Indian Journal of Engineering & Materials SciencesVol. 5, June 1998, pp. 97-105

Modelling of supersonic mixing and shock-wave structure in two jetsinteraction

Mohammad Ali & Toshi Fujiwara

Department of Aerospace Engineering, Nagoya University, Nagoya 464, Japan

Received 20 June 1997; accepted 19 March 1998

Shock-wave structure due to collision of a hypersonic main jet with a transversely injected side jet andflowfield model for good mixing characteristics were investigated solving two-dimensional complete Navier-Stokesequations. Two flowfield models were considered: (i) upper boundary consists of a wall, named the "confinedflow", and (ii) the upper wall was removed making the flowfield as "unconfined". In confined flow the side sonic-jet, associated with upper and lower walls, produced a number of non-uniform reflected shock waves and acted as ablockage for the hypersonic main jet resulting in a large subsonic region. To get the supersonic mixing flowfield,we made the flowfield unconfined and increased the Mach number of side jet from M= 1.0 to M=2.0. The computerprogram was verified by the experimental results on the flow pattern of an air jet in a duct with abrupt areaenlargement.

Interaction between jet and cross flow and theirmixing are encountered in many engineeringapplications. Particularly the fuel injection schemein hypersonic vehicles incorporating SupersonicCombustion Ramjet (SCRAMJET) engines,requires special attention for stable and efficientcombustion. Interaction between side jet and mainflow produces shock waves which lead to turbulentmixing zones that thicken between the reflectedshocks I created by the combustor walls. Geometricconfiguration of fuel injection scheme is alsoimportant for good mixing':' and combustion.Therefore, an extensive investigation on the jetinteraction and mixing flowfield including shock-wave structure is required for efficient high speedvehicle propulsion.

The flowfield of jet interaction with free streamand their mixing have been investigated by manyscientists. Yokota and Kaje investigated thesupersonic flow and mixing with a perpendicularinjection from a finite length slit experimentallyand numerically using two slit angles 90° and 45°and showed that for the slit angle of 45° the mixingwas enhanced. Weidner and Drummond'conducted a parametric study using staged,perpendicular fuel Injectors. They studied themixing of hydrogen by varying the distancebetween injectors and the fuel split (percentage offuel injected per injector). Crabb et al.4 provided

an extensive review of earlier works and reportedthe measurements of the velocity characteristics ofa jet in crossflow encompassing the entire mixingregion. They confirmed the double vortexcharacteristics of the downstream flow anddemonstrated that it was associated with fluidemanating from 'the jet. Catalano et al? reportedmeasurements and computations for a turbulent jetdischarging into a crossflow confined between twoparallel plates, and concluded that the jet trajectoryand the existence of opposite-wall impingementare strongly dependent on the velocity ratio.Thayer III6 performed an experiment showing thatthe jet interaction flowfield depends markedly onthe injectant molecular weight. Rodriguez et a/. I

showed experimentally that the mixing zonescreated by the shock interaction with adiscontinuous interface thickened due to turbulentdiffusion and became wider than the continuousinterface after the second reshock. Thayer III andCorlett' found that the size of the upstreamseparated- flow region was strongly dependent onthe jet to free stream pressure ratio, and injectantconcentration in the separated region was high atall conditions investigated.

The interaction and mixing of a side jet injectedtransversely into a hypersonic jet, as shown inFig.l, have not been investigated yet. When a sidejet is directed transversely into a hypersonic jet,

98 INDIAN J. ENG. MATER. SCI., JUNE 1998

the jets interaction creates shock waves withsignificant increase in surface pressure" and theshocks together with their reflection enhance themixing region I. The enhancement of surfacepressure is particularly effective for controllingvehicle attitude and stability, and enhancement ofmixing for increasing engine efficiency. Toanalyze the interaction and mixing flowfield we,therefore, considered the geometric configurationsof Fig. 1 which consists of two flowfield models:(i) Confined and (ii) Unconfined. The dimensions,and configurations of upper and right boundariesof both cases are shown in Table 1. The main jetconsists of nitrogen, whereas the side jet (injector),injected from lower wall, consists of iodine-seedednitrogen. At the exit of side jet the mole fraction ofiodine is 4.6x 10-5 which is much lower than that ofnitrogen as 99995.4xIO-5

. For both cases, thestagnation pressure and temperature are identicalas shown in Fig.I. For Confined flow, the Machnumbers at the exit of main and side jets are 5.0and 1.0, and accordingly the Reynolds numbers(based on width of jet exit) are 1.08xI04 and

q:l~:il:ii!

