NUMERICAL COMPUTATIONS FOR DESIGNING A SCRAMJET …

25th INTERNATIONAL CONGRESS OF THE AERONAUTICAL SCIENCES

NUMERICAL COMPUTATIONS FOR DESIGNING ASCRAMJET INTAKE

M. Krause, B. Reinartz, J. BallmannDepartment of Mechanics, RWTH Aachen University

Keywords: Hypersonic flow, compression ramp flow, computational air intake design

Abstract

A numerical and experimental analysis of aScramjet intake has been initiated at RWTHAachen University. The paper presents anoverview of the ongoing work on the nu-merical simulations of compression ramp andair intake flow of a Scramjet propulsion us-ing two different, well validated Reynolds av-eraged Navier Stokes flow solvers. The anal-ysed geometry concepts have been definedwithin the frame of the Research TrainingGroup GRK1095:”Aerothermodynamic Designof a Scramjet Engine for a Future Space Trans-portation System”. To optimize the geometry ofthe intake, especially to minimize the separationbubble in front of the isolator inlet, several nu-merical simulations (2D and 3D) are performedusing a variety of turbulence models. Here,the most important question is, which turbu-lence model will reliably predict, whether block-age of the flow will be avoided or not. Thisis the “killer” argument for the design. Theexperimental investigation will start in summer2006 at RWTH Aachen University and the DLRCologne.

1 Introduction

The intake of an air breathing hypersonic propul-sion system with supersonic combustion (Scram-jet) mostly consists of exterior compressionramps followed by a so-called isolator/diffusorassembly (see fig. 1). Important features ofthe flow field can be studied assuming two-

dimensional flow. Oblique shock waves withouta final normal shock are performing the compres-sion of the incoming flow. Concerning the flightconditions the two main difficulties of a hyper-sonic intake are evident. The first one is the in-teraction of strong shock waves with thick hyper-sonic boundary layers, which causes large sep-aration zones that are responsible for a loss ofmass flow and some unsteadinesses of the flow,like e.g. bulging of the separation zones and cor-responding shock movement. Consequences arethat the compression process is affected and theengine performance decreases. The second maindifficulty is that the high total enthalpy of theflow causes severe aerodynamic heating, furtherenhanced by turbulent heat flux. Up to now thefollowing cases were studied: i) the influence ofgeometry changes on the flow, especially on theseparation regions, ii) the impact of the used tur-bulence modeling within the numerical methodon the flow solution and iii) the difference be-tween 2D approach and 3D simulations.

Fig. 1 shows a configuration with sharp lead-ing edges. But in practice, sharp leading edgeswill not withstand the high thermal loading inhypersonic flow, i.e. rounded leading edges aremore realistic. This geometric change has a re-markable influence on the flow in several aspects,for example the shapes and positions of frontshock and cowl shock. These will be detachedand exhibit strong curvature around the bluntedges which generates entropy layers. Along theramp the boundary layer grows inside the entropylayer causing an increase in aerodynamic heating[1]. Another effect of a detached bow shock is

1

M. KRAUSE, B. REINARTZ, J. BALLMANN

that farther downstream changes of the positionof the leading edge shock can diminish the cap-tured mass flow and worsen the flow conditionsin the isolator inlet.

In the past, numerous simulations for hyper-sonic intake flows have been performed in 2D and3D and published in the literature e.g. [2], [3],[4]. Emphasis on physical and numerical model-ing of such flows was put in [5] where as [6] con-centrated on applications and experimental veri-fication.

2 Physical Model

2.1 Conservation Equations

The governing equations for high-speed turbulentflow are the unsteady Reynolds-averaged Navier-Stokes equations for compressible fluid flow inintegral form

∂∂t

Z

VU dV +

I

∂V

(

Fc−Fd

)

n dS= 0 (1)

whereU = [ ρ , ρv , ρetot ]T (2)

is the array of the mean values of the conservedquantities: density of mass, momentum density,and total energy density. The tilde and the barover the variables denote the mean value ofReynolds-averaged and Favre-averaged vari-ables, respectively. The quantityV denotes anarbitrary control volume with the boundary∂Vand the outer normaln. The fluxes are splittedinto the inviscid part

