Abstract
The evolution of disturbances in a hypersonic viscous shock layer on a flat plate excited by slow-mode acoustic waves is considered numerically and experimentally. The parameters measured in the experiments performed with a free-stream Mach number M ∞ = 21 and Reynolds number Re L = 1.44 · 105 are the transverse profiles of the mean density and Mach number, the spectra of density fluctuations, and growth rates of natural disturbances. Direct numerical simulation of propagation of disturbances is performed by solving the Navier-Stokes equations with a high-order shock-capturing scheme. The numerical and experimental data characterizing the mean flow field, intensity of density fluctuations, and their growth rates are found to be in good agreement. Possible mechanisms of disturbance generation and evolution in the shock layer at hypersonic velocities are discussed.
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References
C. L. Chang, M. F. Malik, and M. Y. Hussaini, “Effect of shock on the stability of hypersonic boundary layers,” AIAA Paper No. 90-1448 (1990).
J. F. McKenzie and K. O. Westphal, “Interaction of linear waves with oblique shock waves,” Phys. Fluids, 11, 2350–2362 (1968).
K. F. Stetson and R. L. Kimmel, “On hypersonic boundary-layer stability,” AIAA Paper No. 92-0737 (1992).
H. L. Reed and W. S. Saric, “Linear stability theory applied to boundary layers,” Annu. Rev. Fluid Mech., 28, 389–428 (1996).
Y. Ma and X. Zhong, “Receptivity of a supersonic boundary layer over a flat plate. Part 2. Receptivity to freestream sound,” J. Fluid Mech., 488, 79–121 (2003).
I. V. Egorov, V. G. Sudakov, and A. V. Fedorov, “Numerical simulation of propagation of disturbances in a supersonic boundary layer,” Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza, No. 6, 33–44 (2004).
M. C. Fisher, D. V. Maddalon, L. M. Weinstein, and R. D. Wagner (Jr.), “Boundary-layer Pitot and hot-wire surveys at M∞ ≈ 20,” AIAA J., 9, No. 5, 826–834 (1971).
J. H. Kemp and F. K. Owen, “Nozzle wall boundary layer at Mach numbers 20 to 47,” AIAA J., 10, No. 7, 872–879 (1972).
J. A. Smith and J. F. Driscoll, “The electron-beam fluorescence technique for measurements in hypersonic turbulent flows,” J. Fluid Mech., 72, No. 4, 695–719 (1975).
S. J. Cowley and Ph. Hall, “On the instability of hypersonic flow past a wedge,” J. Fluid Mech., 214, 17–42 (1990).
N. D. Blackaby, S. J. Cowley, and Ph. Hall, “On the instability of hypersonic flow past a flat plate,” J. Fluid Mech., 247, 369–416 (1993).
C. W. Whang and X. Zhong, “Nonlinear interaction of Gortler and second shear modes in hypersonic boundary layers,” AIAA Paper No. 2000-0536 (2000).
X. Zhong, “Leading-edge receptivity to free-stream disturbances waves for hypersonic flow over a parabola,” J. Fluid Mech., 441, 315–367 (2001).
J. Laufer, “Some statistical properties of the pressure field radiated by a turbulent boundary layer, ” Phys. Fluids, 7, No. 8, 1191–1197 (1964).
K. W. Roger, G. B. Wainwright, and K. J. Touryan, “Impact and static pressure measurements in high speed flows with transitional Knudsen numbers,” in: Rarefied Gas Dynamics, Vol. 2, Academic Press, New York (1966), pp. 151–174.
S. G. Mironov and A. A. Maslov, “An experimental study of density waves in hypersonic shock layer on a flat plate,” Phys. Fluids, A, 12, No. 6, 1544–1553 (2000).
A. Suresh and H. T. Huynh, “Accurate monotonicity-preserving schemes with Runge-Kutta stepping, ” J. Comput. Phys., 136, Part 1, 83–99 (1997).
A. N. Kudryavtsev and D. V. Khotyanovsky, “Numerical simulation of compressible shear layer development with weighted ENO schemes,” in: Computational Fluid Dynamics, Proc. of the ECCOMAS Conf. (Athens, Greece, September 7–11, 1998), Vol. 1, Part 2, John Wiley and Sons, Chichester (1998), pp. 900–905.
M. N. Kogan, Rarefied Gas Dynamics [in Russian], Nauka, Moscow (1974).
A. A. Maslov, S. G. Mironov, and V. M. Aniskin, “Hypersonic shear layer stability experiments, ” J. Spacecraft Rockets, 42, No. 6, 999–1004 (2005).
V. M. Aniskin and S. G. Mironov, “Evolution of controlled disturbances in the shock layer on the compression surface,” J. Appl. Mech. Tech. Phys., 44, No. 5, 626–633 (2003).
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 5, pp. 3–15, September–October, 2006.
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Kudryavtsev, A.N., Mironov, S.G., Poplavskaya, T.V. et al. Experimental study and direct numerical simulation of the evolution of disturbances in a viscous shock layer on a flat plate. J Appl Mech Tech Phys 47, 617–627 (2006). https://doi.org/10.1007/s10808-006-0097-x
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DOI: https://doi.org/10.1007/s10808-006-0097-x