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Receptivity of a high-speed boundary layer to temperature spottiness

Published online by Cambridge University Press:  28 March 2013

A. V. Fedorov
Affiliation:
Moscow Institute of Physics and Technology, Dolgoprudny, Moscow region, 141700, Russia
A. A. Ryzhov
Affiliation:
Moscow Institute of Physics and Technology, Dolgoprudny, Moscow region, 141700, Russia Central Aerohydrodynamic Institute, Zhukovsky, 140180, Russia
V. G. Soudakov*
Affiliation:
Moscow Institute of Physics and Technology, Dolgoprudny, Moscow region, 141700, Russia Central Aerohydrodynamic Institute, Zhukovsky, 140180, Russia
S. V. Utyuzhnikov
Affiliation:
Moscow Institute of Physics and Technology, Dolgoprudny, Moscow region, 141700, Russia School of Mechanical, Aerospace and Civil Engineering, University of Manchester, Sackville Street, Manchester M13 9PL, UK
*
Email address for correspondence: vit_soudakov@mail.ru

Abstract

Two-dimensional direct numerical simulation (DNS) of the receptivity of a flat-plate boundary layer to temperature spottiness in the Mach 6 free stream is carried out. The influence of spottiness parameters on the receptivity process is studied. It is shown that the temperature spots propagating near the upper boundary-layer edge generate mode F inside the boundary layer. Further downstream mode F is synchronized with unstable mode S (Mack second mode) and excites the latter via the inter-modal exchange mechanism. Theoretical assessments of the mode F amplitude are made using the biorthogonal eigenfunction decomposition method. The DNS results agree with the theoretical predictions. If the temperature spots are initiated in the free stream and pass through the bow shock, the dominant receptivity mechanism is different. The spot–shock interaction leads to excitation of acoustic waves, which penetrate into the boundary layer and excite mode S. Numerical simulations show that this mechanism provides the instability amplitudes an order of magnitude higher than in the case of receptivity to the temperature spots themselves.