Fc =

ρvρv◦v+ p1v(ρetot + p)

(3)

and the diffusive part

Fd =

0

σ−ρv′′◦v′′

vσ+v′′σ−q−cp ρv′′T ′′

−12 ρv′′v′′◦v′′− vρv′′◦v′′

, (4)

where 1 is the unit tensor and◦ denotesthe dyadic product1. The air is considered tobe a perfect gas with constant ratio of specificheats, γ = 1.4, and a specific gas constant ofR = 287[J/kgK]. Correspondingly the expres-sion for the specific total energy reads:

etot = cvT +12

vv+k . (5)

The last term represents the turbulent kinetic en-ergy

k :=12

ρv′′v′′

ρ. (6)

For isotropic Newtonian fluids, the mean molec-ular shear stress tensor is a linear, homogeneousand isotropic function of the strain rate

σ = 2µS−23

µtr(

S)

1. (7)

The mean strain rate tensor is

S :=12

[

grad(v)+(grad(v))T]

, (8)

and the molecular viscosity ¯µ = µ(T) obeysSutherland’s law. Similarly, the molecularheat flux is considered a linear, homogeneous,isotropic function of the temperature gradient

q = −

cpµ

Prgrad(T), (9)

with the Prandtl numberPr = 0.72.

2.2 Turbulence Closure

To close the above system of partial differen-tial equations, the Boussinesq hypothesis is usedwhere the remaining correlations are modeled asfunctions of the gradients of the mean conser-vative quantities and turbulent transport coeffi-cients. The Reynolds stress tensor thus becomes

−ρv′′◦v′′ = 2µt (S−13

tr(S))−23

ρk1 , (10)

1Scalar Products of dyadics formed by two vectorsaandb with a vectorc are defined as usual, i.e.,a◦ bc =a(bc), ca◦b = (ca)b.

2

Numerical Computations for Designing a Scramjet Intake

with the eddy viscosityµt, and the turbulent heatflux is

cp ρv′′T ′′ = −cpµt

Prtgrad(T), (11)

with the turbulent Prandtl numberPrt = 0.89. Fi-nally, for hypersonic flows the molecular diffu-sion and the turbulent transport are modeled asfunctions of the gradient of the turbulent kineticenergy

v′′σ−12

ρv′′v′′◦v′′ = (µ+µt

Prk)grad(k), (12)

with the model constantPrk = 2.The turbulent kinetic energy and the eddy

viscosity are then obtained from the turbulencemodel. In case of laminar flow, both variables areset to zero to regain the original transport equa-tions. As mentioned, several turbulence modelswere used for the numerical simulations withinthis paper. For description of the models used,we refer to [7], [8], [9] and [10].

3 Numerical Method

3.1 Navier–Stokes Solver FLOWer

One of the codes applied is the DLR FLOWercode [11], which solves the unsteady Navier–Stokes equations for compressible fluid flow us-ing a cell–centered finite volume method onstructured multiblock grids. The implementedadvection upstream splitting method (AUSM)is used for modeling the inviscid fluxes andthe second order accuracy in space is achievedby a monotonic upstream scheme for conserva-tion laws (MUSCL) extrapolation where differ-ent limiter functions guarantee the total variationdiminishing (TVD) property of the scheme. Thediffusive fluxes are discretized by central differ-ences. For time integration a five–step Runge-Kutta scheme of fourth order accuracy in timeis used. Multigrid, implicit residual smooth-ing, and local time stepping for steady–statecomputations can be applied to enhance conver-gence. To simulate turbulent flow, a wide varietyof low Reynolds number turbulence models for

compressible flow are implemented. For exam-ple: Spalart-Allmaras, k-ω, SST, LEA, Baldwin-Lomax and a 7-equation Reynolds stress model.The spatial discretization is performed similarlyto the system of conservation equations using anAUSM upwind scheme for the convective andcentral discretization for the diffusive terms. Toincrease the numerical stability, the time inte-gration of the turbulence equations is decoupledfrom the mean flow equations. The integration iscarried out implicitly using a Diagonal DominantAlternating Direction Implicit (DDADI) scheme[10].