odine &. Nit regen~r.n7Tr.n7T~7T~~~7Tr.n7T~7nr,ry7Bottom Wall

C ----------t

Staenatioa coodilioo.for maiD jetPra~ = 26.7 kPaTemperature = 293.0 K StapaliOll cooditioos

for injectorPrasurc = 6.67 kPaTemperature = 293.0 K

BachWlIl'd-C.alJlllep (0, IS an)

Fig. I-Schematic of flowfield models.(Dimensions andboundary configurations of the flowfields are shown inTable 1)

1.1x103, respectively. At the left boundary ofcalculation domain, 1.5 mm vertical solid wallbetween main jet exit and lower wall may act as abackward-facing step by which we can achieve alarge upstream separated region .. We locate theinjector at 30.0 mm from left boundary to analyzethe effects of backward-facing step on upstreamboundary layer separation. Initially the calculationdomain is assumed to be filled with low densitynitrogen of pressure 50 Pa and temperature 293 K.

The confined flowfield model produces largesubsonic region on the top of injector which seemsimpractical. To look for more practical combustionflowfield, we remove the upper wall of the domainmaking the flowfield unconfined. In practical, thisconfiguration may act as one-half of a symmetriccombustor. The Mach number at the exit of mainjet is considered identical as Confined flow caseand that at the exit of side jet we use 2.0 instead of1.0. The height of domain is increased from 15.0 to50.0 mm to study the effect of removed upper wall.Besides, the width of main jet exit is increasedfrom 12.0 to 13.5 mm. The change in configurationand Mach number of side jet, causes the smallchange in Reynolds numbers and iodineconcentration at the jet exits. At the exit of mainand side jets, the Reynolds number becomes1.2xl04 and 0.9xl03, respectively, and at the exitof side jet the mole fraction of iodine becomes4.19x 10-5

. In both models, the grid system consistsof 194 nodes in horizontal direction and 121 nodesin vertical direction. Particularly the exit ofinjector consists of 12 grid points.

Governing EquationsThe two-dimensional Navier-Stokes and species

continuity equations are solved to analyze the

Table I-Dimensions and boundary configuration of the flowfield models(All dimensions are in ern)

Flowfield a b c ·d Side jetModel width Boundary configuration

Confined 12 3.0 10.0 1.5 0.12 Upper RightConsisting Open

ofa wall

Unconfined U) 3.0 10.0 5.0 0.12 Open Open(No wall)

where, a = width of main jet exit, b = distance of injector axis from main jet exit, c = length of calculation domain and d = heightof calculation domain

ALl & FUJIWARA: JET INTERACTION AND MIXING FLOWFIELD 99

collision and mixing flowfield of nitrogen andiodine-seeded nitrogen. The body forces areneglected. With the conservation-law form, theseequations can be expressed by

oU + of + X = oFv + Xvot ox dy ox oy

where

... (1)

p pu pvpu pu2 +p puv

U= pv F= puv G= pv' + P ,, ,

E (E+p)u (E+p)vpYj P Yju pYjv

o o'yxay

'xyu + ayv + s,my

F=v 'xyaxu+ ,yxv+qx

mx

ns ns R ns

P= "p. R.T = "p. -T E= "p C TL..JJ J L..JJW' L..Jj pjj=1 j=1 J j=1

~ R P 2 2- L..JPj-T+-(u +v )j=1 Wi 2

(ou Ov) (ou) (ou Ov)ax=A, -+- +2Jl - ,ay=A, -+-ox dy ox ox oy

+211(Ov) r, =z =11(ou + Ov)r: oy 'xy yx r: oy ox '

oT o~q=« - +pDI2(hl~2) -,ox ox

me =pl) oYj me =pl)x- UI2-' y- U12ox

oYj ,A,=- ~ f.Loy 3

The transport properties; the viscositycoefficient J.l and thermal conductivity K aredetermined from Sutherland formulae" and thebinary-diffusion coefficient D\2 from Chapman-

Cowling" formula as

1'0+ST+S

... (2)

( )

1.5~_:£ 1'o+S/Co 1'0 T+ S

( )

0.5

0.001858 TI.5 .~ +W2 x 10.13~ W2

... (3)

... (4)P a~2nD

It can be pointed out that the flow field consists ofmainly nitrogen and therefore, the viscosity of themixture will, in practical, be same as that ofnitrogen. Since the flowfield is laminar incharacter and we are conducting the preliminaryinvestigation, no turbulence model has beenincluded at this stage.

