FullPaper ASSC 10th Final

8/11/2019 FullPaper ASSC 10th Final

1/12

Physical Insight into Nozzle Flow Behaviour of Axisymmetric Scramjets for Access-to-Space

via Design Optimisation

Hideaki Ogawa and Russell R. Boyce

Centre for Hypersonics, School of Mechanical and Mining Engineering,The University of Queensland, St. Lucia, Brisbane, QLD 4072, Australia

Summary: Scramjet propulsion is a promising hypersonic airbreathing technology forefcient and reliable access-to-space. Internal-compression axisymmetric scramjet (supersoniccombustion ramjet) engines are now being explored in the SCRAMSPACE project. The

nozzle section plays a key role in producing thrust in scramjet operation. Shape optimisationshave been performed for axisymmetric scramjet nozzles to achieve the maximum thrust withvarious inow conditions at Mach 8. They have resulted in optimum geometries characterisedby similar nozzle length and exit radius for all the tested inow assumptions, while themajor inuence of inow non-uniformity on the optimum contour has been found only inthe vicinity of the nozzle entrance. Comparable performance has been obtained in cross-referencing the optimum geometries under different inow conditions, suggesting detailedgeometric difference apart from that in the nozzle length and exit radius exert rather minorimpact on the off-design nozzle performance for the conditions considered here.

Keywords: hypersonic airbreathing propulsion, axisymmetric scramjet nozzle, design opti-

misation, access-to-space

Introduction

Hypersonic air-breathing propulsion offers great potential for reliable, reusable and eco-nomical systems for access-to-space. In particular, scramjet (supersonic combustion ramjet)propulsion is a promising technology that can enable efcient and exible transport systems.The last decade has seen remarkable milestones achieved by various ight experimentsincluding University of Queensland (UQ)s HyShot II in July 2002 [1, 2], the NASA X-43vehicles in the Hyper-X program in March and November 2004 [3], and the Boeing X-51AWaveRider in May 2010 [4].

The SCRAMSPACE program is now underway as an international collaboration led byUQ, where internal-compression axisymmetric scramjets (Figure 1 (a)) are being investigatedin both ground and ight tests, following the performance demonstrated in shock tunnelexperiment [5]. Featuring innovative techniques such as inlet fuel injection and radical-farmingshock-induced combustion, the elegantly simple axisymmetric geometry offers numerousadvantages in various aspects including aerodynamic and combustion efciency, thermal andstructural management as well as manufacture. Scramjet operation typically relies on thesequential process capture and compression of hypersonic airow in the inlet, fuel injectioninto the air, supersonic combustion in the chamber, and expansion of combustion productsfor thrust through the nozzle (Figure 1 (b)).


2/12

(a) upstream view [5]

nozzlecombustor inlet

(b) schematic diagram

Fig. 1: Axisymmetric scramjet engine

The nozzle plays a primary role in producing the thrust to propel the vehicle. The designof axisymmetric scramjet nozzles requires particular care due to complex aerodynamic phe-nomena and chemical kinetics; the nozzle inow is highly non-uniform due to the presence

of shock-shock and shock wave / boundary layer interactions, which are responsible forthe creation of localised hot pockets that are essential for radical-farming shock-inducedcombustion [6]. Re-association of molecules subsequently occurs in the nozzle as the reactedgas cools in rapid expansion. The xed geometry makes the nozzle susceptible to performancelosses in off-design operation at various velocities and altitudes with / without fuel injectionin the course of the SCRAMSPACE mission.

This paper presents the results of nozzle design optimisations for axisymmetric scramjets atan operating Mach number of 8, aiming at the application of hypersonic airbreathing propul-sion to efcient access-to-space. Various inow conditions have been assumed, includinguniform and proled inows in the presence or absence of fuel, and the owelds associated

with the optimum nozzle geometries have been probed in order to investigate the inuentialfactors and key ow physics.

