1. Investigations of Wind Tunnel Size and Shock Strength on Shock Boundary Layer Interactions John A. Benek, Ph.D. Casimir J. Suchyta III, Ph.D. Rick Graves, Ph.D. April 2015

2. Overview  Hypothesis – Dominant Physics  Modeling and Simulation  Future Work 2 Cleared for public release 88ABW-2015-1433

3. SBLI Flow Phenomena 3 This is how we usually think of SBLI. Incident Oblique, 2D shock wave Fin on a PlateSidewall shock, Corner Flow Cleared for public release 88ABW-2015-1433

4. SBLI as Function of Tunnel W/H 4 Small W/H Flow Regions Separated Flow Incident Shock Impingement Line Moderate W/H Separated Flow Flow Regions Large W/H Flow Regions Separated Flow Incident Shock Impingement Line Sidewall separation sets up a shock system that smears the pressure gradient Cleared for public release 88ABW-2015-1433

5. Dominant Physics With decreasing tunnel width  Corner interactions make up larger portion of flow  Corner shocks change the adverse pressure gradient Affect the character of the SBLI and separated regions  Magnitude of effects depend on size of boundary layer Hypothesis: Separation zone is function of BL thickness & tunnel width 5 Cleared for public release 88ABW-2015-1433

6. Variation of separation with W Cleared for public release 88ABW-2015-1433 6

7. Modeling and Simulation 7 Cleared for public release 88ABW-2015-1433 Modeling and Simulation

8. Computational Domain & BC Hyperbolic tangent stretching function is used to smoothly stretch the grid. 8 Width:Height Ratio NxNyNzCells (10 6 ) 2:1100120140180 1:1.125100120130160 1:41001201 40 Grid spacingMinMax x direction0.000830.0083 y, z direction0.000010.0050 Height is constant Cleared for public release 88ABW-2015-1433

9. Code and Turbulence Models  OVERFLOW: VERSION 2.2g 16 August 2013 Non-equilibrium k-  (Hamlington and Dahm) model Quadratic Constitutive Relation (QCR) CNL1=0.3 9 Standard k-  Non-equilibrium k-  Cleared for public release 88ABW-2015-1433 QCR

10. Solver and Flow Parameters 2 nd order Central difference flux scheme (IRHS=0 FSO=2) DDADI algorithm (ILHS=3) 2 nd order HLLC flux scheme (IRHS=5 FSO=2) SSOR algorithm (ILHS=6) Local time stepping (ITIME=1) Koren limiter (ILIMIT=1 ) 10 Cleared for public release 88ABW-2015-1433

11. Flow Parameters Parameter Value R e /m16x10 6  1.0 p1p1 0.71 T1T1 288 K M1M1 2.52.72.9  810.513810.513810.513  30.01 32.33 34.82 28.0230.2932.7226.3528.5930.96 M2M2 2.17 2.07 1.96 2.342.232.122.522.402.28     1.43 1.58 1.74 1.461.621.791.491.671.84 p2p2 1.18 1.37 1.58 1.221.431.661.261.491.73 T 2 /T 1 1.16 1.21 1.27 1.171.231.291.181.251.31 11 Cleared for public release 88ABW-2015-1433

