N A S A C O N T R A C T O R

R E P O R T

N A S A C R - 2 4 9 4

FILE

SIMULATION OF HYPERSONICSCRAMJET EXHAUST

R. A. Oman, K. M. Foreman, J. Leng, and H. B. Hopkins

Prepared byGRUMMAN AEROSPACE CORPORATION

Bechpage, N.Y. 11714

for Langley Research Center ' '

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION • WASHINGTON, D. C. • MARCH 1975

https://ntrs.nasa.gov/search.jsp?R=19750009272 2018-05-25T15:52:47+00:00Z

1. Report No.

NASA CR-24944. Title and Subtitle

2. Government Accession No.

SIMULATION OF- HYPERSONIC SCRAMJET EXHAUST

7. Author(s)

R. A. Oman, K>. M. Foreman, J. Leng, and H. B. Hopkins

9. Performing Organization Name and Address

Grumman Aerospace CorporationBethpage, N .Y. 11714

12. Sponsoring Agency Name and Address

National Aeronautics and SpaceWashington, D.C. 20546

Administration

• 3. Recipient's Catalog No.

5. Report DateMARCH 1975

6. Performing Organization Code

8. Performing Organization Report No.

RE -473

10. Work Unit No.

760-66-01-02-00

11. Contract or Grant No.

NAS1-12553

13. Type of Report and Period Covered

CONTRACTOR REPORT

14. Sponsoring Agency Code

15. Supplementary Notes

FINAL REPORT

16. Abstract

This report describes a plan and some preliminary analysis for the accurate simulation ofpressure distributions on the afterbody /nozzle portions of a hypersonic scramjet vehicle. Theobjectives fulfilled were to establish the standards of similitude for a hydrogen/air scramjetexhaust interacting with a vehicle afterbody, determine an experimental technique for validationof the procedures that will be used in conventional wind tunnel facilities, suggest a programof experiments for proof of the concept, and explore any unresolved problems in the proposedsimulation procedures. It is shown that true enthalpy, Reynolds number, and nearly exact chemistrycan be provided in the exhaust flow for the flight regime from Mach 4 to 10 by a detonation tubesimulation. A detailed discussion of the required similarity parameters leads to the conclusionthat substitute gases can be used as the simulated exhaust gas in a wind tunnel to achieve thecorrect interaction forces and moments. A proof-of-concept series of experiments is proposedusing the detonation tube as a standard against which substitute gas candidates would be compared.Detailed procedures for selecting the binary mixtures for substitute gas blends are presented,along with calculated comparisons of pressures and forces for the real engine case, thedetonation tube case, and two representative substitute gas mixtures.

17. Key Words (Suggested by Author(s))

Engine/Airframe IntegrationHypersonicSimulationScramjet

19. Security dassif. (of this report)

Unclassified

18. Distribution Statement

Unclassified - UnlimitedSubject category 05 Aircraft Design,Testing and Performance

20. Security Classif. (of this page) 21. No. of Pages 22. Price*

Unclassified 71 $4.25

For sale by the National Technical Information Service, Springfield, Virginia 22151

TABLE OF CONTENTS

Item Page

Introduction and Summary 1

Symbols 6

Similitude and Substitute Gases 10

Similitude Parameters 11

Substitute Gases 17

Mixing Layer Similitude 27

Detonation Tube Simulator 30

Detonation Tube Simulator Running Conditions 32

Two Dimensional Afterbody Pressure and Force Predictions .. 48

Conclusions 57

References 59

Appendix: Calculation Methods for SubstituteGas Mixtures „ 61

111

SIMULATION OF HYPERSONIC SCRAMJET EXHAUST

By Ro A. Oman, K. M, Foreman, Jo Leng, and H. B. HopkinsResearch Department

Grumman Aerospace CorporationBethpage, New York 11714

INTRODUCTION AND SUMMARY

This report describes a plan and some preliminary analysisfor the accurate simulation of pressure distributions on theafterbody/nozzle portions of a hypersonic scramjet vehicle suchas shown in the figure on page 2. It is apparent from the cur-rent design philosophy for these vehicles that the scramjet ex-haust gases will play a major role in the determination of theaerodynamic forces and moments acting on the vehicle. Conven-tional aerodynamic testing methods offer no straightforward ap-proach that will meet all of the vehicle development require-ments. In this first investigation our objectives were to es-tablish the standards of similitude for a hydrogen/air scramjetexhaust interacting with a vehicle afterbody, determine an ex-perimental technique for validation of the procedures that willbe used in conventional wind tunnel facilities, suggest a pro-gram of experiments for proof of the concept, and explore any un-resolved problems in the proposed simulation procedures. We havefulfilled all of these objectives, and the second phase activi-ties of proof-of-concept experiments and more detailed analysisare ready to begin.

The over-all plan for vehicle development that we have de-fined during the program covered by this report has four sepa-rate activities that culminate in a final determination of theafterbody pressure distribution in a wind tunnel. First, theexpansion characteristics of the hydrogen/air combustion productsat true flight enthalpy will be determined by pressure and otherdiagnostic measurements in a special facility called a detonationtube simulator. Second, a. small number of substitute gases willbe tested in the same facility to show that they are capable ofreproducing at moderate temperature levels the pressure distribu-tions of the hot combustion products. Third, a series of experi-ments will be conducted with substitute gases and with combustionproducts to develop methods for assessing such nonuniformities as

Internal .Shock(Overexpanded Case Only)

+ Inlet Shock' Scramjet CombustorCombustor Exit

Side View

ExternalShocks

'Plume Boundary

Plume Boundary

YExternal Shocks \ Afterbody -

Wakes from Module Partitions.

Inlet Shock

Forebody S£5

Inlet CombustorRamp(s) Module(s)

Bottom View

Scramjet Nozzle and Related Flow Fields

combustor partition wakes, combustor wall boundary layers, cor-ner flows, and combustor end effects. Fourth, the qualifiedsubstitute gases will be used in vehicle and combustor develop-"ment testing in conventional wind tunnel facilities. The fouractivities can,, in part, run concurrently.

One of the most difficult simulation problems for thescramjet exhaust is to reproduce the effect of the correct chem-istry along with the high total enthalpy (flight compressionplus combustion heating) in the exhaust flow. To achieve thiscombination with the true combustion mixture in a conventionalwind tunnel model of reasonable size and complexity is a virtualimpossibility. The approach we have taken in the current workis to investigate the use of a cold substitute gas, or blend ofgases, to simulate the scramjet exhaust. In order to selectsuch a substitute gas, we must have a comparison technique forvalidating the gas mixtures chosen to represent the exhaust atdifferent flight conditions. 'The best validation will come frommeasurement of actual pressure distributions over a scale modelof the vehicle afterbody with an exhaust gas consisting of theproducts of combustion of hydrogen and air at an enthalpy levelas close to that of the real engine as possible. These pressuredistributions can then be compared to those obtained with selec-ted substitute gas mixtures.

An extensive analysis of the requirements that must be ful-filled to ensure fidelity of model pressure distributions to theflight case showed that the most critical parameters were match-ing combustor exit Mach number and following the variation ofspecific heat ratio with increasing M in an isentropic expan-sion. Many other important simulation requirements have alsobeen satisfied by the plan we have devised. The requirements ofpressure simulation within the diverging contact surfaces of theunderexpanded exhaust are met to a remarkable degree. Reynoldsnumber is matched, Prandtl number is quite closely matched,and the viscosity variation through the boundary layer is shownto be nearly that needed for an ideal boundary layer match.Slight adjustments in the substitute gas blends can easily bemade to allow for different degrees of chemical equilibrium inthe flight exhaust. Even the strict similitude requirements ofthe turbulent mixing layer between exhaust and external flowcould be fulfilled by the substitute gases if they were used ina special Freon wind tunnel — but we recommend a separate in-vestigation of hypersonic mixing layer similitude for the pur-pose of easing this requirement. In short, the substitute gas

concept looks like a valid approach, and the next step is toprove it by comparison to a valid standard flow.

The only known technique for producing the correct enthalpyand chemistry in the laboratory appears to be the detonationtube concept pioneered by Grumman for the LM program, and usedsubsequently to simulate the exhaust from the hydrogen/oxygenmain engines for the Space Shuttle (Ref. 1). This technique isideally suited to scramjet simulation because it combines shockheating of the gas with the heat of combustion to obtain the re-quired enthalpy. One of the main objectives of our current workwas to investigate analytically the operating range of the deto-nation tube facility and to match it to the proposed flight en-velope of the scramjet aircraft. We have done this and shownthe technique to be capable of high quality simulation through-out the complete flight regime and beyond. Having shown thatoperating range is not a significant problem for the detonationtube system, we selected a nominal Mach 8 flight condition as abaseline condition for the first set of demonstration tests.Picking a single flight Mach number restricts the required modelbuilding to a set with one exit area ratio yet allows a fullrange of experiments on pressure and enthalpy levels, substitutegas matching, and exit plane partition wakes.

The next objective was to examine and select possible sub-stitute gases for subsequent experiments. Three promising bi-nary mixtures were chosen, and two dimensional pressure distri-butions were calculated for the flight baseline conditions onthe real engine, the detonation tube simulation, and the threesubstitute gases. The selection procedures involved a one di-mensional screening technique, after which the two dimensionalmethod of characteristics calculations were made to compare ac-tual pressure distributions over the two dimensional representa-tion of the geometry that we propose to test in the next phase.On page 5, we show a preview of Fig. 16, which describes betterthan words the matches of axial and normal forces that we canget. The blends used are easily prepared and modified, safe,and relatively inexpensive. Although only inviscid flows areshown, the friction drag will also be properly scaled when nor-malized by the exit plane pressure.

In summary, the results of the present investigation showthat the detonation tube simulator should provide an excellentsimulation of the hydrogen/air scramjet exhaust flow over thevehicle afterbody for the entire flight regime. There are

several nontoxic, relatively inexpensive substitute gas mixturesavailable for use in wind tunnels that will give adequate repre-senations of the pressure distributions over the afterbody dueto the scramjet exhaust. In order to choose the best substitutegas mixture for a given flight regime, comparisons with the de-tonation tube results and with mixing layer similitude require-ments will be made. An experimental program to prove this con-cept at a representative point in the flight envelope is pre-sented. We expect that such a program will provide the abilityto simulate correctly the aerodynamic loads due to the engineexhaust in subsequent experiments in Langley facilities.

Relative Normal Forces

£y i_ r P

P3A L J P,d(x)

Prototype - Equilibrium

Prototype - Frozen

Model -

Model -

Model -

Model -

CK00351I

l/8th Scale Det. Tube

Sub. Gas

Sub. Gas

Sub . Gas

Const. > (=1 .4)

0.0339|

0.0279|

0.030l|

0.0339|

0.0292(407. Freon0.0344| 58

% Freon% Ar12,607.

