Study of the non-viscous flows of a radiating gas by means of differential approximations

Abstract

The problem of the hypersonic streamlining of a blunt body by a non-viscous gas flow allowing for radiative transfer in the shock layer was considered and solved in [1, 2]. The solution of the problem was based on the method of integral ratios. The P 1-th (differential) approximation of the spherical harmonics method was used to allow for the two-dimensional nature of the radiation field and the reabsorption of radiation in the shock layer. The selectivity of the radiation was taken into account by the partition of the continuous radiation spectrum into a number of frequency intervals within each of which the absorption coefficient k v ( p, T) was regarded as being independent of the frequency. In this paper higher P 3-th and P 5-th approximations of the spherical harmonic method are considered and are compared with the P 1-th approximation. In view of the unwieldiness of the P 3-th and P 5-th approximations, unlike [1, 2] a simpler gas-dynamical model is considered: the flow of a radiating gas is studied in the neighbourhood of the leading critical point of a blunt body. Moreover, in this paper a two-stage frequency approximation of the real absorption coefficients of air is investigated for the purpose of explaining the possibility of using such a model to allow for radiation selectivity approximately. The results of calculations of temperature profiles and radiative heat flows are presented for different models of the radiating gas. The presence of local thermodynamic equilibrium in the gas is assumed.