| Traditionally, radiative heat transfer is seldom taken into account in the analysis of combustion instability for the solid propellant rocket motor. In a confined domain such as star-shaped propellant surfaces, however, it is quite probable that a considerable portion of heat transfer from the flame to the burning surface is by radiation, as well as by conduction and convection. The main purpose of the present study is, therefore, to investigate the role of radiative heat transfer upon combustion instability as determined from response function calculations.; The formulation is based on the Arrhenius law with a single step forward chemical reaction, idealized two-dimensional mean flow, and impressed arbitrary acoustic wave incidences. Premixed, laminar flame, multi-dimensional radiative heat transfer in participating media will be considered in this study. The response function calculations are ideally carried out using finite elements. Analytical boundary conditions at the flame edge and decomposition zones are implemented via the Lagrange multipliers in finite elements. To this end, we expand the multi-dimensional, nonlinear, time-dependent, simultaneous equations with the relevant boundary conditions into first and second order perturbations.; All excited frequencies are calculated by means of eigenvalue analyses and the combustion response functions corresponding to these frequencies are determined. Effects of radiation, frequencies and incidence angles of impressed pressure waves have been demonstrated. It is also shown that the so-called velocity-coupling stems from the second order perturbation expansion, a phenomenon likely to occur in nonlinear combustion instability. |
