(c)2002 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s)' Sponsoring Organization.

AIAA 2002-0438

CFD VALIDATION FOR BASE FLOWS WITH AND WITHOUT PLUME INTERACTIO N

P.O. Bakker* and WJ. Bannink1

University of Technology Delft, The Netherlands

P. Servel* and Ph. Reijasse§

Onera, Meudon, France

AbstractIn the framework of the NATO-RTO-AVT-WG10 entitled "Technologies for Propelled Hypersonic Flight",base flow test cases have been selected for code validation. Concerning the first dataset devoted to base flow-plume interaction at moderate nozzle pressure ratios, the influence of numerical discretization technique andturbulence models are discussed. The multi-dimensional upwind (MDU) discretization technique onunstructured grids applied to the axisymmetric base flow model with an underexpanded jet predicts basepressures that are consistently lower than the experimental values. If no proper conclusions can be drawn fromthis comparison because of the 3-D model support influence in the experiments, conclusions in relation to theturbulence models and to the axisymmetric results of the other code, the finite-volume technique on multi-block grids (LORE), may be of interest. Concerning the second dataset of a boattailed afterbody flowfield withplume-induced-separation, RANS calculations with transport equations turbulence models reproduce thegeneral organization of the flow, in particular the free separation phenomenon with a X-shock system inducedby the jet/external flow interaction. The afterbody wall-pressure profile on the cylindrical part and during theexpansion wave is well restituted. But it seems difficult to predict accurately the afterbody wall-pressure profileon the boat-tail because turbulence models have difficulties to reproduce positive pressure gradients.Calculations do not reveal the existence of a singular reflection on the symmetry axis for the recompressionbarrel shock of the propulsive jet, with a Mach disc, as it has been experimentally observed.

NomenclatureM^ free stream Mach numberMj jet Mach numberN ratio of chamber pressure to free stream static

pressureTt free stream stagnation temperaturept free stream stagnation pressureptj jet stagnation pressurep^ free stream static pressurepe nozzle exit pressurepb base pressurepbm average base pressureU^ free stream velocity

1. IntroductionFor the development of the next generation of reusablelaunchers and re-entry vehicles, one of the criticalareas is concerned with the proper modelling of baseflow. The low pressures acting on the base region ofbodies in supersonic and hypersonic flight cause asignificant drag. Due to flow separation from the

* Professorf Doctor* Research scientist§ Research scientist

Copyright © by the American Institute of Aeronauticsand Astronautics, Inc. All rights reserved.

afterbody followed by mixing with the hot exhaustplume from the nozzle and the reattaching flow at thebase thereafter also the heat loading may beconsiderable. Furthermore, asymmetric effects andunsteady flow phenomena can cause severe side loadson a launch vehicle. Important aspects influencing thebase flow physics are e.g. the presence of externalflow and the conditions of the exhausting jet(underexpanded or overexpanded), boattailing of theafterbody, base bleed.Two different experimental data sets meeting theobjectives set by the RTO Working Group WG 10 areidentified covering a number of the conditionsmentioned and (partially) their interactions. DatasetNo. 1 (TU Delft) is concerned with the supersonicflow along a cylindrical afterbody with a singleoperating exhaust jet. Dataset No. 2 (ONERA)considers the flow along an axisymmetric boattailedafterbody also with exhaust jet. Dataset No. 1 dealswith overexpanded, accommodated andunderexpanded jet flows and Dataset No.2 only withunderexpanded jets. Comparing them the influence ofboattailing in presence of an exhaust jet may bestudied for underexpanding cases, which is of specialinterest at higher altitudes.

2. Dataset No. 1: Base Flow-Plume Interaction inSupersonic External Flow

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2.1 Description of Model ConfigurationThe selected geometry is an axisymmetric bluntedcone cylinder. The conical forebody and thecylindrical afterbody are about the same length. Themodel is supported at the lower side of the aft part andhas a free base, see Fig. 1. From the center of the basea nozzle protrudes, its outer shape is a circularcylinder. The inner nozzle is conical with a divergenceof 15 deg. The inner exit diameter of the nozzle is 16.4mm, being about 1/3 of the model base diameter. Thenominal jet Mach number was chosen to be 4. Theconical forebody has a semi-apex angle of 11 deg. anda nose radius of 7.5 mm. The total length of the modelis 186.81 mm and the length of the cylindricalafterbody is 90 mm.Along the afterbody 10 pressure taps are provided. Inthe upperpart of the base 17 taps are foreseen. Toincrease the measuring resolution and because oflimitations in manufacturing the taps at the base areprovided in three rays. The location of the taps isshown in Fig. 2.The model is positioned at zero incidence in a uniformsupersonic free stream.The test set-up enables the investigation of the flowfield along the model with a single operating exhaustjet. In the interaction region between jet and externalflow behind the base a turbulent mixing layer, arecirculating region and a shock system (plume shock,barrel shock, Mach disc) are formed.

2.2 Description of ExperimentIn order to ascertain that the boundary layerapproaching the base of the body is turbulent it istripped at 38 mm from the nose of the model.The measurements are made in thetransonic/supersonic wind tunnel TST27, test section27 cm x 28 cm, of the Aerospace Department of theDelft University ot Technology. Tests were performedat free stream Mach numbers of 1.96 and 2.98 and atstagnation pressures pt = 2.06 bar and pt = 5.75 bar,respectively, with an accuracy of 1 %. The stagnationtemperature Tt = 285 ± 2 K. The jet stagnationpressures ranged from ptj = 3.5 bar to 100 bar, with anaccuracy of 1.5 %. The Mach number at the nozzleexit was measured to be Mj = 3.96 ± 0.02.The Reynolds numbers based on the model length are5.MO.6 and 8.7-10.6 at free stream Mach numbers of1.96 and 2.98, respectively.The distinction between underexpanded andoverexpanded jets cannot be given by the ratio of thejet exit pressure pe to the free stream static pressure p^.This is because p^ cannot be considered as the ambientpressure near the nozzle exit. Therefore, as a measurefor the status of the exhausting jet, the ratio of pe tothe mean base pressure pbm has been taken. The basepressure is close to ambient pressure. As will be seenthe ratio Pe/Pbm yields a good appreciation for the jetstatus: pe < Pbm indicates overexpansion and pe > Pbmunderexpansion.

