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On the transition between regular and irregular shock patterns of shock-wave/boundary-layer interactions

Published online by Cambridge University Press:  06 July 2015

Jan Matheis  and
Stefan Hickel Open the ORCID record for Stefan Hickel [Opens in a new window]
Jan Matheis
Affiliation:
Institute of Aerodynamics and Fluid Mechanics, Technische Universität München, D-85747 Garching bei München, Germany
Stefan Hickel*
Affiliation:
Institute of Aerodynamics and Fluid Mechanics, Technische Universität München, D-85747 Garching bei München, Germany Faculty of Aerospace Engineering, Technische Universiteit Delft, P.O. Box 5058, 2600 GB Delft, The Netherlands
*
†Email address for correspondence: [email protected]
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Abstract

The reflection of strong oblique shock waves at turbulent boundary layers is studied numerically and analytically. A particular emphasis is put on the transition between regular shock-wave/boundary-layer interaction (SWBLI) and Mach reflection (irregular SWBLI). The classical two- and three-shock theory and a generalised form of the free interaction theory are used for the analysis of well-resolved large-eddy simulations (LES) and for the derivation of stability criteria. We found that at a critical deflection angle across the incident shock wave, the perturbations related to the turbulent boundary layer cause bi-directional transition processes between regular and irregular shock patterns for a free-stream Mach number of $\mathit{Ma}_{0}=2$. Computational results show that the mean deflection angle across the separation shock is decoupled from the incident shock wave and can be accurately modelled by the generalised free interaction theory. On the basis of these observations, and the von Neumann and detachment criteria for the asymmetric intersection of shock waves, we derive the critical incident shock deflection angles at which the shock pattern may/must become irregular. Numerical data for a free-stream Mach number of $\mathit{Ma}_{0}=3$ confirm the existence of the dual-solution domain predicted by theory.

JFM classification

Aerodynamics: Aerodynamics Compressible Flows: Compressible boundary layers Compressible Flows: Shock waves
Type
Papers
Information
Journal of Fluid Mechanics , Volume 776 , 10 August 2015 , pp. 200 - 234
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Copyright
© 2015 Cambridge University Press 

