Application of immersed boundary method to the simulation of transient flow in solid rocket motors

Abstract

To avoid the cumbersome re-meshing, an easy-to-implement immersed boundary method (IBM) is developed for simulating the coupling of gas flow and burning surface regression in solid rocket motors (SRM). The treatments of the slip wall boundary and the mass flow inlet boundary in the IBM are described. The Euler equations are discretized on a rectangular Cartesian grid based on the HLLC Riemann solver for inviscid fluxes. The interpolated primitive variables on cell boundaries are determined by using the third-order MUSCL method. The solution of the fluid flow is advanced in time by using the second-order TVD Runge–Kutta scheme. The proposed coupling method updates the burning surface and grid classification once when the movement distance is accumulated to half of the grid cell height. The numerical results of Taylor-Culick flow verify that the developed solver has second-order accuracy in space. To conduct the validation of our method, three typical grains are selected for coupling simulations, which are the perforated cylindrical grain with burning on both the ends and the inner surface, the end-slotted end-burning grain, and the perforated cylindrical grain with erosive burning on the inner surface, respectively. The calculation results show that the proposed IBM with the coupling method leads to low-frequency pressure fluctuations within 0.2% of the mean value during the burning surface regression. The accuracy of the calculation results is verified by the comparison with zero-dimensional interior ballistics, the body-fitted grid method, or experiments in literature.