Shock Wave / Boundary Layer Interactions in Hypersonic ... - CiteSeerX

2ND EUROPEAN CONFERENCE FOR AEROSPACE SCIENCES

Shock Wave / Boundary Layer Interactions in Hypersonic Intake Flows B. Reinartz⋆ , J. Ballmann⋆, L. Brown⋆⋆ , Ch. Fischer⋆⋆ and R. Boyce⋆⋆ ⋆ Lehr- und Forschungsgebiet für Mechanik, RWTH Aachen University Templergraben 64, 52062 Aachen, Germany ⋆⋆ School of Aerospace, Civil & Mechanical Engineering, University of New South Wales Northcott Drive, Canberra, ACT 2600, Australia

Abstract A combined experimental as well as computational analysis of hypersonic flows over a heated ramp configuration with a deflection angle of 15o has been initiated. This paper presents an overview of the ongoing work on the numerical simulation using two different, well validated Reynolds averaged Navier–Stokes solvers. The conducted mesh sensitivity analysis yields a strong dependance of the hypersonic flow solution on the resolution. Different surface temperatures are specified to investigate the impact on the shock / boundary layer interaction and on the size of the shock induced separation. Laminar and a combination of laminar and turbulent (transitional) computations as well as preliminary 3D simulations have been conducted and show the experimental shock-tunnel results to be influenced by transition and 3D spillage.

1. Introduction A hypersonic engine inlet consists of a series of exterior compression ramps and a subsequent interior isolator/diffuser assembly. Compression of the incoming flow is thereby achieved through oblique shock waves interacting with thick hypersonic boundary layers. High-speed flows over such compression ramps are usually being tested in short-duration facilities where the model, in contrast to a real flight situation, remains at its initial temperature due to short measuring times. Thus, computational fluid dynamics (CFD) is used to extrapolate to real flight situations. However, CFD needs reliable data by which it can be validated. Furthermore, it is well known that an increase in wall temperature destabilizes the boundary layer and, thus, increases the separation region, however for hypersonic flow there are no proven correlations that allow for an engineering estimate of the size of the separation to be expected. It is not yet clear whether the wall temperature by itself or the wall to freestream temperature ratio is the important physical parameter for separated hypersonic flows. In the present paper, a shock-tunnel experiment1 investigating the flow over a preheated model for different flow conditions is numerically simulated to analyze on the one hand the wall temperature effect and on the other hand to validate the CFD solutions. In addition, the CFD analysis helps to interpret the experimentally gained data. Within the frame of designing a hypersonic engine inlet, a compression ramp configuration with a deflection angle of 15o and a sharp leading edge was selected. Figure 1 shows the flow details of a separated hypersonic compression ramp flow.

REATTACHMENT SHOCK WAVE

LEADING EDGE SHOCK WAVE

SEPARATION SHOCK WAVE

α BOUNDARY LAYER

REATTACHMENT POINT

SEPARATION POINT

Figure 1: Separated hypersonic compression ramp flow.

Copyright © 2007 by B. Reinartz and R. Boyce. Published by the EUCASS association with permission.

SESSION 2.14 & B. REINARTZ ET AL.

2. Numerical Method 2.1 Navier–Stokes Solver FLOWer The FLOWer code2 is applied, which solves the unsteady compressible Navier–Stokes equations using a cell–centered finite volume method on block–structured grids. An advection upstream splitting method (AUSM) Flux Vector splitting is used for the inviscid fluxes and second order accuracy in space is achieved by means of a monotonic upstream scheme for conservation laws (MUSCL) extrapolation where a van Leer limiter function is used to guarantee the total variation diminishing (TVD) property of the scheme. The diffusive fluxes are discretized by central differences. Time integration is performed by a five–step Runge–Kutta method for the mean flow equations and a diagonal dominant alternating direction implicit (DDADI) scheme for the turbulence equations. To enhance convergence, a multigrid method, implicit residual smoothing, and local time stepping for steady–state computations can be applied. In case of turbulent flow, a differential Reynolds stress model, the so–called SSG/LRR-ω model,3 is applied. The model combines a simplified version of the Launder-Reece-Rodi (LRR) model by Wilcox close to the wall with the SpezialeSarkar-Gatski (SSG) in the farfield and Menter’s ω-equation for closure and has previously been successfully applied to hypersonic shock wave / boundary layer interaction flows with separation.4 The FLOWer computations are performed on the SunFire SMP–cluster of the RWTH Aachen University as well as on the IBM p690 cluster of Research Centre Jülich. A complete validation of the FLOWer code has been performed by the DLR prior to its release2 and continued validation is achieved by the analyses documented in subsequent publications.5, 6 The accuracy of the current investigation is evaluated by comparison with experimental and additional numerical results.

