Flow, Turbulence and Combustion

, Volume 97, Issue 1, pp 1–25 | Cite as

Effects of Compressibility and Shock-Wave Interactions on Turbulent Shear Flows

Article

Abstract

Compressibility effects are present in many practical turbulent flows, ranging from shock-wave/boundary-layer interactions on the wings of aircraft operating in the transonic flight regime to supersonic and hypersonic engine intake flows. Besides shock wave interactions, compressible flows have additional dilatational effects and, due to the finite sound speed, pressure fluctuations are localized and modified relative to incompressible turbulent flows. Such changes can be highly significant, for example the growth rates of mixing layers and turbulent spots are reduced by factors of more than three at high Mach number. The present contribution contains a combination of review and original material. We first review some of the basic effects of compressibility on canonical turbulent flows and attempt to rationalise the differing effects of Mach number in different flows using a flow instability concept. We then turn our attention to shock-wave/boundary-layer interactions, reviewing recent progress for cases where strong interactions lead to separated flow zones and where a simplified spanwise-homogeneous problem is amenable to numerical simulation. This has led to improved understanding, in particular of the origin of low-frequency behaviour of the shock wave and shown how this is coupled to the separation bubble. Finally, we consider a class of problems including side walls that is becoming amenable to simulation. Direct effects of shock waves, due to their penetration into the outer part of the boundary layer, are observed, as well as indirect effects due to the high convective Mach number of the shock-induced separation zone. It is noted in particular how shock-induced turning of the detached shear layer results in strong localized damping of turbulence kinetic energy.

Keywords

Compressible turbulence Shock waves Boundary-layers 

References

  1. 1.
    Dolling, D.S.: Fifty years of shock-wave/boundary-layer interaction research: What next? AIAA J. 39(8), 1517–1531 (2001)CrossRefGoogle Scholar
  2. 2.
    Birch, S.F., Eggers, J.M.: A critical review of the experimental data for developed free turbulent shear layers. Tech. Rep., 32 (1973). NASA-SPGoogle Scholar
  3. 3.
    Brown, G.L., Roshko, A.: Density effects and large structure in turbulent mixing layers. J. Fluid Mech. 64, 775–816 (1974)CrossRefGoogle Scholar
  4. 4.
    Bradshaw, P.: Compressible turbulent shear layers. Ann. Rev. Fluid Mech. 9, 33–54 (1977)CrossRefMATHGoogle Scholar
  5. 5.
    Babinsky, H., Harvey, J.: Shock Wave-Boundary-Layer Interactions, Cambridge (2011)Google Scholar
  6. 6.
    Clemens, N.T., Narayanaswamy, V.: Low frequency unsteadiness of shock wave/turbulent boundary layer interactions. Ann. Rev. Fluid Mech. 46, 469–492 (2014)CrossRefMATHMathSciNetGoogle Scholar
  7. 7.
    Gatski, T.B., Bonnet, J.P.: Compressibility, Turbulence and High-Speed Flow. Academic Press (2009)Google Scholar
  8. 8.
    Smits, A.J., Dussauge, J.-P.: Turbulent Shear Layers in Supersonic Flow, 3rd edn. Springer (2006)Google Scholar
  9. 9.
    Gaitonde, D.V.: Progress in shock wave/boundary layer interactions. Prog. Aero. Sci. 72(SI), 80–99 (2015)CrossRefGoogle Scholar
  10. 10.
    Souverein, L.J., Dupont, P., Debieve, J.-F., Dussauge, J.-P., van Oudheusden, B.W., Scarano, F.: Effect of Interaction Strength on Unsteadiness in Turbulent Shock-Wave-Induced Separations. AIAA J. 48(7), 1480–1493 (2010)CrossRefGoogle Scholar
  11. 11.
    Giepman, R.H.M., Schrijer, F.F.J., van Oudheusden, B.W.: High-resolution PIV measurements of a transitional shock wave-boundary layer interaction. Exp. Fluids 56(6), 1–20 (2015)CrossRefGoogle Scholar
  12. 12.
