Study of Parameters Affecting Separation Bubble Size in High Speed Flows using k-ω Turbulence Model

Document Type: Research Paper


Department of Aeronautical Engineering, King Abdul Aziz University, Saudi Arabia.


Shock waves generated at different parts of vehicle interact with the boundary layer over the surface at high Mach flows. The adverse pressure gradient across strong shock wave causes the flow to separate and peak loads are generated at separation and reattachment points. The size of separation bubble in the shock boundary layer interaction flows depends on various parameters. Reynolds-averaged Navier-Stokes equations using the standard two-equation k-ω turbulence model is used in simulations for hypersonic flows over compression corner. Different deflection angles, including q ranging from 15o to 38o, are simulated at Mach 9.22 to study its effect on separated flow. This is followed by a variation in the Reynolds number based on the boundary layer thickness, Red from 1x105 to 4x105. Simulations at different constant wall conditions Tw of cool, adiabatic, and hot are also performed. Finally, the effect of free stream Mach numbers M, ranging from 5 to 9, on interaction region is studied. It is observed that an increase in parameters, q, Red, and Tw results in an increase in the separation bubble length, Ls, and an increase in M results in the decrease in Ls


Main Subjects

[1] Babinsky, H., Harvey, J. K., Shock Wave-Boundary Layer Interactions, Cambridge University Press, 2011.

[2] Bose, D., Brown, J. L., Prabhu, D. K., Gnoffo, P., Johnston, C. O., Hollis, B., Uncertainty Assessment of Hypersonic Aerothermodynamics Prediction Capability, Journal of Spacecraft and Rockets, 50(1), 2013, pp. 12-18.

[3] DeBonis, J. R., Oberkampf, W. L., Wolf, R. T., Orkwis, P. D., Turner, M. G., Babinsky, H., and Benek, J. A., Assessment of Computational Fluid Dynamics and Experimental Data for Shock Boundary-Layer Interactions, AIAA Journal, 50(4), 2012, pp. 891-903.

[4] Sinha, K., Mahesh, K., Candler, G. V., Modeling Shock-Unsteadiness in Shock/Turbulence Interaction, Physics of Fluids, 15(8), 2003, pp. 2290-2297.

[5] Verma, S. B., Stark, R., Haid, O., Relation Between Shock Unsteadiness and the Origin of Side-Loads Inside a Thrust Optimized Parabolic Rocket Nozzle, Aerospace Science and Technology, 10(6), 2006, pp. 474-483.

[6] Dussauge, J. P., Dupont, P., Debieve, J. F., Unsteadiness in Shock Wave Boundary layer Interactions with Separation, Progress in Aerospace Sciences, 10(2), 2006, pp. 85-91.

[7] Estruch, D., Lawson, N. J., MacManus, D. G., Garry, K. P., Stollery, J. L., Measurement of Shock Wave Unsteadiness using a High-Speed Schlieren System and Digital Image Processing, Review of Scientific Instruments, 79(12), 2008, pp. 126108.

[8] Clemens, N. T., Narayanaswamy, V., Low-Frequency Unsteadiness of Shock Wave/Turbulent Boundary Layer Interactions, Annual Review of Fluid Mechanics, 46, 2014, pp. 469-492.

[9] Bertin, J. J., Hypersonic Aerothermodynamics, AIAA Education Series, AIAA, Washington, DC, 1994.

[10] Anderson, J. D., Hypersonic and High Temperature Gas Dynamics, AIAA, 2006.

[11] Holden, M. S., Wadhams, T. P., A Database of Aerothermal Measurements in Hypersonic. Flow in “Building Block” Experiments for CFD Validation, 41st Aerospace Sciences Meeting and Exhibit, 6-9 July 2003, Reno, Nevada, 2003.

[12] Marvin, J. G., Brown, J. L., Gnoffo, P. A., Experimental Database with Baseline CFD Solutions: 2-D and Axisymmetric Hypersonic Shock-Wave/Turbulent-Boundary-Layer Interactions, NASA/TM–2013–216604, 2013.

[13] Narayanaswamy, V., Raja, L. L., Clemens, N. T., Control of Unsteadiness of a Shock Wave/Turbulent Boundary Layer Interaction by using a Pulsed-Plasma-Jet Actuator, Physics of Fluids, 24(7), 2012, p. 076101.

[14] Delery, J., Marvin, J. G., Shock-Wave Boundary Layer Interactions, edited by E. Reshotko, AGARD No. 280, 1986.

[15] Settles, G. S., Dodson, L. J., Supersonic and Hypersonic Shock/Boundary Layer Interaction Data Base, AIAA Journal, 32(7), 1994, pp. 1337-1383.

[16] Arnal, D., Delery, J. M., Laminar-Turbulent Transition And Shock-Wave/Boundary-Layer Interaction, RTO-EN-AVT-116, Chapter 4, 2004, p. 46.

[17] Ostlund, J., Klingmann, B. M., Supersonic Flow Separation with Application to Rocket Engine Nozzles, AppliedMechanics Reviews, 58, 2005, pp. 143-177.

[18] John, B., Kulkarni, V., Effect of Leading Edge Bluntness on the Interaction of Ramp Induced Shock Wave with Laminar Boundary Layer at Hypersonic Speed, Computers and Fluids, 96, 2014, pp. 177-190.