7. Freon

13 Bl.

Ar

13 Bl + 427. Ar

Relative Axial ForcesFx 1 f P- = — / -P3A L J P3

d(y)

Prototype - Equilibrium

Prototype - Frozen

Model -

Model -

Model -

Model -

Const. i

l/8th Scale Detonation Tube - Equilibrium

Sub. Gas - 50% Freon 13B1, 507, Ar

Sub. Gas - 40% Freon 12. 60% Ar

Sub. Gas - 587. Freon 13 Bl + 427. Ar

(=1.4)

0.0648 |

0.0620|

0.0634|

0.0646)

0.0627|

0.0647J

0.0520|

Normal and Axial Forces for 2D ExpansionsM « = 8 , a + 3 = 4°

SYMBOLS

A

Ar

area

v

D12

I

EC

F

Freon 12

Freon 13

Freon 13B1

Freon 14

Freon E5

H

HFA

K

k

L

LM

argon atom

sound speed

specific heat at constant pressure

specific heat at constant volume

binary diffusion coefficient, defined on page 64

first Damkbhler parameter, defined on page 15

third Damkohler parameter, defined on page 16

Eckert number, defined on page 16

fluorine atom; also abreviation for Freon

dichlorodifluoromethane (CClpF?)

chlorotrifluoromethane (CClFo)

bromotrifluoromethane (CBrF-)

tetrafluoromethane (CF.)

a complex fluorinated ether

enthalpy; also hydrogen atom

hydrogen fueled aircraft

Kelvin temperature scale

thermal conductivity

length

NASA/Grumman Lunar Module

Le Lewis number, defined on page 15

M Mach number (= V/a)

fn. molecular weight

tn unit of length (meter)

N nitrogen atom; also unit of force (Newton)

Nu Nusselt number, defined on page 17

n exponent in temperature-viscosity power law

0 oxygen atom

P pressure

Pr Prandtl number, defined on page 14

q heat transfer rate

R universal gas constant

Re Reynolds number (== pVL/|i)

S sulphur atom; also entropy

SCRJ Supersonic Combustion Ramjet

Sc Schmidt number, defined on page 15

T temperature

t time

U velocity (in detonation tube)

V velocity

X coefficient in chemical mixture equation(pp. 34 and 61); also afterbody axial distance

X nondimensional distance (= X/Y-)

y coefficient in chemical mixture equation, page 34;also afterbody radial distance

Y nondimensional distance (= Y/Yv)

a angle of attack

(3 inlet ramp angle

y ratio of specific heats, c /c

7 average 7 between two frozen thermodynamic states

7 average 7 between two equilibrium thermodynamicstates

0 ' temperature difference between two points

ix viscosity, or prefix "micro" (10 )

p density

a. thermodynamic function defined on page 34; alsomolecular collision diameter constant defined onpage 64

T ratio of two different absolute temperatures

* equivalence ratio

cp mixture viscosity parameter defined on page 62

Subscripts

0 refers to total (stagnation) condition

1 refers to an arbitrary thermodynamic state point

2 / refers to an arbitrary thermodynamic state point;also thermodynamic state behind incident shock wavein detonation tube

8

3 refers to combustor exit plane

4 refers to unexpanded, high pressure driver gas

5 refers.to stagnation condition or region behind re-flected shock wave in detonation tube

00 refers to undisturbed free stream

CJ refers to Chapman-Jouguet thertnodynamic state

t~h1 refers to i chemical specie; also internal flow

e refers to external flow; also shock tube nozzleexit plane

m refers to a mixture of gases

s refers to constant entropy

Superscript

* refers to sonic condition

SIMILITUDE AND SUBSTITUTE GASES

The purpose of this part of the investigation is to identi-fy the thermodynamic and transport property relationships neces-sary to ensure that the flow fields of scaled test nozzles willproduce the same pressure distributions as those of the fullscale exhaust nozzles used in supersonic combustion ramjets(SCRJ). Because of the method selected to achieve this result,a critical associated task is the selection of suitable testgases to be substituted in wind tunnel tests for the extremelyhigh temperature exhaust gases produced by the hydrogen fueledaircraft (HFA).

The nondimensional similarity parameters for inviscid andviscous flow are computed for the SCRJ and used to formulatesubstitute gases with the required properties, assuming geomet-ric similarity between the model and full scale nozzle configu-rations. A significant effort has been required to compile themost current and authoritative transport properties for thelikely substitute gas constituents and to determine the mostaccurate combining rules for estimating transport properties ofthe gas mixtures. Sixteen gases considered safe, easily han-dled, chemically stable, relatively inexpensive, and commercial-ly available were considered. The most promising substitute gasblends (binary mixtures) from those sixteen were determined bythe following four-step matching process. Initially, for spe-cific flight conditions, the combustor exit specific heat ratio,73, and the approximate range of y variation in the SCRJ ex-haust gas expansion are used to screen the candidates. Then,the transport similarity parameters (such as Reynolds, Prandtl,and Schmidt numbers) are used to further narrow the choices ofsubstitute gas components. Subsequently, the specific initialtemperature and pressure conditions and fractional compositionof the substitute gases that exhibit the best pressure distri-bution match to the SCRJ gases along the entire nozzle expansionprocess are selected, assuming one dimensional isentropic flowand the particular needs or restrictions of the testing tech-nique to be used. Finally, the best matches of the one dimen-sional computations are confirmed by two dimensional analysis.

As a result of this procedure we have concluded that binarymixtures of four Freon compounds (Freon 12, 13, 13B1, and 14)with argon additive are good substitutes for SCRJ combustiongases for facility testing of model exhaust nozzles at condi-tions simulating flight between Mach 4 and 10. Using these

10

mixtures with about £ scale models provides complete dynamicinviscid simulation of the flow field pressure distributionalong the SCRJ nozzle walls and will closely approximate trans-port similitude as well. These mixtures are compatible witheither the wind tunnel or the detonation tube test facilities.

Similitude Parameters

The nondimensional parameter requirements for dynamic simi-larity of models in fluid dynamic systems without heat transferand chemical reactions have been well developed in the litera-ture (e.g., Ref. 2). For inviscid, two or three dimensional com-pressible flow and geometrically similar systems, the Mach numberof the model and prototype must .be reproduced throughout theflows so that geometric relationships between physical surfacesand the characteristic directions of propagation in the flow arepreserved. A primary additional requirement for this geometricpreservation in a nozzle exit region is that the ratio of pres-sures between the external and internal flows is established suchthat all wave systems that affect regions of measurement areproperly reproduced. In most cases this means a simple matchingof pressure ratio, but in some situations corrections for gasthermodynamics are required. If the region of interest is re-stricted to that inside the Mach cones from the exit lips andtherei are no compression waves from the exit lips, it is neces-sary to ensure only that the external pressure is lower than thecorresponding flight external pressure. For perfect gases inequilibrium it is then also necessary and sufficient for inviscidsimulation that the ratio of specific heats, y, be the same inmodel test and in prototype flight. However, the gases involvedin SCRJ flows show very significant variations in specific heatwithin the flow, but in the exhaust region of interest they arewell represented by the equation of state P=pRT/#i, where Ris the universal gas constant and the molecular weight #1 can beregarded as a local constant (see additional discussion below).This type of behavior is referred to as thermally perfect, andour subsequent discussion and analysis will employ that simpli-fication. , ,

We will show below 'that a thermally perfect gas flow willbe dynamically similar to another flow for matched geometries asdefined above whenever the local ratio of specific heats, y,is the same at corresponding geometric points in the two flowsand molecular weight changes along the streamlines of each floware negligible. Because temperature levels in the two flows

11

(model and prototype) may be radically different, the proper wayto ensure this match is to ensure that y(T/Tref) is the samefunction for both gases, where Tref is the temperature at anyconvenient geometric reference point common to the two flows.We have chosen the combustor exit plane temperature, 13, asour reference temperature. The y function used here is thelocal ratio of specific heats, Cp/cv, which should not beconfused with the isentropic exponent or the effective y thatcan be used to characterize a shock or other finite propertychange of a process. These latter effective y's characterizea process in terms of an equivalent process for which the localspecific heat ratio would be unchanging, while the y we usechanges throughout the flows. We will henceforth use y onlyto characterize relationships among gas properties at a pointor for infinitesimal processes, not across finite state changes.For finite processes we will use y.

The flows of greatest concern in SCRJ simulation are eitherlocally isentropic, or include shock processes. Starting withthe shock case, we can write the Rankine-Hugoniot equations torelate properties on either side of a shock wave

PaVa * PbVb

-a'a' Pb +

H + i V2

Normalizing all properties by their conditions at the exitplane (subscript 3), the local velocity can be expressed interms of the local Mach number

V

and the total enthalpy is expressed

H cpdT = RT37

—^rp I

12

The above system of relationships is closed by the equation of state

so that any property ratio at b is determinable by knowledgeof the state a and the functions 7(1/13) and (1/13). Notethat although "ft. is not a function of temperature ratio aloneit is in a particular flow system where p and T are coupledto a particular relationship.

Similarly, for external flow the continuity constraintequation is set by the geometry and the constraint of constantentropy is added

T ' T

The internal energy E can be written

CvdT = RT3

so we get

^-) + frt dl— = constant

Thus we see that if the Mach number at the boundaries iseverywhere the same, matching of the functions y(T/T3) and#i(T/T3) is sufficient to ensure that all property ratios(e.g., P/P3, P/P3, etc.) are matched in two different inviscidflows, with or without shock processes.

For the Mro = 10 flight case we find that with no shockwaves present, the equilibrium molecular weight varies fromabout 24.3 at the combustor exit to 24.6 at the end of theafterbody. Even if the flow were shocked back to the sonic con-dition, the molecular weight would not go below 22.7. For theMOO = 8 flight case, the #i variations are even less. We have

13

therefore concluded that the molecular weight can be treated asa constant in the SCRJ exhaust, even in the presence of shocks,and that substitute gases need only have matching y and Machnumber distributions for inviscid similarity. Note again thatty of the substitute gas and SCRJ flow need not be the same.

Inclusion of viscous regions in the similitude requiresmatching of Reynolds number, Re. Also necessary for dynamicsimilarity in either the viscid or inviscid case is the similari-ty of properties of the gas used for model testing and the gasassociated with the prototype. Principal inviscid gas proper-ties are represented by Prandtl number, Pr., and the variationof viscosity and thermal conductivity with temperature, wherePr = Cp p.k-1, which can be considered the ratio of momentumdiffusion to thermal diffusion.

