ON THE DEVELOPMENT OF A NEAR WALL-MODEL FOR ABLATING SOLID FUEL REACTING BOUNDARY LAYERS

The focus of this study is to develop a near-wall model for Large Eddy Simulations (LES) of full-scale hybrid rocket motors. The wide span in flow length scales ranging from the turbulent flow structures in the core of the engine to the reacting ablating boundary layer, necessitate the use of subgrid scale (SGS) wall models. Most existing wall models assume non-reacting flows with low or no surface blowing. These models are not suitable for application to hybrid rocket motors. The fundamental challenge in describing these boundary layers is the coupling of flow expansion, chemical reactions with conjugate heat and mass transfer with the fuel surface. Local modeling formulations are therefore desirable. Early attempts at localized solutions include the work of Marxman and co-workers in the 1960s. To explore the limits of Marxman theory, Direct Numerical Simulations of a slab burner configuration are conducted. The DNS is validated using temporal and local experimental regression rate data from a PMMA - GO2 slab burner system and is shown to agree in reasonably well. Analysis of the DNS reveal that Marxman’s assumed momentum profiles are not good approximations, due to the neglection of volumetric expansion from the reacting flame. Further investigation of the DNS also revealed the existence of self-similar solutions using a new set of conservative variables. A similarity formulation is derived by assuming that vertical and streamwise mass flux, total enthalpy and mass fractions are functions of the normalized boundary layer height. By assuming the mass flux profiles from the DNS, the chemical state predicted by the solutions to the similarity problem are shown to agree well to the values from the the DNS.