3.2 QUADFLOW

QUADFLOW is an adaptive and fully implicitnew flow solver to the Navier–Stokes equationsfor compressible flow using a fully unstructuredcell–centered finite volume method. It followsan integrated concept of surface-based discretiza-tion, adaptivity governed by multiscale analysisand grid generation and refinement based on B-splines. The method has been developed withincollaborative research center SFB 401:”FlowModulation and Fluid Structure Interaction atAirplane Wings” and the GRK 5:”Transport Pro-cesses in Hypersonic Flow” at RWTH AachenUniversity and is still in process for 3D flowproblems. So far, several turbulence modelshave been implemented, validated and tested in2D calculations, for example Spalart-Allmaras,LEA, SST,k−ω. The parallelisation using MPIis realized with the PETSc software.

3.3 Boundary Conditions

At the inflow and outflow boundaries, a locallyone–dimensional flow normal to the boundary isassumed. The governing equations are linearizedbased on the theory of characteristics and theincoming and outgoing number of characteris-tics are determining the directions of informationtransport. For incoming characteristics, the statevariables are corrected by the freestream values atthe inlet of the test section using linearized equa-tions. Else the variables are extrapolated fromthe interior. The turbulent values are determined

3


by the specified freestream turbulence intensityTu∞: k∞ =1.5(Tu∞u∞)2. At solid walls, the no-slip condition is enforced by setting the velocitycomponents to zero. Additionally, the turbulentkinetic energy and the normal pressure gradientare set to zero. The energy boundary condition isdirectly applied by prescribing the wall temper-ature when calculating the viscous contributionof wall faces. In case of quasi two–dimensionalcomputations, periodic boundary conditions areapplied in the third space direction.

3.4 Computations

The FLOWer computations are performed on theSunFire SMP–cluster of RWTH Aachen Univer-sity, the Jump- and BlueJean-cluster of the Re-search Centre Jülich and the NEC SX–8 clus-ter at Stuttgart University. The parallelization ofFLOWer is jointly based on it’s block–based MPI(message passing interface) formulation as wellas on an OpenMP shared memory paralleliza-tion. The QUADFLOW computations are doneon the SunFire SMP– and the Opteron–clusterof RWTH using MPI, based on the PETSc soft-ware.

3.5 Numerical Accuracy

A complete validation of the FLOWer code hasbeen performed by the DLR prior to its release[11, 12] and continued validation is achieved bythe analyses documented in subsequent publica-tions e.g. [6]. QUADFLOW is also a well val-idated solver for 2D computations [13], its 3Dversion is still in progress.

The numerical research reported in this papercontains a grid convergence study and compari-son of the mass flow over all boundaries as shownin chapter 5.

4 Geometry and Farfield Flow Conditions

The farfield flow conditions are the same for allcomputations shown in this paper. The condi-tions belong to an altitude of 25000m and are asfollows: M = 7.0, Re= 5.689·106, T∞ = 222Kand p∞ = 2511Pa. A sketch of the plainflow

geometry is shown in fig. 1. All gradients in

Fig. 1 Hypersonic inlet model sharp leading edges

the third space direction are assumed to be zero.In the corresponding boundary conditions on thesides symmetry conditions are used for fictitiouspoints.

5 Validation

So far, no experimental results for comparisonare available. That is why validation is performedon the basis of grid convergence, a mass flowbalance and they+ values. The grid conver-gence simulations were done for 3 different tur-bulence models on two grids in 2D. The first onehad 77000 points and the second one has 310000points for the same geometry. Mach and pressurecontours were compared and showed the same re-sults qualitatively. To insure it, a mass flow bal-ance was calculated for all non-wall boundaries.For both grids the differences in the mass flowfor a certain wall segment were between 0.2 and0.5%. This mass flow balance was scrutinizedfor all simulations performed. It could be shown,that the difference between inflow and outflowwas at maximum 1%. That insured convergencewithin the computations. For all simulations they+ values were at least below 2.

6 Results

6.1 Grid Generation for Geometries withSharp Leading Edges

The grid generation for the considered intakegeometry was performed by using the Mega-Cads program, which has been developed andused at DLR and was further developed in theMEGAFLOW project [11].

