Occurrence conditions and high-speed overlap effect value in shocked gases' mixture

Fluid, gas and plasma mechanics


Аuthors

Kuznetsov M. M.*, Kuleshova Y. D.**, Reshetnikova Y. G.***, Smotrova L. V.****

Moscow Region State University, 10a, Radio str., Moscow, 105005, Russia

*e-mail: kuznets-omn@yandex.ru
**e-mail: juliaybogdanova@mail.ru
***e-mail: gau1972@mail.ru
****e-mail: lilysmotrova@mail.ru

Abstract

In the previous articles the authors formulated two theorems on the high velocity translational non-equilibrium in a shock wave of a one-component (ordinary) gas. It was noted herewith that the proofs of those theorems in case of shocked gas mixture required overcoming of several significant difficulties. The main difficulty consists in the fact that bimodal distribution of molecules velocities in gas mixtures cannot be used without doubt to determine the structure of a shock-wave, as it was done for the ordinary gas. As a rule, the area of applicability of the classic Tamm – Mott-Smith bimodal distribution with constant approximation of the auxiliary macroscopic velocities and kinetic temperatures for the groups of molecules in the supersonic and subsonic “wings” of such distribution is limited by the small values of concentrations of one of the mixture’s components. Only in this case it is possible to keep all the advantages of the bimodal approximation of partial distribution functions in binary gas mixture to obtain a simple analytical solution for shock wave structure. That is why obtaining necessary and sufficient conditions for high velocity translational non-equlibrium for arbitrary values of gas mixtures’ component concentration becomes much more complex.

The paper presents rigorous formulation and substantiation of these conditions.

These conditions are applicable to the case of variable auxiliary approximation macro parameters of “hot” wing of a binary gas mixture bimodal distribution. At the same time, the values of auxiliary macroscopic velocities and kinetic temperatures for groups of molecules in subsonic «wing» are kept constant. In binary gas mixtures with distribution functions for both the light and heavy components three types of functions of molecules’ pairs distribution throughout their relative velocity module exist. These functions are: G(ll) is the distribution function of pairs inside a light-light component, G(lh) the function of molecules’ pairs of light-heavy component and G(hh) is a function of molecules’ pair inside a heavy component. The numerical calculations of the corresponding “overlap” effect of bimodal distributions for pair of molecules was performed for a special case of small concentration values of heavy component in binary gas mixture (Rayleigh gas). It is known that in Rayleigh gas this effect for function G(hh) is most noticeable. While its computation, the molecules’ rotating degrees of freedom were accounted for.

Keywords:

kinetic, equation, non-equilibrium, gas mixture, shock wave

References

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