The viscosity of gases is independent of pressure at rela-tively low pressure and generally increases with temperature.For nonpolar gas molecules, the viscosity varies as a power oftemperature, n, where n approaches 0.5 for high tempera-ture gases and is nearer 1.0 for low temperatures. Polargases, such as the H20 which comprises approximately one thirdof the SCRJ exhaust gas composition, cannot have their viscosityvariation so easily characterized. However, over a finite tem-perature range of interest, the viscosity calculations or datafor SCRJ and test gases can be fitted locally by a law such asM-l/M-2 = (Tl^T2)n> or by a two-constant Sutherland equation suchas u. = bT3/2(S + T) , where b and S are constants. Inthis way the model test and prototype operation conditions canbe examined for similarity of the viscosity distributions.Thermal conductivity of gases, k, increases nearly linearlywith temperature. However, for diatomic and polyatomic gasesno general temperature relation has been found satisfactory.Curve fitting of k to a polynomial in temperature using testor computed data is one way of representing this transport pro-perty. The use of Pr as a similarity parameter characterizesthe relationship between p, and k, but the relationship isstrictly corr "*: only if Pr is invariant with temperature.

In combustion, chemical reactions, and heat transfer pro-cesses, four additional independent similarity parameters arenecessary. The diffusion of mass from one part of the multi-specie system to another must be considered. The Schmidt num-ber, Sc, ratios the diffusion of momentum to mass

14

Sc -

From Sc and Pr the Lewis number, Le, is derived to give theratio of mass diffusion to thermal diffusion:

Le = ~ "

The first and third Damkbhler parameters, Dj andalso are important, especially in chemically reacting flows. Theratio of residence time of a reacting gas mixture in a flow chan-nel, L/V- to the duration of the controlling chemical reaction,t^, is given by the first Damkohler grouping, Dj = L/Vt^. ForDj » 1, the gas can be considered in local equilibrium eventhough several secondary reaction products may not have reachedfinal concentrations. For Dj « 1 the reaction products willbe nearly frozen in composition during the process. For accuratedetails of the flow chemical kinetic rate data must be used with-the flow equation. In both the SCRJ exhaust gas flow and detona-tion tube simulator, the kinetics can be important in determiningthe flow field and pressure distribution for high Mach number(altitude) cases, although the coupling to pressure is ratherweak. For the binary substitute gas mixture, the components arechemically unchanging, and the only relevant kinetic process isvibrational relaxation of the polyatomic molecules in the blend.For conditions characteristic of the use of substitute gases(i.e., moderate temperature and near atmospheric pressure), theirvibrational relaxation time is on the order of 10~8 to 10~6'seconds (Ref. 3), which corresponds to vibrational relaxationlengths very much smaller than crucial flow field dimensionsalong stream tubes. Equilibrium y values should therefore bevalid for substitute gas flows.

If the SCRJ combustor is efficient, the value of D-j- at thecombustor exit should be of the order of unity because ti 10' sfor nearly complete energy release in the supersonic diffusionflame (Ref. 4). As the exhaust flow expands, the local tempera-ture and pressure decrease , the reaction rate decreases (or reac-tion time increases), and Dj < 1. This case describes a condi-tion in which an essentially frozen composition experiences theexpansion process. The detonation tube gases at the model testsection can be tailored to provide the same composition as theflight SCRJ combustor exit condition, but at a much higher pres-sure to achieve proper scaling. The higher pressure results in

15

more recombination reactions and tends to defer the onset offreezing. Calculations (Ref . 5) showed that this effect nearlycompensates for the high dissociation in the stagnation region ofthe detonation tube. Although the chemical reaction history isnot identical, the detonation tube system provides the closestreproduction of flight chemistry of any available simulationmethod. For the substitute gases, Dj » 1, and when used inSCRJ simulation facilities, they should always be in a thermody-namic equilibrium condition.

The Dm parameter involves the relation of combustionenergy release, and the ratio of residence to reaction time (orDI) to the thermal energy transferred to the working fluid. Ex-amination of the test concepts we propose does not show any sig-nificant relevance of DJJJ to the SCRJ simulation process.

The Eckert number is useful in characterizing the heattransferred from the SCRJ exhaust products to the afterbody sur-face and cowl, and thereby the effect of heat transfer on growthof the boundary layer. This parameter relates the prevailingtemperatures of the exhaust products and the boundaries to theheat transferred to the walls, or

where 6 is the temperature difference between the exhaust gasat the outer edge of the boundary layer and the nozzle wall tem-perature. The SCRJ value for this parameter will not be dupli-cated directly in the detonation tube, unless the SCRJ wall iscooled to near room temperature, or the model is heated greatly.Fluid dynamic and fluid properties simulation is almost com-pletely reproduced, so Eckert number is reproduced only if walltemperatures are equal. We have concluded that the secondaryeffect of EC on pressure distribution does not justify thelarge expense of heating the model wall and the resultant ef-fects on instrumentation.

In substitute gas flow, the Eckert number can be matched tothe SCRJ condition, despite the fact that Q and the heat trans-fer is much smaller for the relatively cool test mixtures. Thisis possible because the model test gas velocity and Cn valuesare each quite different for the SCRJ gases at comparable modelstations. Thus, for example, a model wall at room temperature,

16

using 400°K substitute gas, can match EC for the SCRJ, wherethe exhaust gases are over 2000°K.

It should be noted that the usual inviscid heat, transfersimulation, which involves only duplicating Nusselt number (Nu =qL(kAQ)"-'- and geometry, is not adequate for the SCRJ exhaustnozzle process because of the large compressibility effects(i.e., large density changes) as well as viscous .dissipation.

Substitute Gases

Substitute gases appear to be the best solution to the con-flict between the required thermodynamic behavior in afterbodymodel testing and the present lack of a method for generating hightemperature exhaust gas chemistry and thermodynamics in a windtunnel test. Low specific heat ratio, y, gases have been usedwith success for simulating high temperature air flows in hyper-sonic testing (e.g., Refs. 1, 6, and 7), and those experienceswere the initial stimulus to their application in SCRJ simulation.Typical candidates for these substitute gases are several Freoncompounds and sulfur hexafluoride (SFg) that can be used atmoderate operating temperatures and pressures in a wind tunnelfor supersonic speeds and are chemically stable over a wide tem-perature range. However, some of the best Freon compounds andSF6 require too low a temperature to duplicate the specific heatratio of SCRJ gases at the entrance of the exhaust nozzle, and,consequently, they experience phase change (condensation) alongthe expansion process. This undesirable test gas property can beovercome by fractional additives of high specific heat ratio,stable noble gases, such as argon. We thereby create binary andternary mixtures capable of matching the ratios of thermodynamicproperties of virtually any SCRJ high speed flight propulsion sys-tem (exemplified by the values of y of the combustion products) .Figure 1 shows the y(T) behavior of several such blends as wellas that of the SCRJ exhaust flow in equilibrium. It should benoted that we do not wish to match y(T) ; instead, we wish to re-produce y(X) at a much lower temperature level, which can beviewed in the previous context as matching

Thus, by selection of appropriate and convenient workingtemperature, pressure, and binary gas mixture composition, theSCRJ exhaust distributions of 7, M, and Re can be matched ina test facility using small scale models. Furthermore, the dif-ferent working requirements of different test techniques can be

17

T°K (For SCRJ Exh-Gas Only)1000 1200 1400 1600 1800 2000 2200 2400

1.40-,

1.35-

1.30-

1.25.

1.20-

1.15-

1.1-

1.OS-

T

SCRJ Exhaust(Equilibrium)

Range offor matchingto SCRJ exhaustat M oo =8Flight Condition

40% F13B1 + 20% SF6 + 40% Ar

70% F13B1 + 30% Ar

0 100 200 300 400 500 600 700 800 900 1000T°K

Fig. 1 Variation ofy with Temperature forSCRJ Exhaust and Substitute Gas .Formulations

18

accommodated. Figure 2 presents curves of how changes in compo-sition affect the temperature at which there is an exact matchto Y and M at the exit for flight conditions of M«, = 8, 6,and 4; an effective angle of attack (a + 3) of 4°; andequivalence ratios (<t>) of 1.0, 1.0, and 0.6, respectively.These representative trends are for binary mixtures of Freon 12,13; 13B1, and 14 with argon additive and can readily be extendedto match requirements of other flight conditions or for othermatching points in the flow.

Table 1 compares several similarity parameters and thermo-dynamic and transport properties of a M^ = 8 SCRJ operationalcondition with two typical substitute gas mixtures of Freon 12and 13B1 with argon,additive. Figure 3 shows that these mix-tures are designed to produce the best pressure distributionmatch to the 1-D computed SCRJ exhaust gas along the nozzlewalls. Small compositional changes in the selected substitutegas mixture can result in significantly lower stagnation tem-perature requirements, with relatively minor alteration in pres-sure distribution match. Other flight Mach numbers can also bematched similarly. It is necessary to prevent the Freon com-ponent gas from condensing within the model flow field. To il-lustrate this point, the required 622 K stagnation temperaturefor the 50 percent Freon 13B1 4- 50 percent Argon mixture (seeTable 1) can be lowered to 485 K by changing to a 58 percentFreon 13B1 & 42 percent Argon mixture. The Freon fraction thenwill still be well within the vapor phase — a static tempera-ture of 185 K and partial pressure of 4500 Newton/m2 (0.653psia) — for Mach 4.06 flow at the end of the model afterbody.The 22 percent lower stagnation temperature can be extremelyeffective in simplifying the utilization of existing wind tun-nels. Computational methods are described in the appendix.Subsequent calculations discussed in the Two Dimensional After-body Pressure and Force Predictions section will show how two-dimensional calculations using the same substitute gas behaviorcompare to the SCRJ case.

The SCRJ exhaust gas properties and similarity parametersare obtained from the standard NASA Lewis Research Center Com-puter Program (Ref. 8) for an equilibrium kinetics expansionprocess of hydrogen/air reaction products. The program resultsare augmented by our additional, calculations of Sc and Le,which use a mutual diffusivity value computed for the SCRJ ex-haust gases. This value was obtained by assuming that the

19

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400

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M = 8, 0 = 1a+ 0 = 4°

T3 = 1.178= 2.36

Mm= 5= 1, «+-j8 = 4°= 1.182

Fig. 2 Composition-Temperature Requirements for Binary GasMixtures to Simulate SCRJ Nozzle Entrance GasConditions

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principal SCRJ exhaust components of N2 and H20 can be ap-proximated as a binary mixture. Calculations of the substitutegas properties and parameters are described in the appendix.

