free-stream flow in the far-field (x/d > 9). The convection velocity of ethylene

structures were slower than the hydrogen eddies due to the low jet exit velocities.

Tracking different parts of the ethylene large eddies, a wide convection velocity dis-

tribution was shown to exist across the shear layer ranging between 750-1750 m/s.

The differences in the bow shock steepness could result in the observed differences

in the convection velocity between the cases. The properties of the free-stream (the

bow shock shape and the shock-induced flow properties) were directly influenced

by the convection characteristics of the large-scale eddies.

• The ethylene jet penetrates deeper into the free-stream than the hydrogen jet.

This was an unexpected result as all of the previous studies showed that the jet-

to-free-stream momentum flux ratio (J) was the primary penetration controlling

mechanism. We therefore expected to observe identical penetration heights as the

J was identical for both cases in our studies. This interesting and surprising result

could again be attributed to the evolution of the jet shear layer under large velocity

gradients. The thickness of the penetration band, used as the representation of

the jet-shear-layer thickness was considerable in the ethylene injection case, due

to the tilting-stretching-tearing mechanism and also due to the larger growth rate

of the jet shear layer.

8.1.4 Density and Velocity Ratio Effects

• Following the observations of the previous section, we investigated the stability of

the jet shear layer at various speed ratios and density ratios via flow visualization

(schlieren). The high shear stresses induced by the large velocity difference across

the jet shear layer had a large effect on the structure of the layer. For the unstable

case, we noticed: 1) loss of Kelvin-Helmholtz structures with the tilting-stretching-

tearing mechanism, 2) increased growth rates with decreasing values of jet-to-

free-stream velocity ratio, 3) large intrusions of crossflow in between the eddies,


4) distortion of the bow shock around the large eddies. Stable layers showed well-

defined Kelvin-Helmholtz rollers.

• An “effective velocity ratio” parameter, λ = (1− r2)/√

1 + r2 was suggested. The

results plotted in a density-effective velocity ratio (s-λ) diagram demonstrated two

separate regions of “stable” and “unstable” jet shear layers.

8.1.5 Ignition and Flame-Holding Capability of a Hydrogen Trans-

verse Jet

The problem of hydrogen transverse injection and its flame-holding capability was

studied in very high-speed, high-total-enthalpy flow conditions. The experiments ap-

plied simultaneous OH-PLIF and schlieren imaging to map the regions where combus-

tion occurs relative to the jet position. The main results are summarized as follows:

• At the flight Mach 10 condition, OH fluorescence was mainly observed along the

outer edge of the jet plume. Simultaneous OH-PLIF/schlieren revealed that the

structural evolution of the reaction zone is in good agreement with the jet shear

layer position determined by the schlieren imaging. The ignition was initiated in

the recirculation region upstream of the jet. The ignition product OH, convected

downstream along with the large eddies, was mainly detected along the jet shear

layer periphery in a continuous and very thin filament.

• At the flight Mach 13 condition, OH-PLIF demonstrated high signal levels of OH

fluorescence starting in the upstream recirculation region and along the jet shear

layer. The ignition delay times in this condition were effectively zero (∼ 1− 5µs)

due to the high total enthalpies (namely high total temperatures) of the free-

stream.

• At the low total enthalpy Mach 8 condition, the ignition was limited to a small

region behind the bow shock and no OH fluorescence could be observed farther

downstream.

8.1.6 Cavity Flame-Holders

In this part of the thesis, we have first provided a review of cavities in supersonic flows

and their use for flame-holding in supersonic combustors. Second, we have performed a


preliminary investigation, where the primary objective was to demonstrate the feasibility

of the experimental set-up to provide information for cavity flameholder studies. These

appear to be the first cavity experiments performed in such high total enthalpy flows.

