Numerical Simulation of Complicated Grain Burnback in Three Dimensions

Instantaneous grain geometry is one of the most affecting parameters on the performance of the solid rocket motors (SRMs). This paper presents the simulation of geometrically complicated solid propellant grain burnback using the level set method. The initial form of the grain is assumed in this method. Propagation of the grain boundaries in a velocity field is described using the Hamilton-Jacobi type equation. The solution of this equation in successive time steps gives the new burning boundaries of the grain. For this purpose, the initial geometry of grain is modeled in any CAD software. Then, the initial burning surfaces of grain are implicitly defined by the sign distance function and are used as the initial conditions of the level set equation. The geometrical characteristics of grain, such as burning surface area, port area, burning perimeter, and port volume are determined by Heaviside and Delta Dirac functions. The result of simulation is validated by an analytically predictable case, which shows excellent agreement. Burnback analysis is done for some practical grains including two cases that the test data were available. Using an unsteady zero dimension interior ballistic analysis, the resulting motor pressure curves are compared with the experimental data showing good agreement. The capability of the approach to handle the analyzing of problems, including non uniform burning velocity and arbitrary burnout configurations of grain are shown in examples.