    Adams, N.A.: Direct numerical simulation of turbulent compression ramp flow. Theor. Comp. Fluid Dyn. 12(2), 109–129 (1998)CrossRefMATHGoogle Scholar
  13. 13.
    Adams, N.A.: Direct simulation of the turbulent boundary layer along a compression ramp at M=3 and Re-theta=1685. J. Fluid Mech. 420, 47–83 (2000)CrossRefMATHGoogle Scholar
  14. 14.
    Yee, H.C., Sandham, N.D., Djomehri, M.J.: Low-dissipative high-order shock-capturing methods using characteristic-based filters. J. Comp. Phys. 150(1), 199–238 (1999)CrossRefMATHMathSciNetGoogle Scholar
  15. 15.
    Ducros, F., Ferrand, V., Nicoud, F., Weber, C., Darracq, D., Gacherieu, C., Poinsot, T.: Large-eddy simulation of the shock turbulence interaction. J. Comp. Phys. 152(2), 517–549 (1999)CrossRefMATHGoogle Scholar
  16. 16.
    Johnsen, E., Larsson, J., Bhagatwala, A.V., Cabot, W.H., Moin, P., Olson, B.J., Rawat, P.S., Shankar, S.K., Sjoegreen, B., Yee, H.C., Zhong, X., Lele, S.K.: Assessment of high-resolution methods for numerical simulations of compressible turbulence with shock waves. J. Comp. Phys. 229(4), 1213–1237 (2010)CrossRefMATHMathSciNetGoogle Scholar
  17. 17.
    Gerritsen, M., Olsson, P.: Designing an efficient solution strategy for fluid flows. 1. A stable high order finite difference scheme and sharp shock resolution for the Euler equations. J. Comp. Phys. 129(2), 245–262 (1996)CrossRefMATHMathSciNetGoogle Scholar
  18. 18.
    Sandham, N.D., Li, Q., Yee, H.C.: Entropy splitting for high-order numerical simulation of compressible turbulence. J. Comp. Phys. 178(2), 307–322 (2002)CrossRefMATHGoogle Scholar
  19. 19.
    Pirozzoli, S.: Numerical Methods for High-Speed Flows. In: Davis, S.H., Moin, P. (eds.) Annual Review of Fluid Mechanics, vol. 43, pp 163–194. Annual Reviews Inc. (2011)Google Scholar
  20. 20.
    Garnier, E., Adams, N.A., Sagaut, P.: Large Eddy Simulation for Compressible Flows. Springer (2009)Google Scholar
  21. 21.
    Vreman, B.: Direct and Large-Eddy Simulation of the Compressible Mixing Layer. PhD Thesis. University of Twente, Enschede (1995)Google Scholar
  22. 22.
    Hickel, S., Egerer, C.P., Larsson, J.: Subgrid-scale modeling for implicit large eddy simulation of compressible flows and shock-turbulence interaction. Phys. Fluids 26(10), 106101 (2014)CrossRefGoogle Scholar
  23. 23.
    Papamoschou, D., Roshko, A.: The compressible turbulent shear-layer - an experimental-study. J. Fluid Mech. 197, 453–477 (1988)CrossRefGoogle Scholar
  24. 24.
    Slessor, M.D., Bond, C.L., Dimotakis, P.E.: Turbulent shear-layer mixing at high reynolds numbers: effects of inflow conditions. J. Fluid Mech. 376, 115–138 (1998)CrossRefMATHGoogle Scholar
  25. 25.
    Vreman, A.W., Sandham, N.D., Luo, K.H.: Compressible mixing layer growth rate and turbulence characteristics. J. Fluid Mech. 320, 235–258 (1996)CrossRefMATHGoogle Scholar
  26. 26.
    Breidenthal, R.E.: Sonic eddy - a model for compressible turbulence. AIAA J. 30(1), 101–104 (1992)CrossRefMATHGoogle Scholar
  27. 27.