• In the first part of the review, the basic flow-field features of cavities studied by

various researchers are summarized, including: different flow regimes of cavities

based upon the length-to-depth ratio (open and closed), oscillations, techniques

to suppress these oscillations, drag penalties for different cavity geometries, and

flow residence time inside a cavity which is crucial to initiate the ignition. Both

experimental and numerical studies still need to be performed to answer some of

the contradictory results that have been observed by different investigators (drag

penalties of angled back wall cavities, amplitude of pressure fluctuations, flow

residence time inside an unsteady cavity).

• In the second part of the review, studies demonstrating the feasibility of cavities

to achieve ignition and to enhance flame-holding in subsonic and supersonic com-

bustors, are described. Finally, we have introduced several questions followed by

comments that need to be addressed in the development of cavities for practical

combustors.

• Through a combination of simultaneously performed fast response pressure mea-

surements, established cavity oscillations were observed and a sequence of os-

cillation cycles were captured during the limited test time ( 270µs) of the flow

facility. The results demonstrated that short duration pulse facilities can be used

to study gasdynamic aspects of cavities, though with small dimensions (depth of

D = 3 mm), in hypersonic flows.

• In the first part of the preliminary study, flows around 2-D cavities (D = 3mm,

L/D =3, 5 and 7) in a supersonic flow were investigated. Significant changes

in the shock wave structure around the cavities were observed as the length-to-

depth ratio were systematically changed. Leading edge shock waves diminished

in cavities with large L/D. In all cases a strong reattachment shock wave at the

trailing edge of the cavity was observed. A transition from an open cavity flow

to a closed cavity flow was obtained for L/D = 7. An angled back wall reduced

the leading edge shock strength. Schlieren movies of the cavities reveal the shock


wave fluctuations around the jet are caused by the pressure oscillations inside the

cavity.

• In the second part of the preliminary study, ignition properties of a 30o hydrogen

jet combined with a downstream cavity (L/D = 3) were investigated. While

both cavities (with and without an angled back wall) provided an autoignition in

and around the cavity, flame-holding seems to require an improved cavity design.

Recommended configurations are presented in the following section.

8.2 Recommendation For Future Work

Recommended future work can be summarized in the following topics:

Extension of Ignition Measurements of Transverse Jets

We have shown that a fundamental supersonic combustion study can be performed

using an expansion tube, providing realistic free-stream conditions with relatively accu-

rate chemical composition. We therefore recommend the study of the near-field ignition

mechanism of transverse jets in more detail by taking advantage of the various free-

stream conditions. For example, this study can be performed using a set of free-stream

conditions with reasonably similar velocities and total enthalpies but with significantly

different static temperatures. Table 8.1 summarizes a set of recommended conditions

which were actually characterized in the expansion tube. Maps of Fig. 2.7 guided us in

determining the appropriate initial pressures.

Observation of the ignition processes for decreased static temperatures, while keeping

the other flow parameters constant, can reveal information about the source of the

ignition and the parameters controlling the ignition process.

Ignition in Cavity Flame-Holders

The effects of the jet in crossflow in conjunction with a cavity can easily be studied

in the current facility setup. Fig. 8.1 shows three possibilities to produce a reacting jet

in crossflow which is stabilized by a cavity flame-holder. A preliminary examination

of a 30o angled hydrogen injection upstream of the cavity showed autoignition inside

the cavity. However, a detailed investigation is still required to reveal the flame-holding


TABLE 8.1 Recommended free-stream flow conditions for further ignition studies.

Condition U∞ P∞ T∞ M∞ Htot

m/s atm K MJ/kg

600/0.5/20 2360± 25 0.32 1290 3.38± 0.04 3.84

600/1/20 2365± 27 0.31 977 3.86± 0.03 3.52

600/2/20 2286± 26 0.30 717 4.32± 0.05 3.06

600/3/20 2143± 45 0.29 604 4.39± 0.09 2.62

600/4/20 2212± 24 0.29 516 4.89± 0.05 2.68

properties of the configuration. Injection in the upstream wall of the cavity might

provide a larger volume of combustible mixture of fuel and air within the cavity flow.