12. Corner Flow 12 Cleared for public release 88ABW-2015-1433 hllcQCR Mach = 2.5 empty tunnel, x = 0

13. M=2.5 Wedge=8 W/H=2 RL=2.5 13 hllc QCR Cleared for public release 88ABW-2015-1433 cent

14. M=2.5 Wedge=8 W/H=2 RL=5.5 14 hllc With QCR Cleared for public release 88ABW-2015-1433 cent

15. M=2.9 Wedge=13 W/H=2 RL=2.5 15 hllc QCR Cleared for public release 88ABW-2015-1433 cent

16. M=2.9 Wedge=13 W/H=2 RL=5.5 16 hllc QCR Cleared for public release 88ABW-2015-1433 cent

17. M=2.5 Wedge=8 W/H=1/4 RL=2.5 17 hllc RL=2.5 Cleared for public release 88ABW-2015-1433 QCR cent

18. M=2.5 Wedge=8 W/H=1/4 RL=5.5 18 RL=5.5 Cleared for public release 88ABW-2015-1433 hllc QCR cent

19. M=2.9 Wedge=13 W/H=1/4 RL=2.5 19 Cleared for public release 88ABW-2015-1433 RL=2.5 hllc QCR cent

20. M=2.9 Wedge=13 W/H=1/4 RL=5.5 20 Cleared for public release 88ABW-2015-1433 RL=5.5 cent hllc QCR

21. M=2.5 Wedge=8 W/H=2 RL=2.5 21 Inviscid flow incident shock impingement line Cleared for public release 88ABW-2015-1433 x=0 hllc QCR x=0 x=-1/2

22. M=2.5 Wedge=8 W/H=1/4 RL=2.5 22 Cleared for public release 88ABW-2015-1433 x=0 hllc QCR x=0 x=-1/2

23. M=2.9 Wedge=13 W/H=2 RL=2.5 23 Cleared for public release 88ABW-2015-1433 x=0 hllc QCR x=0 x=-1/2

24. M=2.9 Wedge=13 W/H=1/4 RL=2.5 24 Cleared for public release 88ABW-2015-1433 x=0 hllc QCR x=0 x=-1/2

25. M=2.5 Wedge=8 W/H=2 RL=2.5 25 Isosurface ∂ x  planes ∂ x  hllc QCR Cleared for public release 88ABW-2015-1433

26. M=2.5 Wedge=8 W/H=1/4 RL=2.5 26 Isosurface ∂ x  planes ∂ x  hllc QCR Cleared for public release 88ABW-2015-1433

27. M=2.9 Wedge=13 W/H=2 RL=2.5 27 Isosurface ∂ x  planes ∂ x  hllc QCR Cleared for public release 88ABW-2015-1433

28. M=2.9 Wedge=13 W/H=1/4 RL=2.5 28 Isosurface ∂ x  planes ∂ x  hllc QCR Cleared for public release 88ABW-2015-1433

29. Summary M=2.5 29 Cleared for public release 88ABW-2015-1433 xx

30. Summary M=2.9 30 xx Cleared for public release 88ABW-2015-1433

31. Design of Experiments  Determine the range of input parameters and the outputs to be modeled.  Create a list (matrix) of simulations to run.  Run the simulations (this is the long part).  Fill in matrix with outputs.  Run software to determine sensitivities.  Create response surface. 31 Cleared for public release 88ABW-2015-1433

32. Boundary Layer Thickness 32 Cleared for public release 88ABW-2015-1433 MachW/HRL 2.54.05.5 2.5 2:10.032330.06208 1:1.1250.04918 1:40.036160.06876 2.7 2:10.04711 1:1.1250.031810.047680.06252 1:40.05232 2.9 2:10.031230.06179 1:1.1250.04695 1:40.034710.06860

33. DoE Boundary Layer Thickness  Three input parameters Mach number Tunnel Width Run Length, RL  Most sensitive to RL  Least sensitive to Mach number  Response surface is a good fit to data 33 Cleared for public release 88ABW-2015-1433

34. DoE Separation Length  Four input parameter Mach number Wedge angle,  Tunnel Width Run Length, RL  Exploring polynomial response surfaces 34 Cleared for public release 88ABW-2015-1433

35. Shock Strength 35 Cleared for public release 88ABW-2015-1433 MM SW/HRL 2.54.05.5 2.5 8 0.6574 2:10.025440.03341 1:1.1250.04427 1:40.050700.00000 2.7 10.5 0.9970 2:10.05254 1:1.1250.048600.122680.16886 1:40.12302 2.9 13 1.4330 2:10.116850.09616 1:1.1250.27706 1:40.156500.00000 S = (M perp 2 – 1)*2*  /(1+  )

36. Future Work  Compare Dahm to k-   Further investigation with DoE  Fill in our Summary curves  Effect on interactions of  Height  Acquire  x/  vs  /W from literature and compare with computations  Experiments in Cambridge corner flow suction/blowing 36 Cleared for public release 88ABW-2015-1433