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Zababakhin Scientific Talks - 95
October 1995

http://www.ch70.chel.su/vniitf/events/1995/zab/abstr73.txt

NUMERICAL SIMULATION OF A THIN HEATED LAYER SEPARATION UNDER INTERACTION WITH A SHOCK WAVE

B.N. Gordeichik, M.D. Scherbin, V.N. Zabavin
Central Institute of Physics and Technology, Defence Ministry of Russian Federation, Sergiev Posad-7

Let us take a nonviscous flow with a shock wave moving along a surface to which a heated layer of gas is adjoined. It is well known that a stationary flow with curved front is formed in case the layer temperature is not too high and it can penetrate into a region behind a shock front. If the layer temperature exceeds some threshold value the global alteration of the whole flow takes place: a precursor is formed in front of shock wave, a vortex separating the heated layer from the surface is formed in the area of interaction, and the flow turns into a non-stationary one. In practical tasks size of disturbance may exceed the layer depth by two or three orders. It is impossible to use direct numerical simulation for tasks of this type due to limited computer resources. Boundary conditions for numerical simulation of flows with a thin heated layer separation are presented in this study. The depth of the layer here is supposed to be small in comparison with the size of one cell.

Preliminary analysis of Euler equations shows that thin heated layer cannot change the general balance of mass, impulse and energy in the flow but it alters the circulation rate variation which is an integral flow characteristic. And the alteration in its first approximation does not depend upon the layer depth but is determined by layer temperature and shock characteristics. The mode of interaction may be stationary when all generated vorticity is taken down by the flow away from the region. Yet the rate of circulation taking away may not exceed a certain value depending upon shock parameters while circulation generation rate may increase unlimitedly when heated layer density decreases. Therefore if layer density is less than some threshold value the produced vorticity cannot be taken away out of the interaction region. As a result a growing vortex is formed which evokes layer separation and a precursor wave generation.

The above interpretation allowed to produce boundary conditions imitating an infinitely thin heated layer near the surface. This is the way to avoid thin heated layer simulation in the analyzed region and the inner mechanism of interaction - vortex formation being intact.

The physical analysis of the task allowed to clear out interaction mechanism between a shock and a thin heated layer and to produce a method of numerical simulation of this phenomenon.