[19] Sriram , R., Srinath, L., Manoj, K., Devaraj, K., Jagadeesh, G., On the Length Scales of Hypersonic Shock-Induced Large Separation Bubbles Near Leading Edges, Journal of Fluid Mechanics, 806, 2016, pp. 304-355.

[20] Neuenhahm T, Olivier H., Influence of the Wall Temperature and Entropy Layer Effects on Double Wedge Shock Boundary Layer Interactions, 14th AIAA/AHI Space Planes and Hypersonic Systems and Technologies Conference, International Space Planes and Hypersonic Systems and Technologies Conferences, 2006-8136, 2006.

[21] Brown, L., Fischer, C., Boyce, R. R., Reinartz, B., Olivier, H., Computational Studies of the Effect of Wall Temperature on Hypersonic Shock-Induced Boundary Layer Separation, Shock WavesIn: Hannemann K., Seiler F. (eds) Shock Waves. Springer, Berlin, Heidelberg, 2009.

[22] Xiaodong, Z., Zhenghong, G., A Numerical Research on a Compressibility-correlated Langtry’s Transition Model for Double Wedge Boundary Layer Flows, Chinese Journal of Aeronautics, 24, 2011, pp. 249-257.

[23] Yang Z., Large-Eddy Simulation: Past, Present and the Future, Chinese Journal of Aeronautics, 28(1), 2015, pp. 11-24.

[24] Knight, D. D., Degrez, G., Shock Wave Turbulent Boundary Layer Interactions In High Mach Number Flows a Critical Survey of Current Numerical Prediction Capabilities, AGARD Advisory Report, 319(2), 1998, pp. 1-35.

[25] Knight, D., Yan, H., Panaras, A. G., Zheltovodov, A., Advances in CFD Prediction of Shock Wave Turbulent Boundary Layer Interactions, Progress in Aerospace Sciences, 39(2-3), 2003, pp. 121-184.

[26] Roy, C. J., Blottner, F. G., Review and Assessment of Turbulence Models for Hypersonic Flows, Progress in Aerospace Sciences, 42(7-8), 2006, pp. 469-530.

[27] Guohua, T. U., Xiaogang, D., Assessment of Two Turbulence Models and Some Compressibility Corrections for Hypersonic Compression Corners by High-Order Difference Schemes, Chinese Journal of Aeronautics, 25, 2012, pp. 25-32.

[28] Rui, Z., Chao, Y., Jian, Y.,  Xinliang, L., Improvement of Baldwin-Lomax Turbulence Model for Supersonic Complex Flows, Chinese Journal of Aeronautics, 26(3), 2013, pp. 529-534.

[29] Li, M., Lipeng, L. , Jian, F., Qiuhui, W., A Study on Turbulence Transportation and Modification of Spalart-Allmaras Model for Shock-Wave/Turbulent Boundary Layer Interaction Flow, Chinese Journal of Aeronautics, 27(2), 2014, pp. 200-209.

[30] Georgiadis, N. J., Yoder, D. A., Vyas, M. A., Engblom, W. A., Status Of Turbulence Modeling For Hypersonic Propulsion Flow paths, Theoretical and Computational Fluid Dynamics, 28(3), 2014, pp. 295-318.

[31] Panaras, A. G., Turbulence Modeling of Flows with Extensive Cross Flow Separation, Aerospace, 2, 2015, pp. 461-481.

[32] Gaitonde, D. V., Progress in Shock Wave/Boundary Layer Interactions, Progress in Aerospace Sciences, 72, 2015, pp. 80-99.

[33] Elfstrom, G. M., Turbulent Hypersonic Flow at a Wedge- Compression Corner, Journal of Fluid Mechanics, 53(1), 1972, pp. 113-127.

[34] Wilcox, D. C., Turbulence Modeling for CFD, La Canada CA: 2nd edition, DCW Industries, 2000.

[35] Sinha, K., Candler, G. V., Convergence Improvement of Two Equation Turbulence Model Calculations, 29th AIAA, Fluid Dynamics Conference, Fluid Dynamics and Co-located Conferences, Minneapolis, Albuquerque, U.S.A., 1998.

[36] Wilcox, D. C., Formulation of the k-ω Turbulence Model Revisited, AIAA Journal, 46(11), 2008, pp. 2823-2838.

[37] MacCormack, R. W., Candler, G.V., The Solution of Navier-Stokes Equations Using Gauss-Siedal Line Relaxation, Computers and Fluids, 17(1), 1989, pp. 135-150.

[38] Wright, M. J., Candler, G. V., Bose, D., Data-Parallel Line Relaxation Method for the Navier-Stokes Equations, AIAA Journal, 36(9), 1998, pp. 1603-1609.

[39] Sinha, K., Mahesh, K., Candler, G. V., Modeling the Effect of Shock-Unsteadiness in Shock Turbulent Boundary-Layer Interactions, AIAA Journal, 43(3), 2005, pp. 586-594.

[40] Pasha, A. A., Sinha, K., Shock-Unsteadiness Model Applied to Oblique Shock Wave/Turbulent Boundary-Layer Interaction, International Journal of Computational Fluid Dynamics, 22(8), 2008, pp. 569-582.

[41] Pasha, A.A., Sinha, K., Shock Unsteadiness Model Applied to Hypersonic Shock Wave Turbulent Boundary-Layer Interactions, Journal of Propulsion and Power, 28(1), 2012, pp. 46-60.

[42] Menter, F. R., Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications, AIAA Journal, 32(8), 1994, pp. 1598-1605.