Injection further downstream might provide a pool of radicals both upstream, as well as

downstream of the jet. It is however impossible to predict the interaction of jet/cavity

shear layers in those configurations. A detailed experimental study is therefore needed

for a better understanding of the coupling between the jet and the cavity flow. Finally,

it should be noted that for hydrocarbon fuels with chemical kinetic rates notably slower

than hydrogen, a cavity may be the only viable means for flame stabilization.

Shock Wave/Jet Interaction

Oblique shock wave impingement into the jet is one method known to enhance the

molecular mixing between supersonic air and gaseous fuel. Waves are also unavoidable

in SCRAMJETS and often originate in the inlet isolator leading to the combustion zone

or from ramps and the bow-shock in front of the jet in crossflow. Thus, we propose

to use wedge generated waves to interact with the jet injection flow-field. A schematic

showing the expected features of shock impingement into a transverse jet is drawn in

Fig. 8.2.

It is well known that vorticity is generated when a shock wave interacts with a shear

layer due to the baroclinic torque (in general, the pressure gradient caused by the shock

and the density gradient in the shear layer will not be colinear). Amplified turbulence

and vorticity have immediate significance to the mixing enhancement in supersonic

flows. Furthermore, the shock directs the airflow towards the fuel jet, increasing the air

entrainment rate, the static pressure, the static temperature, and therefore the reaction


Jet

Shear Layer - Jet

Interaction

Jet

Free Shear Layer

InjectantFree Shear Layer

Jet

(c)

(a)

(b)

FIGURE 8.1 Flow-field schematics demonstrating different concepts of angled jet injection combined withcavity flame-holder. a) upstream injection, b) base injection , c) cavity injection.

rates. There are few works (Hwanil and Driscoll 1996; Menon 1989; Marble 1994) which

have studied the effect of shock-wave/shear-layer interaction on mixing enhancement in

a supersonic combustor. The results indicated that the spreading rate of the shear-

layer may be enhanced by the shock impingement, resulting in enhanced mixing and

combustion efficiency.

Shock wave jet interaction can easily be studied using the current facility/injection

system. A 25o angled wedge is actually designed to generate an oblique shock wave as

illustrated in Figure 8.3. The wedge, positioned 22 mm above the injection plate, has a

window made of sapphire to pass the OH-PLIF laser sheet into the imaged region.

A typical schlieren image demonstrating the oblique shock wave jet interaction is

shown in Fig. 8.4. The relatively strong shock, generated by the 25o wedge, directs the

air flow inward toward the hydrogen jet. In a different experiment in which simultaneous


INJECTANT

(Hydrogen)

BOW SHOCK

BARREL SHOCK

RECIRCULATION

ZONE

MM¥

>1>1

RECIRCULATION

ZONE

BOUNDARY LAYER

SEPARATED

REGION

SHOCK-ENHANCED

COMBUSTION

MACH DISK

SHOCK GENERATOR PLATE

OBLIQUE

SHOCK

FIGURE 8.2 Flow-field schematic of a shock-wave/jet interaction.

FIGURE 8.3 Schematic of the 25o wedge to generate a shock wave above the injection plate.


OH-PLIF and schlieren was applied (see Fig. 8.4b), no change in the OH signal level

was observed behind the shock impingement; meanwhile the thin filament of OH was

directed along the jet contour.


PLIF Sheet

Jet: Hydrogen, djet = 2 mm, Mjet=1, J=3

M¥

= 4.7

V¥

= 3200 m/s

P¥

= 4 kPa

T¥

= 1250 K

Air

2525oo

Slit for

OH-PLIF

Laser Sheet

0 2 4 6 8 10 12 14 16 18

0 2 4 6 8 10 12y/djet

Region Illuminated byPLIF Sheet

y/djet

FIGURE 8.4 (a) An oblique shock wave impinging the hydrogen jet as visualized using schlieren imaging.The shock was produced by a 25 o angled wedge mounted above the injection plate. FlightMach 13 free-stream condition. (b) Combined OH-PLIF and schlieren images visualizing theeffect of shock/jet interaction on OH number density.

