| Abstract: | This article discusses self-similar statements of the problem of the motion of a completely radiating and absorbing gas. The field of radiation is assumed to be quasi-steady-state, and the contribution of the radiation to the internal energy, as well as the pressure and the viscosity of the medium, are not taken into account. The presence of local thermodynamic equilibrium is assumed. The absorption coefficient is approximated by a power function of the pressure and the density. Scattering of the radiation is not taken into account. Under these assumptions, there exist self-similar statements of the problem for one-dimensional unsteady-state flows (a strong detonation, the problem of plug-flow, motion under the effect of a radiation source, and others) and two-dimensional steady-state flows (flow in a diffuser, supersonic flow around a wedge or a cone). It is shown that there exists a non steady-state spherically symmetrical flow depending on four parameters; this flow is adiabatic in spite of the presence of radiation. This article is made up of seven sections. It is shown in the first section that the presence of radiation leads to the appearance of new dimensional constants, entering into the equations of the problem. The second section is devoted to self-similar nonsteady-state one-dimensional flows. The third section contains a detailed study of one class of such flows. In a partial case, adiabatic flows of a radiating gas are obtained. In the fourth and fifth sections, a detailed analysis is made of the initial and boundary conditions from the point of view of dimensionality. The sixth section describes self-similar two-dimensional steady-state flows of a radiating-absorbing gas. The seventh section consists of remarks with respect to approximations of the transfer equation.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 8–22, July–August, 1970. |