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References

Anderson, J. D. 2001 Fundamentals of Aerodynamic. McGraw-Hill Science/Engineering/Math.Google Scholar
Babinsky, H. & Harvey, J. K. 2011 Shock Wave-Boundary-Layer Interactions. Cambridge University Press.Google Scholar
Bardsley, O. & Mair, W. A. 1950 III. The interaction between an oblique shock-wave and a turbulent boundary-layer. Phil. Mag. 7 42 (324), 29–36.Google Scholar
Ben-Dor, G. 2010 Shock Wave Reflection Phenomena. Springer.Google Scholar
Bermejo-Moreno, I., Campo, L., Larsson, J., Bodart, J., Helmer, D. & Eaton, J. K. 2014 Confinement effects in shock wave/turbulent boundary layer interactions through wall-modelled large-eddy simulations. J. Fluid Mech. 758, 5–62.CrossRefGoogle Scholar
Bogdonoff, S. M. 1955 Separation of a supersonic turbulent boundary layer. J. Aeronaut. Sci. (Inst. Aeronaut. Sci.) 22 (6), 414–430.Google Scholar
Campo, L. M. & Eaton, J. K. 2015 Shock boundary layer interactions in a low aspect ratio duct. Intl J. Heat Fluid Flow 51, 353–371.Google Scholar
Carrière, P., Sirieix, M. & Solignac, J. L.1969 Similarity properties of the laminar or turbulent separation phenomena in a non-uniform supersonic flow. In Applied Mechanics—Proceedings of the Twelfth International Congress of Applied Mechanics, Stanford University, August 26–31, 1968 pp. 145–157.Google Scholar
Chapman, D. R., Kuehn, D. M. & Larson, H. K.1958 Investigation of separated flows in supersonic and subsonic streams with emphasis on the effect of transition. NACA Tech. Rep. 1356.Google Scholar
Charwat, A. F. 1970 Supersonic flows with imbedded separated regions. Adv. Heat Transfer 6, 1–131.Google Scholar
Chpoun, A., Passerel, D., Li, H. & Ben-Dor, G. 1995 Reconsideration of oblique shock wave reflections in steady flows. Part 1. Experimental investigation. J. Fluid Mech. 301, 19–35.CrossRefGoogle Scholar
Coles, D. E.1953 Measurements in the boundary layer on a smooth flat plate in supersonic flow. PhD thesis, California Institute of Technology.Google Scholar
Delery, J. & Dussauge, J. P. 2009 Some physical aspects of shock wave/boundary layer interactions. Shock Waves 19 (6), 453–468.Google Scholar
Delery, J. & Marvin, J. G.1986 Shock-wave boundary layer interactions. Tech. Rep. AGARD-AG-280.Google Scholar
Dolling, D. S. 2001 Fifty years of shock-wave/boundary-layer interaction research: what next? AIAA J. 39 (8), 1517–1531.CrossRefGoogle Scholar
Dussauge, J.-P., Dupont, P. & Debieve, J.-F. 2006 Unsteadiness in shock wave boundary layer interactions with separation. Aerosp. Sci. Technol. 10 (2), 85–91.Google Scholar
Edney, B. E.1968 Anomalous heat transfer and pressure distributions on blunt bodies at hypersonic speeds in the presence of an impinging shock. Tech. Rep. FFA Report 115, Stockholm.Google Scholar
Erdos, J. & Pallone, A.1963 Shock-boundary layer interaction and flow separations. In Proceedings of the 1962 Heat Transfer and Fluid Mechanics Institute.Google Scholar
Fernholz, H. H. & Finley, P. J.1977 A critical compilation of compressible turbulent boundary layer data. Tech. Rep. AGARD-AG-223.Google Scholar
Foysi, H., Sarkar, S. & Friedrich, R. 2004 Compressibility effects and turbulence scalings in supersonic channel flow. J. Fluid Mech. 509, 207–216.Google Scholar
Gadd, G. E., Holder, D. W. & Regan, J. D. 1954 An experimental investigation of the interaction between shock waves and boundary layers. Proc. R. Soc. Lond. A 226 (1165), 227–253.Google Scholar
Gottlieb, S. & Shu, C. W. 1998 Total variation diminishing Runge–Kutta schemes. Maths Comput. 67 (221), 73–85.Google Scholar
Green, J. E. 1970 Reflexion of an oblique shock wave by a turbulent boundary layer. J. Fluid Mech. 40 (1), 81–95.CrossRefGoogle Scholar
Grilli, M., Hickel, S. & Adams, N. A. 2013 Large-eddy simulation of a supersonic turbulent boundary layer over a compression–expansion ramp. Intl J. Heat Fluid Flow 42, 79–93.Google Scholar
Grilli, M., Schmid, P. J., Hickel, S. & Adams, N. A. 2012 Analysis of unsteady behaviour in shockwave turbulent boundary layer interaction. J. Fluid Mech. 700, 16–28.Google Scholar
Guarini, S. E., Moser, R. D., Shariff, K. & Wray, A. 2000 Direct numerical simulation of a supersonic turbulent boundary layer at Mach 2.5. J. Fluid Mech. 414, 1–33.Google Scholar