The properties of the two substitute gas flows shown inTable 1 were established by matching the Mach number and Rey-nolds number exactly for the conditions at the cotnbustor exitof a £ the scale model once the gas blends were chosen. Thegas flows were all assumed to be homogeneous. The initial 7of each of the substitute gases is larger than that of the SCRJ,but these selected binary mixtures produce nearly the same over-all pressure distribution as the SCRJ along the nozzle expan-sion. As was shown in Fig. 1, the 7 versus T trends of theSCRJ gas and substitute test gases are not identical; however,it is possible for the latter to reproduce the working range of7 for the SCRJ, but at much lower temperatures. As shown byFig. 3, the matching of the different substitute gas isentropesto the SCRJ expansion pressure distributions is very close.

In preliminary selection of substitute gas candidates, thebest similarity parameter to be used is the value of 7 charac-terizing the over-all expansion process. For isentropic expan-sion of the chemically nonreactive substitute gas mixtures, con-sidered as a perfect gas, the process-averaged 7 is the isen-tropic exponent of the relation (P/p)* = constant. Then

- _ log <W log (F2/Pi)

7 = log (pg/pp log (P2/P1) - log (T2/T1)

where the subscripts 1 and 2 refer to .the nozzle entranceand exit conditions, respectively. For the three candidate sub-stitute gas compositions whose gas dynamic properties are givenby Table A-l (see p. 68), the 7 for the nozzle expansion pro-cess (between Mach numbers 2.36 to 4.06) is as follows:

50 percent Freon 13B1 + 50 percent Argon - 7 = 1.24

40 percent Freon 12 + 60 percent Argon - 7 = 1.27

58 percent Freon 13B1 + 42 percent Argon - 7 = 1.20

The expansion of SCRJ gases involves small changes in equilib-rium chemical composition leading to slight changes in molecularweight dependent on the local pressure and temperature. In thispolytropic process, the process -averaged exponent, 7 , governing

23

the (PXp)'V relation is now defined as

log (P2/P1)—c7 = log (P2/PP - log

to account for the molecular weight changes. From the equilib-rium gas dynamic data generated by the method of Ref. 8 for theM~ = 8> a lc^ = 4 , 9 = 1.0 SCRJ operational condition, thevalue of 7 equals 1.24. For the frozen composition SCRJ gasdynamic properties the value of 7 is calculated by the samerelation as for the substitute gases,and for the M^ = 8 SCRJcondition has a value of 1.277. From data shown in Fig. 16 itwill be seen that the resulting forces produced by the SCRJpressure distribution along the nozzle surface is nearly exactlysimulated by substitute gas expansions where 7 is very nearlyequal to 7 , in the SCRJ equilibrium case, and where the y'sare £qual for the frozen SCRJ case. Note again that the purposeof 7 is only for preliminary selection; the actual 7(1/13)function for the substitute gas must be used in a multidimen-sional calculation before it can be accepted as a valid substi-tute gas.

Other similarity trends shown by the data of Table 1 are:

* Prandtl No. The low value (Pr ~ 0.50) for theSCRJ exhaust shows that thermal diffusion is strongerthan momentum diffusion. The substitute gas selec-tions will ha\e a somewhat less dominant thermal dif-fusion process, being more like the familiar levelsof low temperature air. In this regard, the Freon 12and argon mixture is a better simulation than theFreon 13Bl-argon composition. Note that Pr is notchanged significantly by pressure changes, nor does achange in Pr have a large effect on pressure dis-tribution in nearly adiabatic attached flows."

* Schmidt No. In view of the large Sc value forboth the SCRJ and the substitute gases, the mass dif-fusion in each case is % to 3 of the diffusion ofmomentum in the flow field. .All cases are comparablealthough the Freon 12 + argon component mixture is aslightly better match to the SCRJ case.

24

* L£Wi-S No. The very low value of the SCRJ and sub-stitute gases indicates that in both situations, thediffusion of the temperature field is almost an orderof magnitude greater than mass diffusion.

As previously discussed, dynamic similarity requires simu-lation of gas properties; for detailed nozzle boundary layer de-velopment the simulation of transport property variation withtemperature is of great importance because of the large tempera-ture gradients in the gas adjacent to the nozzle wall. Whilethe Reynolds number matching of model and SCRJ governs the over-all flow process, the boundary layer bears special considerationbecause of its possibly significant interaction with the flowfield pressure distribution. The viscosities of the binary sub-stitute gas mixtures listed in Table 1 are about one third thatof the SCRJ exhaust gas at the nozzle entrance. This reflectsprimarily the large difference in temperature of the two workingfluids.

Perhaps of greater significance is the temperature varia-•tion of viscosity of the substitute gases compared to the SCRJgases in their respective temperature ranges of operation asshown by Fig. 4.- This variation can be characterized by thevalue of the exponent, n, in a power law approximation of p.versus T. As shown in Table 1, the n value for the binarysubstitute gases is about 10-12 percent larger than the SCRJgases.

It is well-known that the viscosity-temperature exponentwill have a greater effect on boundary layer growth and relatedparameters at supersonic Mach number than will relatively largechanges in Pr. Because the inviscid similitude laws provide acorrespondence in temperature ratios between corresponding adia-batic points in substitute and SCRJ flows [i.e., (T2/T ) sub-stitute gas ~ (T2/T]J SCRJ], we can establish reference vis-cosity ratios for the afterbody boundary layer characterized byadiabatic temperature levels — say, stream and stagnation tem-perature. These will ensure corresponding viscosity distribu-tions in the wall cooling (Eckert number) are all the same. Itis our feeling that the matches of n and Pr shown in Table 1are more than adequate for their relatively weak coupling topressure distribution, but the final test of this opinion willcome when substitute gases are tested against detonation tubeSCRJ flows in Phase II of this program.

25

900 n

800-

700 -

600 -

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f> 500vOIo

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400-

> 300 -

200 -

100 -

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• - Denotes Temperaturefor y o Simulation

SCRJ Exhaust Gasfor MO, = 8.0<f> = 1.0, « + /5 = 4°

0 400 800 1200 1600 2000 2400 2800

Temperature,°K

Fig. 4 Temperature Variation of Viscosity for SCRJ ExhaustGas and Several Substitute Gas Compositions

26

The viscosity properties of a ternary mixture are alsoshown by Fig. 4 where a Freon 13Bl-sulfur hexafluoride-neonmixture formulation is plotted.

The ternary mixture was examined to see if its 7(T) vari-ation would prove superior to the best binary mixtures, or ifthere were significant advantages in the transport properties ofthe ternary mixture. The limited data we generated on ternarymixtures did not indicate any significant advantage for them; infact the (I - T exponent moved further from that of the SCRJexhaust gas.

A slightly better (i.e., lower) value of n could beachieved by using a substitute gas mixture of Ne and Freon13B1 at a stagnation temperature of about 1600 K, While thiscould be easily done in a shock tunnel, it would create opera-tional difficulty and expense in the subsequent wind tunneltesting that would preclude its selection.

In summary, the distribution of transport property effectsin the SCRJ exhaust and binary mixture substitute test gasesfollow the same relative order of dominance, namely

thermal > momentum > mass ,

and very similar viscous aerodynamic behavior should be encoun-tered within each working medium.

Mixing Layer Similitude

Complete SCRJ exhaust simulation eventually will involvethe mixing of simulated exhaust and external flow fields. Thescaling laws for turbulent mixing are not known reliably, soeither all of the suspected important scaling parameters must bematched or an experimental investigation must be designed inwhich any imperfect matching can be varied and evaluated for itseffect. The major mixing similitude parameters are: Re, ini-tial boundary layer properties on the internal and external sur-faces (perhaps scaled to the inviscid flow properties), and theratios of internal to external density, velocity, viscosity, andtemperature. For inviscid similitude, a simple analysis indi-cates that the parameter (T /Te) O g/ ), where ffl is molecu-lar weight, will simulate some of these mixing properties ifmaintained equal in the model and prototype. (The subscripts iand e refer to internal and external flows, respectively.)

27

For example, the density ratio across the mixing layer is:

p \P /\T.Ke e i e

and the velocity ratio is:

V. M.. 7.T.501

V \M -y T 01.e e re e i

For the SCRJ, the magnitude of the parameter (Ti/TgX 55 /5 ) atthe cowl lip is approximately 8.5. This value should be matchedin the detonation tube simulator tests and in wind tunnel testswhere relatively low temperature substitute gases are used.

For the detonation tube, the ratio (1±/ ±) is about 80so the required (Te/#!e) ratio is about 9.5 for exact match-ing. This condition is easily obtained by using air (57<e = 29)for the external flow, and setting test conditions to produce aTe of about 275 K at the cowl lip station.

For the wind tunnel test situation, the types of substitutegases selected for SCRJ internal flow simulation give a (T / i)ratio of 3.7 to 4.7. This establishes a (Te// e) ratio re-quirement of 0.43 to 0.55 for the external flow substitutegas. For the safe Freon compounds and binary mixtures consideredfor SCRJ exhaust gas simulation, the molecular weight will be inthe range of 70 to 150. If used as an external gas, thiswould result in a need for extremely low temperature, Te (onthe order of 50 K to 100 K), at the cowl lip location with itsaccompanying danger of phase change for the Freon component atpractical pressure levels. To obtain more practical temperatureand pressure levels a different class of f luorocarbons is needed.A preliminary survey of safe, chemically stable candidates forthis purpose indicates that the Freon "E" series of high molecularweight, low 7, compounds, with (Te/W(e) values of 0.52 to0.72 at their boiling points could be useful components of a bi-nary mixture with high molecular weight noble gases. Freon E5,for example, has a molecular weight of 950 and a boiling point,at atmospheric pressure, of 497 K. Using these "E" seriesfluorinated ethers at lower pressures than atmospheric could re-duce the temperature requirements and decrease the (Te/ e) ratioto the full extent needed to examine mixing processes in wind tun-nels. Clearly, this problem requires more extensive study which

28

could be pursued in the context of a research program concernedwith mixing phenomena of high speed parallel flows of dissimilargases. Also requiring further consideration are the methods andcosts of implementation by which the external and internal flowscan be supplied and sequenced in short duration tests in boththe wind tunnel and detonation tube simulator test techniques.However, a conceptual solution for substitute gas simulation ofSCRJ mixing processes appears available within the framework ofpresent technology.