Appendix A

Expansion Tube Equations

In this appendix we summarize the equations used to calculate the test gas properties

at the exit of the expansion tube assuming one-dimensional, adiabatic and inviscid flow.

The nomenclature corresponds to Fig. 2.2 which defines the flow states at different

sections of the expansion tube.

As the expansion tube includes two-shock tubes in tandem, the common shock tube

equations (Gaydon and Hurle 1963) can be used in the intermediate calculations to fully

describe the test gas conditions at the exit of an expansion tube. Initially, the shock

wave strength and the post-shock conditions of the test gas (defined as state 2) in the

driven section and that of the acceleration gas (defined as state 20) in the expansion

section, must be calculated using the slightly modified shock tube equations. The test

gas flow conditions at the exit of the tube (state 5) can then be obtained by assuming

an isentropic expansion from the pressure in state 2 to the pressure in state 20.

Initially, as the primary (driver/driven) diaphragm is broken, the high-pressure

driver gas expands into the lower pressure driven section. A shock wave is formed

propagating into the test gas in the driven section. We can estimate the strength of this

incident shock for a given set of initial filling pressures. Assuming that the shock tube

is of uniform area, and that the driver gas expands isentropically from the driver into

the driven section, we find that

P4

P1=

2γ1M2s1 − (γ1 − 1)γ1 + 1

1− γ4 − 1

γ1 + 1· a1

a4

(Ms1 − 1

Ms1

)−(

2γ4γ4−1

)

(A.1)

where Ms1 is the shock Mach number in the driven section. The propagation of the

175

APPENDIX A. EXPANSION TUBE EQUATIONS 176

shock wave along the tube induces a velocity in the test gas behind the wave and causes

an increase in the pressure and temperature. These shock-induced properties of the

test gas can, therefore, be calculated using the calorically perfect and 1-D normal shock

relations, given by:

U lab2 =

2a1

γ1 + 1

(Ms1 − 1

Ms1

)(A.2)

P2

P1=

2γ1M2s1 − (γ1 − 1)γ1 + 1

(A.3)

T2

T1=

(γ1M

2s1 − (γ1−1)

2

) (γ1−1

2 M2s1 + 1

)

(γ1+1

2

)2M2

s1

(A.4)

U2, P2 and T2 represent the velocity in the laboratory reference frame, the pressure and

the temperature of the shocked test gas in the driven section, respectively.

When the secondary diaphragm breaks due to the shock-induced high pressure in

the driven section, a new shock is formed propagating into the expansion section. The

expression to calculate the shock strength in this section, taking into account the velocity

of the test gas in the driven section (the driver gas in Eq. A.1 was motionless), therefore,

includes an additional term, resulting in:

P2

P10=

2γ10M2s2 − (γ10 − 1)γ10 + 1

1− γ2 − 1

γ10 + 1· a10

a2

(Ms2 − 1

Ms2

)+

γ2 − 12

M2

−(

2γ2γ2−1

)

(A.5)

where M2 = U lab2 /

√γ2 R2T2.

Equations to predict the shock-induced properties of the acceleration gas are similar

to that of the driven section gas:

U lab20 =

2a10

γ10 + 1

(Ms2 − 1

Ms2

)(A.6)

P20

P10=

2γ10M2s1 − (γ10 − 1)γ10 + 1

(A.7)

T20

T10=

(γ10M

2s2 − (γ10−1)

2

) (γ10−1

2 M2s2 + 1

)

(γ10+1

2

)2M2

s2

(A.8)

APPENDIX A. EXPANSION TUBE EQUATIONS 177

As the shocked test gas in the driven section is suddenly confronted with the much

lower pressure acceleration gas in front of it, simultaneously expands and accelerates to

match the pressure and velocity of the shocked acceleration gas (helium), namely:

P5 = P20 (A.9)

U5 = U20 (A.10)

The corresponding temperature of the expanded test gas can be obtained by assum-

ing an isentropic expansion from condition 2 to condition 5.