2.2 CFD++ The commercial code CFD++, developed by Metacomp Technologies,7 can solve both the steady or the unsteady (timeaccurate) Navier–Stokes equations for compressible flows, including multi–species and finite–rate chemistry modeling. It is basically an unstructured code, but handles Cartesian structured curvilinear and unstructured grids (with various cell types and shapes), including hybrids. A variety of turbulence models are available in CFD++, ranging from one– to three–equations transport models. Multi–grid relaxation provides a fast and accurate solution methodology for both steady and (with dual–time stepping) unsteady flows. Most importantly, CFD++ has had considerable investment concerning code validation and has been used with great success on similar problems in the past.8–10 The CFD++ computations have been performed on an AMD opteron linux cluster of the University of New South Wales in Canberra.

2.3 Boundary Conditions At the inflow boundary, the freestream conditions of the experimental investigation listed in Table 1 are prescribed. The turbulence quantities are determined by the specified freestream turbulence intensity of T u∞ = 0.5: k∞ = 1.5(T u∞u∞ )2 and ω∞ = k∞ /(0.001×µ). For the supersonic outflow, the variables are extrapolated from the interior. At solid walls, the no-slip condition is enforced by setting the velocity components, the turbulent kinetic energy and the normal pressure gradient to zero. The specific dissipation rate is set proportionally to the wall shear stress and the surface roughness. The energy boundary condition is directly applied by prescribing the wall temperature when calculating the viscous contribution of wall faces. Four different wall temperatures are simulated for each test condition: T W,I = 293 K, 480 K, 640 K and 805 K and T W,II = 293 K, 546 K, 750 K and 819 K, respectively. For FLOWer computations, a constant wall temperature is assumed whereas the CFD++ computations take into consideration that in the front part a length of 0.179 m (17%) of the flat plate is not heated and remains at ambient temperature.

Condition I II

2

Table 1: Test conditions M∞ Re∞ [106 /m] T 0 [K] 7.7 4.16 1607 7.42 3.66 2720

T ∞ [K] 125 265

B. Reinartz et al. SHOCK WAVE / BOUNDARY LAYER INTERACTIONS

3. Results 3.1 Mesh Sensitivity Because preliminary computations of the shock induced separation in hypersonic flows have shown a strong mesh dependance, a sensitivity analysis was initiated using CDF++. Figure 2 shows the applied mesh (left) and its decompositon (right). Structured quadrilaterals, better suited to resolve wall-bounded high Reynolds number flow, are used 0.2

Y [m]

0.15

0.1

0.05

0

-0.05

0

0.1

0.2

0.3

X [m]

0.4

Figure 2: Hybrid mesh (left) and domain decomposition (right) for mesh sensitivity analysis using CFD++ . Structured quadrilaterals are used for boundary layer resolution (block AITK), otherwise unstructured triangles are applied. inside the boundary layer (block AITK in Fig. 2). The separation region and the shear layer are resolved by a dense clustering of unstructured triangles which grow in size towards domain boundaries. In the streamwise direction, the cells are clustered in the nose region (ABLK) and evenly spaced in the separation region (CGRM). The mesh sensitivity analysis focuses on the structured cells near the wall. The hybrid mesh was chosen because it allows the refinement of the cell sizes in the boundary layer region without affecting other areas of the mesh. Different normal resolutions of the boundary layer are combined with varying streamwise resolutions (see Table 2).

0.0014

∆ξmin=2e-4 ∆ξmin=1e-4 ∆ξmin=5e-5 ∆ξmin=5e-5, sep only

∆ξ

cP 0.03

BL-y coarse, ∆ξmin=2e-4 BL-y coarse, ∆ξmin=1e-4 BL-y coarse, ∆ξmin=5e-5 BL-y coarse, ∆ξmin=5e-5, sep only BL-y fine, ∆ξmin=2e-4 BL-y fine, ∆ξmin=1e-4 BL-y fine, ∆ξmin=5e-5 BL-y fine, ∆ξmin=5e-5, sep only