    Pantano, C., Sarkar, S.: A study of compressibility effects in the high-speed turbulent shear layer using direct simulation. J. Fluid Mech. 451, 329–371 (2002)CrossRefMATHGoogle Scholar
  28. 28.
    Wilcox, D.C.: Turbulence Modeling for CFD, 3rd edn. McGraw-Hill (2006)Google Scholar
  29. 29.
    Sarkar, S., Erlebacher, G., Hussaini, M.Y., Kreiss, H.O.: The analysis and modeling of dilatational terms in compressible turbulence. J. Fluid Mech. 227, 473–493 (1991)CrossRefMATHGoogle Scholar
  30. 30.
    Yoder, D.A., DeBonis, J.R., Georgiadis, N.J.: Modeling of turbulent free shear flows. Comp. Fluids 117, 212–232 (2015)CrossRefMathSciNetGoogle Scholar
  31. 31.
    Barre, S., Bonnet, J.P.: Detailed experimental study of a highly compressible supersonic turbulent plane mixing layer and comparison with most recent DNS results: Towards an accurate description of compressibility effects in supersonic free shear flows. Int. J. Heat Fluid Flow 51, 324–334 (2015)CrossRefGoogle Scholar
  32. 32.
    Duan, L., Martin, M.P.: Direct numerical simulation of hypersonic turbulent boundary layers. Part 4. Effect of high enthalpy. J. Fluid Mech. 684, 25–59 (2011)CrossRefMATHMathSciNetGoogle Scholar
  33. 33.
    Touber, E., Sandham, N.D.: Large-eddy simulation of low-frequency unsteadiness in a turbulent shock-induced separation bubble. Theo. Comp. Fluid Dyn. 23(2), 79–107 (2009)CrossRefMATHGoogle Scholar
  34. 34.
    Maeder, T., Adams, N.A., Kleiser, L.: Direct simulation of turbulent supersonic boundary layers by an extended temporal approach. J. Fluid Mech. 429, 187–216 (2001)CrossRefMATHGoogle Scholar
  35. 35.
    Pirozzoli, S., Grasso, F., Gatski, T.B.: Direct numerical simulation and analysis of a spatially evolving supersonic turbulent boundary layer at M =2.25. Phys. Fluids 16(3), 530–545 (2004)CrossRefMATHGoogle Scholar
  36. 36.
    Huang, P.G., Coleman, G.N., Bradshaw, P.: Compressible turbulent channel flows: DNS results and modelling. J. Fluid Mech. 305, 185–218 (1995)CrossRefMATHGoogle Scholar
  37. 37.
    Sarkar, S.: The stabilizing effect of compressibility in turbulent shear-flow. J. Fluid Mech. 282, 163–186 (1995)CrossRefMATHGoogle Scholar
  38. 38.
    Redford, J.A., Sandham, N.D., Roberts, G.T.: Numerical simulations of turbulent spots in supersonic boundary layers: Effects of Mach number and wall temperature. Prog. Aerosp. Sci. 52(SI), 67–79 (2012)CrossRefGoogle Scholar
  39. 39.
    Fischer, M.C.: Spreading of a turbulent disturbance. AIAA J. 10, 957–959 (1972)CrossRefGoogle Scholar
  40. 40.
    Krishnan, L., Sandham, N.D.: Effect of Mach number on the structure of turbulent spots. J. Fluid Mech. 566, 225–234 (2006)CrossRefMATHGoogle Scholar
  41. 41.
    Jocksch, A., Kleiser, L.: Growth of turbulent spots in high-speed boundary layers on a flat plate. Int. J. Heat Fluid Flow 29(6), 1543–1557 (2008)CrossRefGoogle Scholar
  42. 42.
    Gad-El-Hak, M., Blackwelder, R.F., Riley, J.J.: On the growth of turbulent regions in laminar boundary-layers. J. Fluid Mech. 110, 73–95 (1981)CrossRefGoogle Scholar
  43. 43.