T5

T2=

(P5

P2

)(γ2−1

γ2

)

(A.11)

Appendix B

Maps of Estimated Expansion

Tube Test Conditions

178

APPENDIX B. MAPS OF ESTIMATED EXPANSION TUBE TEST CONDITIONS 179

(a)

0.1

2

3

4

5

6

7

89

1

2

3

4

5

Dri

ven

Gas (

Nit

rog

en

) In

itia

l P

ressu

re, P

1 (p

sia

)

12 3 4 5 6 7 8 9

102 3 4 5 6 7 8 9

100Expansion Gas (Helium) Initial Pressure, P10 (torr)

2200 K

1800 K

1400 K

1000 K

600 K

400 K

300 K

0.8

atm

0.6

atm

0.4

atm

0.3

atm

0.2

atm

0.1

atm

0.0

5 a

tm

800 K

(b)

0.1

2

3

4

5

6

7

89

1

2

3

4

5

Dri

ve

n G

as

(N

itro

ge

n)

Init

ial

Pre

ss

ure

, P

1

(ps

ia)

12 3 4 5 6 7 8 9

102 3 4 5 6 7 8 9


2.5

3200 m

/s

3000 m

/s

2800 m

/s

2600 m

/s

2400 m

/s

2200 m

/s

2000 m

/s

1800 m

/s

6 MJ/kg

3.5

3 MJ/kg

5.5

4 MJ/kg

4.5

5 MJ/kg

1600 m

/s 2 MJ/kg

FIGURE B.1 Maps of estimated test gas (nitrogen) conditions at the exit of an expansion tube: a) pressureand temperature, b) total enthalpy and velocity of the test gas are plotted for different ini-tial driven and expansion section pressures. Calculations are performed using the inviscid 1Dequations for a given driver pressure of P4 = 300 psig (helium).


(a)

0.1

2

3

4

5

6

7

89

1

2

3

4

5

Dri

ve

n G

as

(N

itro

ge

n)

Init

ial

Pre

ss

ure

, P

1

(ps

ia)

12 3 4 5 6 7 8 9

102 3 4 5 6 7 8 9


3200 K

0.8

atm

0.6

atm

0.4

atm

0.3

atm

0.2

atm

0.1

atm

0.0

5 a

tm 400 K

300 K

200 K

1400 K

4000 K

2000 K

2600 K

600 K

1000 K

4800 K

Temperature Pressure

(b)

0.1

2

3

4

5

6

7

89

1

2

3

4

5

Dri

ve

n G

as

(N

itro

ge

n)

Init

ial

Pre

ss

ure

, P

1

(ps

ia)

12 3 4 5 6 7 8 9

102 3 4 5 6 7 8 9


2 MJ/kg

30

00

m/s

M = 8

26

00

m/s

24

00

m/s

22

00

m/s

20

00

m/s

18

00

m/s

16

00

m/s

28

00

m/s

M = 4

M = 5

M = 6

M = 3

M = 7

M = 2 4 MJ/kg

6 MJ/kg

Velocity Mach number Total enthalpy

5 MJ/kg M = 1.5

3 MJ/kg

FIGURE B.2 Maps of estimated test gas (Argon) conditions at the exit of an expansion tube: a) pressureand temperature, b) total enthalpy, velocity and Mach number of the test gas are plotted fordifferent initial driven and expansion section pressures. Calculations are performed using theinviscid 1D equations for a given driver pressure of P4 = 300 psig (helium).


(a)

0.1

2

3

4

5

6

78

1

2

3

4

5

6

78

10

Dri

ven

Gas (

Arg

on

) In

itia

l P

ressu

re, P

1

(ps

ia)

12 3 4 5 6 7 8 9

102 3 4 5 6 7 8 9

1002


1.8

atm

1.2

atm

0.8

atm

0.4

atm

0.2

atm

0.1

atm

0.0

5 a

tm 400 K

300 K

200 K

1400 K

4000 K

2000 K

2800 K

600 K

1000 K


5000 K

(b)

