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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 ,
A. A. Ryzhov ,
V. G. Soudakov  and
S. V. Utyuzhnikov
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
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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.

JFM classification

Compressible Flows: Compressible Flows

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Type
Papers
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Journal of Fluid Mechanics , Volume 722 , 10 May 2013 , pp. 533 - 553
Copyright
©2013 Cambridge University Press

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