Abstract
The influence of a local change in surface temperature of a contoured nozzle corresponding to the Mach number M = 6 on the boundary layer stability and laminar-turbulent transition is numerically studied. The profiles of the laminar boundary layer are obtained by solving the Navier-Stokes equations with the use of the Ansys Fluid software system. N-factors of the growth rates of the Goertler vortices and also disturbances of the first and second Mack modes are calculated in the approximation of the linear stability theory. It is demonstrated that local heating ensures lower growth rates of the amplitudes of the Goertler vortices and the first Mack mode as compared to the base case; the more intense the heating, the more expressed this effect. The growth rate of the amplitude of the second-mode disturbances decreases during local heating of the nozzle to a temperature close to the stagnation temperature and increases at higher temperatures of local heating. It is found that local cooling leads to an increase in the growth rates of the amplitudes of the Goertler vortices and second Mack mode. The amplitude of the first Mack mode in the cooling region is smaller than that in the base case; however, further downstream, it is much greater than that in the base case. It is found that the surface of contoured nozzles should be heated in the region of the maximum growth rates of the amplitudes of the Goertler vortices; the higher the temperature, the more pronounced the expected effect. However, the maximum possible temperature is determined by the growth of the second Mack mode. The optimal option is to use the temperature of local heating of the surface at which the growth rate of the amplitude of the second mode is smaller than that of the Goertler vortices.
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References
I.E. Beckwith, M.R. Malik, F.-J. Chen, and D.M. Bushnell, Effects of nozzle design parameters on the extent of quiet test flow at Mach 3.5, in: Proc. Laminar-Turbulent Transition, IUTAM Symp., Novosibirsk, 1984, ed. V.V. Kozlov, Springer-Verlag, Berlin, Heidelberg, 1985, P. 589–600.
T. Brogan and A. Demetriades, Effects of surface heating on instabilities in a supersonic nozzle boundary layer, AIAA Paper No. 1998-779, 1998.
S.P. Schneider, Design and fabrication of a 9.5-inch Mach-6 quiet-flow Ludwieg tube, AIAA Paper No. 998–2511, 1998.
A. Demetriades, Stabilization of a Nozzle boundary layer by local surface heating, AIAA J., 1996, Vol. 34, No. 12, P. 2490–2495.
A.V. Dovgal, V.Ya. Levchenko, and V.A. Timofeev, Boundary layer control by a local heating of the wall, in: Proc. Laminar-Turbulent Transition, IUTAM (Springer, Berlin, Heidelberg, 1990, P. 113–121).
R.-S. Lin, V. Iyer, and M.R. Malik, Throat heating effect on critical roughness and nozzle wall boundary-layer stability, AIAA J., 2003, Vol. 41, No. 4, P. 612–622.
N.M. El-Hady and A.K. Verma, Instability of compressible boundary layers along curved walls with suction or cooling, AIAA J., 1984, Vol. 22, No. 2, P. 206–213.
N.V. Semionov and A.D. Kosinov, Method of laminar-turbulent transition control of supersonic boundary layer on a swept wing, Thermophysics and Aeromechanics, 2007, Vol. 14, No. 3, P. 337–341.
S.V. Lukashevich, S.O. Morozov, and A.N. Shiplyuk, Experimental study of the effect of a passive porous coating on disturbances in a hypersonic boundary layer. 2. Effect of the porous coating location, J. Appl. Mech. Tech. Phys., 2016, Vol. 57, No. 5, P. 873–878.
A.V. Fedorov, V.G. Soudakov, I.V. Egorov, A.A. Sidorenko, Y.V. Gromyko, D.A. Bountin, P.A. Polivanov, and A.A. Maslov, High-speed boundary-layer stability on a cone with localized wall heating or cooling, AIAA J., 2015, Vol. 53, No. 9, P. 2512–2524.
S.O. Morozov and A.N. Shiplyuk, Laminar boundary layer stability calculation for contoured Mach 6 nozzle, Thermophysics and Aeromechanics, 2020, Vol. 27, No. 1, P. 35–44.
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This work was financially supported by the Russian Foundation for Basic Research (Project No. 19-08-00794).
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Morozov, S.O., Shiplyuk, A.N. Investigation of the influence of a local change in surface temperature on the laminar boundary layer stability in a hypersonic nozzle. Thermophys. Aeromech. 27, 633–642 (2020). https://doi.org/10.1134/S0869864320050017
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DOI: https://doi.org/10.1134/S0869864320050017