    Brinkerhoff, J.R., Yaras, M.I.: Numerical investigation of the generation and growth of coherent flow structures in a triggered turbulent spot. J. Fluid Mech. 759, 257–294 (2014)CrossRefGoogle Scholar
  44. 44.
    Casper, K.M., Beresh, S.J., Schneider, S.P.: Pressure fluctuations beneath instability wavepackets and turbulent spots in a hypersonic boundary layer. J. Fluid Mech. 756, 1058–1091 (2014)CrossRefGoogle Scholar
  45. 45.
    Monkewitz, P.A., Huerre, P.: Influence of the velocity ratio on the spatial instability of mixing layers. Phys. Fluids 25(7), 1137–1143 (1982)CrossRefGoogle Scholar
  46. 46.
    Gaster, M., Kit, E., Wygnanski, I.: Large-scale structures in a forced turbulent mixing layer. J. Fluid Mech. 150, 23–39 (1985)CrossRefGoogle Scholar
  47. 47.
    Morris, P.J., Giridharan, M.G., Lilley, G.M.: On the turbulent mixing of compressible free shear layers. Proc. Roy. Soc. Math. Phys. Sci. 431(1882), 219–243 (1990)CrossRefMATHGoogle Scholar
  48. 48.
    Suzuki, T., Colonius, T.: Instability waves in a subsonic round jet detected using a near-field phased microphone array. J. Fluid Mech. 565, 197–226 (2006)CrossRefMATHGoogle Scholar
  49. 49.
    Ragab, S.A., Wu, J.L.: Linear instabilities in two-dimensional compressible mixing layers. Physics of Fluids A-Fluid Dynamics 1(6), 957–966 (1989)CrossRefGoogle Scholar
  50. 50.
    Sandham, N.D., Reynolds, W.C.: Compressible mixing layer - linear theory and direct simulation. AIAA J. 28(4), 618–624 (1990)CrossRefGoogle Scholar
  51. 51.
    Sandham, N.D., Reynolds, W.C.: Three-dimensional simulations of large eddies in the compressible mixing layer. J. Fluid Mech. 224, 133–158 (1991)CrossRefMATHGoogle Scholar
  52. 52.
    Mayer, C.S.J., von Terzi, D.A., Fasel, H.F.: Direct numerical simulation of complete transition to turbulence via oblique breakdown at Mach 3. J. Fluid Mech. 674, 5–42 (2011)CrossRefMATHGoogle Scholar
  53. 53.
    Sandham, N.D., Sandberg, R.D.: Direct numerical simulation of the early development of a turbulent mixing layer downstream of a splitter plate. J. Turbul. 10 (1), 1–17 (2009)CrossRefGoogle Scholar
  54. 54.
    Kumar, G., Bertsch, R.L., Girimaji, S.S.: Stabilizing action of pressure in homogeneous compressible shear flows: effect of Mach number and perturbation obliqueness. J. Fluid Mech. 760, 540–566 (2014)CrossRefMathSciNetGoogle Scholar
  55. 55.
    Coleman, G.N., Kim, J., Moser, R.D.: A numerical study of turbulent supersonic isothermal-wall channel flow. J. Fluid Mech. 305, 159–183 (1995)CrossRefMATHGoogle Scholar
  56. 56.
    Goldstein, D., Chu, J., Brown, G.: Lateral Spreading Mechanism of a Turbulent Spot an a Turbulent Wedge. In: Proceedings of the International Symposium on Turbulence and Shear Flow Phenomena, pp. Paper 6B–2, 1–6. Melbourne (2015)Google Scholar
  57. 57.
    Chu, B.-T., Kovásznay, S.G.: Non-linear interactions in a viscous heat-conducting compressible gas. J. Fluid Mech. 3, 515–522 (1958)CrossRefMathSciNetGoogle Scholar
  58. 58.