0.0012

0.001

0.0008

0.02 0.0006

0.0004

0.01 0.0002

0 -0.45

0

-0.4

-0.35

-0.3 x/L

-0.25

-0.2

-0.8

-0.7

-0.6

-0.5

x/L

Figure 3: Wall distributions for the pressure coefficient in the area of separation (left) and the streamwise structured grid spacings prior to separation (right) using different hybrid meshes of Table 2 (condition II and T W = 750 K) Figure 3 shows the pressure coefficient distribution of the separation region (left) and the distribution of the streamwise cell sizes ∆ξ on the flat plate in the region upstream of separation (CGRM) for the eight meshes of Table 2. Except for the curve labeled ’sep only’, the streamwise distributions are linearly scaled from each other, for example the streamwise cell size for ∆ξmin = 2e − 4 is everywhere exactly twice the streamwise cell size for ∆ξmin = 1e − 4 at the same x-location. On the other hand, the ’sep only’ ∆ξmin = 5e − 5 case represents a modification of the ∆ξmin = 5e − 5 distribution in the upstream region but leaving the separation region mesh the same. Three mesh-dependency issues are 3

SESSION 2.14 & B. REINARTZ ET AL.

Table 2: Sizes and spacings of hybrid CFD++ meshes mesh Nall NBL,η ∆ξmin [m] 1 232k 50 2 · 10−4 2 303k 50 1 · 10−4 3 471k 50 5 · 10−5 4 399k 50 5 · 10−5 5 293k 100 2 · 10−4 6 427k 100 1 · 10−4 7 720k 100 5 · 10−5 8 609k 100 5 · 10−5

observed. Firstly, refining the number of points in the direction normal to the wall NBL,η from 50 (BL-y coarse) to 100 (BL-y fine) increases the separation size indicating mesh dependancy. Secondly, the separation point is NOT sensitive to the streamwise cell size for a given wall-normal spacing, as long as the streamwise spacing has been linearly scaled everywhere. Thirdly, mesh-dependence of the separation point IS observed when only the streamwise spacing upstream of separation is modified - the nonlinear ’sep only’ case. There is clearly a dependancy of the separation region on the resolution of the upstream unseparated boundary layer, emphazising the complexity of mesh sensitivity in hypersonic flows. The FLOWer code uses block-structured grids. Earlier analysis of separated hypersonic flows have shown that clustering of cells in the separation region can trigger separation. Therefore, the nodes in the FLOWer grids are evenly spaced in the streamwise direction, except for the leading edge. The grid shown in Fig. 4 resulted from an earlier grid sensitivity analysis of a Mach 10 compression ramp flow and is used for the computations of condition I. For condition II computations, this grid had to be refined (see Table 3) because additional turbulent and transitional simulations are performed. Also given in Table 3 are details of a 3D simulation which is currently being investigated.

y [m]

0.2

FLOWer grid 450 x 125 nodes uniformly spaced, clustered in nose region

0.1

0

-0.2

-0.1

0

x [m]

0.1

0.2

-0.01

0

x [m]

0.01

Figure 4: Block-structured grid used for FLOWer computations. The overall grid (left) and a cut-out of the discretization in the separation area (right) are shown.

grid condition I condition II condition II, 3D

Table 3: Sizes and spacings of block-structured FLOWer grids Nξ Nη Nζ Nall NBL,η ∆ξmin [m] ∆ηmin [m] 450 125 56.2k 85 1.6 · 10−5 8 · 10−6 −5 800 200 2720 160k 160 1.5 · 10 7.5 · 10−6 −6 384 128/152 152 7.7M 155 1 · 10 1 · 10−6

∆ζmin [m] 1 · 10−6

3.2 Laminar 2D Computations The experimental set–up was designed to yield nominally two–dimensional laminar flow along the center plane. Therefore, 2D laminar computations were initiated at first. The computed wall distributions for pressure coefficient and Stanton number are compared to the measurements in Figs. 5 and 6. Figure 5 shows the prediction of the separation size to be satisfying, even though there is a tendency to slightly overpredict the size with increasing wall temperature. 4

B. Reinartz et al. SHOCK WAVE / BOUNDARY LAYER INTERACTIONS

The plateau pressure in the separation region is also overpredicted. However, the agreement in the reattachment region with strong compression and peak pressure is again satisfying. There is an unaccountable pressure overshoot visible in the measurements for the highest wall temperature. The strong discrepancy between CFD and experiment in the expansion region is caused by 3D spillage over the model edge as has been shown in an earlier analysis.11 The spillage also causes the plateau pressure to drop slightly, possibly explaining the differences between CFD and experiment in this region. There seems to be no effect of wall temperature on the plateau and on the peak pressure level. Comparison

