Radiation heat transfer in ablating boundary layer combustion theory used for hybrid rocket motor analysis

Marxman theory is often used for developing correlations of fuel regression rate for hybrid rocket motor analysis. Effects of radiation are accounted for in this theory as a perturbation to the non-radiating blowing limit allowing for the leading order effects of blowing blockage from radiation heat transfer to influence convective heat flux. The theory does not, however, account for the non-linear changes in radiative gas absorption properties to allow for tightly coupled descriptions of heat transfer and surface blowing. In this study, Marxman theory is expanded in a new fully coupled approach, employing Schvab-Zeldovich coupling functions, unsteady heat transfer response of the fuel, and solution of the gas-phase radiation heat transfer. To develop this theory, Marxman's theory is generalized to allow for expanded functional forms of friction coefficient and account for changes in gas properties. To validate the modeling approach, measurements from a simplified slab burner experiment are conducted. Paraffin wax is used as the fuel and relatively low oxidizer fluxes are employed so the dominate effects of radiation heat transfer can be understood. Measurements of temperature, soot volume fraction, and fuel radiative heat flux rely on two-color pyrometry analyses using high-speed camera color images. Comparisons of model predictions to data indicate the new tightly coupled approach provides good predictions of regression rate, temperature, and radiative heat flux to the fuel surface over the range of oxidizer flow rates considered. Model sensitivity studies reveal commonly used one-way coupling strategies may result in significant over prediction in fuel regression rate that are most likely compensated for by errors in simplified treatments of radiation heat transfer. (C) 2020 The Combustion Institute. Published by Elsevier Inc. All rights reserved.