ApproachesCongurations

Nozzle geometry

The present study is conducted with focus on the nozzle section of an axisymmetric scramjetengine, as seen in Fig. 2. Both internal and external nozzle surfaces are considered herein order to take into account the ow interactions downstream of the trailing edge. Thenozzle radius at entrance is xed at a nominal value 0.03512 m. The inner nozzle surfaceis represented by an arc dened by the radius r a and angle a at the entrance followed bya cubic B ezier curve dened by the front vector magnitude n and an inner trailing-edgecurve represented by a vector of magnitude ite and direction ite , which is an angle relativeto the straight line that connects both ends of the inner nozzle curve (shown by a dashedline). This geometric representation is adopted particularly because thrust values comparableto those yielded by thrust-optimised nozzles can generally be produced by parabolic nozzles,whose inner surface is represented by a cubic B ezier curve [7]. The position of the trailing

edge is dictated by the nozzle length ln and exit radius r n . The external nozzle surface is alsorepresented by a cubic B ezier curve dened by vector magnitudes r and ote and a relativedirection ote in a similar manner to the inner curve.


3/12

Fig. 2: Parameterisation of the scramjet nozzle geometry

Flow conditions

The freestream condition considered in this study is M = 8 .0, p = 1197 Pa, and T =226.5 K, assuming scramjet operation at an altitude of 30 km on a constant dynamic pressuretrajectory of 53.6 kPa. The Reynolds number based on the nozzle entrance radius is Re =1.06 105 .

Computational uid dynamics

Computational methods

Nozzle owelds are computed by utilising the state-of-the-art commercial solver CFD++ [8].An implicit algorithm with second order spatial accuracy is used to solve the Navier-Stokesequations for steady owelds and convergence is accelerated by the multigrid technique.The nozzle surface is assumed to be an isothermal cold wall of 300K. The boundary layeris assumed to be turbulent and modelled by the two-equation SST k RANS model [9].Computations are performed until the energy residual drops to the order of 10 5 , based ona convergence dependency study, where all objective functions have been found to vary lessthan 0.01% at higher orders. Standard air in thermochemical equilibrium state is assumed forthe gas in the fuel-off case, whereas the gas composition and nite-rate chemical reactionsare represented by Evans and Schexnayders model [10], which consists of 25 elementaryreactions among 12 species including hydrogen-air combustion as well as nitrogen chemistry.

Computational mesh

The computational domain is represented by a two-dimensional structured mesh generated byGlyph scripting within the commercial grid generator Pointwise [11]. The numbers of nodesand cells for the mesh resolutions considered in the present research are tabulated in Table 1 1 .Fig. 3 shows a coarse computational mesh for the baseline geometry with a conical nozzle of a semi-vertex angle of 25 . The minimum grid width is 10 5 m at the rst grid point off thewall (non-dimensional distance y+ = 0 .32 on average) in order to assure good resolution of the viscous sublayer. The coarse resolution level is adopted for the present study, based on apreliminary mesh convergence study for the baseline geometry (results of the mesh sensitivitystudy are not presented here but this topic is revisited later in the results section).

1In the absence of the nozzle entrance arc, the number of nodes along the wall is 10 / 20 / 40 less than those shown forthe coarse, ne and superne mesh, respectively.


4/12

Table 1: Mesh resolutions

resolution along the wall wall-normal direction total number of cellscoarse 262 100 25,839

ne 524 200 104,077

superne 1048 400 417,753

x [m]

r

[ m ]

0.9 1 1.1 1.20

0.1

0.2

0.3

0.4

0.5

0.6

Fig. 3: Computational mesh (baseline)

internal inflow

external inflow

isothermalwall

freestream

supersonicoutflow

symmetry axis

Fig. 4: Boundary conditions

Flow and boundary conditions

Fig. 4 schematically shows the conditions that are imposed on the boundaries of the computa-tional domain. The surface is assumed to be isothermal walls of 300 K. Imposed at the nozzleentrance are inow boundary conditions given by either ow proles or uniform ows, asshown by solid and dashed lines in Fig. 5 (b), respectively. The proles are obtained by slicingthe owelds calculated in separate axisymmetric CFD runs for the nominal SCRAMSPACEspecication 2 , except the one with fuel on, which is obtained by circumferentially averagingthe sliced ow quantities from a three-dimensional CFD run in the presence of inlet fuel(hydrogen) injection through multiple portholes. The uniform ows are represented by stream-thrust-average [12] values of the proles. The freestream condition is also applied to the topboundary, while a supersonic outow condition is imposed on the right hand boundary, whichis positioned 0.15m downstream of the trailing edge.