Numerical SchemeThe system of governing equations has been

solved, using an explicit Harten-Yee Non-MUSCLModified-flux-type TVD scheme". For betternumerical simulation, the grid points near the wallsand side jet are clustered which causes non-uniformity in the physical coordinate system.Therefore, the two-dimensional, rectangularphysical coordinate system (x, y) is transformedinto the computational coordinate system (~ ,1]) inorder to solve the problem on uniform grids. Thephysical and computational coordinate system canbe related byx=x(~ 1]), y=y(~ 1]) (5)From the chain rule of differential calculus, wehave

[i] ~[~~~] [i] ~[;:;:{i]Eq.(6) can be written as

... (6)

... (7)

100 INDIAN J. ENG. MATER. sci., JUNE 1998

Here the transformation Jacobian J is

J= 1

x~Y,.,-x,.,Y~The relationship between thecomputational coordinate systemwritten as

... (8)

physical andcan also be

~=.;:(x.y).'1=7]{x.y)

and by differential calculus,

[£] [o~ 0'1][ 0] [£]ox = ox ox o~ = [~x 'Ix] o~~ o~ 0'1 0 ~y 'ly ~oy oy oy 0'1 0'1

where the transformation Jacobian J is

Using Eqs.(6-8), (10), and (11), we can write

[~x 'lx][x~ y~] =[1 0]~y n, x,., v; 0 1

and the grid metric terms and Jacobian J are

J=~x 'ly- ~y 'lx= ----x~y,.,-x,.,y~

... (9)

... (10)

... (11)

.. .(12)

... (13)

After applying the transformation, Eq.(I) can beexpressed as

oU of-+ -+ot o~oG0'1

" "where U = r'u, F =,rI(~xF+~yG)." AG =,rI('lxF+'lyG). F y=,rl(~x r.+~y Gy).A

G =J" ('Ix r,+ 'ly GJ.

... (14)

For the left hand side of Eq.(14), the explicit Non-MUSCL TVD scheme can be written as

~ +1 ~ Ilt ~ ~U", =u.n -J .._(Fn I . _Fn I .)I,j I,j I,j Il~ 1+1 2,j I-I 2,j

!It ~ ~-Jj,j Il'l (Gj~j+112 -Gtj-112 ) (15)

" AThe variables F and G can be described as

... (16)

where Rj+1/2 IS an eigen vector matrix. Moredetails about the Scheme can be found inreferences (10) and (11) .

Boundary ConditionsA Navier-Stokes analysis imposes that the

normal and tangential velocity components arezero on the walls. The walls are assumed thermally

adiabatic, so that (~:) =0. For non-catalyticw

walls, the normal derivative of species massfraction also vanishes, and consequently thegradient of total density becomes zero. Thepressure is determined from the equation of state .The temperature, pressure and density at inflowboundary are assumed steady. At the outflowboundary the variables are determined by first-order extrapolation when flow character issupersonic and by zero order extrapolation whenflow character is subsonic.

Verification of the CodeBefore applying the numerical code to compute

the interaction and mixing flowfield, itsverification is necessary. Accordingly acomparison has been made with the experimentalresults found by Nakano et al," The geometricconfiguration of the experiment is shown in Fig.2,where air was injected at sonic condition from a3.0 mm nozzle exit into a rectangular duct of 160.0mm length and 10.0 mm height. Using the samegeometric configuration we calculated the jetflowfields for two cases: (i) Pc/Po = 3.1, and (ii)Pc/PI ~3.65, where Po was the stagnation pressureand P. atmospheric pressure. Our computational

ALl & FUJIWARA: JET INTERACfION AND MIXING FLOWFIELD 101

domain consists of 166 and 101 nodes in thehorizontal and vertical directions, respectively.

The results are shown in Figs 3 and 4. Fig. 3shows the comparison of experimental andcomputed flow patterns along with internal shockwaves. Both near the jet exit and far down stream,computed flow patterns (Fig. 3a) agree with theexperiment (Fig. 3b). Fig. 3a indicates that jetboundary, exit shock, regular reflection, Machreflection and Mach stem are similar with

Dimensions are in mm

Two-Dimensional Nenzel

Fig. 2-Geometric configuratioa of experiment.

