Linear burning rate dynamics of solids subjected to pressure or external radiant heat flux oscillations

Linearized analysis of burning solids subjected to pressure or external radiant heat flux oscillations results in relatively simple expressions for the burning rate response, particularly when combined with quasisteady gas and surface zone assumptions. In this article, a linear expression for the radiant heat flux response function Rq as a function of primary experimental parameters is obtained. The implications of this expression and its relationship to the pressure coupled response function Rp are examined. In particular, the linearized effects of the mean radiant heat flux level and in-depth absorption on Rq are investigated. The linear response to a series of radiant pulses is also presented to suggest an alternate method of experimentally measuring Rq. The effects of nonlinearities are investigated using numerical calculations. It is shown that, in general, the relationship between Rp and Rq is more complicated than a constant scaling factor. The results demonstrate that in-depth absorption of the thermal radiant energy in the solid significantly affects Rq for many practical conditions. Furthermore, even when the equivalence principle holds in the steady case, an equivalent change in the initial temperature does not have the same effect on Rq, in general, as an equivalent mean radiant flux. Also, the mean radiant flux is seen to have a significant effect on Rq. An attempt is made throughout this article to further clarify the relationship and differences between the flame modeling (FM) and the Zeldovich-Novozhilov (ZN) phenomenological approaches in the prediction of Rq and Rp.