A. Design Optimisation

1) Optimisation algorithms

Design optimisation is performed in an iterative manner as per the optimisation loop shownin Fig. 6, which consists of mesh generation (pre-processing), CFD computation (evaluation),post-processing and optimisation algorithms.

2r t = 0 .0005 m, l1 = 0 . 1994 m, 1 = 5 .90

, l2 = 0 .069 m, 2 = 3 .18

, l3 = 0 .040 m, 3 = 3 .13

, r c = 0 . 035 m,l c = 0 . 5 m, c = 0 , r a = 0 m, a = 0

, n = 0 m, ln = 0 . 242 m, r n = 0 . 148 m, ite = 0 m, ite = 0 , lf = 0 .280 m,

f = 20 . 0 , bf = 0 .528 m, r = 0 .1 m, ote = 0 m and ote = 0

in Fig.2.


5/12

0 1 2 3 4 5 6 7

x 104

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

p [Pa]

r

[ m ]

Fuel On (profile)Fuel On (uniform)Fuel Off (profile)Fuel Off (uniform)

(a) pressure

0 200 400 600 800 10000

0.005

0.01

0.015

0.02

0.025

0.03

0.035

T [K]

r

[ m ]

Fuel On (profile)Fuel On (uniform)Fuel Off (profile)Fuel Off (uniform)

(b) temperature

0 0.005 0.01 0.015 0.02 0.025 0.030

0.005

0.01

0.015

0.02

0.025

0.03

0.035

cH

2

r

[ m ]

Fuel On (profile)

Fuel On (uniform)

(c) hydrogen mass fraction

Fig. 5: Internal inow proles

mesh generation CFD computation post-processing

decision variablesoptimisation algorithms

objective / constraint function values

mesh solution

Fig. 6: Optimisation loop

Population-based evolutionary algorithms developed at UNSW@ADFA are employed foroptimisation [13, 14]. In particular, use is made of the elitist non-dominated sorting geneticalgorithm (NSGA-II) [15]. Optimisation occurs over generations with a population of 32individuals. A simulated binary crossover and polynomial mutation are used as recombinationoperators at a given probability (1.0 and 0.1, respectively) with a specied distributionindex (10 and 20, respectively). The optimisation process is efciently assisted by varioussurrogate models including the response surface models, kriging approximations and radialbasis functions. Among these models the one with the least error within a threshold of 10%is adopted to predict the objective and constraint functions in lieu of actual CFD evaluationand all individuals that are estimated to be superior to the present elitists are veried by trueCFD evaluation. All members in the population pool are truly evaluated by CFD every 5generations, when the surrogate models are trained by using 90% of the solutions from thearchive, which stores all solutions that are evaluated by true evaluation.

2) Optimisation problem

The nozzle performance is assessed by the sum of the forces acting on the inner and outernozzle surface: F F inner + F outer . This parameter is used as the objective function to bemaximised 3 in order to set the goal of the design optimisation. No constraint function isemployed for the present study. The 10 design parameters that dene the nozzle geometry(Fig. 2) are used as the decision variables, the upper and lower bounds of which are shownlater at the top and bottom of the columns in the graph Fig. 8. Design optimisation has beenperformed with four different assumptions for the gas and internal inow boundary condition(refer to Fig. 4) as tabulated below:

3Note that the sign of F is negative for positive thrust due to the denition of the x axis.


6/12

Table 2: Nozzle inow conditions

fuel (hydrogen) gas assumption internal inowon non-equilibrium proledon non-equilibrium uniform

off equilibrium proledoff equilibrium uniform

Results

Optimisation results

Optimisation progress

The nozzle geometry has been optimised to attain maximum possible thrust for the fourinow assumptions. Fig. 7 shows the progression of the thrust values for each case duringoptimisation. It is seen that convergence has been achieved as at the 30 th generation in allcases.

80

90

100

110

120

130

140

150

0 5 10 15 20 25 30

- F [ N ]

generation

Fuel On (profile)

Fuel On (uniform)

Fuel Off (profile)

Fuel Off (uniform)

Fig. 7: Optimisation progress

Optimum geometries

The values of the objective function ( F ) as well as the 10 decision variables (designparameters) are plotted in Fig. 8 for the optimum geometries along with the baseline values.

