Burning rate distributions for boundary layer flow combustion of a PMMA plate in forced flow

Abstract

Solutions of Navier-Stokes (NS) equations were obtained for burning rate Nu and temperature distributions for a flat, PMMA plate using an iterative method to impose steady-state, pyrolysis kinetics at the surface. The NS solutions show that Nu depends on both Reynolds number Re and air velocity U unlike the classical solutions, which include the boundary layer (BL) approximations. However, at large values of Re (Re >1000) and U (U >120 cm/s), the NS solutions can be represented by Nu = ε +0.1 Re 1/2, where the intercept ε increases with U and the slope is identical to that given by the classical BL solutions. The NS solutions are compared with experiments, in which short (10 cm) PMMA plates were ignited uniformly and burnt for different lengths of time. The comparisons show that the steady-state surface pyrolysis approximation holds in the middle region of the pyrolysis zone, where the NS solutions agree with the data for Nu. Near the leading edge, where the heat feedback is high, the NS solutions over-predict the measurements as the initially flat surface becomes curved (concave) and forms a valley due to the moving boundary. As the valley size increases with time, the deviations between the NS solutions and data increase and extend to increasing distance from the leading edge. Far from the leading edge, where the heat feed back is low, NS solutions also over-predict the data due to transient effects caused by in-depth pyrolysis. As the melt approaches the pyrolysis temperature, the data approach NS solutions with increased burn times. Therefore, the curvature and in-depth heat transfer/pyrolysis effects are significant within the pyrolysis zone at large and small burn times, respectively.