Hankey, W. L. Jr. & HJrolden, M. S. 1975 Two-dimensional shock wave-boundary layer interactions in high speed flows. Tech. Rep. AGARD-AG-203.Google Scholar
Henderson, L. F. 1967 The reflexion of a shock wave at a rigid wall in the presence of a boundary layer. J. Fluid Mech. 30 (04), 699–722.Google Scholar
Hickel, S., Adams, N. A. & Domaradzki, J. A. 2006 An adaptive local deconvolution method for implicit LES. J. Comput. Phys. 213 (1), 413–436.Google Scholar
Hickel, S., Egerer, C. P. & Larsson, J. 2014 Subgrid-scale modeling for implicit large eddy simulation of compressible flows and shock-turbulence interaction. Phys. Fluids 26, 106101.Google Scholar
Hopkins, E. J. & Inouye, M. 1971 An evaluation of theories for predicting turbulent skin friction and heat transfer on flat plates at supersonic and hypersonic Mach numbers. AIAA J. 9 (6), 1–11.CrossRefGoogle Scholar
Hornung, H. G. 1982 Transition from regular to Mach reflection of shock waves Part 2. The steady-flow criterion. J. Fluid Mech. 123, 155–164.Google Scholar
Hornung, H. G. 1986 Regular and Mach reflection of shock waves. Annu. Rev. Fluid Mech. 18, 33–58.Google Scholar
Hornung, H. G., Oertel, H. & Sandeman, R. J. 1979 Transition to Mach reflexion of shock waves in steady and pseudosteady flow with and without relaxation. J. Fluid Mech. 90 (3), 541–560.Google Scholar
Hu, Z. M., Myong, R. S. & Kim, M. S. 2009 Downstream flow condition effects on the RR - MR transition of asymmetric shock waves in steady flows. J. Fluid Mech. 620, 43–62.Google Scholar
Humble, R. A., Scarano, F. & van Oudheusden, B. W. 2009 Unsteady aspects of an incident shock wave/turbulent boundary layer interaction. J. Fluid Mech. 635, 47–74.Google Scholar
Ivanov, M. S., Ben-Dor, G., Elperin, T., Kudryavtsev, A. N. & Khotyanovsky, D. V. 2002 The reflection of asymmetric shock waves in steady flows: a numerical investigation. J. Fluid Mech. 469, 71–87.Google Scholar
Ivanov, M. S., Gimelshein, S. F. & Beylich, A. E. 1995 Hysteresis effect in stationary reflection of shock waves. Phys. Fluids 7 (4), 685–687.Google Scholar
Ivanov, M. S., Gimelshein, S. F. & Markelov, G. N. 1998 Statistical simulation of the transition between regular and mach reflection in steady flows. Comput. Maths Applics. 35 (1–2), 113–125.Google Scholar
Ivanov, M. S., Kudryavtsev, A. N., Nikiforov, S. B., Pavlov, A. A. & Shiplyuk, A. N.2003 Study of transition between regular and Mach reflections in various wind tunnels. In 41st Aerospace Sciences Meeting and Exhibit.CrossRefGoogle Scholar
Ivanov, M. S., Vandromme, D., Fomin, V. M., Kudryavtsev, A. N., Hadjadj, A. & Khotyanovsky, D. V. 2001 Transition between regular and Mach reflection of shock waves: new numerical and experimental results. Shock Waves 11 (3), 199–207.Google Scholar
Klein, M., Sadiki, A. & Janicka, J. 2003 A digital filter based generation of inflow data for spatially developing direct numerical or large eddy simulations. J. Comput. Phys. 186 (2), 652–665.CrossRefGoogle Scholar
Komminaho, J. & Skote, M. 2002 Reynolds stress budgets in Couette and boundary layer flows. Flow Turbul. Combust. 68 (2), 167–192.Google Scholar
Krehl, P. & van der Geest, M. 1991 The discovery of the Mach reflection effect and its demonstration in an auditorium. Shock Waves 1 (1), 3–15.Google Scholar
Kudryavtsev, A. N., Khotyanovsky, D. V., Ivanov, M. S., Hadjadj, A. & Vandromme, D. 2002 Numerical investigations of transition between regular and Mach reflections caused by free-stream disturbances. Shock Waves 12 (2), 157–165.Google Scholar
Li, H. & Ben-Dor, G. 1997 A parametric study of mach reflection in steady flows. J. Fluid Mech. 341, 101–125.CrossRefGoogle Scholar
Li, H., Chpoun, A. & Ben-Dor, G. 1999 Analytical and experimental investigations of the reflection of asymmetric shock waves in steady flows. J. Fluid Mech. 390, 43.Google Scholar
Liepmann, H. W., Roshko, A. & Dhawan, S.1951 On reflection of shock waves from boundary layers. Tech. Rep. 1100 ADA382023.Google Scholar
Maeder, T., Adams, N. A. & Kleiser, L. 2001 Direct simulation of turbulent supersonic boundary layers by an extended temporal approach. J. Fluid Mech. 429, 187–216.Google Scholar
Mouton, C. A. & Hornung, H. G. 2007 Mach stem height and growth rate predictions. AIAA J. 45 (8), 1977–1987.Google Scholar
Mouton, C. A. & Hornung, H. G. 2008 Experiments on the mechanism of inducing transition between regular and Mach reflection. Phys. Fluids 20 (12), 126103.Google Scholar