For a complete report of the experiments one isreferred to Refs. 1, 2 and 3. In the present article onlythose cases will be considered that are of interest forthe validation of CFD capacity. In Table 1 a selectedtest matrix is given.

No

123456

M..

2.982.981.961.961.961.96

P.(bar)0.16130.16180.28300.28300.28300.2830

Ptj(bar)31.3no jetno jet3.6512.4549.2

N=Ptj/P-194.1........12.944.0173.9

Pbm/P.

0.2440.3260.5130.4390.2990.363

Pe/P..

1.348............0.0900.3061.208

Pe/Pb

5.518............0.2041.0223.332

Table 1 : Test matrix for validated cases, Mj = 3.96

The dynamic behaviour of the base flow has beentested in two series of measurements at free streamMach numbers of M.. = 1.96 and 2.98, each series atseveral jet stagnation pressures. During these tests thebase pressures were measured with high sensitivepiezo resistive transducers. The pressure signalsshowed a noise rubble of a few percent of the meanstatic base pressure with a frequency of 10 kHz or less.

2.3 Computational Methods

The results of two CFD codes will be discussed. Thefirst code is based on a multi-dimensional upwindmethod on unstructured grids (Refs. 4 and 5). Thecode has been applied on the flow around the modelwithout support, thus on an axisymmetric flowproblem. Naturally, this will involve disagreementwith the experimental results. Four turbulence modelsare considered (see section 2.3.1).The second code (Ref. 5) is based on a cell-centeredfinite-volume method using the flux-difference-splitting scheme of Van Leer. Structured multiblockgrids are employed and two turbulence models areapplied. In this simulation the flow around the 3-Dconfiguration including the support effect, as well asan axisymmetric configuration has been computed.

2.3.1 Multi-Dimensional Upwind method (MDU)The MDU method is decribed in great detail in Vander Weide's Ph.D thesis, Ref. 4 and its references. It isa well established method for scalar convectionproblems for which it leads to improved schemes withcompact stencils. The method has been generalized byVan der Weide to non-commuting hyperbolic systemsand it is constructed such that for any decoupledequation of the system it automatically reduces to thescalar distribution scheme on which it is based. Theinviscid part of the Navier-Stokes equations has beendiscretized by a nonlinear monotone, second-order,multi-dimensional upwind scheme, the PSI-scheme.The Petrov-Galerkin finite element interpretation ofthe scheme allows a straightforward discretization ofthe viscous terms. The discretization of these terms onlinear elements through integration by parts condenses

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to the Galerkin method. The time integrator is thebackward Euler method.The governing equations for the turbulence models aresolved in a fully coupled manner on the explicit level,but its off-diagonal entries are ignored in the Jacobianmatrix of the backward Euler method. This techniqueappears to be more stable than the fully coupledapproach. The convection terms of the turbulenttransport equations are discretized with the second-order PSI-scheme.The turbulence models used are the following one-equation or two-equation models:• Spalart-Allmaras: an empirical one-equation

model;• k-co: a two equation model;• BSL: the baseline two-equation model, which is a

blending of the k-e and k-co models;• SST: the two-equation shear stress transport model.

The computations with the MDU method have beenperformed for Case No.l of Table 1. A hybridstructured/unstructured approach (Ref. 7) is used togenerate a coarse and a fine grid. The coarse version(Fig. 3) has 15,505 nodes of which approximately12,000 are located in the structured part near the walls.The unstructured part is much too coarse to predict thebase flow accurately. Therefore, a very fine gridconsisting of 119,519 nodes is generated in the baseregion, see Fig. 4. To investigate the solution in thisregion in even more detail it has been computedseparately on a 925 x 481 triangulated structured grid,which is on the average 5 times finer in each co-ordinate direction than that of Fig. 4.

2.3.2 Finite-Volume Flux-Difference method (LORE)The LORE computational method (Ref. 6) is a fullNavier-Stokes solver for high temperature flowsincluding chemical and thermal nonequilibriumeffects. The governing equations are discretized basedon a cell-centered finite volume method. It is providedwith second-order accurate upwind discretizationsaccording to the flux-difference splitting scheme ofVan Leer. Higher order spatial discretizations areobtained with Monotone Upstream Schemes forConservation Laws (MUSCL), an interpolationtechnique with a Van Albada limiter to suppressspurious oscillations at discontinuities. Structuredmulti-block grids are used to compute flows aroundcomplex geometries.Two turbulence models of the two equation type areapplied in the present application of the LORE code(see also Ref. 8):• k-co;• SST, of which two versions are used: SST-0 and

SST-1, without and with compressibilitycorrection, respectively.

The computations have been made for Cases No's 2 - 6of Table 1. Two multi-blocked structured grids aregenerated: one grid is axisymmetric containing onlythe model and the other grid is three-dimensional,

containing model and its wind tunnel support. In bothcases a coarse and a fine grid is used. The fine grid isobtained by a refinement of the coarse grid by a factor2 in the co-ordinate directions. The coarseaxisymmetric grid consists of a total of 17,404 cellsand the fine grid 4 times as much, 69,616 cells. In the3-D case these numbers are 353,026 and 2,824,208,respectively. Figs. 5 and 6 show the coarse grids forthe 3-D configuration. The wind tunnel wall isrepresented as circular tube with a diameter of 270mm, being the height of the actual test section. Theoutflow boundary is chosen at 400 mm behind themodel nose, there the flow is supersonic andconsequently no boundary conditions need to beimposed.