4


The generated grid is split up into 3 blockswith approximately 60000 points each, to facil-itate the use of MPI and OpenMP for calcula-tions performed on parallel computer systems.The whole grid has a total of 168960 points andhas been densified at solid walls and at the in-flow boundary as well as at the isolator inlet. Theminimum grid resolution is 10−6 in x and y di-rection.

6.2 Sharp Leading Edges

So far, there are several results of 2D compu-tations available for the geometry with sharpleading edges (sketched in fig.1) which wereachieved using different turbulence models. Theresults shown within this subchapter have allbeen found using the flow solver FLOWer. Sim-ulations have been performed using the origi-nal k− ω -turbulence Model from Wilcox, theSpalart-Allmaras and a Reynolds stress model,called SSG -ω - model (Speziale, Sarkar, Gatski,1993, [14]). It should be mentioned that also in-viscid flow computations were carried out. Theresults showed a shock system that is generatedwithin the intake as it was expected during thefirst design by using a 2D characteristics methodfor steady supersonic flow.

In the following, we report on 2D turbulentflow computations. At first, the differences be-tween an adiabatic wall and an isothermal wall(Twall = 300K) have been investigated. The flowconditions for all calculations were the same asdescribed in chapter 4. Fig. 2 shows contourlines of Mach number in the Scramjet intake foran adiabatic wall. Fig. 3 shows results for thesame geometry with an isothermal wall at 300 Kwall temperature. It can be seen that the wall tem-perature has a remarkable effect on the flow field,especially on the separation regions between thedouble ramp and the inlet of the isolator. Therethe cowl shock interacts with the boundary layerat the expansion region. This interaction creates aseparation bubble, which fills about 35 percent ofthe overall intake height for the isothermal wall.In the case of an adiabatic wall (fig. 2) the separa-tion fills about 55 percent of the intake. A higher

X [m]

y[m

]

0 0.1 0.2 0.3 0.4 0.50

0.1

0 0.8 1.6 2.4 3.2 4 4.8 5.6 6.4

Mach

leading edge shock

2nd ramp shockcowl shock

reflected shocks

separation bubble

separation between ramps

grid boundary

Fig. 2 Mach contours for Scramjet intake (ge-ometry 1) adiabatic wall, SA turbulence model(M∞= 7.0,Rel = 5.689·106 [1/m], T∞=222 K).

X [m]

y[m

]0 0.1 0.2 0.3 0.4 0.5

0

0.1

0 0.8 1.6 2.4 3.2 4 4.8 5.6 6.4

Mach

leading edge shock

2nd ramp shockcowl shock

reflected shocks

separation bubble

separation between ramps

grid boundary

Fig. 3 Mach contours for scramjet intake (geom-etry 1) isothermal wallTwall = 300K, SA turbu-lence model (M∞= 7.0, Rel = 5.689· 106 [1/m],T∞=222 K).

wall temperature produces thicker boundary lay-ers, which leads to a steeper shock and a largerseparation. Furthermore, a steeper shock reducesthe mass flow entering the isolator. Concerningthese results it is obvious that the wall tempera-ture strongly influences the flow field, which isconfirmed when looking at the Mach contours infig. 4 and fig. 5. It can be asserted that byreaching a certain wall temperature using the k-

X [m]

y[m

]

0.35 0.4 0.45

0.1

0 0.6 1.2 1.8 2.4 3 3.6 4.2 4.8 5.4 6 6.6

Mach

cowl shock

front shock

2nd ramp shock

Fig. 4 Mach contours for scramjet intake (ge-ometry 1) adiabatic wall,k−ω turbulence model(M∞= 7.0,Rel = 5.689·106 [1/m], T∞=222 K).

5


X [m]

y[m

]

0.35 0.4 0.45

0.1

0 0.6 1.2 1.8 2.4 3 3.6 4.2 4.8 5.4 6 6.6

Mach

cowl shock

TW=300K

front shock

2nd ramp shock

Fig. 5 Mach contours for scramjet intake (geom-etry 1) isothermal wallTwall = 300K, k−ω tur-bulence model (M∞= 7.0,Rel = 5.689·106 [1/m],T∞=222 K).