29

DETONATION TUBE SIMULATOR

The Grumman detonation tube simulator to be used for the mea-surement of exhaust flows and validation of the substitute gasesis capable of giving nearly correct chemistry and total enthalpyfor the hydrogen/air combustion system throughout the entire pro-posed flight regime. Reynolds numbers can easily be maintainedat flight values by running at elevated pressures with both com-bustion and substitute gases. Comparisons of pressure distribu-tions over a model afterbody obtained with the combustion gasesagainst those obtained with candidate substitute gases will beused to select the proper substitute gas and operating conditionsfor subsequent wind tunnel tests so that the necessary dynamicsimilitude prevails.

A schematic of the detonation tube facility is shown inFig. 5. It consists of a 6.1 meter long, 7.62 cm insidediameter driver section initially separated from a 10 meterlong, 12.7 cm inside diameter driven tube by a metallic dia-phragm. The driven tube is terminated by a supersonic nozzle de-signed to produce a flow that will match the expected exit planeconditions of the proposed scramjet engine. The nozzle exhaustsinto a 1.83 meter diameter, 3.66 meter long test section.Mounted within the section, and mating to the supersonic nozzleis the model afterbody. For the proof-of-concept experiments,the upper afterbody surface will be a flat plate instrumentedwith up to 20 pressure transducers. The test section can beevacuated prior to a run to any desired pressure down to5 x 10~5 torr. The facility has been designed to handle com-bustible hydrogen mixtures safely. Various interlocks and leakdetection devices are incorporated into the automatic gas handlingsystem. Details of this system may be found in Ref. 1.

The facility has available up to 35 channels to carry modeldata. All data are recorded through FM/FM multiplexing on mag-netic tape and reduced by a special off-line computer. Heattransfer rates are measured using thin film platinum resistancegauges. Pressures in the past have been measured with standardpiezoelectric gauges for pressures above 7000 N/nr or with spe-cial Grumman designed gauges for low pressure work. For theafterbody pressure measurements above 7000 N/m^ we intend touse a new system using unbonded semiconductor strain gauges.Those are much lower impedance devices than the piezoelectrictype and will lead to much less mechanical noise. These instru-ments use a bridge circuit; differential amplifiers can therefore

30

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bO•H

31

be used which will allow the elimination of common-mode noise., Other facility induced noise problems will be unknown until we) actually try the system. Since capability for accurate pressure: measurement is critical to the successful conclusion of the nextphase of the program, we are devoting considerable effort outsidethe coverage of this contract to achieving the maximum instrumentcapability possible. For pressures above 7000 N/m^. gauges areavailable with sufficient frequency response and with accuracy to•5- of one percent of full scale. In the pressure range from

' 70 N/m2 to 7000 N/nr we are currently investigating the use ofmicrophone-type gauges to obtain similar accuracies.

Photographic coverage available includes time-exposure glowphotographs in color or black and white, high speed movies, and,where there is sufficient density, schlieren photographs. We hopethat the schlieren photographs will be sufficiently sensitive tomeasure relative boundary layer growth in substitute gas and de-tonation tube tests.

Two modes of detonation tube operation are possible. In thefirst, called the incident or forward-running detonation tech-nique (Ref. 9), the driver section is pressurized with helium toa pressure high enough to insure detonation of the combustiblegases when the main diaphragm ruptures. The diaphragm is scribedto a predetermined depth so that it will rupture at a specificpressure. The shock wave formed will rapidly become a self-propagating detonation wave -that will reflect from the nozzle endof the driven tube as a shock wave. The gas is heated and pres-surized by the combustion behind the detonation wave and furtherby the energy addition behind the reflected shock wave. A weakdiaphragm at the entrance to the nozzle is ruptured by the arrivalof the incident wave and the high energy slug of gas expandsthrough the nozzle into the test section. In order to prevent therapid expansion that exists behind a free-running detonation wave,the initial helium driver gas pressure is chosen so that when itexpands after the rupture of the diaphragm its pressure matchesthat immediately behind the detonation wave. This produces quasi-steady flow conditions for two to four milliseconds»

The second mode of operation is called the backward-runningdetonation technique. This technique was developed specificallyfor the simulation of hydrogen/oxygen rocket engine plumes (Ref. 1)where the incident technique would.have produced an enthalpy higherthan the actual engine case because of the shock wave heating addedto the heat of combustion. A very weak shock wave is sent into thecombustible mixture in this method (through the use of a low driver

32

pressure and weak main diaphragm). The idea is to prevent igni-tion on the incident wave, but have the gas ignite when the in-cident wave reaches the nozzle end of the tube. The detonationwave then travels away from the nozzle back towards the driversection. The expansion following this wave drops the pressureand enthalpy in the test gas, which then expands through thenozzle. We have found in previous work (Ref» 1) that the igni-tion at the end of the tube is best accomplished by a timedelectrical spark, although under certain conditions spontaneousignition behind the reflected wave will occur.

The choice of technique to be used for the scramjet simula-tion depends on the final conditions required and to some extenton operational experience during exploratory tests to be madeduring the next phase of this program. Further discussion ofthis choice is given in the next section where calculated runningconditions for various mixtures are presented.

For running the inert substitute gases in the detonationtube we run the facility as a conventional reflected shock tun-nel. That is, the test gas mixture is placed in the driven tube.Helium driver gas is used. The shock wave formed on rupture ofthe main diaphragm reflects from the nozzle end of the driventube to produce a slug of high energy gas which expands throughthe nozzle into the test section. The stagnation conditions ofthe substitute gas are determined by the strength of the incidentshock wave in the driven tube, which may be easily controlled.

Detonation Tube Simulator Running Conditions

We have been able to show that by the use of one of our twodetonation tube techniques we will be able to simulate the HRAexhaust nozzle flow with exact total enthalpy (flight and com-bustion) , full scale Reynolds number, and nearly exact chemistry(exact elemental composition, with nearly exact molecular compo-sition) . Calculations were made for the three basic flight con-ditions specified in NASA Langley Statement of Work 1-53-3387,March 12, 1973, plus the M^, •= 8 flight conditions. It appearsat this stage that the detonation tube techniques will give ex-act total enthalpy simulation only up to M^ = 10 at * = 1,but close simulation is available to higher flight Mach numbers.In the following pages we give some details of the calculationswhich show the broad range of simulation capability of the deto-nation tube and how the above mentioned flight conditions fallwithin our operating range.

33

Total Enthalpy and Chemical Composition

With the backward-running detonation tube technique we cangive exact total enthalpy and equilibrium chemical compositionsimulation for M00 = 4 at 4> = 0.6, M*, = 6 at <t> = 1, and wemay use this method as high as M^, = 8 at 4> = 1.

The procedure for determining the tunnel stagnation condi-tions is as follows (see also Ref. 1). For a given incident wavespeed at the end of the tube, the state properties and particlevelocity behind the wave are calculated, assuming real-gasthermodynamic properties and frozen composition. The reflectedwave is assumed to be a Chapman-Jouguet (C-J) detonation whoseinitial conditions are the conditions behind the weak incidentshock wave. The unsteady expansion from the C-J state to thetunnel stagnation conditions is calculated assuming an isentropicexpansion with equilibrium thermodynamic properties. The govern-ing equation for this expansion is a - U = constant, where

a = (a/p)g dp

Pref

For the C-J state, U = (Ucj - U2), and for the end wallstate (Region 5), U = 0. The chemical equilibrium program ofRef. 8 is used throughout these calculations.

There are a wide variety of gas mixtures and initial shockwave speeds that we could use to achieve these simulations. Mix-tures would consist basically of H2,02, 2 > an<* Ar, with vari-ous amounts of NH3 or N20 added to achieve the desired en-thalpy. For <t> = 0.6 the gas mixtures could be (Y)NH3 +(0.2511 - 3/2 Y)H2 + (0.2095)02 + (0.7809 - 1/2 Y)N2 + (0.0096)Arwith 0 < Y < 0.1674, or they could be (X)N20 + (0.2511)H2 +(0.2095 - 1/2 X)02 + (0.7809 - X)N2 + (0.0096)Ar0 •< X < 0.4190.

with

For <D = 1 the mixtures could be (Y)NH3 + (0.4190 -3/2 Y)H2 + (0.2095)02 + (0.7809 - 1/2 Y)N2 + (0.0096)Ar with0 < Y < 0.27933, or (X)N20 + (0.4190)H2 + (0.2095 - 1/2 X)02 +(OT7809 - X)N2 + (0.0096)Ar with 0 < X < 0.4190.

The actual gas mixture used will be chosen for operationalconvenience in obtaining the desired stagnation pressure, P^.

34

Figures 6 and 7 show the variation of total enthalpy with initialshock wave speed for these gas mixtures. The problem of achiev-ing the Moo = 8 flight case with the backward-running techniqueoccurs because the incident shock wave Mach number must be greaterthan 2.5 (see Fig. 7). If this high speed causes an incidentdetonation, we will use the front-running technique to simulateMOO = 8. The backward-running technique is preferable because itrequires a much lower driver gas pressure to achieve the samestagnation pressure. The higher driver pressure required by thefront-running technique is due to the high contact surface ve-locity required to match the pressure behind the detonation wave.

With the front-running detonation tube technique we will beable to achieve exact total enthalpy simulation at <t> = 1 fromabout Moo = 7 to -Mo,, = 10, overlapping the conditions simu-lated by the backward-running technique. For a given gas mixturethe forward-running technique generates a higher total enthalpybecause the burned gas is further heated by a reflected shockwave, rather than cooled by an expansion wave as with the back-ward-running technique.

The stagnation conditions for each gas mixture are determinedby first calculating the conditions behind the detonation waveassuming the C-J condition (see Ref. 9). The steady flow con-servation equations and the equation of state are then appliedacross the reflected shock wave assuming a constant ratio of spe-cific heat, 7, equal to that behind the detonation wave.

Figure 8 is a graphical presentation of the variation oftotal enthalpy with the <!> = 1 gas mixtures specified at thebeginning of this subsection. For a specified total enthalpy,X and Y are only weak functions of the stagnation pressure,P5, since the initial shock Mach number is now fixed at the pre-determined Chapman-Jouguet detonation wave speed for each mixture.It is fortuitous that to simulate M^ = 8, the flight conditionagreed upon for our initial experimental work, no other molecularforms of the elements in the combustion gases are required to beadded to the basic H2/air mixture (see Fig. 8).