2.4 Results

2.4.1 Results of the MDU methodComputational and experimental results for Case No.l(axisymmetric flow) of Table 1 are shown in Figs. 7and 8. Fig. 7 represents the pressure distribution onthe cylindrical part of the model; it may be observedthat the boundary layer thickness has some influencenear the edge of the base (compare the turbulent andlaminar solutions). The pressure distribution along thispart is mainly determined by the inviscid solutions(Ref. 5). All results are nearly identical and fit theexperimental data very well, apparently no influenceof the model support is felt there.In Fig. 8 the computed pressure distributions at thebase are compared with the experimental values. Thelaminar distribution may only serve as illustration,since it is not realistic in the practice of thisapplication. In particular Fig. 8c shows this. On thetriangulated structured grid the laminar solution ishighly unsteady. Numerically Von Karman vortexsheets are observed. Due to numerical difusion thelaminar solutions on the coarse and fine grid (Fig. 8a,8b) are steady (see Ref. 4).All solutions on the coarse grid are not grid converged,as shows the sequence in Fig. 8. The solution obtainedwith the Spalart-Allmaras model on the fine grid isidentical to that computed on the triangulatedstructured grid, compare Figs. 8b and 8c.Consequently, this solution is grid converged.However, it is clear that the solutions of the two-equation models on the fine grid are not gridconverged, since the base pressures on the triangulatedstructured grid shown in Fig. 8c are 25 to 50 % higher.All turbulence models predict the base pressure toolow compared with the experimental values. Thisobservation is even more cumbersome if one realizesthat the influence of the model support is to decreasethe base pressure, see Ref. 9.In case of the Spalart-Allmaras turbulence model muchof the difference may be explained by the deficiency ofthe turbulence model itself, this model shows gridconvergence whereas for the two-equation models thesolutions cannot be assumed to be grid converged.

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However, also for the latter models the situation is notevident either. It might be possible that on finer gridsthe base pressure increases further. Furthermore, it isnot at all clear what is the effect of imposing the entiresolution (interpolated from the fine grid solution) onthe flow boundaries of the triangulated structured gridin the base region. Ref. 4 speaks of strong changes ofthe solution in the interaction region so that a wrongsolution is imposed there.On the triangulated structured grid, Fig. 8c, the k-comodel predicts a significantly higher base pressurethan the BSL and SST models, whose formulations arealmost identical to the k-e model in this part of theflow field.The correct prediction of the base flow characteristicsrequires extremely fine grids, in particular for the two-equation models. As the refinement of the gridincreases the relative difference between the resultsincreases also, although they remain quite close toeach other, see Fig. 8b. The result obtained with k-coon a very fine structured grid (Fig. 8c) is stillincreasing. It is believed in Ref. 4 that the base flowcharacteristics cannot be predicted accurately by eddy-viscosity turbulence models. Apparently this is not thecase here as long as sufficiently fine grids are used.Ref. 4 states such a conclusion might be a coincidenceand that more cases should be computed for a decisiveconclusion.

2.4.2 Results of LORE

Case No. 2: M_ = 2.98, no exhaust jetThe influence of grid (coarse/fine) and of turbulencemodels (k-co, SST-0, SST-1) will be discussed for theaxisymmetric case with plume off.The axisymmetric flow topologies in the base regionare shown in Fig.9. Like the MDU method the laminarresults are included as a comparison. The differentturbulence models show basically similar topologies.The number of vortices and their location is almost thesame. There is influence on the size of the vortex nearthe base, this will of course have its effect on the basepressure distribution. The grid size does not seem togive great topological differences with the exceptionof the SST-0 model. The solutions are shown to begrid independent in Ref. 10, where also theconvergence of the solutions is proved.Fig. 10 contains the base flow topologies of the 3-Dconfiguration (model with support) computed on thecoarse mesh (353,026) cells. The number of vorticesobtained with the various turbulence models isdifferent, i.e. compare the upper base region for k-coand SST and the lower region for all turbulencemodels.The surface shear stress computed with the SST-1model is compared to the experimental oil flowvisualization in Fig. 11. The agreement ie surprisinglygood, not only on the model itself but also on thesupport near the junction with the model where theseparation lines are very well simulated.

Finally, for Case 2, the radially distributed basepressures are presented in Fig. 12. Disregarding thelaminar distribution which is not well understood, onemay conclude that the discrepancy between numericalresults of the different turbulence models is not verylarge, particularly not in the 3-D case. In addition, itmay be noticed that the presence of the supportapparently decreases the base pressure. This is inagreement with the experimental results of Ref. 9where the influence of aft fin locations were studied onthe base pressures of axisymmetric models insupersonic flow. The 3-D simulations made with theSST-1 model (with compressibility correction) areclosest to the experimental data. SST-1 together withthe fine mesh (2) shows that the pressure levelcompared to the SST-0 solution is maintained but thatthe resolution at the edge of the base is improved.