0.3

0.3

condition II

condition I cP 0.2

TW=293K TW=480K TW=640K TW=805K

peak pressure

TW=293K TW=546K TW=819K

cP 0.2

0.1

0.1

CP= (p-p∞) / (0.5 ρ∞u2∞)

plateau pressure

0

0

δ=15 -1

-0.5

0

x/L

δ=15

o

0.5

1

-1

-0.5

0

x/L

0.5

o

1

Figure 5: Computed (FLOWer, solid lines) and measured (symbols) pressure coefficients for different wall temperatures of heated compression ramp model.

of the wall heat fluxes in Fig. 6 yields the measured peak heating in the reattchment region to be closer to turbulent than laminar values. However, the flow cannot be fully turbulent because a turbulent boundary would not separate under those conditions. The analysis of a comparable shock tunnel experiment under similar conditions has shown that the flow is transitional.11 It is assumed that for the current test case the flow turns turbulent somewhere along the separated shear layer. Thus, additional computations were performed to model this transitional behavior.

10

-2

10

condition I

St

-2

condition II

St

TW=293K TW=480K TW=640K TW=805K

TW=293K TW=546K TW=819K

10-3

10-3

self similar solutions

10

TW

-4

ramp hinge line 10

-0.5

0

-4

10

-5

St = qW / [ρ∞u∞cp (T0-TW) ]

δ=15o

δ=15o

-5

-1

10

x/L

0.5

1

-1

-0.5

0

x/L

0.5

1

Figure 6: Computed (FLOWer, solid lines) and measured (symbols) Stanton number distributions for different wall temperatures of heated compression ramp model.

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SESSION 2.14 & B. REINARTZ ET AL.

3.3 Transitional 2D Computations Because there is no transition model available in the FLOWer code, the process of transition has to be modeled otherwise. In the above mentioned analysis of a double wedge configuration,11 good results were obtained by running a laminar computation and turning on the turbulence model along the hinge line. Out of a variety of turbulence models applied, the SSG/LLR-ω model proved to be best suited for that kind of simulations. Thus, the same procedure is applied here. Figures 7 and 8 compare the laminar and combined laminar/turbulent CFD results with the measurements for two different wall temperatures of condition II. Even though the transition modeling is a crude approximation of

10

-2

0.3

condition II, TW= 293 K

condition II, TW= 293 K

St

lam / SSG/LLR-ω laminar

lam / SSG/LLR-Ω laminar Exp.

cP

Exp. 0.2 10-3

self similar solutions 0.1 10

-4

0

ramp hinge line 10

δ=15

δ=15o

o

-5

-1

-0.5

0

x/L

0.5

1

-1

-0.5

0

x/L

0.5

1

Figure 7: Stanton number and pressure coefficient distributions for condition II and T W = 293 K. Comparing results of laminar and combined laminar/turbulent computations with experimental data taken from Bleilebens and Olivier1

10

-2

0.3

condition II, TW= 819 K

St

lam / SSG/LLR-ω laminar

condition II, TW= 819 K lam / SSG/LLR-Ω laminar Exp.

cP

Exp. 0.2 10-3

self similar solutions 0.1 10

-4

0

ramp hinge line 10

δ=15

δ=15o

o

-5

-1

-0.5

0

x/L

0.5

1

-1

-0.5

0

x/L

0.5

1

Figure 8: Stanton number and pressure coefficient distributions for condition II and T W = 819 K. Comparing results of laminar and combined laminar/turbulent computations with experimental data taken from Bleilebens and Olivier1

the real physical process, the agreement of the peak heating levels is greatly improved by it. Furthermore, the pressure levels in the reattachment zone and the subsequent expansion region increase due to the introduction of turbulence. However, in contrast to the findings for the double wedge test case where the point of separation moved downstream for transitional simulations, no such upstream effect is visible for the ramp configuration. 6

B. Reinartz et al. SHOCK WAVE / BOUNDARY LAYER INTERACTIONS

Figure 9 summarizes the numerical findings for the position of separation and reattachment. The results suggest an almost linear dependance of the separation length on the wall temperature to total temperature ratio where the separation point is more sensible to changes of the temperature ratio. As mentioned before, there seems to be no upstream effect concerning separation for the combined laminar/turbulent simulations (lam / SSG/LLR-ω). The point of reattachment on the ramp, however, is moved upstream, reducing the overall separation size.

