Convective heat exchange in a radiating gas

Abstract

The problem of radiating gas flow past a blunt body has been studied by many authors. A quite complete review of these studies is presented in [1, 2]. Basic attention has been devoted to determining the radiant fluxes to the body surface and calculation of the parameter distribution across the shock layer. In many studies, particularly the foreign ones, use has been made of the approximation of “bulk” luminescence. In this approximation a term is added to the energy equation in order to account for the effect of the radiant heat exchange. This term is equivalent to the heat flux, whose intensity depends on the local thermodynamic state of the gas. With the use of this assumption the gas enthalpy in the inviscid flow vanishes at the stagnation point. The singularity resulting from the use of various approximations was revealed in [3–5]. This singularity is caused by the fact that a gas particle moving along the stagnation streamline to the body is retarded over an infinitely long time. Obviously, if we take into account the dissipative processess (for example, thermal conduction) which really take place, the singularity disappears. For a perfect gas it may be shown that the enthalpy and velocity are equal to zero along the entire surface of the body. Then the use of conventional boundary layer theory becomes impossible. The concept of a viscous and heat-conducting shock layer has been used in [5,6] and also by the present authors to eliminate this difficulty. However, this approach leads to unjustified complication of the problem and forces the introduction of more or less rough assumptions in carrying out the calculations. In the present study we have investigated a form of the boundary layer equations and the corresponding boundary conditions for flows with “bulk” gas luminescence and approximating flow regimes with small “optical” thickness of the shock layer. The solution was carried out with the aid of the method of inner and outer expansions (for example, [7]). The form of the equations and the boundary conditions differed depending on which of the dissipative processes-thermal conduction or absorption of the radiation by the gas in a narrow layer cooled by luminescence of the near-wall layer, was dominating. (The existence in the inviscid shock layer with small but finite “optical” thickness of an absorbing near-wall sublayer was discovered by V. N. Zhigulev, and also in [2].) In the present study we have used the “Newtonian” approximation, analogous to that considered for the nonradiating gas by Shidlovskii [8], This made it possible to obtain most of the results in a simple, easily visualized form. However, the flow regimes considered and the corresponding parameters do, of course, have general significance.