Cases No. 3 to 6: M,. = 1.96, with jet exhaustSince the results in the plume-off case using the SST-1turbulence model showed the best agreement with theexperimental data the Cases No's 3 to 6 are computedwith SST-1 only. The axisymmetric computations areperformed on two meshes to show meshindependence. Because of this and the CPU timeconsuming character of the 3-D simulations only thecoarse mesh is used for the configuration with support.Fig. 13 illustrates the difference in base flow topology.The plume-off case may be compared to that of CaseNo. 2 at M^ =2.98 shown in Fig. 10, which is alsocalculated with SST-1. The number and location ofvortices is different; due to the higher free streamMach number the more intense shear layer emanatingfrom the edge of the base appears to have its effect onthe base flow topology.The radial base pressure distribution of all flow casesis presented in Fig. 14. The trend for the plume-offcase is similar to that at M^ = 2.98: as may be expectedthe axisymmetric pressures do not agree with theexperimental results and the 3-D simulations are closeto the measured values.The 3-D overexpanded and accommodated jetcomputational data are quite satisfactory, although theconstant character of the distributions disappears athigher jet pressures. The maxima in the pressuredistributions may indicate a reattaching flow at thebase. However, there is no strong evidence in thestreamline patterns of Fig. 13. All cases with jetexhaust show basically similar flow topologies.The nice agreement with experiments seems todecrease for higher pressure ratios, since the pureunderexpanded jet at N = 173.9 causes all computedbase pressures to give an underestimation of about 25% to the measurements.An explanation for the discrepancy may be found inthe grid size. As can be observed in Fig. 6 the shearlayer region between exhaust and ambient flow doesnot have a very dense grid point distribution.Considering Fig. 14 it appears that the differencebetween the axisymmetric results on the coarse and the

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fine grid increases with increasing chamber pressure.The fine mesh contains more grid points andtherefore a better capturing of the gradients isachieved, leading to a better simulation of the baseflow. The coarse grid shown in Fig. 6 may be suited tocompute the plume-off and overexpanded casesbecause the gradients in the shear layer are not solarge. So, again, as in the application of the MDUmethod, the conclusion may be that finer grids shouldbe used to predict the base flow more accurately.

2.5 ConclusionsThe multi-dimensional upwind (MDU) discretizationtechnique on unstructured grids applied to theaxisymmetric base flow model with an underexpandedjet predicts base pressures that are consistently lowerthan the experimental values. Naturally, no properconclusions can be drawn from this comparisonbecause of the 3-D model support influence in theexperiments. However, conclusions in relation to theturbulence models and to the axisymmetric results ofthe other code, the finite-volume technique on multi-block grids (LORE), may be of interest.

The conclusions are summarized in the following.• The MDU code needs extemely fine meshes to

obtain a grid converged solution.• With the exception of the one-equation Spalart-

Allmaras model the other turbulence modelsapplied (k-co, SST, BSL) show almost nodifference in results on the coarse and fine grids.

• Only on the very fine triangulated structured gridin the base region the k-co model predicts asignificantly higher base pressure than the BSL andSST models.

• The Spalart-Allmaras model is unable to predictthe physical phenomena in the base regioncorrectly.

• The computations made with LORE have shownthat, in agreement with experiments, the presenceof a model support causes a decrease of the basepressure.

• In the plume-off case LORE does not show asignificant effect of grid size on the results. Gridindependence exists also in the axisymmetricplume-on cases, where the 3-D computations areonly made on a coarse grid.

• From the turbulence models used (k-co, SST-0,SST-1) the LORE 3-D results show the best basepressure prediction for the SST-1 model (withcompressibility correction).

• Very good agreement with the experimental data isobtained for the plume-off, overexpanded and jet-accommodated flow cases. The results for theunderexpanded jet are underpredicted.

• Qualitative comparison between the axisymmetricresults of MDU and LORE reveals that MDUunderpredicts the base pressures considerably withrespect to LORE.

• Among each other both methods show largedifferences in base flow topologies.

3. Dataset No. 2: Plume-Induced Separation on aBoattailed Afterbody in Supersonic External Flow

3.1 Model Configuration and Stagnation ConditionsTests have been performed in the continuousatmospheric research wind tunnel S8Ch of Onera atChalais-Meudon Center. The wind tunnel is equippedwith two planar half-nozzles, producing a uniformMach 2 flow in a 120mm-side square test section. Thestagnation conditions of the external flow are : pt =0.975bar for the pressure, and Tt = 298K for thetemperature. The axisymmetric model is mounted atthe extremity of a centerbody fixed in the settlingchamber. The afterbody geometry (Fig. 15) consists ina 9.5deg.-conical boattail with a length of 31.5mm.The external diameter of the model is D = 30mm. Theexternal Mach number of the unperturbated incomingflow is MM = 1.94. The length of the centerbody fromthe wind tunnel throat to the model boattail is L =212.5mm. The Reynolds number based on the length Lis 2.65 106. The model is equipped with a lOdeg.-conical nozzle fed by dessicated air. The stagnationtemperature of the jet is Ttj = 298K. The exit diameterof the model nozzle is 14.9mm and the exit Machnumber on the centerline is Mj = 1.75. The stagnationpressure of the jet is ptj = 7.75bar.

3.2 The Onera Laser Doppler Velocimetry (LDV)BenchThe LDV system, which was operated in the forwardscatter mode, has been used in its two-componentversion. The light source is a 15W argon ion laseroperating at 8W for all lines. The crossing of dichroicplates allows selection of the green and blue lines,their wavelengths being 0.5145 and 0.4880nm,respectively. Each beam is divided when it crossesbeam splitters. The two resulting monochromaticbeams are then focused in order to create aninterference fringe pattern. The diameter of the probevolume, constituted by the two fringe systems, is200|im and the focal distance is 1m. The blue andgreen fringe spacings are 13.165 and 12.684jim,respectively. Frequency shifting at 15MHz is used todiscriminate the direction of the measured velocitycomponent. The external stream is seeded withsprayed olive oil by the means of a movable tubeplaced in the settling chamber of the wind tunnel. Theseeding of the jet is ensured by submicron (0.5jumdiameter) magnesium oxide (MgO) particles injectedfar upstream of the model nozzle throat.