Östlund, J.2002 Flow processes in rocket engine nozzles with focus on flow separation and side-loads. PhD thesis, KTH, Stockholm.Google Scholar
Pasquariello, V., Grilli, M., Hickel, S. & Adams, N. A. 2014 Large-eddy simulation of passive shock-wave/boundary-layer interaction control. Intl J. Heat Fluid Flow 49, 116–127.Google Scholar
Piponniau, S., Dussauge, J. P., Debiêve, J. F. & Dupont, P. 2009 A simple model for low-frequency unsteadiness in shock-induced separation. J. Fluid Mech. 629, 87–108.Google Scholar
Pirozzoli, S. & Bernardini, M. 2011 Turbulence in supersonic boundary layers at moderate Reynolds number. J. Fluid Mech. 688 (1), 120–168.Google Scholar
Pirozzoli, S. & Grasso, F. 2006 Direct numerical simulation of impinging shock wave/turbulent boundary layer interaction at $M=2.25$ . Phys. Fluids 18 (6), 065113.Google Scholar
Pirozzoli, S., Grasso, F. & Gatski, T. B. 2004 Direct numerical simulation and analysis of a spatially evolving supersonic turbulent boundary layer at $M=2.25$ . Phys. Fluids 16 (3), 530–545.Google Scholar
Quaatz, J. F., Giglmaier, M., Hickel, S. & Adams, N. A. 2014 Large-eddy simulation of a pseudo-shock system in a Laval nozzle. Intl J. Heat Fluid Flow 49, 108–115.Google Scholar
Reijasse, P.2005 Aérodynamique des tuyères propulsives en sur-détente: décollement libre et charges latérales en régime stabilisé (Aerodynamics of overexpanded propulsive nozzles: free separation and side loads in stabilized regime). PhD thesis, Université Pierre-et-Marie-Curie, Paris.Google Scholar
Reijasse, P. & Birkemeyer, J.2002 Semi-empirical flow separation model for subscale nozzles. In Fourth Symposium on Aerothermodynamics for Space Vehicles, p. 407. Capua (IT).Google Scholar
Schlatter, P. & Örlü, R. 2010 Assessment of direct numerical simulation data of turbulent boundary layers. J. Fluid Mech. 659, 116–126.Google Scholar
Settles, G. S., Bogdonoff, S. M. & Vas, I. E. 1976 Incipient separation of a supersonic turbulent boundary layer at high Reynolds numbers. AIAA J 14 (1), 50–56.Google Scholar
Shang, J. S., Hankey, W. L. Jr. & Law, C. 1976 Numerical simulation of shock wave-turbulent boundary-layer interaction. AIAA J. 14 (10), 1451–1457.CrossRefGoogle Scholar
Simens, M. P., Jiménez, J., Hoyas, S. & Mizuno, Y. 2009 A high-resolution code for turbulent boundary layers. J. Comput. Phys. 228 (1), 4218–4231.Google Scholar
Smits, A. J. & Dussauge, J. P. 2006 Turbulent Shear Layers in Supersonic Flow. Springer.Google Scholar
Smits, A. J., Matheson, N. & Joubert, P. N. 1983 Low Reynolds number turbulent boundary layers in zero favourable pressure gradients. J. Ship Res. 27, 147–157.Google Scholar
Souverein, L. J., Bakker, P. G. & Dupont, P. 2013 A scaling analysis for turbulent shock-wave/boundary-layer interactions. J. Fluid Mech. 714, 505–535.Google Scholar
Souverein, L. J., Dupont, P., Debiêve, J. F., Dussauge, J. P., van Oudheusden, B. W. & Scarano, F. 2010 Effect of interaction strength on unsteadiness in turbulent shock-wave-induced separations. AIAA J. 48 (7), 1480–1493.Google Scholar
Touber, E. & Sandham, N. D. 2009 Large-eddy simulation of low-frequency unsteadiness in a turbulent shock-induced separation bubble. Theor. Comput. Fluid Dyn. 23 (2), 79–107.Google Scholar
Touber, E. & Sandham, N. D. 2011 Low-order stochastic modelling of low-frequency motions in reflected shock-wave/boundary-layer interactions. J. Fluid Mech. 671, 417–465.CrossRefGoogle Scholar
van Driest, E. R. 1956 The problem of aerodynamic heating. Aeron. Engng Rev. 15 (10), 26–41.Google Scholar
Vuillon, J., Zeitoun, D. & Ben-Dor, G. 1995 Reconsideration of oblique shock wave reflections in steady flows. Part 2. Numerical investigation. J. Fluid Mech. 301, 37–50.Google Scholar
Zheltovodov, A. A.1996 Shock waves/turbulent boundary-layer interactions – fundamental studies and applications. AIAA Paper 96-1977, 1–27.Google Scholar
Zheltovodov, A. A. & Yakovlev, V. N.1986 Stages of development, gas dynamic structure and turbulence characteristics of turbulent compressible separated flows in the vicinity of 2-D obstacles. Preprint No. 27–86. Inst. Theor. Appl. Mech. (ITAM), Novosibirsk.Google Scholar
Zukoski, E. E. 1967 Turbulent boundary-layer separation in front of a forward-facing step. AIAA J. 5 (10), 1746–1753.Google Scholar