ω turbulence model the separation bubble in theisolator inlet becomes so big, that it blocks theflow. A strong shock in front of the isolator willbe the consequence with subsonic flow behind itand disabling of supersonic combustion.

Contemplating fig. 4 and 2, which presentresults computed with different turbulence mod-els, remarkable differences can be seen, althoughthe boundary and flow conditions are identical.That means the differences are produced simplyand solely by the turbulence models. To empha-size such influence on the results of the numericalsimulations, several models were used for com-putation, as mentioned above. The biggest differ-ences are observed in the boundary layer thick-ness and the separation bubble height. Anyway, agreater separation bubble leads to a steeper shockand therewith to different flow conditions behindit. For optimising the geometry to realize super-sonic combustion it is essential to know the po-sitions of the shocks as well as the size of theseparation bubble.

6.3 Grid Generation for Geometry with de-fined Leading Edge Radii

Two grids were created using the MegaCads pro-gram. The first one consists of 5 Blocks with ap-proximately 15000 points each. Altogether thisgrid has a total of 77000 points with densifiedgrid lines at solid walls and at the inflow bound-ary as well as at the isolator inlet. The minimumresolution is 10−5 in x- and 10−6 y-direction.

The second one was created to do a grid con-vergence study (see chapter 5). It has a total of310000 points split into 5 blocks.

6.4 Influence of rounded Leading Edges onthe Intake Flow Field

Up to now several flow computations have beendone using different turbulence models (SA,LEA, LLR, SST, Standard k-ω model fromWilcox and a Reynolds stress model (SSG -ω))and both flow solvers. Fig. 6 shows the Machnumber distribution for the whole intake whenthe SA model was used. Within this chapter thedifferences to the geometry with sharp leadingedges will be pointed out, followed by a com-parison of the results achieved with different tur-bulence models. Furthermore, two different flowsolvers are applied, the FLOWer- and QUAD-FLOW code, that are described in chap. 3.

x [m]

y[m

]

0 0.1 0.2 0.3 0.4 0.50

0.1

0.2 0.2 0.6 1 1.4 1.8 2.2 2.6 3 3.4 3.8 4.2 4.6 5 5.4 5.8 6.2 6.6

leading edge bow shock

2nd ramp shock

cowl bow shockreflected cowl shock

Mach

Fig. 6 Mach contours for scramjet intake(FLOWer) isothermal wall,TWall = 300K, SAturbulence model, rounded leading edges (M∞=7.0,Rel = 5.689·106 [1/m], T∞=222 K)

It can be ascertained that detached bowshocks are generated in front of the first ramp andin front of the cowl. As expected, the round lead-ing edge at the first ramp forces the shock to takea more upstream position. At the cowl the bowshock interacts with the second ramp shock di-rectly in front of the cowl. This interaction hasno influence on the body side part of the cowlshock and thus not on the isolator flow. The en-tropy layers caused by the strong shock curva-ture at the leading edges of ramp and cowl willbe a matter of further study. Fig. 9 shows theinlet of the isolator and fig. 10 shows a close

6


x [m]

y[m

]

0.37 0.38 0.39 0.4 0.41

0.1

0.2 0.6 1 1.4 1.8 2.2 2.6 3 3.4 3.8 4.2 4.6 5 5.4 5.8 6.2 6.6

Mach

2nd ramp shockhits bow shockin front of cowl

merged bow and2nd ramp shock

front shock

cowl shock

merged front-, cowl -and ramp shock

separation bubble

Fig. 7 Mach contours for isolator intake(FLOWer) isothermal wall,TWall = 300K, SAturbulence model, rounded leading edges (M∞=7.0,Rel = 5.689·106 [1/m], T∞=222 K)

up view of the cowl (both Mach distribution).

x [m]

y[m

]

0.374 0.376 0.378 0.38

0.1

0.2 0.6 1 1.4 1.8 2.2 2.6 3 3.4 3.8 4.2 4.6 5 5.4 5.8 6.2 6.6

cowl bow shock

2nd ramp shock

stagnation point

Fig. 8 Mach contours for cowl (FLOWer)isothermal wall,TWall = 300K, SA turbulencemodel, (M∞= 7.0, Rel = 5.689 · 106 [1/m],T∞=222 K)