3.3 Computational Methods

3.3.1 Presentation oftheNASCA codeThe numerical simulations presented below have beenperformed with an axisymmetric version of theReynolds Averaged Navier-Stokes (RANS) NASCA

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research code (Ref. 11). In this code, we solve the fullsystem of Navier-Stokes equations for perfect gas bymeans of a finite volume technique in which the time-averaged Navier-Stokes equations, in theirconservative form, are integrated on each cellsurrounding each calculation point with a spatiallysecond-order-accurate method.This is an implicit first-order-accurate in time codeusing an ADI-type (Alternating Direction Implicit)factorisation for each direction in space whileinverting the matrix of the system. The numericalprocedure described in Ref. 11 for the scheme of theNASCA code uses a classical central-differenceapproximation for the diffusion terms and a high-resolution TVD (Total Variation Diminishing) shock-capturing method for the inviscid part of the Navier-Stokes equations (i.e. the non-linear Euler equations).Thus, we evaluate the convective fluxes at theinterfaces between the integration cells in an upwindmanner for the Steger and Warming flux-vectorsplitting (based on the sign of the eigenvalues of theJacobian matrix of the convective operator). Then, thespatially first-order-accurate implicit part of theconvective terms uses an approximate Riemann solverdue to Roe while the spatially second-order-accurateexplicit part is an extension of the Osher andChakravarthy scheme to a non-uniform and non-orthogonal grid.In order to solve the fully turbulent Navier-Stokesequations, the eddy viscosity related to the turbulentshear and normal stresses by the Boussinesqhypothesis (analogy of the Reynolds tensor to theviscous tensor) has to be calculated. For this purpose,turbulence models of two types are proposed (Ref.12):• the algebraic Baldwin-Lomax turbulence model,based on the mixing-length theory,• the two transport equations k-£ turbulence model dueto Chien.In this last case, in order to calculate the eddyviscosity, the transport equations for the turbulentkinetic energy k and its dissipation rate 8 are solvedthanks to the same method as mentioned above for themean flow variables (see Ref. 13 for more details).

3.3.2 Grids, boundary conditions and computationalprocedureThe computational grid for the following numericalcalculations contains 265 points in the X-direction and190 points in the Z-direction, with mesh refinements indirections perpendicular to the afterbody and basewalls determined after a careful analysis of spatialconvergence, especially for the transverse griddistribution on the base and on the boat-tail (Ref. 12).The upwind and the upper boundaries of thecalculation grid are considered as supersonic inletswhere all the variables of the flow are imposed,especially the boundary layers of the external flow atX / D = -2, far upstream from the base which is locatedat X / D = 0, and the internal propulsive jet at the

nozzle lip, both evaluated from the experiments (Ref.12). The downstream boundary constitutes asupersonic outlet where all the variables areextrapolated from the interior of the mesh. The lowerboundary is treated with an axial symmetry conditionwhile the afterbody and the base walls, where k = e =0, have adiabatic wall conditions ( u = w = 3P/8N =3T/ 3N = 0).A steady solution was reached through the solution ofthe pseudo-unstationary Navier-Stokes equations andthe convergence in time is obtained in 8000 iterationsfor this case of propelled afterbody supersonic flow.This convergence has needed about 3 hours on CrayYMP using the Baldwin-Lomax turbulence model and5 hours using the Chien k-e model.

3.4 ResultsThe Mach number levels obtained from the results ofthe Navier-Stokes calculations with the NASCA codewhen using the Baldwin-Lomax turbulence model areshown in Fig. 16, where the general organisation of theflow around the propelled boat-tailed afterbody can beseen and is equivalent to the flow organisationobtained with the Chien k-£ model. Upstream of theboat-tail, the external supersonic flow is quite uniformalong the cylindrical part of the afterbody, except theboundary layer near the wall.Then, the angle of the conical boat-tail induces adeflection of the external flow and the point at thebeginning of the boat-tail (X / D = -1) constitutes theorigin of a centred expansion wave, visible on Fig. 16.Correlatively, the external wall-pressure suddenlydecreases, which favours the jet expansion ratio. Thisboat-tail angle induces such a high nozzle expansionratio so that the underexpanded internal jet expandslargely at the nozzle exit. There results an obstacleeffect for the external stream that induces a deflectionof this last flow upon the conical part of the afterbody,accompanied by a strong shock-wave and a separationof the afterbody boundary layer. A second obliqueshock issuing from the confluence region between thethe external flow and the propulsive jet is joining theformer separation shock. Thus, this plume/afterbodyflowfield is characterized by a X-shock systemconstituted by the separation shock and the confluence-or trailing- shock. In fact, we can notice here a freeseparation occurring on the afterbody boat-tail inducedby the pluming of the jet.For the jet, the flow well separates at the nozzle lip,undergoing a centred expansion wave, as we canobserve in Fig. 16. In this case of base flow withplume-induced separation, the separated zone alsocalled dead-air region, consists in a recirculatingbubble enveloping the base and the ending part of theboat-tail. This recirculation zone is in fact barelyvisible in Fig. 16 due to its small size.The trailing shock of the jet, named barrel shockbecause of its shape, reflects downstream in a regularmanner on the symmetry axis. Downstream from theconfluence region between the two co-flowing

7 - 6 RTO-TR-AVT-007-V3

(c)2002 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s)' Sponsoring Organization.