TW/T0 Condition I Condition II Cond II - lam / SSG/LLR-ω

0.6

0.4

0.2

0 -0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

x/L

0.3

Figure 9: Separation and reattachment positions for different temperature ratios T W /T 0 .

4. Conclusions In order to accurately compute scramjet propulsion inlets, the physical effect of elevated surface temperatures on the flow field has to be investigated and the reliability of the simulations has to be tested. Therefore, a shock-tunnel experiment analyzing hypersonic flow over a preheated compression ramp model is numerically simulated. The combined numerical and experimental analysis proved to be mutually beneficial: The experiment was designed to yield nominally laminar 2D flow along the center plane. However, the numerical analysis shows the measurements being affected by boundary layer transition and 3D spillage. Thus, CFD helps to interpret the experimental findings and, at the same time, valuable knowledge is gained of how such flows have to be simulated. A conducted mesh sensitivity analysis emphasizes the strong dependence of separated hypersonic flows on the cell distribution. Therefore, the applied mesh has to be generated with great care using small, evenly spaced structured cells for the computation of the complete boundary layer. Modeling the process of transition in the shear layer by switching on an adequate turbulence model at the hinge line between flat plate and ramp yields satisfying results. In contrast to earlier findings for a double wedge configuration, there is no upstream influence on the size of the separation for the combined laminar/turbulent computations. However, the introduction of turbulence moves the point of reattachment upstream and increases the computed levels of peak heating and peak pressure. The level of the plateau as well as the peak pressure seem to be unaffected by an increase in surface temperature. Overall, the results indicate a linear dependance of the size of the separation on the wall temperature to total temperature ratio. Currently, additional 3D laminar and laminar/turbulent computations are being conducted. First results will be presented at the conference.

Acknowledgments This work has been financially supported by the Deutsche Forschungsgemeinschaft (DFG). Appreciation is expressed to the Shock Wave Laboratory at RWTH Aachen University for the supply of measurement data.

References [1] Bleilebens, M. and Olivier, H., “On the Influence of Elevated Surface Temperatures on Hypersonic Shock Wave / Boundary Layer Interaction at a Heated Ramp Model,” ShockWaves, Vol. 15, No. 5, 2006, pp. 301–312. 7

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[2] Kroll, N., Rossow, C.-C., Becker, K., and Thiele, F., “The MEGAFLOW Project,” Aerospace Science and Technology, Vol. 4, No. 4, 2000, pp. 223–237. [3] Eisfeld, B. and Brodersen, O., “Advanced Turbulence Modelling and Stress Analysis for the DLR-F6 Configuration,” AIAA Paper 2005-4727, 2005. [4] Reinartz, B. and Ballmann, J., “Computation of Hypersonic Double Wedge Shock / Boundary Layer Interaction,” 26th International Symposium on Shock Waves (ISSW 26), Göttingen, Germany 16-20 July 2007, Softbound Ed. [5] Coratekin, T. A., van Keuk, J., and Ballmann, J., “On the Performance of Upwind Schemes and Turbulence Models in Hypersonic Flows,” AIAA Journal, Vol. 42, No. 5, May 2004, pp. 945–957. [6] Reinartz, B. U., Ballmann, J., Herrmann, C., and Koschel, W., “Aerodynamic Performance Analysis of a Hypersonic Inlet Isolator using Computation and Experiment,” AIAA Journal of Propulsion and Power, Vol. 19, No. 5, 2003, pp. 868–875. [7] Goldberg, U., Peroomian, O., Chakravarthy, S., and Sekar, B., “Validation of CFD++ Code Capability for Supersonic Combustor Flowfields,” AIAA Paper 97–3271, 1997. [8] Boyce, R. R., Gerard, S., and Paull, A., “The HyShot Scramjet Flight Experiment - flight data and CFD calculations compared,” AIAA Paper 2003-7029, 2003. [9] Boyce, R. R., Frost, M., and Paull, A., “Combustor and Nozzle CFD Calculations for the HyShot Scramjet Flight Experiment,” CFD Journal, Vol. 12, No. 2-3, 2003. [10] Boyce, R. R. and Hillier, R., “Shock-Induced Three-Dimensional Separation Of An Axisymmetric Hypersonic Turbulent Boundary Layer,” AIAA Paper 2000-2226, 2000. [11] Reinartz, B. U., Ballmann, J., and Boyce, R. R., “Numerical Investigation of Wall Temperature and Entropy Layer Effects on Double Wedge Shock / Boundary Layer Interactions,” AIAA Paper 06-8137, 2006.

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