Fig.3--Characteristics of flow patterns for P';P.(a) computed, (b) experiment.

geCO)U

.J::o

]1~T \: (a)

-~(bl

Fig.4-Characteristics of flow patterns for P';P.(a) computed, (b) experiment.

experiment. There is a difference in the distance ofMach stem from jet exit plane, where computedflowfield takes a longer distance than theexperiment. This discrepancy originates probablyfrom calculation of viscosity and viscous layeralong the plates for lower pressure ratio, i.e., forpofPa ~ 3.1. For higher pressure ratio, i.e., for pofPa= 3.65, computed flowfield (Fig. 4a) shows the'similar flow patterns with size, shape and positionof oblique shocks and regular reflections ofexperiment in Fig. 4b. Thus, from Figs 3 and 4 wecan conclude that the overall computed resultsagree with the experiment qualitatively. The codeis, therefore, justified suitable for presentinvestigation.

Grid Refinement StudyThe unconfined flowfield model has been used

for this purpose. Our present grid system is 194nodes along the horizontal direction and 121 nodesalong the vertical direction. Using grid system, 322nodes along the horizontal direction and 227 nodesalong the vertical direction, we calculated themixing flowfield. From the calculation it seemsthat the mesh size has more influence on mixing

(a)

(b)

3.1; 5.0 B.O 1.0 1.0 8.0 10.0Distance (em)

.n.

••

.08.010.0(em)

Fig.5--Comparison between penetrations and mole fraction3.65; contours of 12 (Unconfined flow); (a) grid system 194x121,

(b) grid system 322x227.

102 INDIAN 1. ENG. MATER. sci., JUNE 1998

characteristics than that on the other flowfieldproperties. We, therefore, compare the penetrationand mixing of iodine between two grid systems.From Figs 5a and b, it can be seen that there is nosignificant difference in penetration anddistribution of iodine both in upstream anddownstream of side jet. In downstream, negligiblysmall numerical diffusion occurs for grid system194x121 which causes higher penetration of iodineand larger mixing region. Since the difference inpenetration and mixing region between the twogrid systems is negligible small, we concluded 'thatthe grid system 194x121 is a reliable one forpresent analysis.

Results a'dd DiscussionStatic pressure distributions along the lower wall

Fig. 6 compares the static pressures, normalizedby that of main jet exit, along the lower wallamong three flow configurations: (i) confined flowwithout side jet, (ii) confined flow with side jet,and (iii) unconfined flow with side jet. This figure,together with Figs Te-e will be used to discussshock structures and their effects on pressure alongthe lower wall. Intentionally we show very densecontours in Figs 'le-e for better understandingabout shocks and their reflections. For the confinedflow without side jet, pressure at the beginning oflower wall is less than unity due to expansion ofmain jet. The expansion wave interacts with lowerwall at about 0.5 em from left boundary where thepressure begins to rise. The interaction andreflection of shock is evident in Fig. 7a in whichthe shock wave structure including Mach reflectionis clear to see. The pressure ratio rises gradually to2.5, flattens out to a plateau at about 4.0 ern and

<>

_"'-6- Confined now without iqjectionII II Confined now with injection

<> <> Unconfined naw with iqjectionp.r=Sl.38kPa

Distance from left bound8ry (an)

Fig.~Pressure distributions along lower wall.

after reaching the first plateau there is a slightpressure drop at 5.4 em, where Mach reflectionoccurs. At far downstream pressure rises up to 3.0due to Mach reflection and regular reflection. It isclear that smooth shock reflections and pressurevariation are present in confined flow without sidejet; on the other hand, in presence of injection fromlower wall rapid and frequent pressure variationscan be observed. Due to (i) side injection and (ii)backward-facing step, strong separation of main jetoccurs at the beginning of lower wall resulting inan increase of the pressure ratio. The strongseparation shock interacts with the expansionshock produced by main jet, and makes thepressure 21.5 times greater than that of main jetexit. The shocks, their interactions and reflectionsare evident in Fig. 7b. Fig. 6 shows that due torelief of separation .shock the pressure dropsrapidly and becomes 14.5 for confined flow withside jet at about 2.0 em from left boundary, whichis still much higher than that of unconfined flow.The strong interaction between main and side jet

!!

Distance from left boundary (em)

.0 1.0 1.0 10.0

Distance from left boundary (an)

Fig.7-Total density contours; (a) confined flow without sideinjection, (b) confined flow with side injection, (c) unconfinedflow with side injection.