streams, the external flow and the propulsive jet arecontiguous on each side of a common boundary alongwhich a viscous wake develops, a shear layer alsoobservable in Fig. 16.Fig. 17 shows the repartitions of static pressure alongthe walls of the cylindrical and conical parts of theafterbody, upstream from the base which is at X / D =0. The results of the calculations executed with thealgebraic Baldwin-Lomax turbulence model (in solidline) and with the two-transport-equations Chien k-emodel (in dashed line) are drawn in comparison to theexperimental pressure values, (see symbols in Fig. 17).The experimental base pressure are given thanks tofour pressure holes distributed in each quadrant.The simulated profiles seem in good agreement withthe experimental values on the cylindrical part of theafterbody and for the brutal expansion at the beginningof the boat-tail. We note that the base pressure value,given in Fig. 17 at X / D = 0, is well predicted, but thecalculations, with both turbulence models andparticularly the k-8 one, do not fit satisfactorily theafterbody wall-pressure profile through the interaction.Calculations anticipate the beginning of thecompression on the middle of the boat-tail, and givemore gentle evolution of pressure profiles with lesssteep pressure slopes. Thus, the numerical simulationsover-predict the abscissa of the separation point (X / D= -0.24 and -0.35, for respectively the Chien k-8 andBaldwin-Lomax turbulence models) compared to theexperimental value (X / D = -0.4). The simplest model(Baldwin-Lomax) presents curiously the smallest over-prediction but is better adapted for separated flowsthan the Chien model for which, moreover, theturbulent quantities have not been precisely initializednear the wall from the experimental values.The radial distribution of field properties are shown inthe three last figures which give the mean axialvelocity profiles (Fig. 18), the mean radial velocityprofiles (Fig. 19) and the turbulent shear stress profiles(Fig. 20). The first four stations of the three figures(the three profiles upstream from the base : X / D = -1,-0.33 and -0.13, and the profile at the base : X / D = 0)repeat what has been noticed for the static wallpressure : if the calculated profiles seem in agreementwith the experimental values away from the wall,calculations delay the apparition of the separated zone,especially with the Chien k-£ turbulence model.In the dead-air region just downstream from the base,at X / D = 0.13, the discrepancies of the turbulencemodels are visible in the size of the recirculation zoneand in the levels of mean and turbulent quantities(Figs. 18-20). Firstly, this is a consequence of whathappens upwind in the external flow around theafterbody, i.e. an underprediction of the size of theseparated region due to the X-choc. Secondly, there isa lack of information on the nozzle boundary layer,which induces an uncertainty in the initialization of theinternal flow. The last five stations of Fig. 18-20 showa better agreement between experimentalmeasurements and numerical simulations, except for

the prediction of the position of the viscous shear layerseparating the external flow and the propulsive jet.The jump in the profiles of the three quantities (u, wand u'w) is situated in the calculation results at a loweraltitude than in the experiments. It is correlated to thefact that the results of numerical simulationsperformed with the Navier-Stokes NASCA code havenever predicted the Mach disk seen in theexperimental visualisations (Ref. 12). This can beenobserved in the last picture of Fig. 18 where theexperimental profile of the axial velocity u at X / D =3.5 presents a jump near Y / D - 0.32 which revealsthe subsonic area downstream from the Mach disk, thissingular reflection of the barrel shock not existing onthe results of the calculations (Figs. 16,18). The non-restitution of the Mach disk pattern could be explainedthrough a difference in the way of establishing the twoflows between experiments and calculations: while, inthe simulations, the two flows, the external one and theinternal jet, are calculated together, in the wind tunnel,the jet starts after having firstly established the mainflow.

3.5 ConclusionRANS calculations with transport equations turbulencemodels can give a good description of the afterbodyflowfield in plume-induced-separation configurations.In particular they reproduce the free separationphenomenon with a X-shock system induced by thejet/external flow interaction :• The general organization of the flow is wellreproduced, in particular the viscous boundary andshear layers, the expansion-compression waves and thesystem of shocks.• The afterbody wall-pressure profile on thecylindrical part and during the expansion wave is wellrestituted.But it seems difficult to predict accurately thefollowing flow field details of such a plume inducedseparation :• The afterbody wall-pressure profile on the boat-tailis not well predicted because turbulence models havedifficulties to reproduce positive pressure gradients.• Calculations do not reveal the existence of a singularreflection on the symmetry axis for the recompressionbarrel shock of the propulsive jet, with a Mach disc, asit has been experimentally observed.

References1. Bannink, W.J., Bakker, P.O. and Houtman, E.M.,

FESTIP Aerothermodynamics: ExperimentalInvestigation of Base Flow and Exhaust PlumeInteraction, Memorandum M-775, AerospaceEngineering, Delft University of Technology,1997.

2. Bannink, W.J., Houtman, E.M. and Bakker, P.O.,Base Flow/Underexpanded Exhaust PlumeInteraction in a Supersonic External Flow, AIAA8th Internat. Space Planes and Hypersonic Systems

RTO-TR-AVT-007-V3 7 - 7

(c)2002 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s)' Sponsoring Organization.

and Technology Conf., Norfolk VA, 1998, PaperAIAA-98-1598.

3. Bannink, W.J., Proot, M.MJ. and Donker Duyvis,F.J., Final Experimental Results FESTIPAerothermodynamics Phase 2 (1998-1999),CriticalPoint Analysis, ESA Contract 11.534/95/NL/FG,2000.

4. Van der Weide, E., Compressible Flow Simulationon Unstructured Grids Using Multi-DimensionalUpwind Schemes, Ph.D thesis, AerospaceEngineering, Delft University of Technology,1998.

5. Houtman, E.M., Van der Weide, E., Deconinck, H.and Bakker, P.O., Computational Analysis of BaseFlow/Jet Plume Interaction, Proc. 3d EuropeanSymp. on Aerothermodynamics for SpaceVehicles, ESA SP-426, pp 605-612, 1998.