    Mahesh, K., Lele, S.K., Moin, P.: The influence of entropy fluctuations on the interaction of turbulence with a shock wave. J. Fluid Mech. 334, 353–379 (1997)CrossRefMATHMathSciNetGoogle Scholar
  59. 59.
    Ryu, J., Livescu, D.: Turbulence structure behind the shock in canonical shock-vortical turbulence interaction. J. Fluid Mech. 756, R1 (2014)CrossRefGoogle Scholar
  60. 60.
    Larsson, J., Bermejo-Moreno, I., Lele, S.K.: Reynolds- and Mach-number effects in canonical shock-turbulence interaction. J. Fluid Mech. 717, 293–321 (2013)CrossRefMATHMathSciNetGoogle Scholar
  61. 61.
    Pirozzoli, S., Bernardini, M., Grasso, F.: Direct numerical simulation of transonic shock/boundary layer interaction under conditions of incipient separation. J. Fluid Mech. 657, 361–393 (2010)CrossRefMATHMathSciNetGoogle Scholar
  62. 62.
    Lawal, A.A.: Direct Numerical Simulation of Transonic Shock/Boundary-Layer Interactions. PhD Thesis. University of Southampton, Southampton (2002)Google Scholar
  63. 63.
    Pagella, A., Babucke, A., Rist, U.: Two-dimensional numerical investigations of small-amplitude disturbances in a boundary layer at Ma=4.8: Compression corner versus impinging shock wave. Phys. Fluids 16(7), 2272–2281 (2004)CrossRefMATHGoogle Scholar
  64. 64.
    Matheis, J., Hickel, S.: On the transition between regular and irregular shock patterns of shock-wave/boundary-layer interactions. J. Fluid Mech. 776, 200–234 (2015)CrossRefGoogle Scholar
  65. 65.
    Doerffer, P., Hirsch, C., Dussauge, J.-P., Babinsky, H., Barakos, G.N.: Unsteady Effect of Shock Wave Induced Separation, Notes on Numerical Fluid Mechanics and Multidisciplinary Design, vol. 114. Springer (2010)Google Scholar
  66. 66.
    Garnier, E.: Stimulated detached eddy simulation of three-dimensional shock/boundary layer interaction. Shock Waves 19(6), 479–486 (2009)CrossRefMATHGoogle Scholar
  67. 67.
    Garnier, E., Sagaut, P., Deville, M.: Large eddy simulation of shock/boundary-layer interaction. AIAA J. 40(10), 1935–1944 (2002)CrossRefGoogle Scholar
  68. 68.
    Dupont, P., Haddad, C., Debiève, J.F.: Space and time organization in a shock-induced separated boundary layer. J. Fluid Mech. 559, 255–277 (2006)CrossRefMATHGoogle Scholar
  69. 69.
    Piponniau, S., Dussauge, J.P., Debiève, J.F., Dupont, P.A.: simple model for low-frequency unsteadiness in shock-induced separation. J. Fluid Mech 629, 87–108 (2009)CrossRefMATHGoogle Scholar
  70. 70.
    Touber, E.: Unsteadiness in Shock-Wave/Boundary-Layer Interactions. PhD Thesis. University of Southampton, Southampton (2010)Google Scholar
  71. 71.
    Ganapathisubramani, B., Clemens, N.T., Dolling, D.S.: Effects of upstream boundary layer on the unsteadiness of shock-induced separation. J. Fluid Mech. 585, 369–394 (2007)CrossRefMATHGoogle Scholar
  72. 72.
    Pirozzoli, S., Grasso, F.: Direct numerical simulation of impinging shock wave/turbulent boundary layer interaction at M =2.25. Phys. Fluids 18(6), 065113 (2006)CrossRefGoogle Scholar
  73. 73.
    Robinet, J.: Bifurcations in shock-wave/laminar-boundary-layer interaction: global instability approach. J. Fluid Mech. 579, 85–112 (2007)CrossRefMATHMathSciNetGoogle Scholar
  74. 74.
