Regression rates in boundary layer combustion

Abstract

This paper is concerned with the re-examination of the hybrid regression rate equation proposed by Marxman and co-workers and long accepted in the combustion literature. The important conclusion of the theory that the regression rate, being a weak function of the mass transfer number B, is nearly independent of the properties of the fuel and oxidiser is shown not to be borne out by the experimental studies including those of Marxman et al. Experiments specifically designed by the present authors to elucidate the dependence of the mass transfer number B are described. It is shown that the exponent on B is 0.5 instead of 0.23 from the data on rubber-oxygen+nitrogen system. A theory is proposed here to explain these results. One element of the theory is that the density variation across the boundary layer as affected by temperature and, more importantly, molecular weight has significant effect on the blocking effect (reduction in skin friction coefficient with injection). It is first shown that the theory explains the long standing results on the blocking effectwith denser gas injection. This result is then combined with the known fact that in polymer combustion environment the mean molecular weight of fueld gases near the surface is much larger than monomer molecular weight by a factor of 4-6 to obtain modified predictions on regression rate. A new regression rate law has been obtained incorporating these features and it reads as ρ_pr=0.056G^0.8(x/μ)^-0.2(ρ_f/ρ_e)^0.71(ρ_w/ρ_e)^0.14. B(1+B)^{−0.73+0.002ρ_w/ρ_e} where ρ_w, ρ_e and ρ_f are the densities at the central core, wall and the flame respectively. The predicted results are shown to remove the anomalies present in the earlier prediction procedures. The new regression rate law may have far reaching consequences in hydrbrid regression rate theory as well as erosive combustion in solid propellants.