In the experimental work conducted, two cases have been considered for the six- finned internal star cylinder: the semi-elliptic natural crack and a machined V-cut crack extending the length of the cylinder, both originating from the axis of symmetry of the fin tip. The V-cut crack constitutes a plane strain approximation and is used in current design rationale. Results show that the normalized stress intensity factor (SIF) for the V-cut case are at least equal to, but in most cases are greater than, the natural crack cases. These results were compared to experimental results from Smith and his associates for motor grains having similar shaped off-axis cracks, and similar trends were achieved. Comparisons were also made between the natural crack models and the modified boundary element method of Guozhong, Kangda, and Dongdi (GKD) for a semi-elliptic crack in a circular cylinder and the V-cut crack models to the modified mapping collocation technique of Bowie and Freese (BF), which constitutes the plane strain solution to a circular cylinder with a crack extending the length of the bore. For both cases general trends were similar. Using the numerical results, a relation for estimating the plane strain SIF for the finned cylinder models was developed. The situation of a finned cylinder containing a crack the length of the bore constitutes the worst case scenario. Testing has shown, however, that under normal loading conditions this case is conservative. Penetration tests have shown that a crack penetrating the outer boundary retains its semi-elliptic shape, thus the use of a semi-elliptic crack in design more accurately represents reality. / Master of Science

Design process of a solid rocket motor with the objective of meeting certain mission requirements can be specified as a search for a best set of design parameters within the overall design constraints. In order to ensure that the best possible design amongst all achievable designs is being achieved, optimization is required during the design process. In this thesis, an optimization tool for internal ballistic design of solid rocket motors was developed. A direct search method Complex algorithm is used in this study. The optimization algorithm changes the grain geometric parameters and nozzle throat diameter within the specified bounds, finally achieving the optimum results. Optimization tool developed in this study involves geometric modeling of the propellant grain, burnback analysis, a 0-dimensional ballistic performance prediction analysis of rocket motor and the mathematical optimization algorithm. The code developed is verified against pretested rocket motor performance.

Within the scope of this thesis study, an optimization tool for the ballistic design of three-dimensional grains in solid propellant rocket motors is developed. The modeling of grain geometry and burnback analysis is performed analytically by using basic geometries like cylinder, cone, sphere, ellipsoid, prism and torus. For the internal ballistic analysis, a quasi-steady zero-dimensional flow solver is used. Genetic algorithms have been studied and implemented to the design process as an optimization algorithm. Lastly, the developed optimization tool is validated with the predesigned rocket motors.

The performance prediction of solid propellant rocket motor depends on the calculation of internal aerodynamics of the motor through its operational life. In order to obtain the control volume, in which the solutions will be carried out, a process called &ldquo / grain burnback calculation&rdquo / is required. During the operation of the motor, as the interface between the solid and gas phases moves towards the solid propellant in a direction normal to the surface, the combustion products are generated and added into the control volume. This phenomenon requires handling of moving boundaries as the solution proceeds. In this thesis, Fast Marching Method is implemented to the problem of grain burnback. This method uses the upwinding nature of the propellant interface motion and solves the Eikonal type equations on a fixed three-dimensional tetrahedron mesh. The control volume is coupled to a one-dimensional and a three-dimensional Euler aerodynamic solver in order to obtain the performance of the engine. The speed by which the interface moves depends on the static pressure on the surface of the propellant and comes from the solver. Therefore an iterative method has been proposed between the interface capturing algorithms and the flow solver. Both of the calculation results, which are obtained from one-dimensional and three-dimensional solvers are compared with actual rocket firing data and validated.