    Touber, E., Sandham, N.D.: Low-order stochastic modelling of low-frequency motions in reflected shock-wave/boundary-layer interactions. J. Fluid Mech. 671, 417–465 (2011)CrossRefMATHGoogle Scholar
  75. 75.
    Plotkin, K.J.: Shock-wave oscillation driven by turbulent boundary-layer fluctuations. AIAA J. 13(8), 1036–1040 (1975)CrossRefGoogle Scholar
  76. 76.
    Poggie, J., Bisek, N.J., Kimmel, R.L., Stanfield, S.A.: Spectral Characteristics of Separation Shock Unsteadiness. AIAA J. 53(1), 200–214 (2015)CrossRefGoogle Scholar
  77. 77.
    Agostini, L., Larcheveque, L., Dupont, P.: Mechanism of shock unsteadiness in separated shock/boundary-layer interactions. Phys. Fluids 27(12) (2015)Google Scholar
  78. 78.
    Sartor, F., Mettot, C., Bur, R., Sipp, D.: Unsteadiness in transonic shock-wave/boundary-layer interactions: experimental investigation and global stability analysis. J. Fluid Mech. 781, 550–577 (2015)CrossRefGoogle Scholar
  79. 79.
    Sansica, A., Sandham, N.D., Hu, Z.: Forced response of a laminar shock-induced separation bubble. Phy. Fluids 26, 957–959 (2014)CrossRefGoogle Scholar
  80. 80.
    Grilli, M., Schmid, P.J., Hickel, S., Adams, N.A.: Analysis of unsteady behaviour in shockwave turbulent boundary layer interaction. J. Fluid Mech. 700, 16–28 (2012)CrossRefMATHGoogle Scholar
  81. 81.
    Fang, J., Yao, Y., Zheltovodov, A.A., Li, Z., Lu, L.: Direct numerical simulation of supersonic turbulent flows around a tandem expansion-compression corner. Phys. Fluids 27(12) (2015). Article no. 125104Google Scholar
  82. 82.
    Eagle, W.E., Driscoll, J.F.: Shock wave-boundary layer interactions in rectangular inlets: three-dimensional separation topology and critical points. J. Fluid Mech. 756, 328–353 (2014)CrossRefGoogle Scholar
  83. 83.
    Helmer, D.B., Campo, L.M., Eaton, J.K.: Three-dimensional features of a Mach 2.1 shock/boundary layer interaction. Expt. Fluids 53(5), 1347–1368 (2012)CrossRefGoogle Scholar
  84. 84.
    Campo, L.M., Eaton, J.K.: Shock boundary layer interactions in a low aspect ratio duct. Int. J. Heat Fluid Flow 51, 353–371 (2015)CrossRefGoogle Scholar
  85. 85.
    Bermejo-Moreno, I., Campo, L., Larsson, J., Bodart, J., Helmer, D., Eaton, J.K.: Confinement effects in shock wave/turbulent boundary layer interactions through wall-modelled large-eddy simulations. J. Fluid Mech. 758, 5–62 (2014)CrossRefGoogle Scholar
  86. 86.
    Wang, B., Sandham, N.D., Hu, Z., Liu, W.: Numerical study of oblique shock-wave/boundary-layer interaction considering sidewall effects. J. Fluid Mech. 767, 526–561 (2015)CrossRefGoogle Scholar
  87. 87.
    Edgington-Mitchell, D., Oberleithner, K., Honnery, D.R., Soria, J.: Coherent structure and sound production in the helical mode of a screeching axisymmetric jet. J. Fluid Mech. 748, 822–847 (2014)CrossRefGoogle Scholar
  88. 88.
    Aubard, G., Gloerfelt, X., Robinet, J.C.: Large-Eddy Simulation of Broadband Unsteadiness in a Shock/Boundary-Layer Interaction. AIAA J. 51(10), 2395–2409 (2013)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Aerodynamics and Flight Mechanics Group, Faculty of Engineering and the EnvironmentUniversity of SouthamptonSouthamptonUK

Personalised recommendations