6. Walpot, L.M.G.F., LORE: a 3-D Navier StokesSolver for High Temperature Chemical andThermal Nonequilibrium Gas Flows, Ph.D thesis inpreparation, Aerospace Engineering, DelftUniversity of Technology.

7. Carette, J.-C, Adaptive Unstructured MeshAlgorithms and SUPG Finite Element Method forHigh Reynolds Number Compressible Flows, Ph.Dthesis, Universite Libre de Bruxelles, 1997.

8. Ottens, H.B.A., Gerritsma, M.I. and Bannink, W.J.,Computational Study of Support Influence on BaseFlow of a Model in Supersonic Flow, AIAA 15thAIAA Computational Fluid Dynamics Conf.,Anaheim CA, 11-14 June 2001, Paper AIAA-2001-2638.

9. Heyser, A. Maurer, F. and Oberdorffer, E.,Experimental Investigation on the Effect of TailSurfaces and Angle of Attack on Base Pressure inSupersonic Flow, In: The Fluid Dynamic Aspectsof Ballistics, AGARD CP 10, 1966.

10. Ottens, H.B.A., FESTIP Aerothermodynamics: AComputational Study of Base Flow and ExhaustPlume Interaction, Master's thesis. AerospaceEngineering, Delft University of Technology,2000.

11.Benay R. and Servel P., Applications d'un codeNavier-Stokes au calcul d'ecoulements d'arriere-corps de missiles ou d'avion. La RechercheAerospatiale, 1995, n°6, pp. 405-426.

12.Benay R., Corbel B., Reijasse Ph. and Servel P.,Etude experimental et numerique d'un arriere-corps muni d'un retreint avec jet propulsiffortement eclate. ONERA, RTS n° 37/4361 AY(January 1997).

13.Benay R. and Servel P., Modelisation deI'ecoulement autour d'un arriere-corps d'avion decombat. ONERA RSF n° 24/4361 AY (September1993).

Figures

7 - 8 RTO-TR-AVT-007-V3

(c)2002 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s)' Sponsoring Organization.

Figl: Blunt cone-cylinder configuration showingexhaust nozzle and construction details.

© © <D © Fig 4: Unstructured fine grid in base region,119,519 nodes (MDU code).

FES75P1 SCCOO

Fig 5: Three-dimensional coarse grid (mesh 1),353,026 cells (LORE code).

Fig 2: Location of pressure taps along cylindricalafterbody and at the base.

Fig 3: Unstructured coarse grid, 15,505 nodes Fig 6: Three-dimensional coarse grid (mesh 1) near(MDU code). base (LORE code).

RTO-TR-AVT-007-V3 7 - 9

(c)2002 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s)' Sponsoring Organization.

0.40.100 0.140x<m)

0.160 0.180

Fig 7: Pressure distribution along cylindricalafterbody computed with MDU code.

0.4

0.3

fO.2

0.1

- Spalait-Allmaras• SST•BSL-k-(D-LaminarExperiment

y(m) 0.025

coarse grid

0.4 r

0.3

0.1

- Spatert-Almaras-SST-BSL-k-co-Laminar

Experiment

0.015 0.020y(m)

0.025

b) fine grid

0.4 r

0.1

- Spalart-AHmaras-8ST-BSL-k-o)-Laminar

Experiment

0.015 0.020y(m) QJ02S

c) very fine grid

Fig 8a, b, c: Radial base pressure distributioncomputed with MDU code.

107 - 10 RTO-TR-AVT-007-V3

(c)2002 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s)' Sponsoring Organization.

a) Laminar flow a) Laminar flow

b) k-co k-co

c) SST-0 SST-0

d) SST-1Fig 9 a,b,c,d: Axisymmetric base flow computed withLORE code on grids, mesh 1 = coarse mesh and mesh2 = fine mesh; M^ = 2.98, plume off.

d) SST-1Fig 10 a,b,c,d: Three-dimensional base flowtopologies computed with LORE code on coarse grid(mesh 1); M.. = 2.98, plume off.

RTO-TR-AVT-007-V3 7 - 11

(c)2002 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s)' Sponsoring Organization.

No plume

Fig 11: Comparison of computational surface shearstress lines on 3-D configuration (coarse grid, SST-1turb. mod.) with experimental oil streak lines; M^ =2.98, plume off.

N=12.9

0.5

0.4

0.3

$0.2

0.1

0

- - - - Turbulent k-(o mesh 1_._._._ Turbulent SST-0 mesh 1_. _.._ ._ Turbulent SST-1 mesh 1—— —— Turbulent SST-1 mesh 2

• Experimental data

\̂ ju? — -^rx'- "*>]

L ! , , . , ! , I L ll I , I 1 , • 1 I 1 , . 1 • 1 1

0.4 0.5 0.6 0.7 0.8 0.9 1r /R

Axisymmetric

0.5

0.4

0.3

10.2

0.1

0

- - - - Turbulent k-o> mesh 1 :_._._._ Turbulent SST-0 mesh 1-.._ ._._ Turbulent SST-1 mesh 1— — — - Turbulent SST-1 mesh 2

• Experimental data

| "1

0.4 0.5 0.6 0.7 0.8 0.9 1r /R3D

Fig 12: Radial base pressure distribution for plume-off case at M = 2.98.

d) N= 173.9Fig 13 a,b,c,d: Three-dimensional base flowtopologies for turbulence model SST-1 at different jetstagnation pressures and at M^ = 1.96.

127 - 12 RTO-TR-AVT-007-V3

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__A.