0.1

2

3

4

5

6

78

1

2

3

4

5

6

78

10

Dri

ven

Gas (

Arg

on

) In

itia

l P

ressu

re, P

1 (p

sia

)

12 3 4 5 6 7 8 9

102 3 4 5 6 7 8 9

1002


6

2 MJ/kg

34

00

m/s

22

00

m/s M = 4

M = 10

M = 3

M = 2

4 MJ/kg

6 MJ/kg

5 MJ/kg

3 MJ/kg

M = 8

M = 6

30

00

m/s

26

00

m/s

18

00

m/s

Temperature Mach number Total enthalpy

M = 5

FIGURE B.3 Maps of estimated test gas (Argon) conditions at the exit of an expansion tube: a) pressureand temperature, b) total enthalpy, velocity and Mach number of the test gas are plotted fordifferent initial driven and expansion section pressures. Calculations are performed using theinviscid 1D equations for a given driver pressure of P4 = 600 psig (helium).


(a)

0.1

2

3

4

5

6

7

89

1

2

3

4

5

Dri

ve

n G

as (

Heli

um

) In

itia

l P

ress

ure

, P

1

(ps

ia)

12 3 4 5 6 7 8 9

102 3 4 5 6 7 8 9


0.8

atm

0.6

atm

0.4

atm

0.3

atm

0.2

atm

0.1

atm

0.0

5 a

tm

400 K

300 K

200 K

600 K

1000 K


(b)

0.1

2

3

4

5

6

7

89

1

2

3

4

5

Dri

ven

Gas

(H

eli

um

) In

itia

l P

res

su

re, P

1

(ps

ia)

12 3 4 5 6 7 8 9

102 3 4 5 6 7 8 9


32

00

m/s

24

00

m/s

20

00

m/s

16

00

m/s

28

00

m/s

M = 4 M = 3

M = 2

4 MJ/kg

6 MJ/kg


5 MJ/kg

M = 1

36

00

m/s

8 MJ/kg

7 MJ/kg

FIGURE B.4 Maps of estimated test gas (Helium) conditions at the exit of an expansion tube: a) pressureand temperature, b) total enthalpy, velocity and Mach number of the test gas are plotted fordifferent initial driven and expansion section pressures. Calculations are performed using theinviscid 1D equations for a given driver pressure of P4 = 300 psig (helium).


(a)

0.1

2

3

4

5

6

78

1

2

3

4

5

6

78

10

Dri

ve

n G

as (

Heli

um

) In

itia

l P

res

su

re,

P1

(ps

ia)

12 3 4 5 6 7 8 9

102 3 4 5 6 7 8 9

1002


1.8

atm

1.2

atm

0.8

atm

0.4

atm

0.2

atm

0.1

atm

0.0

5 a

tm

400 K

300 K

200 K

600 K

1000 K


800 K

(b)

0.1

2

3

4

5

6

78

1

2

3

4

5

6

78

10

Dri

ven

Gas (

Heliu

m)

Init

ial P

ressu

re, P

1

(ps

ia)

12 3 4 5 6 7 8 9

102 3 4 5 6 7 8 9

1002


40

00

m/s M = 4

M = 3

M = 2

6 MJ/kg

5 MJ/kg

32

00

m/s

16

00

m/s


M = 5

M = 1

36

00

m/s

28

00

m/s

24

00

m/s

9 MJ/kg

20

00

m/s

8 MJ/kg

7 MJ/kg

4 MJ/kg

FIGURE B.5 Maps of estimated test gas (Helium) conditions at the exit of an expansion tube: a) pressureand temperature, b) total enthalpy, velocity and Mach number of the test gas are plotted fordifferent initial driven and expansion section pressures. Calculations are performed using theinviscid 1D equations for a given driver pressure of P4 = 600 psig (helium).

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EXPERIMENTAL INVESTIGATION OF MIXING AND IGNITION OF ... · EXPERIMENTAL INVESTIGATION OF MIXING AND IGNITION OF TRANSVERSE JETS IN SUPERSONIC CROSSFLOWS a dissertation submitted