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

Marxman theory is often used to develop 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. However, this theory does not account for the non-linear changes in radiative gas absorption properties to allow for tightly coupled descriptions of heat transfer and surface blowing. Marxman theory can be modified to a fully coupled approach, by employing Schvab-Zeldovich coupling functions, and solutions of the gas-phase radiation heat transfer to account for this non-linear change in radiative properties. During the development of this theory, Marxman’s analysis 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 compared. Paraffin wax is used as the fuel and relatively low oxidizer fluxes are employed so the dominate effects of radiation heat transfer are present. Experimental data and model comparisons indicate the tightly coupled approach provides good predictions of regression rate over the 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.