"All & FUJIWARA: JET INTERACfION AND MIXING FLOWFIELD 103

forms a bow shock and increases pressure at 2.5cm from left boundary. The average pressure overthe separated region is about 18.0 times greaterthan that of main flow which results in a reactionforce useful for rapid manoeuvering of hypersonicvehicle. At downstream of side jet a pair of shockscan be seen; one strong compression shock appearsat 4.5 cm caused by the reattachment of side jet,the other is at 8.4 em caused by the reflection ofbow shock. The downstream compression shockreflects and forms another weak shock at the endof lower wall. There is small pressure riseimmediately downstream of side jet caused bydownstream recirculation created by the suctionand bending of side jet. Though several pressuredrops can be found in downstream caused by therelief of shocks, pressure is always higher than thatat main flow exit which is also a good indicationfor the enhancement of reaction force.

In mixing and combustion application frequentshock reflections may cause the localized heatingproblem on combustor walls which leads us toconsider the flowfield model 2 for analyzing themixing and combustion characteristics. Using thisflowfield configuration the reflected shocksdisappear as shown in Fig. 7c. Three shocks can beseen from this figure; (i) main jet separation shock,(ii) bow shock and (iii) recompression shock.

!Fig. -6 shows that pressure at low locations ismuch lower in the unconfined flow than that of theconfined flow with side jet. Due to separation of

II(8)

-..•..~.-. ,., .~- - - -

Irr~' , . '••..__•••••••••...• AIlJMDiscancc from left boundary (an)

.0 .0 .0Distance from left boundary (an)

Fig.8-Velocity vector field; (a) for confined flow, (b) forunconfined flow.

main jet, pressure rises up to 4.5 and remainsalmost same up to the formation of bow shock. Inthis case interaction between main and side jet isnot so strong as that in the confined flow, thereforethe pressure rise is not very large. Immediatelydownstream of side jet pressure decreases down toless than unity due to suction of side jet. Becauseof upward-deflection of main flow, pressure islower than that of the confined flow without sideinjection at all downstream locations. Smooth riseand fall in pressure make this configuration moreappropriate to investigate mixing characteristicsfor future combustion.

Analyses of MixingFigs 8a and 8b show the recirculation regions

and flow patterns by vectors for the two flowfieldmodels. In upstream of injector Fig. 8a shows (i)two large and elongated primary recirculations(adjacent to lower, and upper wall) caused by theseparation of main jet, (ii) one very smallsecondary recirculation immediately upstream ofinjector caused by primary recirculation andsuction of injector. Between the two large primaryrecircuiations the bottom one is the bigger andcontains higher percentage of iodine due toconvection and diffusion mechanisms. Thisrecirculation is very important for mixing in bothupstream and downstream of injector. For theunconfined flow, although the same number ofupstream recirculations can be found in Fig. 8b,from vector length we can differentiate theintensity of recirculations. Though upstreambottom recirculation is extended up to leftboundary, its overall size is smaller than that in theconfined flow indicating weak interaction betweenmain and side jet in the unconfined flow. In theconfined flow one recirculation appears at fardownstream due to reflection of shocks as shownin Fig. 8a, and disappears when the upper wall isremoved.

From mole fraction contour in Fig. 9a we cansee that due to strong injection and existence ofupper wall, the side jet acts as a barrier of main jetresulting in large upstream recirculation containingrich-iodine. Large upstream recirculation withiodine makes high mixing region in downstream.Moreover, the blockage of main jet results insubsonic region on the top of side jet plume shown

104 INDIAN 1. ENG. MATER. set, JUNE 1998

Injector Distance (em)(Maximum mole fraction of 12= 4.6E-05)

Subsonic region (b)

Injector Distance (em)

Fig.9--Confined flow showing, (a) mole fraction contour of 12and (b) Mach contour.

in Fig. 9b, and together with upper elongatedrecirculation, causes the injected iodine to reachthe upper-left comer of flowfield as shown in Fig.8a. A number of shock waves and their reflectionscaused by jets interaction together with upper andlower walls make the contour lines oscillatory. Thegeneration of subsonic region on the top of side jetplume in the confined flow model makes itinappropriate for SCRAMJET application. Fig. lOashows iodine contour and flowfield pattern of theunconfined flow model where shock reflectionshave disappeared. In Fig. lOb the shock structure,including bow shock, recompression shock, andflowfield pattern are evident. From this figure wecan see that most of the flowfield, particularly onthe top of side jet plume, is supersonic which isapplicable for hypersonic vehicle propulsionsystem.