Model Size and Reynolds Number

Both the backward-running and forward-running techniques re-quire reflected shock waves. As a general rule, to produce thedesired stagnation conditions behind a reflected shock wave, thethroat area in the end wall of the shock tube should not exceed

35

3.0 -

2.5 -

2.0on)

oo

c0)T3•HOC!M

1.5

1.0

0.5

-200_L _L

0 200 400 600 800

Total Enthalpy (Flight & Comb), cal/gm

Fig. 6 Backward Running Detonation Tube Total Enthalpy forVarious Gas Mixtures for Simulating I^/Air ScramjetCombustor Exit Conditions at * =0.6

36

3.0 -

2.5 -

oS3

2.0 -

ootn•u6 i c;<u 1. _>

OCH

1.0

.5

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0 200 400 600 800

Total Enthalpy (Flight & Comb), cal/gm

8

1000

Fig. 7 Backward-Running Detonation Tube Total Enthalpy for VariousGas Mixtures for Simulating H^/Air Scramjet Combustor ExitConditions at 0 = 1.0

37

O

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53

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0.5-

0.4-

0.3-

0.2-

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II

8

Y = 0.2793

0 200 400 600 800

Total Enthalpy (Flight & Comb.), cal/gm

1000

Fig. 8 Forward-Running Detonation Tube Total Enthalpy for VariousGas Mixtures for Simulating H2/Air Scramjet Combustor ExitConditions at <t> = 1.0

38

10 percent of the shock tube cross section area. The combustorexit plane Mach numbers and shock tube nozzle exit to throatarea ratios required to generate those Mach numbers are givenbelow for the cases under consideration.

Shock TubeM 4> M ... A /A*00

4

6

8

10

0.6 -

1.0

1.0

1.0

1.29

1.68

2.34

3.00

1.07

1.40

3.10

8.30

Note: The variation,of Mgxit and Ae/A* with a + 3 isvery small. The above numbers are average valuesfor the 3 a + P's at each M^.

If we assume a two dimensional combustor with a square exitplane and a throat area A* equal to one-tenth that of the de-tonation tube cross section, the maximum exit plane dimensionsbecome:

M Maximum Exit Plane°° _ Dimensions, cm

4

6

8

10

A rectangular exit plane with an aspect ratio greater than1 was chosen, primarily because it will give a relatively largervolume of two dimensional flow than the alternatives, givingmeasurements which could be more easily compared to theory. TheM^, = 8 flight condition was also chosen as the nominal baselinefor the first series of experiments required to prove the con-cept of detonation tube simulation for a SCRJ. In Fig. 9 we showthe maximum combustor exit plane dimensions for various aspectratios for the four flight conditions under consideration. Given

3

4

6

10

.683

.318

.1

.16

X

X

X

X

3.

4.

6.

10.

683

318

1

16

39

Bo

T3••-I

0)cPL,

4-)•HX

15 --

10--

0 10

Exit Plane Height (Throat Length), cm

Fig. 9 Maximum Exit Plane Dimensions for 12.7cm DiameterShock Tube Operation with A.. = 0.1Ar throat TDet. Tube

40

the restraints of a 12.7 cm i.d. detonation tube with throatarea one tenth of the detonation tube area and M^, = 8, we chosea 3:1 aspect ratio for the combustor exit plane with a widthof 11.43 cm and a height of 3.81 cm. With the 3.81 cmheight we can also fit three 3.81 cm x 3.81 cm square com-bustor nozzles in the end wall of the detonation tube, thus simu-lating the 3:1 aspect ratio with and without separators. Fig-ure 10 is a sketch showing the proposed single nozzle arrangementand Fig. 11 shows the same shock tube and afterbody model, butwith the three smaller nozzles installed in the detonation tubeend wall. •

To achieve full scale Reynolds number we first determinedthe exhaust flow Reynolds number .per meter at the prototype com-bustor exit plane, using the NASA/Lewis computer program (Ref. 8).These results are presented in Table 2. Since we chose a modelcombustor height of 3.81 cm while the prototype is assumed tobe 30.48 cm, we will be doing 1/8 scale testing based oncombustor exit height and must achieve in the model combustor aReynolds number per meter eight times that of the prototype forproper viscous flow development on the afterbody.

To determine the stagnation conditions in the detonationtube that are required to achieve the desired Reynolds number atthe model combustor exit, we assumed the following:

1. The total enthalpies of the prototype and modelflows are identical.

2. The equivalence ratios of the prototype and modelflows are identical.

3. The flow from the detonation tube stagnation regionto the model combustor exit is in equilibrium.

4. The combustor exit to sonic throat area ratio inthe model (A3/A*) is the same as the theoreticalcombustor exit to sonic throat area ratio in theprototype.

The last assumption required calculating a theoretical sonic con-dition for the prototype. The differences in exit Mach number,between model and prototype, were on the order of a few hundredthsof a Mach number, not enough to justify additional calculations toachieve an exact match. Using these assumptions with the computerprogram of Ref. 8, we determined the detonation tube stagnation

41

Detonation Tube

CowlModel

Array of Pressureand Heat TransferGauges

Fig. 10 Sketch of Detonation Tube and Model Installationfor Unsegmented, <& = 3 Scramjet Combustor Exit Plane

42

Detonation Tube

CowlModel

Array of Pressureand Heat TransferGauges

6°

Fig. 11 Sketch of Detonation Tube and Model Installation forSegmented .41 = 3 Scramjet Combustor Exit Plane

43

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44

required to achieve the desired Reynolds number, together-withthe other thermodynatnic and transport properties at the modelcotnbustor exit plane.

Table 3 summarizes the results of these calculations for theMOO = 8 flight cases. The differences between the 1/8 scalemodel and prototype exit plane Mach numbers and other stateproperties may be seen by comparing Tables 2 and 3. Achieving astagnation pressure between 60 and 110 atmospheres with back'ward-running detonations is no problem in our facility. We haverepeatedly run different simulated propellants at pressures be-tween 10 and 400 atmospheres. The driver pressure, P^, re-quirements for these backward-running detonations are not at allsevere — 10 to 20 atmospheres at the most.

To achieve stagnation pressures, P5> of several hundredatmospheres with front-running detonations, higher driver pres-sures are required. For the Mach 8 flight cases using room tem-perature helium as the driver gas, the driver pressures will bebetween 200 and 300 atmospheres. We have routinely run for-ward-running detonations with P /s between 300 and 400 at-mospheres and have the capability to operate at double thatlevel. Thus, simulating the M^ = 8 flight case with 1/8 scalemodels at full scale Reynolds number is well within the operatingrange of the Grumman Detonation Tube Simulator.

Ensuring that the edges of the exhaust expansion regionswill be properly configured requires that the contact surfacesbetween external and internal gas in the detonation tube test lieoutboard of the contact surfaces in the flight and wind tunnelcases, this is achieved by ensuring that the test chamber pres-sure in the detonation tube is well below the static pressure ofthe flight contact surface (i.e., the pressure at which internaland external flows can turn to the same flow direction). Thedomain of validity for the test is then determined analyticallyfor each flight condition.

Experimental Verification of Simulation Technique

The next phase of this program will include proof-of-conceptexperiments to validate the proposed technique. During theseexperiments measurements of the wave speeds and stagnation pres-sure, PS, will be made to insure that the desired stagnationconditions have been achieved. Calibration of the flow from thecombustor exit will be accomplished by stagnation pressure and

45

TABLE 3

EQUILIBRIUM THERMODYNAMIC AND TRANSPORT PROPERTIES AT f-SCALEMODEL COMBUSTOR EXIT PLANE FOR SIMULATING FULL SCALE REYNOLDS

NUMBER WITH CORRESPONDING DETONATION TUBE ISENTROPIC STAGNATIONCONDITIONS, M 8.0, * = 1.0

a + P (deg)

P» (atm)

T f ° V^o \ ^/

V~ (m/sec)

M, *A3/A

Rey. No.~ (m )

^3lj.3 (M. poise)

/ u. cal \~3 VCm-sec-°K/

/ cal \Po ^gm-°K/

4

4.2731

2310.0

2317.28

2.386

3.1233

1.736 x 107

1.2045

24.524

738.0

642.0

0.5183

0.5953

DETONATION TUBE ISENTROPIC

P (atm)

T f°K \c \ **•/

H I cal ir- V /5 \gm /

a,, (m/sec)

"5

66.96

3365.0

578.4

1173.3

1.1636

23.651

8

6.1788

2316.0

2316.93

2.380

3.0833

2.500 x 107

1.2077

24.536

739.0

622.0

0.5073

0.6029

12

8.0730

2368.0

2272.87

2.311

2.8142

3.081 x 107

1.2051

24.522

752.0

650.0

0.5167

0.5979

STAGNATION CONDITIONS

95.623

,3397 .0

578.4

1178.7

1.1665

23.712

109.45

3409.0

578.4

1180.8

1.1676

23.735

Note: 1 atm 1.01325 x 105 N/m2

46

heat transfer surveys using instrumented rakes at several sta-tions along the afterbody. A limited amount of spectroscopic/radiometric analysis for exhaust composition and temperatureassessment will also be conducted.

Calculation procedures proven in previous plume simulationwork (such as reported on in Ref. 9), will be used for compari-son with the measured data. We have shown in the past that suchcomparisons give a valid indication of the fidelity of a givendetonation tube simulation. In addition, IR measurements ob-tained in plumes simulated by the detonation technique have beenshown to give remarkable agreement with other experimental tech-niques as well as with detailed theoretical calculations (Ref.10). The methods used in such theoretical computations are pre-sently limited to axisymmetric nozzles, so their application tothe nonuniform three dimensional afterbody flow of this projectwill only be an intermediate step. Final and complete theoreti-cal substantiation of our data in the flight situation mustawait the completion of theoretical methods now under develop-ment by other contractors.

47

TWO DIMENSIONAL AFTERBODY PRESSURE

AND FORCE PREDICTIONS

The goal of this program is to provide a system of substitutegases for use in a wind tunnel model that will duplicate the dis-tribution of forces produced by the scramjet engine exhaust overthe vehicle afterbody. In this section we present calculationsof pressure distributions for several different cases, and, inaddition, show integrated axial and normal force values. All cal-culations in this section are for a flight Mach number of 8.The results are the basis of our conclusion that it is possibleto select a substitute gas to fulfill the goal stated above.

We have performed two dimensional method of characteristicscalculations for nine separate cases. For the full scale flighthydrogen/air combustion system, we did four calculations: equi-librium and exit plane frozen, each at inlet ramp angles (a + p)of 4° and 12°. We have similarly calculated pressure distri-butions for an eighth scale detonation tube simulation, matchingall conditions at the exit plane to that of full scale, butraising the pressure to duplicate Reynolds number. The eighthscale calculations were carried out for a.+ f3 of 4° and 12°,but only for equilibrium chemistry. An exact nonequilibrium twodimensional kinetic calculation has not been carried out.