Type
Papers
Copyright
©2013 Cambridge University Press

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References

Bushnell, D. 1990 Notes on initial disturbance fields for the transition problem. In Instability and Transition (ed. Hussaini, M. Y. & Voigt, R. G.), vol. I, pp. 217232. Springer.Google Scholar
Choudhari, M. 1994 Theoretical prediction of boundary-layer receptivity. AIAA paper 94-2223.Google Scholar
Choudhari, M. & Streett, C. 1990 Boundary-layer receptivity phenomena in three-dimesnional and high-speed boundary layers. AIAA paper 90-5258.Google Scholar
Djakov, S. P. 1957 Interaction of shocks with small disturbances. J. Expl Theor. Phys. 33, 948961 (in Russian).Google Scholar
Egorov, I. V., Fedorov, A. V. & Soudakov, V. G. 2005 Direct numerical simulation of supersonic boundary-layer receptivity to acoustic disturbances. AIAA Paper 2005-97.Google Scholar
Egorov, I. V., Fedorov, A. V. & Soudakov, V. G. 2006 Direct numerical simulation of disturbances generated by periodic suction–blowing in a hypersonic boundary layer. Theor. Comput. Fluid Dyn. 20 (1), 4154.Google Scholar
Egorov, I. V., Fedorov, A. V. & Soudakov, V. G. 2008 Receptivity of a hypersonic boundary layer over a flat plate with a porous coating. J. Fluid Mech. 601, 165187.Google Scholar
Fedorov, A. V. 2003 Receptivity of a high-speed boundary layer to acoustic disturbances. J. Fluid Mech. 491, 101129.Google Scholar
Fedorov, A. 2011 Transition and stability of high-speed boundary layers. Annu. Rev. Fluid Mech. 43, 7995.Google Scholar
Fedorov, A. V. & Khokhlov, A. P. 1991 Excitation of unstable modes in supersonic boundary layer by acoustic waves. Fluid Dyn. 9, 456467.Google Scholar
Fedorov, A. V. & Khokhlov, A. P. 2001 Prehistory of instability in a hypersonic boundary layer. Theor. Comput. Fluid Dyn. 14 (6), 359375.Google Scholar
Fedrorov, A. V. & Kozlov, M. V. 2011 Receptivity of high-speed boundary layer to solid particulates. AIAA Paper 2011-3925.Google Scholar
Fedorov, A. V. & Tumin, A. M. 2003 Initial-value problem for hypersonic boundary-layer flows. AIAA J. 41 (3), 379389.Google Scholar
Fedorov, A. & Tumin, A. 2010 Branching of discrete modes in high-speed boundary layers and terminology issues. AIAA Paper 2010-5003.Google Scholar
Gaydos, P. & Tumin, A. 2004 Multimode decomposition in compressible boundary layers. AIAA J. 42 (6), 11151121.Google Scholar
Goldstein, M. E. 1983 The evolution of Tollmien–Schlichting waves near a leading edge. J. Fluid Mech. 127, 5981.Google Scholar
Goldstein, M. E. 1985 Scattering of acoustic waves into Tollmien–Schlichting waves by small streamwise variation in surface geometry. J. Fluid Mech. 154, 509529.Google Scholar
Heitmann, D. & Radespiel, R. 2011 Simulation of the interaction of a laser generated shock wave with a hypersonic conical boundary layer. AIAA Paper 2011-3875.Google Scholar
Heitmann, D., Radespiel, R. & Knauss, H. 2011 Experimental study of Mach 6 boundary layer response to laser generated disturbances. AIAA Paper 2011-3876.Google Scholar
Huang, Y. & Zhong, X. 2010 Numerical study of laser-spot effects on boundary-layer receptivity for blunt compression-cones in Mach-6 freestream. AIAA Paper 2010-4447.Google Scholar
Jaffe, N. A., Okamura, T. T. & Smith, A. M. O 1970 Determination of spatial amplification factors and their application to predicting transition. AIAA J. 8 (2), 301308.Google Scholar
Jiang, G.-S. & Shu, C.-W. 1996 Efficient implementation of weighted ENO schemes. J. Comput. Phys. 126, 202228.Google Scholar
Kimmel, R. 2003 Aspects of hypersonic boundary layer transition control. AIAA Paper 2003-0772.Google Scholar
Ma, Y. & Zhong, X. 2001 Numerical simulation of receptivity and stability of nonequilibrium reacting hypersonic boundary layers. AIAA Paper 2001-0892.Google Scholar
Ma, Y. & Zhong, X. 2003 Receptivity of a supersonic boundary layer over a flat plate. Part 2. Receptivity to free-stream sound. J. Fluid Mech. 488, 79121.Google Scholar
Ma, Y. & Zhong, X. 2005 Receptivity of a supersonic boundary layer over a flat plate. Part 3. Effects of different types of free-stream disturbances. J. Fluid Mech. 532, 63109.Google Scholar
Mack, L. M. 1969 Boundary layer stability theory. Part B. Doc. 900-277, JPL, Pasadena, California, May.Google Scholar
Malik, M. R. 1997 Boundary-layer transition prediction toolkit. AIAA Paper 97-1904.Google Scholar
Malik, M. R. & Balakumar, P. 2005 Receptivity of supersonic boundary layers to acoustic disturbances. AIAA Paper 2005-5027.Google Scholar
Malik, M. R., Zang, T. & Bushnell, D. 1990 Boundary layer transition in hypersonic flows. AIAA Paper 90-5232.Google Scholar
Maslov, A. A., Shiplyuk, A. N., Sidorenko, A. & Arnal, D. 2001 Leading-edge receptivity of a hypersonic boundary layer on a flat plate. J. Fluid Mech. 426, 7394.CrossRefGoogle Scholar
McKenzie, J. F. & Westphal, K. O. 1968 Interaction of linear waves with oblique shock waves. Phys. Fluids 11 (11), 23502362.Google Scholar
Reshotko, E. 2008 Transition issues for atmospheric entry. J. Spacecr. Rockets 45, 161164.CrossRefGoogle Scholar
Ruban, A. I. 1984 On Tollmien–Schlichting waves generation by sound. Izv. Akad. Nauk SSSR Mekh. Zhidk. Gaza (6), 6067.Google Scholar
Salyer, T. R., Collicott, S. H. & Schneider, S. P. 2006 Characterizing laser-generated hot spots for receptivity studies. AIAA J. 44 (12), 28712878.Google Scholar
Schmeisseur, J. D., Schneider, S. P. & Collicott, S. H. 2002 Supersonic boundary-layer response to optically generated freestream disturbances. Exp. Fluids 33, 225232.CrossRefGoogle Scholar
Schneider, S. P., Collicott, S. H. & Schmeisseur, J. D. 2000 Laser-generated localized freestream perturbations in supersonic and hypersonic flows. AIAA J. 38 (4), 666671.Google Scholar
Schneider, S. P., Wheaton, B. M., Julinao, T. J., Berridge, D. C., Chou, A., Gilbert, P. L., Casper, K. M. & Steen, L. E. 2009 Instability and transition measurements in the Mach-6 quiet tunnel. AIAA Paper 2009-3559.Google Scholar
Soudakov, V. G. 2010 Numerical simulation of the effect of acoustic wave inclination angle on a hypersonic boundary-layer receptivity. TsAGI Sci. J. 41 (3), 269284.Google Scholar
Wu, X. 1999 Generation of Tollmien–Schlichting waves by convecting gusts interacting with sound. J. Fluid Mech. 397, 285316.Google Scholar
Zhigulev, V. N. & Fedorov, A. V. 1987 On boundary layer receptivity to acoustic disturbances. J. Prikl. Mekh. Tekh. Fiz. (6), 4349.Google Scholar
Zhigulev, V. N. & Tumin, A. M. 1987 Onset of Turbulence. Nauka (in Russian).Google Scholar
Zhong, X. 2001 Leading-edge receptivity to free-stream disturbance waves for hypersonic flow over parabola. J. Fluid Mech. 441, 315367.Google Scholar