For comparison of results, a flow simulation withthe SA turbulence model has been performed us-ing the same grid and flow conditions with theflow solver QUADFLOW. It has to be mentionedthat for this comparison the adaptivity conceptof QUADFLOW was switched off. Results areshown in fig. 9 and 10. It can be pointed out,that the first and second ramp shock is a littlebit steeper in the FLOWer results. Therefore thesecond ramp shock hits the bow shock of the

cowl nearer to its stagnation point than in theFLOWer result. This causes a stronger interac-tion between the shocks, leading to a greater re-gion with high temperature and thus to a biggerheat load upon the structure. Under the compara-bly chosen code parameters, both solvers gener-ated nearly the same result.

x [m]y

[m]

0.37 0.38 0.39 0.4 0.41

0.1

0.2 0.6 1 1.4 1.8 2.2 2.6 3 3.4 3.8 4.2 4.6 5 5.4 5.8 6.2 6.6

Mach



front shock

cowl shock


separation bubble

Fig. 9 Mach contours for isolator intake (QUAD-FLOW) isothermal wall,TWall = 300K, SA tur-bulence model, rounded leading edges (M∞= 7.0,Rel = 5.689·106 [1/m], T∞=222 K)

x [m]

y[m

]

0.374 0.376 0.378 0.38

0.1

0.2 0.6 1 1.4 1.8 2.2 2.6 3 3.4 3.8 4.2 4.6 5 5.4 5.8 6.2 6.6

cowl bow shock

2nd ramp shock

stagnation point

Fig. 10 Mach contours for cowl (QUAD-FLOW) isothermal wall,TWall = 300K, SA tur-bulence model, (M∞= 7.0, Rel = 5.689 · 106

[1/m], T∞=222 K)

In the following some results for 2 equationturbulence models will be shown, all generatedwith FLOWer. Four models were tested (SST,LEA, LLR and original k− ω from Wilcox).

7


x [m]

y[m

]

0.37 0.38 0.39 0.4 0.41

0.1

0.2 0.6 1 1.4 1.8 2.2 2.6 3 3.4 3.8 4.2 4.6 5 5.4 5.8 6.2 6.6

Mach



front shock

cowl shock


separation bubble

Fig. 11 Mach contours for isolator intake(FLOWer) isothermal wall,TWall = 300K, SSTturbulence model, rounded leading edges (M∞=7.0,Rel = 5.689·106 [1/m], T∞=222 K)

It was asserted, that even using the same grid,boundary- and flow conditions not the same re-sults were achieved for different turbulence mod-els. Fig. 11 shows the Mach contours for a sim-ulation with the SST model from Menter in com-parison to fig. 12 showing the results for a sim-ulation with the LLR turbulence model. One cansee that there are great differences in the predic-tion of the separation bubble size in the isola-tor inlet and the thickness of the boundary lay-ers. Followed by different positions of the firstand second ramp shock. The LLR model pro-duces thicker boundary layers that increase theoffset of the first bow shock from the round lead-ing edge. Therefore it hits the cowl shock as wellas the second ramp shock, further upstream re-ducing the shock - shock interactions. Never-theless the thick boundary layers cause the bigseparation resulting in a blockade of the isolatorinlet. The result of the SST model is quantita-tively comparable with the ones of the SA modeland the SSG -ω - Reynolds stress model shown infig. 13. Considering the results of the LEA andk−ω - models, the separation within the isolatorintake blocks it and generates a Mach one crosssection. Afterwards the flow expands in the isola-tor so that a Mach number of two is achieved at itsexit. In that case only 60% of the maximum cap-turable mass flow exits the isolator. That means

x [m]

y[m

]

0.37 0.38 0.39 0.4 0.41

0.1

0.2 0.6 1 1.4 1.8 2.2 2.6 3 3.4 3.8 4.2 4.6 5 5.4 5.8 6.2 6.6

Mach



front shock

cowl shock


separation bubble

Fig. 12 Mach contours isolator intake (FLOWer)isothermal wall, TWall = 300K, LLR turbu-lence model, (M∞= 7.0,Rel = 5.689·106 [1/m],T∞=222 K)

the whole intake would generate a spill of 40%.The spill for the other turbulence models is lowerthan 20% (SA: 14.2%; SST: 19.2%; SSG -ω:15.4%). An exception is the LLR model whichproduces a spillage of 25%. But in fig. 12 onecan see that the separation takes about 80% ofthe overall intake height. That means that it willblock the inlet here, too.