Plotted and compared in Fig. 9 (a) are the optimised and baseline geometries (note that thecontours are not to scale). Somewhat similar shapes with relatively straight inner and outernozzle contours have been obtained for all four cases. A closer look in the vicinity of thenozzle entrance (Fig. 9 (b)) reveals pronounced curvature for both fuel on and off cases with

inow proles, as also indicated by large values of the nozzle arc radius r a in Fig. 8.


7/12

0

0.1

0.2

0.3

0.4

0.50.6

0.7

0.8

0.9

1

v a

l u e s

( r e l

. )

0

150

F

0.2

1

l n

0.05

0.2

rn

0.005

0.15

ra

2

20

a

0

0.2

n

5

5

ite

0

0.3

ite

5

5

ote

0

0.3

ote

0

0.3

r

Fuel On (profile)Fuel On (uniform)Fuel On (baseline)Fuel Off (profile)Fuel Off (uniform)Fuel Off (baseline)

Fig. 8: Objective function and decision variable values (at 30 th generation)

0.9 1 1.1 1.2 1.3 1.4 1.5

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

x [m]

r

[ m ]

Fuel On (profile)Fuel On (uniform)Fuel Off (profile)Fuel Off (uniform)baseline

(a) overall

0.81 0.82 0.83 0.84 0.85 0.86 0.87 0.88 0.89 0.9

0.036

0.038

0.04

0.042

0.044

0.046

0.048

0.05

x [m]

r

[ m ]

Fuel On (profile)Fuel On (uniform)Fuel Off (profile)

Fuel Off (uniform)baseline

(b) close-up

Fig. 9: Optimum and baseline nozzle geometries

Flowelds

Flow characteristics

The owelds are visualised in Fig. 10 for the nozzle geometry optimised for the proledinow case with fuel on, compared with the baseline owelds. It can be noted that theoptimised nozzle allows moderate expansion of the internal ow by its extended slendershape, whereas the baseline geometry experiences over-expansion due to drastic broadeningof the channel, as characterised by the emergence of an incidental oblique shock to compensatefor the pressure drop (at the bottom of Figs. 10 (a) and (c)). This effectively allows the near-surface high pressure to hold over a longer extent in the optimum case, which lends itself toproducing greater thrust than the baseline nozzle (Fig. 10 (b)).

Compared in Fig.11 is the difference in the owelds between the two inow assumptions,i.e. proled and uniform inows, in the presence of fuel. Rather minor as the difference may


8/12

(a) Mach number (b) pressure (c) temperature

Fig. 10: Flowelds around optimum and baseline nozzles (Fuel On, proled inow)

(a) Mach number (b) pressure (c) water mass fraction

Fig. 11: Flowelds around optimum nozzles with proled / uniform inow (Fuel On)

seem, it is noticeable in the top image of Fig.11 (a) that the incoming shock wave brought bythe inow interacts with the kernel ow in the case of the proled inow. In effect the highpressure that is present between the internal shock and nozzle wall is felt over a larger surfacearea for the proled inow case, as seen in Fig.11 (b) 4 . Fig.11 (c) shows the distributions of the mass fraction of the water, which is a product of hydrogen-air combustion. It can be seenthat this species, which is carried over from the combustor, is smoothly diffused downstreamthrough the nozzle.

4This is partly attributed to the difference in the initial expansion region as a result of optimisation, which is scrutinisedlater in the surface ow analysis.


9/12

The owelds are plotted in Fig.12 for the optimum and baseline geometries with theinow prole in the absence of fuel. It can be observed that an oblique shock wave carriedfrom upstream (as also seen in Fig.5 (a) and (c)) reects on the centreline and intersect withthe internal shock wave (Fig.12 (a)). This interaction occurs downstream, as compared to thefuel-on case in Fig.10, causing the kernel ow to stretch farther and making the high pressurezone between the internal shock and wall more distinct (Fig.12 (b)).