<7

0.6

O.b

0.4

0.3

0.2

0.1

' n^^g ' Exp.fte8.-96

- - - Axtsym. Mesh 1_._._. Axisym.M«h2

sji |: i

Ii-

0.4 0.5 0.6 0.7 0.8 0.9 1rlR

f0.7

0.6

0.5

0.4

0.3

0.2

0.1

_

- - - Axwym. Meeh 1_._._. Axi8ym.Meeh2

-

^—^^ "vir ̂ —— v 1

^ \

7

'-

0.4 0.5 0.6 0.7 0.8 0.9 1rtR

0.6 0.7 0.8 0.9rtR 0.6 0.7 0.8 0.9

rtR

Fig 14: Radial base pressure distribution forturbulence model SST-1 at different jet stagnationpressures and at M^ = 1.96.

X / D-1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3

Mach number levels.

experiments 0=0°experiments 4^90°

experiments 4>=270Batdwm-Lomax

X / D

Fig 17 : Boattailed afterboby wall pressure profiles.

31.5

dimensions in mm

Fig 15 : Boattailed afterbody geometry.

13RTO-TR-AVT-007-V3 7 - 13

(c)2002 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s)' Sponsoring Organization.

X/D = -1. X/D = -0.33 X/D = -0.13 X/D = 0. X/D = 0.13

1.2

1

0.8

0.6

0.4

0.2

Z / D

_ /

1.2

1

0.8

0.6

0.2

A

•1.2

1

0.8

0.6

0.4

0.2

A

^^L.

1.2

1

0.8

0.6

0.4

0.2

A

• j

\

1.2

1

0.8

0.6

0.4

0.2

— — — k-eCh»n• *xp«rim«nti

J

^-0.5 0 0.5 1 1.5 "0.5 0 0.5 1 1.5 3).5 0 0.5 1 1.5 3>.5 0 0.5 1 1.5 3).5 0 0.5 1 1.5

U/Uo

X / 0 = 0.27 X / 0 = 0.47 X/D = 1. X/D = 3. X / 0 = 3.5

1.2

1

0.8

0.6

0.4

0.2

Z / D

i.i1.2

1

0.8

0.6

0.4

0.2

A

/i i 1.2

1

0.8

0.6

0.4

0.2

A

}

|

; I1.2

1

0.8

0.6

0.4

0.2

A

Hijf\

; 1

1.2

1

0.8

0.6

0.4

0.2

A

•"

•

3).5 0 0.5 1 1.5 -W0.5 0 0.5 1 1.5 3).5 0 0.5 1 1.5 3).5 0 0.5 1 1.5 3).5 0 0.5 1 1.8u/U

Fig 18 : Axial velocity profiles.

X/D = -1. X/D = -0.33 X/D = -0.13 X/D = 0. X/D = 0.131.4

1.2

1

0.8

0.6

0.4

0.2

Z / D

I

1.2

1

0.8

0.6

0.4

0.2

A • L

1.2

1

0.8

0.6

0.4

0.2

\

1.2

1

0.8

0.6

0.4

0.2

A

ii1.2

1

0.8

0.6

0.4

0.2

A

im Bj Idwin-Lomax. — — — k Chten

• i p«riments

i' \

Y°-1 -0.5 0 0.5 1 "-1 -0.5 0 0.5 1 "-1 -0.5 0 0.5 1 w-1 -0.5 6 0.5 1 "-1 -0.5 0 0.5 1

w / U

X/D = 0.27 X / 0 = 0.47 X/D = 1. X / D = 3. X / 0 = 3.51.4

1.2

1

0.8

0.6

0.4

0.2

Z / D

i*

^***s^t

1.2

1

0.8

0.6

0.4

0.2

A

\}

1.2

1

0.8

0.6

0.4

0.2

A

i

•11.2

1

0.8

0.6

0.4

0.2

n A.

1.2

1

0.8

0.6

0.4

0.2

n A.,..°-1 -0.5 6 0.5 1 "1 -0.5 6 0.5 1 "-1 -0.5 0 0.5 1 "-1 -0.5 0 0.5 1 -1 -0.5 0 0.5 1

W / U

Fig 19 : Radial velocity profiles.

147 - 14 RTO-TR-AVT-007-V3

(c)2002 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s)' Sponsoring Organization.

X/D X / D = -0.33 X/D = -0.13 X/D = 0. X/D = 0.13

1.2

1

0.8

0.6

0.4

0.2

Z / D

02-0.01 0 0.01 0.

1.4

1.2

1

0.8

0.6

0.4

0.2

02 -0

r •"-

02-0.01 0 0.01 0.

1.4

1.2

1

0.8

0.6

0.4

0.2

02 -0

4.

02-0.01 0 0.01 0.

1.4

1.2

1

0.8

0.6

0.4

0.2

02 -0

- ><

02-0.01 0 0.01 0.

1.4

1.2

1

0.8

0.6

0.4

0.2

02 -0

- - - -

-

k-eChienexperiments

*.

•*'

06-0.03 0 0.03 0.(uW/L

X/D = 0.27 X / D = 0.47 X/D X/D = 3. X/D = 3.51.4

1.2

1

0.8

0.6

0.4

0.2

n

z

4

D

fc* • • •

. . . , ! . . . .

0.02 0.04

1.2

1

0.8

0.6

0.4

0.2

Jl

-

i

f

01 0 0.01 0.02 0.

1.2

1

0.8

0.6

0.4

0.2

003 -0.

<

.

r»"x

02-0.01 0 0.01 0.

1.2

1

0.8

0.6

0.4

0.2

02 -0

if

^

\

*•

02-0.01 0 0.01 0.

1.2

1

0.8

0.6

0.4

0.2

032 -0.

. t

\

:

02-0.01 0 0.01 0.(uW/L

Fig 20 : Turbulent shear stress profiles.

15RTO-TR-AVT-007-V3 7 - 15

CFD Validation for Base Flows With and Without Plume Interaction

7 - 16 RTO-TR-AVT-007-V3