Simulations using QUADFLOW were pro-duced for the LEA andk−ω turbulence mod-els, so far. Results are similar. That means theseparation blocks the isolator inlet and the shockpositions are equal, except for very small differ-ences.

In the following we will present results of a3D flow simulation. The grid is based on the oneused for 2D. It was made up by multiple repeti-tion in the third dimension to create a 3D intake.In 3D one boundary of the grid is given by thesidewall the other one is assumed as a symmetrycondition in the middle of the intake. The num-ber of points in the third dimension is 80, gen-erating a grid with a total of 6.1 million points.The flow conditions still remain the same. Thefirst simulation in 3D was performed using theflow solver FLOWer. Considering the 2D resultsand the smaller amount of simulation effort, theSA turbulence model was chosen for the compu-tation. Fig. 14 shows slices of Mach contours

8


x [m]

y[m

]

0.37 0.38 0.39 0.4 0.41

0.1

0.2 0.6 1 1.4 1.8 2.2 2.6 3 3.4 3.8 4.2 4.6 5 5.4 5.8 6.2 6.6

Mach



front shock

cowl shock


separation bubble

Fig. 13 Mach contours for isolator intake(FLOWer) isothermal wall,TWall = 300K, SSGturbulence model, rounded leading edges (M∞=7.0,Rel = 5.689·106 [1/m], T∞=222 K)

for the 3D simulation where the x-coordinate hadbeen held constant which means, the slices arenormal to flow direction. Fig. 15 shows the Machcontours in flow direction for the middle of theintake. One can see, that there is a great influ-

Fig. 14 Mach contours isolator intake (FLOWer)isothermal wall,TWall = 300K, SA turbulencemodel, (M∞= 7.0, Rel = 5.689 · 106 [1/m],T∞=222 K)

ence of the third dimension. The sidewall cre-ates a boundary layer and a shock. The bound-ary layer grows and the shock plain interacts withthese of the ramps. This reduces the Mach num-ber near the wall, dramatically as expected in thecorner between the side walls and the ramps. Up-

x [m]

y[m

]

0 0.1 0.2 0.3 0.4 0.50

0.1

0.2 0.2 0.6 1 1.4 1.8 2.2 2.6 3 3.4 3.8 4.2 4.6 5 5.4 5.8 6.2 6.6

leading edge bow shock

2nd ramp shock

cowl bow shockreflected cowl shock

Mach

separation bubble

Fig. 15 Mach contours for isolator intake(FLOWer) isothermal wall,TWall = 300K, SAturbulence model, rounded leading edges (M∞=7.0,Rel = 5.689·106 [1/m], T∞=222 K)

stream of the isolator inlet the area of small Machnumber and the size of the subsonic corner flowregion is so big that it leads to a great separa-tion bubble. Contrary to the 2D simulation withthe SA turbulence model, this separation blocksthe isolator. Comparison of the shock angels be-tween 2D and 3D show a difference, that meansthe angle of the first ramp shock in 3D is 0.2◦

and of the second ramp shock 1.3◦ steeper thanin the 2D result. This leads to a decrease of theMach number at the isolator inlet, leading to adecreased velocity after the expansion and, there-fore, to a greater separation. It can be assertedthat the sidewall shock bends the ramp shocks up-stream. Future studies will show if this is the casewhen using the other turbulence models.

Finally, it can be asserted that geometrychanges have to be introduced. The separationbubble in the isolator inlet is too big and must bereduced. Furthermore, the point where the 2ndramp shock hits the bow shock has to be moveddownstream, that means, this convergence pointmust stand above the cowl, so that the influenceon the isolator flow is as small as possible. Toachieve that it might be necessary to extend theisolator height, move the cowl lip downstream orchange the ramp angles.