(a) Mach number (b) pressure (c) temperature

Fig. 12: Flowelds around optimum and baseline nozzles (Fuel Off, proled inow)

Surface force

Total surface force

The force acting on an axisymmetric surface can be obtained by integrating the pressure andshear stress as follows:

F = s ( p sin

cos ) 2rds (1)

The total force that acts on both sides of the nozzle, i.e. F = F inner + F outer , is compared inFig.13 for the optimum geometries that have been achieved with three different computationalmesh resolutions (as tabulated in Table 1) under the four assumed inow conditions. Littledifference is found between different mesh resolutions for all conditions, with the largestdeviation of 1.1% seen for the fuel-off case with the inow prole, which justies the choiceof the (coarse) mesh resolution adopted in this study.

Plotted in Fig.14 are the contributions of the pressure and viscous forces to the total surface

force for the optimum geometries with fuel on (those for the fuel-off case are not presentedhere since they are similar to the fuel-on case), compared with the baseline cases. It is notable


10/12

80

90

100

110

120

130

140

150

Fuel On, profile Fuel On, uniform Fuel Off, profile Fuel Off, uniform

- F [ N ]

conditions

CoarseFineSuperfine

Fig. 13: Total surface force (mesh sensitivity)

0

20

40

60

80

100

120

140

160

Pressure force Viscous drag

f o r c e [ N ]

optimum (Fuel On, profile)optimum (Fuel On, uniform)

baseline (Fuel On, profile) baseline (Fuel On, uniform)

Fig. 14: Pressure / viscousbreakdown of inner nozzle force

(Fuel On)

that substantial increase in pressure force has been achieved by design optimisation for bothcases with moderate viscous penalty, leading to appreciable gain in the overall nozzle thrust.

Surface pressure distributions

0.8 0.9 1 1.1 1.2 1.30

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5x 10

4

x [m]

p [ P a

]

Fuel On (profile)Fuel On (uniform)Fuel On (baseline)Fuel Off (profile)Fuel Off (uniform)Fuel Off (baseline)

(a) surface pressure

0.8 0.9 1 1.1 1.2 1.30

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

x [m]

s i n

Fuel On (profile)Fuel On (uniform)Fuel Off (profile)Fuel Off (uniform)baseline

(b) sin

Fig. 15: Inner nozzle surface properties

In order to investigate the driving factors of shape optimisation, the surface owelds areexamined in detail here 5 . Fig.15 shows the pressure distributions and sine variations of thesurface inclination on the inner nozzle surface for the optimum and baseline geometries.High pressure level of the incoming gas emitted from the combustion chamber is maintainedover extensive ranges of the inner nozzle section (Fig.15 (a)) for the optimum geometries, incontrast to the baseline nozzle geometry. The presence of a local pressure rise is indicatedby a hump in the cases of proled inows. It is noteworthy that the initial gradients of the

5Only the surface pressure is discussed here because the contributions of the viscous force to the thrust have been foundto be rather minor in Fig.14.


11/12

optimum contours for the proled inow cases are less steep than those for the uniforminows in Fig.15 (b). This allows the surface pressure for the proled inow cases to vary insuch a gradual manner that it increases towards the points where the localised pressure riseis present due to shock impingement. This allows the nozzle to benet the most from highpressure in thrust production (as in p sin in Eqn.(1)), without incurring losses that couldarise from ow separation and associated interactions due to the adverse pressure gradientsat the humps in case the gradients were too steep.

Cross reference

The performance of the nozzle geometry optimised for various inow assumptions has beenevaluated under off-design inow conditions. The thrust force is compared in Fig. 16 for theoptimum contours along with the baseline case. It can be seen that the nozzle geometriesoptimised for a certain inow assumption is able to exert comparable thrust force under otherow conditions with a maximum difference of 2.5%, demonstrating the robustness of the

optimised geometries as regarding thrust production.

0

20

40

60

80

100

120

140

160

Fuel On, profile Fuel On, uniform Fuel Off, profile Fuel Off, uniform

- F [ N ]

conditions

optimum geometry for Fuel On, profileoptimum geometry for Fuel On, uniformoptimum geometry for Fuel Off, profileoptimum geometry for Fuel Off, uniform

baseline geometry

Fig. 16: Thrust force comparison in cross referencing

Conclusions

Design optimisation has been conducted to maximise the thrust of the axisymmetric scramjet nozzle for various inow assumptions (in the presence / absence of fuel with uniform / proled inow) at Mach 8. The owelds associated with the optimum geometries have beenscrutinised in order to identify the key ow physics and driving factors that determine theoptimium shapes and nozzle performance.