Three substitute gases were chosen using the methods de-scribed earlier to match the full scale case of a + (3 = 4° andequilibrium chemistry. The first consisted of 50 percent byvolume Freon 13B1 and 50 percent argon, the second 40 percentFreon 12 and 60 percent argon, and the third 58 percent Freon13B1 and 42 percent argon. Mach number and Reynolds number atthe nozzle exit were matched for the substitute gas calculations.We also calculated a pressure distribution assuming y = 1.4 airwith the same exit Mach number as an illustration of the sensi-tivity of loads to large errors in gas characteristics.

In all cases the two dimensional method of characteristicscomputer program of Ref. 11 was employed. The thermodynamicvariables for the combustion gases were generated by the computerprogram of Ref. 8, while those for the substitute gases were cal-culated as described in the appendix. The flow properties at thecombustor exit were assumed uniform, parallel, and in equilibriumfor all cases.

48

The geometries of the afterbody nozzle surface and the cowlsurface are described by the following equations:

Afterbody

Y

Y

0.7187 X2 + 1.0

0.35935 X + 0.95508

0 < X < 0.25

0.25 < X < 18.54

Cowl

0 0 < X < 1.11

Y = -0.4204 X + 0.933 X - 0.518

Y = -0.1051 X + 0.1232

1.11 < X < 1.235

1.235<X < 3.12

where Yexit.

Y/Y3, X = X/Y3, and Y3 is the height of the nozzle

A sketch of this geometry showing the origin of the coordi-nates is shown in Fig. 12. Also shown in this figure is thecharacteristic diagram calculated for the full scale engine, forMOT = 8, a + p = 12°, and assuming fully equilibrium flow. Theflow fields for all other cases mentioned above with the exceptionof the air case differed from the one shown only in small detail.Regions of uniform flow are labeled "U." At the cowl lip thereis a Prandtl-Meyer expansion to match the local external pressure.In all of the cases considered except the 7 = 1.4 case the firstcharacteristic line from the lip intersected the upper surface atX *z 15.5. The characteristic line that intersects the downstreamend of the upper surface corresponds to an expansion of about 3°(through a pressure ratio of 1.15). It has been shown that theturning pressure ratio at the cowl lip is close to 2 for theprototype flight case. This point is very important, as it in-dicates that at least for two dimensional testing the internalflow is all that need be simulated to ensure that the afterbodyramp pressures are valid. Mixing effects are not likely to de-stroy this independence of the external flow as long as the corn-bus tor exit is everywhere underexpanded, but three dimensional ef-fects at the ends of the combustor will require more completesimulation for regions near and outside the diverging lateralcontact surfaces.

49

Y =

0 2 4 6 8 10 12 14 16 18 20

_ XX = —

Y3

Fig. 12 Nozzle Afterbody Geometry and Characteristic Diagramfor Full-Scale Engine at M»= 8,<*+/? = 12°

50

In Fig. 13 we have plotted the pressure distributions, non-dimensionalized by the combustor exit plane pressure for eachcase, for the combustion gases at exit conditions correspondingto a + p = 4° . In Fig. 14, we show pressure distributions fora + P = 12°. It. can be seen that the pressures calculated as-suming fully equilibrium flow are slightly higher than those cal-culated using frozen chemistry. Also the excellent agreementwith the case calculated for the detonation tube simulation isevident. In Fig. 15 we have compared the calculated pressuresfor the eighth scale detonation tube simulation with those calcu-lated for the three substitute gas mixtures for an a + p of 4°.For comparison we have shown the pressure distribution that wouldbe obtained by expanding air at a constant y of 1.4, assumingthe exit Mach number matches that of the actual engine.

We have integrated the pressure distributions shown inFigs. 13 through 15 to obtain relative values for the forces inthe normal and axial direction. We normalize the two dimensionalforces by P3A, where A is the (unit) width times L, theafterbody length. We have not calculated any pitching momentchanges, because the shifts in center of pressure are extremelysmall. Figure 16 is a bar graph comparing all of the forces cal-culated for the case of a + p = 4°, and Fig. 17 is a comparisonof those for the a + p = 12° case. The differences in normalforce between frozen and equilibrium flow appear to be more sig-nificant than a quick look at the pressure distributions wouldindicate. This apparent disparity exists because the net normalforces are only 20 to 30 percent of the individual (cowl orafterbody) normal forces, and the percentage change in pressurelevel introduced by chemical reaction is much greater on theafterbody than it is on the cowl lip. The detonation tube simu-lation falls between the two cases. The axial forces are allwithin a few percent of one another with the exception of theconstant 7 «• 1.4 air case. Of the three substitute gas mix-tures chosen for this comparison, 50 percent Freon 13B1 and 50percent argon can be seen to give forces very close to the equi-librium full scale engine, and the detonation tube simulationlies between the frozen and equilibrium values. Once the truechemical state of the real engine exhaust flow field is known,there should be no trouble selecting a substitute gas to matchthe pressure distribution to any required system fidelity.

51

P/P,

l.Oi

0.9

0.8

0.7

0.6

0.5

30.4

0.3

0.2

0.1

Full ScaleEquilibriumFrozen

l/8th ScaleEquilibrium

0

1

rt Cowl

Afterbody

0 2 8 10 12 14 16 18 20

X/Y,

Fig. 13 Flight Afterbody Pressure Distributions - CombustionGases, M«,= 8 , a + 0 =4°

52

P/P3

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.1

0.2

n

Cowl

Full Scale

Equilibrium

Frozen

I/8th Scale

Equilibrium

Afterbody

8 10 12 14 16 18 20

X/Y

Fig. 14 Flight Afterbody Pressure Distributions -Combustion Gases, Moo = 8, a +0 = 12°

53

l.U

0.8

0.9

0.7

0.6

P./P3

0.5

0.4

0 0. J

0.2

0.1

1 / O j_1_ O 1 _ T*~.._'.!1.21-U.?_.M«l/otn bcaie JiquiiiDriuni

Substitute Gas 50% Freon 13B1, 50% Ar

Substitute Gas 40% Freon 12,60%Ar

L== y= 1-4 Air

'1 Cowl

\1

\1 " " '\ Afterbody

i i i i i i i i i) 2 4 6 8 10 12 14 16 18 2

X/Y3

Fig. 15 Simulated Afterbody Pressure Distributions,Moo= 8,a +0~ 4°

54

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56

CONCLUSIONS

There are several substitute gas blends that should giveexcellent representations of the pressure, force, and momentdistributions for scramjet exhaust flows over vehicle afterbodies.These binary gas mixtures can be used in wind tunnels and in ashock tunnel, and they show excellent promise for representingthe viscous behavior of the SCRJ flow as well as its inviscidcharacteristics. Different blends can be designed to compensatefor small differences in the expected chemical reaction rates ofthe flight engine or for changes in flight conditions.

The detonation tube system provides the best available lab-oratory simulation of the chemical, dynamic, and thermodynamicbehavior of the flight SCRJ exhaust. This enables the detonationtube to be used as a standard of comparison against which substi-tute gas representations of the flight pressure distribution canbe evaluated.

Analysis shows that relatively small changes in flow thermo-chemistry and resultant pressure distributions can produce sig-nificant changes in vehicle loading, especially in afterbodynormal force. This means that the efforts to overcome the dif-ficulties of creating and employing accurate methods of matchingpressure distributions are, in fact, necessary, and that evenrelatively minor three dimensional flow details will need carefulstudy in later stages of development.

Proof-of-concept tests are required to show that the analyti-cally predicted matching of the SCRJ exhaust can be realized inpractice. These tests will also indicate the degree to which thedetonation tube system can be used to investigate the effects ofthree dimensional flow details such as the dividers between seg-ments of the combustor.

There is a need to develop a better understanding of thesimilitude requirements for the viscous mixing layer between in-ternal and external flow. If complete fidelity to all possiblesimilitude requirements is enforced, the external flow will haveto be of very low temperature or very high molecular weight, e.g.,chilled Freon gas. It is likely that these constraints could berelaxed significantly to allow a much simpler test system, butonly after experiments on the hypersonic mixing layer have shown

57

this to be permissible. We suggest that another set of experi-ments be planned and conducted while the detonation tube proof-of-concept is under way, so that ultimate wind tunnel testingwill be as simple as possible without loss of validity.

58

REFERENCES

1. Hopkins, H., Konopka, W., Leng, J., and Oman, R., "Simula-tion Experiments Using Hydrogen/Oxygen Gas Mixtures in aHigh-Pressure Detonation Tube," Final Report, Contract No.NAS 9-12447, Grumman Research Department Report RE-456,May 1973; also published as NASA Report MSC-05836.

2. Goldstein, S. (Ed.), Modern Developments in Fluid Dynamics^Vol. 1, Oxford: Clarendon Press, 1938.

3. Griffith, W., "Vibrational Relaxation Times in Gases,"J. Appl. Phys.. Vol. 21, No. 12, pp. 1319-1325, December 1950.

4. Ferri, A., "Mixing Controlled Supersonic Combustion," inAnnual Review of Fluid Mechanics, Vol. 5, Annual Reviews,Inc., Palo Alto, California, p. 319, 1973.

5. Leng, J. and Oman, R., "On the Simulation of HypersonicScramjet Engine Plumes in a Detonation Tube Facility,"Grumman Research Department Note RN-339, December 1972.

6. Jones, R. and Hunt, J., "Use of Tetrafluoromethane toSimulate Real-Gas Effects on the Hypersonic Aerodynamics ofBlunt Vehicles," NASA TR-R-312, June 1969.

7. Huber, P. W., "Use of Freon-12 as a Fluid for AerodynamicTesting," NAGA TN-1024, April 1946.

8. Svehla, R. and McBride, B., "FORTRAN IV Computer Programfor Calculation of Thermodynamic and Transport Propertiesof Complex Chemical Systems," NASA TN-D-7056, January 1973.

9. Leng, J., Oman, R., and Hopkins, H., "A Detonation TubeTechnique for Simulating Rocket Plumes in a Space Environ-ment," J. Spacecraft and Rockets, Vol.. 5, No. 10, pp. 1148-1154, October 1968.

10. Slack, M. W., "Measurements of Infrared and Vacuum Ultra-violet Radiation from Simulated Rocket Exhaust Plumes (U),"Final Contract Report No. S-046-277, Grumman Research De-partment Report RE-465, 15 December 1973 (SECRET).

59

11. Ratliff, A., Smith, S., and Penny, M., "Rocket Exhaust PlumeComputer Program Improvement, Volume I - Final Report, Sum-mary Volume, Method-of-Characteristics Nozzle and PlumePrograms,11 Lockheed Missiles and Space Company ReportLMSC/HREC D162220-1, January 1972.

