Effect of Regressing Walls and Skin Friction on Supersonic Solid Fuel Combustion

Solid fuel combustors feature a time-deforming geometry that supports changes in the wall boundary layers. The optimization of the fuel chemistry and combustor geometry requires an understanding of the burn rate response to changes in the boundary-layer characteristics. One key metric of cavity-stabilized flames for supersonic combustion is the wall shear stress and its effect on the burn rate near the aft end of the cavity. A new flamelet model based on the ignition of stagnation-point flames against fuel surfaces is presented that is significantly more accurate than previous models based on flamelet extinction. An erosive burn rate response model is designed and validated against experiments for three stages of deformation using large-eddy simulations. This model approximates turbulent eddy penetration toward the walls using a mixing length damping approach. The erosive model provides much improved regression rates in the late stages of burning, when the combustor operates in scramjet mode, demonstrating the importance of shear stress to the burn rate response. Key to the success of the model is simulating the relaminarization supported by favorable pressure gradients.