A physics-based two-dimensional comprehensive mathematical model to predict non-uniform regression rate in solid fuels for hybrid rocket motors

A numerical study using a comprehensive physics based mathematical model is conducted to predict the fuel regression rate in hybrid rocket fuels. The physical model adopted for the study is based on an unsteady, two-domain (solid fuel and gaseous oxidizer coupled through a moving interface) concept where both domains are assumed to be two-dimensional. The oxidizer gas flow is assumed to be compressible and turbulent with Navier-Stokes Assumptions. The radiative heat transfer is incorporated to the energy equation for the gas domain using the Rosseland diffusion approximation. Fuel is assumed to be a nontransparent isotropic solid. The two domains are coupled through an energy balance at the interface that includes heat transfer due to radiation, conduction, and ablation. The regression rate of the fuel surface due to ablation is modeled using the first-order Arrhenius Equation. The combustion of the ablated fuel is modeled by single step, three species chemical reaction equation of second order Arrhenius type. The solution to the governing differential equations of the present model is obtained by first transform the solution domain using a time and space dependent transformation. In the gas domain the transformed set of differential equations is discretized by a fully implicit finite-difference technique then linearized by using Newton linearization method. The resulting set of algebraic equations are transformed by the Coupled Modified Strongly Implicit Procedure (CMSIP) for the primitive variables of the problem. Validation of the solution algorithm and the CMSIP that is developed for this study is validated through the study of two bench mark cases: driven cavity and flow through channel. Furthermore, the results of the comprehensive model are compared to those of the parabolic incompressible model. Finally the proposed comprehensive mathematical model is used to predict the unsteady temperature and pressure distributions, and the velocity field in the gas domain and temperature distribution in the solid fuel as well as the regression rate at the gas-solid interface during the ignition and burning of the a typical hybrid rocket solid fuel. The effect of oxidizer mass flow rate (Mach number), chamber pressures on regression rate is also studied using the proposed comprehensive model.