Application of the level set method in solid propellant grain burnback with dogbone grain as a case study

Solid propellant grain burnback is a crucial step internal ballistic module. There are different methods to predict grain burnback; the oldest method is the drafting technique where the burning surface is tracked using manual drawing applying surface regression rules. Then there is the analytical method, where a geometric analysis of the surface is performed and analytical expressions for the burning surface segments are derived. These expressions are evaluated at different values of burnt distance to find the evolution of burning surface and port areas with time. A level set method is a different approach which, in some aspects, may be considered a drafting technique where the burning surface segments are tracked. From another point of view, it is a numerical method that tracks the burning surface with no need of trying to derive analytical expressions for burning segments. Dogbone grain is known for its structural superiority; however, researches dealing with dogbone grain design parameters are scarce. In this paper, the level set method is introduced and the main steps for its implementation are elaborated. Validation of the level set method is performed against the drafting technique using CAD and analytical expressions for the well-known star grain. Finally, dogbone grain geometry with different configurations is introduced and a parametric study for the governing parameters that affect dogbone grain burnback is performed.