Stationary combustion modes with allowance for heat losses

Abstract

An attempt is made to investigate the number of possible stationary combustion modes in a continuous-flow semi-infinite pipe with allowance for heat losses through the walls. Cases of a zero-order reaction in the reaction mixture or similarity of the concentration and temperature fields are considered. The equations are averaged with respect to the transverse coordinate η. Within the framework of these approximations it is found that the number of stationary combustion modes is determined by the roots θ_n of some function. The roots θ_2k correspond only to trivial unstable solutions. The roots θ_2k−1 correspond to modes possible within broad regions of variation of the parameters characterizing the temperature of the mixture, the mixture feed rate, and the rate of heat removal. These regions intersect, forming zones where several stationary modes coexist. In these zones, apart from monotonic solutions there may also be solutions that initially make several oscillations. It is shown that the latter are obviously unstable and, in the last analysis, lead to one of the monotonic modes. The common case of not more than three roots is examined in detail.

If the heat release function can change sign, then a similar picture is also observed in the absence of heat losses through the walls (the roots θ_2k−1 and θ_2k may change roles). In this case it is no longer necessary to average the equations with respect to η, since there will not be any corresponding derivatives.