60

APPENDIX

CALCULATION METHODS FOR SUBSTITUTE GAS MIXTURES

A. Thermodynamic Properties

The usual thermodynamic properties of homogeneous mixturesof two or more gases are computed from the component gas properties by use of the relationships:

a)' m

SX.c piZXi(c - R)

ratio of specific heats

b) in' - molecular weight&

c) H = ZX.H.

d) S = SX.S.

enthalpy

entropy

where X^ is the mole (volume) fraction of each component of themixture .

B. Transport Properties

The transport properties, viscosity, thermal conductivity,and mutual diffusivity of binary and ternary mixtures are deter-mined by mixture estimation formulas.

For viscosity, the Wilke method (Ref. A-l) has been employedbecause it yields results rapidly and has been verified by manyexperimental measurements and found to give comparable accuracyto the rigorous kinetic-theory relations (Ref. A-2). The Wilkerelation for a binary mixture viscosity is:

1 H *2

*1 "12

• -f *

1 -Hx2 *21

61

where

M-

'

viscosity, (gm/cm - sec) x 10 (micropoise)

mole fraction of gas component 1 and 2, respectively

8( 1 + sr12

'I 2

Tfi = molecular weight of gas component.

Average deviations of computed values from data for many binarymixtures have been reported as typically one percent for the Wilkeequation; this is considered adequate for our purposes.

The viscosity estimation equation for a ternary mixture byWilke's method takes the general form:

3

I i

-1

where q> and cp_ have been previously defined, and

i n2 Hr

K31

62

23

,2

32

We have selected the Mason-Saxena (Ref. A-3) estimationmethod for determining thermal conductivity, 1^, of binary mix-tures. This method is a simplified version of the classic Was-siljewa formulation, has the similar convenient form of the Wilkeequation for mixture viscosity, and yields, typically, errors ofless than 2 percent from actual data. The Mason-Saxena equa-tion for binary mixtures is:

m

2

l

X

4

8i i i e-V -1- T <w.

with units of cal/cm - sec - °K where the subscripts 1, 2, mrefer to the two gas components and the binary mixture properties,respectively.

Another transport property needed for two similarity parame-ters is the diffusion coefficient for a binary gas system. This

63

coefficient is independent of component gas concentration andquantifies the mutual diffusion of the gas mixture components foran isothermal process.

The binary diffusion coefficient, D-j > has been computedwith the theoretical equation derived from modern nonuniform gastheory, using a Lennard-Jones model to characterize the mole-cules, where:

3/2 1 2 2D19 = 0.001858 TJ/2 - - - - - L~LL- , ci//sec

where P is pressure in atmospheres and T is temperature in°K. The diffusion collision integral, n^, is tabulated(Ref. A-2) as a function of the normalized temperature, T/(e/k),where the molecular attraction law constant, e/k, for the mix-ture is obtained by use of the combining rule:

(e/k)12 =[ (.e/k (e/k)2]

Similarly, the molecular collision diameter constant, a-^> f°r

the gas mixture is determinable from the rule:

012 = al + °2)

where the component a's as well as (e/k)'s were obtainedprincipally from Svehla's (Ref. A-4) listing.

As a result of the computational investigation we have per-formed, the effect of the monomolecular gas additive in binarymixtures with Freon compounds can be characterized for severalsimilarity parameters as follows:

• For sufficiently high inicial temperature to avoidphase change during an expansion process, increasingthe additive increases the value of Y.

• For a given initial temperature, pressure, and modelsize, increasing the additive fraction decreases theReynolds number. As a result the model size for match-ing the full scale Reynolds number of the SCRJ increases

64

as additive is increased at the same pressure. For-tunately, these blends are all much higher in molecularweight than air, so they produce higher Re at smallscale, and matching is not difficult.

For a given initial temperature, the Mach number ismatched at increasingly greater flow velocities in themodel as the additive is increased. However, the modelexhaust velocity is much lower than in the full scaleapparatus.

For a given initial temperature, the Prandtl numberdecreases with increase in additive fraction. Thesubstitute gas mixtures have a similar but slightlygreater magnitude of Prandtl number compared to theSCRJ combustion products.

For a given initial temperature, the Schmidt number in-creases with increase in additive fraction. Both thesubstitute gases and SCRJ combustion products havesimilar magnitude of Schmidt numbers with the latterslightly greater.

The transport properties of viscosity and thermal con-ductivity increase with increase in additive fraction.The viscosity of a substitute gas in its properoperating range is generally about one third that ofthe SCRJ exhaust, and the thermal conductivity is morethan an order of magnitude smaller than that of thehot SCRJ gases.

The mutual diffusivity of binary mixtures is greaterthan the single Freon-type component but is independentof mixture composition. The hot SCRJ exhaust gaseshave about two and one half orders of magnitude greaterdiffusivity than the relatively cool binary mixturesconsidered as substitute gases.

C. One Dimensional Gas Dynamics

The one dimensional gas dynamic properties of a substitutegas mixture flow have been determined with a minicomputer pro-gram, assuming an isentropic process and a thermally perfect gas.To justify these assumptions for the calorically imperfect (i.e.,7 ^ constant) binary gas mixtures, an over-all flow process has

65

been calculated on the basis of a series of small sequentialstep changes in temperature. An average 7 for the incrementalchange is determined, and used in calculating the new flowproperties at the end of the step change, using the equations:

"D / "D /T* /T1

YP1 = (T2/T1'1

P2/Pl = (T2/T1)T"1

where 1 and 2 denote the beginning and end conditions, re-spectively, of the chosen small step interval in temperature:

T2/T1 = T ,

and

It is further assumed that across the small step, To - To ,

and the new Mach number at the end of the step change is found by:

The calculation starts with inputs of initial values of M, 7, T,and p based on matching of substitute gas mixtures to SCRJ ex-haust gas properties. Generally, the Mach number is taken as thevalue at the combustor exit station, assuming homogeneous flowprofiles. Initial values of 7, T, and P are taken to matchSCRJ combustor exit 73 and Re, although the value of T canbe selected for convenient test facility operation; the initialvalue of P can be taken as one and corrected for exact Rematching at a later time. Similarly, the value of initial Ymcan be taken as a value greater than the SCRJ 7, so as to pro-duce an over-all substitute gas expansion process that betterapproximates the SCRJ process.

The ym variation with temperature for a particular binarymixture is precalculated using Eq. (a) of Section A of this ap-pendix, and the JANAF table data of cp for different temperatures

66

of each mixture component. These discrete calculated values ofYm are curve fitted by a third order polynomial in T, storedin the minicomputer, and retrieved in the gas dynamic program toyield values of Ym for each new temperature in the stepwisecalculations through the flow channel.

Additional inputs needed to commence the computation arethe individual values of T to be used and the total number ofprescribed repetitive steps. For directing the calculation toincreasing values of M beyond the initial value, T is takenas slightly less than unity (e.g., 0.97). For decreasingvalues of M toward the stagnation point (M = 0), a valueof T slightly greater than 1 (e.g., 1.01) is selected.As the calculation approaches M = 0, an ongoing test for thenext step being projected beyond M = 0 (i.e., to a virtualnegative M) stops the calculation at the current step. If afiner grid size is desired to obtain nearly stagnation stateconditions, the computation can be restarted at any small sub-sonic Mach number with a value for T closer to 1 than pre-viously used. It has been found that a final T = 1.0001usually is sufficient to obtain stagnation state conditions tofive figure accuracy in temperature.

Table A-l presents representative results of the one dimen-sional gas dynamic calculations for three good substitute gas bi-nary mixtures. These results have been used in the two dimen-sional method of characteristics computations described else-where in this report in the Two Dimensional Afterbody Pressureand Force Prediction section.

67

TABLE A-l

REPRESENTATIVE ONE DIMENSIONAL GAS DYNAMIC PROPERTIES FOR THREE SUBSTITUTE GAS MIXTURES

Substitute.Gas Mixture

50% Freon 13B1+,50% Argon

f

40% Freon 12 +60% Argon <

^*

58% Freon 13B1 +42% Argon (

\*

MMachNo.

1.3088

1.7205

2.0287

2.36

2.9691

3.5295

4.0662

4.5885

5.1113

1.4519

1.7051

2.0224

2.3314

2.6537

3.2078

3.7313

4.2441

4.7479

5.0046

1.5466

2,299

2.365

2.655

2.9025

3.173

3.4099

3.821

3.9977

4.06

WMolecular

Wt.

94.42

172.324

1 r

103 . 15

v

y

1.1795

1.1853

1.1911

1.1994

1.2181

1.2407

1.2667

1.2970

1.3304

1.2054

1.2092

1.2153

1.2232

1.2328

1.2531

1.2788

1.3079

1.3423

1.3600

1.1786

1.1951

1.197

1.2056

1.2142

1.2244

1.2338

1.2508

1.2594

1.260

T

(°K)

539.123

488.066

446.26

400.00

324.00

262.44

212.576

172.1865

139.471

533.756

497.875

450.725

404.0

360.0

291.. 6

236.2

191.318

154.97

139.47

401.98

329.45

322.96

295.30

272,70

249.35 '

230.27

200.33

188.72

185.0

P..

(N/m2)

2.558 x 105

1.286 x 105

7.126 x 104

3.607 x 104

1.065 x 104•i

3.486 x 10

1.274 x 103

5.168 x 102

2.330 x 102

1.891 x 105

1.233 x 105

6.829 x 104

3.678 x 104

1.978 x 10A3

6.758 x 10

2.530 x 103

1.044 x 103

4.762 x 102

3.344 x 102

1.284 x 106

2.634 x 105

2.270 x 105

1.196 x 105

6.961 x 104A

3.941 x 10

2.452 x 104

1.150 x 104

8.542 x 103

7.751 x 103

P

(atm)

2.5247

1.2693

0.7033

0.356

0.1051

0.0344

0.01257

0.0051

0.0023

1.866

1.217

0.674

0.363

0.1952

0.0667

0.02497

0.0103

0.0047

0.0033

12.67

2.60

2.24

1.18

0.687

0.389

0.242

0.1135

0.0843

0.0765

68

REFERENCES

A-l Wiike, C., "A Viscosity Equation for Gas Mixtures,"J. Chem. Phys.. Vol. 18, p. 517, 1950.

A-2 Hirschfelder, J., Curtiss, C., and Bird, R., MolecularTheory of Gases and Liquids, J. Wiley and Sons, New York,1954.

A-3 Mason, E. and Saxena, S., "Approximate Formula for theThermal Conductivity of Gas Mixturest" Phys. Fluids.Vol. 1, p. 361, 1958.

A-4 Svehla, R. A., "Estimated Viscosities and Thermal Con-ductivities of Gases at High Temperatures," NASA TR R-132.,1962.

NASA-Langley, 1975 CR-2494 69

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