7 Summary

Results of 2D and first 3D flow computations arebe presented. Two different intake geometrieshave been studied numerically, one with sharp

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leading edges and the other one with roundedleading edges. It was found, that there are greatdifferences in the results created by different tur-bulence models. These differences are much big-ger than those produced by the change of the ge-ometry from sharp to rounded leading edges. Itwas also asserted that the SA, SST andSSG−ωmodel qualitatively yielded similar results, wherethe LEA and originalk− ω turbulence modelfrom Wilcox showed much greater separationand thicker boundary layers. The LLR modelproduced a result somewhere in between. There-fore these results have to be compared with ex-perimental ones in future when available. So far,one result for a 3D computation was presented. Itwas found out, that the side wall shock bends theramp shocks upstream resulting in reduced veloc-ity, followed by a greater separation bubble thatblocks the isolator inlet.

Further numerical investigation is of greatimportance, because one aim of the research isto garantee the functioning of the hypersonicScramjet intake. The future experimentals withinthe frame of GRK1095 will allow to check andvalidate the computational predictions, so that theconfidence on these numerical predictions of thefunctioning Scramjet can be improved.

References

[1] Anderson, J.,Hypersonic and High Tempera-ture Gas Dynamics, MacGraw–Hill, 1989.

[2] Hien, T. L. and Kim, S. C., “Calculation ofScramjet Inlet with Thick Boundary-Layer In-gestion,” Journal of Propulsion and Power,Vol. 10, No. 5, 1994, pp. 625–630.

[3] Bourdeau, C., Blaize, M., and Knight, D., “Per-formance Analysis for High Speed Missile In-lets,” Journal of Propulsion and Power, Vol. 16,No. 6, 2000, pp. 1125–1131.

[4] Hasegawa, S., Tani, K., and Sato, S., “Aerody-namic Alanysis of Scramjet Engines under theFlight Condition of Mach 6,”11th AIAA/AAAFINTERNATIONAL CONFERENCE, , No. 2002-5128, 2002.

[5] Coratekin, T. A., van Keuk, J., and Ballmann, J.,“Preliminary Investigations in 2D and 3D Ram-

jet Inlet Design,” AIAA Paper 99–2667, June1999.

[6] Reinartz, B. U., Ballmann, J., Herrmann, C.,and Koschel, W., “Aerodynamic PerformanceAnalysis of a Hypersonic Inlet Isolator usingComputation and Experiment,”AIAA Journal ofPropulsion and Power, Vol. 19, No. 5, 2003,pp. 868–875.

[7] Wilcox, D. C., “Turbulence Energy EquationModels,”Turbulence Modeling for CFD, Vol. 1,DCW Industries, Inc., La Canada, CA, 2nd ed.,1994, pp. 73–170.

[8] Spalart, P. R. and Allmaras, S. R., “A One-Equation Turbulence Model for AerodynamicFlows,” AIAA Paper 92–0439, January 1992.

[9] Menter, F. R., “Two-Equation Eddy-ViscosityTurbulence Models for Engineering Applica-tions,” AIAA Journal, Vol. 32, No. 8, Aug. 1994,pp. 1598–1605.

[10] Bardina, J. E., Huang, P. G., and Coakley, T. J.,“Turbulence Modeling Validation, Testing, andDevelopment,” NASA Technical Memorandum110446, April 1997.

[11] Kroll, N., Rossow, C.-C., Becker, K., andThiele, F., “The MEGAFLOW Project,”Aerospace Science and Technology, Vol. 4,No. 4, 2000, pp. 223–237.

[12] Radespiel, R., Rossow, C., and Swanson, R.,“Efficient Cell-Vertex Multigrid Scheme for theThree-Dimensional Navier-Stokes Equations,”AIAA Journal, Vol. 28, No. 8, 1990, pp. 1464–1472.

[13] Bramkamp, F. D., Lamby, P., and Müller, S.,“An adaptive multiscale finite volume solver forunsteady and steady flow computations,”Jour-nal of Computational Physics, Vol. 197, 2004,pp. 460–490.

[14] Rung, T., Statistische Turbulenzmodel-lierung, Herman-Föttinger-Institut für Strö-mungsmechanik, Umdruck zur Vorlesung,2004.

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