Slender nozzle contours have been yielded as a result of design optimisation under all inowconditions considered here, maximising the benet of high pressure nozzle inow, comparedto the baseline geometry. Proled inows have been found to result in curved surface in thevicinity of the nozzle entrance in order to make the most of the high surface pressure dueto the impingement of the shock waves from the combustor section. The robustness of theoptimum geometries in terms of thrust production has been demonstrated by cross-referencingthe nozzle contours under off-design inow conditions.


12/12

Acknowledgments

The authors are grateful to Dr. Tapabrata Ray and Amitay Isaacs at UNSW@ADFA forproviding the advanced MDO capability developed in the group. We are also thankful toMr. Yohan Alazet at Ecole Nationale Sup erieure de lA eronautique et de lEspace for hisassistance in developing the mesh generation and optimisation methodology.

References

[1] Paull,A., Alesi,H. and Anderson,S., HyShot Flight Program and How it was Developed,AIAA Paper 2002-5248, Sep 2002.

[2] Boyce,R.R., Gerard,S. and Paull,A., The HyShot Scramjet Flight Experiment ightdata and CFD calculations compared, AIAA Paper 2003-7029, Dec 2003.

[3] McClinton,C.R., X-43 Scramjet Power Breaks the Hypersonic Barrier: Dryden Lec-tureship in Research for 2006, AIAA Paper 2006-1-317, Jan 2006.

[4] Boeing, X-51A WaveRider Breaks Record in 1st Flight, http://boeing.mediaroom.com,May 2010.

[5] Hunt, D. C., Paull, A., Boyce, R. R. and Hagenmaier, M., Investigation of an axisym-metric scramjet conguration utilising inlet-injection and radical farming, in Proceedingsof the 19 th International Symposium on Airbreathing Engines (ISABE 2009) , Montr eal,Sep 2009.

[6] McGuire, J. R., Boyce, R. R. and Mudford, N. R., Radical farm ignition processes intwo-dimensional supersonic combustion, Journal of Propulsion and Power , Vol. 24, No.6, pp. 1248-1257, 2008.

[7] Ostlund, J., Flow Processes in Rocket Engine Nozzles with Focus on Flow Separationand Side-Loads, Licentiate Thesis, Royal Institute of Technology, Stockholm, 2002.

[8] CFD++, Software Package, Ver. 8.11, Metacomp Technologies, Inc., CA, 2009.[9] Menter, F. R., Zonal Two Equation k Turbulence Models for Aerodynamic Flows,

AIAA Paper 93-2906, 1993.[10] Evans, J. S. and Schexnayder, C. J. Jr., Inuence of Chemical Kinetics and Unmixedness

on Burning in Supersonic Hydrogen Flames , AIAA Journal , Vol. 18, No. 2, pp. 188-193,1980.

[11] Pointwise, Software Package , Ver.16.02, Pointwise,Inc., TX, 2008.[12] M older, S. and McGregor, R. J., Analysis and Optimization of Scramjet Inlet Perfor-

mance, ICAS Paper 90-4.7.3, 17 th Congress of the Aeronautical Sciences, Stockholm,

Sweden, Sep 1990.[13] Ray, T. and Smith, W., A Surrogate Assisted Parallel Multiobjective Evolutionary

Algorithm for Robust Engineering Design, Engineering Optimization , Vol. 38, No. 8,pp. 997-1011, 2006.

[14] Ray, T., Isaacs, A. and Smith, W., Multi-objective optimization using surrogate as-sisted evolutionary algorithm, ( Introduction G.P.Rangaiah ), Multi-objective Optimization:Techniques and Applications in Chemical Engineering , pp. 131-151, World Scientic,Singapore, 2008.

[15] Deb, K., Pratap, A., Agarwal, S. and Meyarivan, T., A fast and elitist multiobjectivegenetic algorithm: NSGA-II, IEEE Transactions on Evolutionary Computation , Vol. 6,No. 2, pp. 182-197, 2002.

Documents

FullPaper ASSC 10th Final