Abstracts - KTH Mechanics

48
Interaction of acoustic disturbances with a hypersonic shock layer
on a flat plate
S. G. Mironov 1, A. N. Kudryavtsev 1, T. V. Poplavskaya 1,
I. S. Tsyrjulnikov 1
The problem of receptivity and evolution of disturbances in a shock layer on a
temperature-controlled flat plate at zero angle of attack subjected to a hypersonic
nitrogen flow with a Mach number equal to 21 and the Reynolds number based on the
free-stream parameters and on the plate length ReL= 1.44 10 5 has been solved for the
first time by methods of direct numerical simulation on the basis of two-dimensional
Navier-Stokes equations. The temperature factor of the surface is 0.25. Interaction of
the shock layer with external acoustic slow-mode disturbances propagating in the
streamwise direction is considered. The results of simulations are the mean flow field
and the field of fluctuating parameters.
Simulations are compared with the mean density and Mach number measured in
the shock layer, which displays good qualitative and quantitative agreement in the
entire shock-layer flow. The computations also show that there are two maximums of
density fluctuations in the shock layer; one of them (with a higher amplitude) is
located on the shock wave, and the other (with a lower amplitude) is located in the
region of rapid variations of the mean temperature and density across the shock layer.
The phases of density fluctuations in these maximums are shifted by 180 relative to
each other. Electron-beam measurements confirm the presence of these maximums of
density fluctuations and reveal good qualitative and quantitative agreement with
computations in terms of intensity of density fluctuations on the shock wave.
Visualization of the numerical vector field of velocity fluctuations displays pairs of
counterrotating vortices between the shock wave and the region of rapid variations of
density and temperature. The presence of two maximums of density fluctuations and
the magnitude of the phase shift between them can be attributed to the dominating
effect of vortex disturbances on the mean flow in the shock layer. To check this
hypothesis, it was demonstrated within the framework of the linear theory of
interaction of acoustic waves with the shock wave that the conditions of existence of
acoustic disturbances behind the shock wave are not satisfied for all angles of
interaction of acoustic waves with the bow shock wave, which are observed in
experiments and numerical simulations. On the other hand, entropy-vortex
disturbances can arise and propagate behind the shock wave for all angles of
interaction, which is actually observed in direct numerical simulations of interaction of
external acoustic disturbances with the shock layer on a flat plate.
This work was supported by the Russian Foundation for Basic Research (Grants
04-01-00474 and 05-08-33436).
1 Institute of Theoretical and Applied Mechanics SB RAS, 630090, Novosibirsk, Russia