ConclusionsFlowfield model for supersonic mixing and the

effects of shock waves on surface pressure for twojets interactions were investigated. The computercode was verified with the experimental resultsshowing qualitative agreement. Two flowfieldmodels: (i) confined by upper wall and (ii)removed upper wall (unconfined), were used forinvestigation. The confined flow model showed: (i)number of shocks and their reflections, (ii) highpressure ratios on the lower wall, and (iii) largesubsonic region on the top of side jet plume. Highpressure on lower wall may be useful for resultant

(a) sf'

····::::·:··.:::··~~.c:.r::.:]: ':'. .

.; ---_.' .. _ ... -

cot - - . - •• ~ •• - ••. : - •. - - •• .

o .•Injector Distance (em)

(Maximum mole fraction oCI2 = 4.19E-05)

3.0

'<;2.0

1.0

10.0

Injector Distance (cm)

Fig. IO-Unconfined flow showing, (a) mole fraction contourOfI2 and (b) Mach contour.

reaction force in rapid manoeuvering of hypersonicvehicle. More investigations are required aboutshock wave structures and wall pressuredistributions to control the stability of a vehicle inpractical. Prediction of subsonic region on the topof side jet plume made the system impractical forsupersonic combustion application. Theunconfined flow model made the mixing flowfieldsupersonic, particularly on the top of side jetplume, and this flowfield model is useful for moreanalyses about mixing and combustion. Transverseinjection of iodine into nitrogen and their mixinghave been reported here, therefore investigationsare necessary for mixing of fuel with oxidizerusing the unconfined flowfield model.

NomenclatureCp = specific heat at constant pressure, J/(kg.K)D12 = binary-diffusion coefficient, m2/sE = total energy, J/m3

F = flux vector in x-directionG = flux vector in y-directionh = enthalpy, l/kgJ =.transformation Jacobian

ALl & FUnW ARA: JET INTERACI10N AND MIXING FLOWFIELD,. 105

m = mass flux of species, kg/sM = Mach numberp = pressure, Paq = conduction of heat, W1m2

R = universal gas constant, J/(kg.moI.K)S = Sutherland constant, Kt = physical time, sT = temperature, Ku = horizontal velocity, mlsv = vertical velocity, mlsW = molecular weight of species, g/molx =horizontal Cartesian coordinate, my = vertical Cartesian coordinate, mY = mass fraction of speciesp = mass density, kg/m'a = normal stress, Pal' = shear stress, Paf.J = coefficient of viscosity, kglm.sK = thermal conductivity, W/m:Kno = diffusion collision integrala12 = effective collision diameter, A~ = transformation coordinate in horizontal direction'7 = transformation coordinate in vertical direction

SuperscriptII = index for calculation stepns = number of species

Subscripta = atmospheric conditionIJ = index for species or grid pointsv = index for viscous termx = horizontal direction

y = vertical directionxy = reference of planeo = reference value or stagnation condition1 = species iodine2 = species nitrogen

References1 Rodriguez G, Galametz I, Thorembey M-H, RayerC &

Haas J-F, Proc 20th Int Symp Shock Waves, California,USA (1995) 647-652.

2 Yokota K & Kaji S, Trans Jpn Soc Aeronautical Space&i, 39(1996) 173-183.

3 Weidner E H & Drummond J P, AIAA Paper 81-1468(1981).

4 Crabb D, Durao D F G & Whitelaw J H, J Fluids Eng ,103 (1981) 142-153.

5 Catalano G D, Chang K S & Mathis J A, AIAA J, 27(1989) 1530-1535.

6 Thayer III W J, AIAA J, 9 (1971) 539-541.7 Thayer III W J & Corlett R C, AIAA J, 10 (1972) 488-493.8 Mudford N R, Roberts G T, Schuricht P H, Ball G J &

East R A, Proc 20th Int Symp Shock Waves, California,USA (1995) 173-178.

9 White F M, Viscous Fluid Flow (McGraw-Hili, NewYork) 1974,27-36.

JO Yee H C, NASA TM-101088 (\989).11 Hishida M, Turbulent Flow and Flame Structure

Generated by Interaction between Non-steady Multi-dimensional Flame and Flowfield, Ph D Dissertation,Department of Aerospace Engineering, NagoyaUniversity, Japan (1997).

12 Nakano K, Matsuoka M & Iwamoto J, Proc Symp ShockWaves, Tokyo, Japan (1996) 481-484.