Congratulations Dr. Boyd and Dr. Meier!

Emma Boyd’s Thesis: A Diffuse Interface Approach for Modeling Solid/Fluid Phase Boundaries with Mass and Heat Transfer
Abstract: Solid rocket motors are the predominant propulsion technology for high-thrust, prolonged-storage applications, notably in missile systems and space launch vehicles. These fuels are heterogeneous and often consist of a mono-propellant embedded in a rubber binder. Melting, dissociation, and pyrolysis all play a role in determining the shape of the burn front and the effectiveness of the burn. Modeling this deflagration poses significant computational challenges due to topological changes such as the formation of fuel binder islands, extreme interface curvatures, and diverse phase change mechanisms. This work introduces a novel diffuse interface approach for modeling multi-phase problems on a single computational mesh that implicitly handles complex topological changes. The method establishes a framework for representing boundary fluxes as interface potentials and captures, among other boundary phenomena, heat transfer, vortex generation, and mass transfer. Focusing on the fluid phase and solid-fluid boundaries, we demonstrate the method’s effectiveness by solving several classical computational fluid dynamics problems. Examples involving heat transfer, varying surface pressure, and complex surface geometries illustrate the method’s relevance to solid propellant deflagration.

Maycon Meier’s Thesis: Thermal-elastic model of regression of solid composite propellants
Abstract: Solid composite propellants (SCPs) are widely used in propulsion due to their stability in long-term storage and simplicity in production and operation. Accurately predicting the regression of SCP burn surfaces is crucial for designing and controlling solid rocket motors. This complex process involves thermal, mechanical, and chemical interactions that result in extreme morphological changes and topological transitions. Previous models have used sharp interface methods that rely on strong assumptions about the topology of the interface, but diffuse interface methods like phase field (PF) offer distinct numerical advantages in modeling such processes. This work presents a thermodynamically-based phase-field model for predicting SCPs burn behavior. We employ a diffuse-species-interface field to capture complex burn chemistry in a reduced-order fashion, enabling the solid phase to be modeled without a fluid solver. The computational implementation uses block-structured adaptive mesh refinement for increased performance and employs adaptive temporal substepping. We apply the model for test cases for homogeneous AP systems and complex heterogeneous AP/HTPB systems. Furthermore, the model is applied to macroscale homogenized SCPs’ geometries to compute the total burning interface as a means of predicting total thrust over time. We observe reasonable quantitative agreement in all cases, even when applied predictively, demonstrating the efficacy of the proposed phase-field model as a numerical design tool for future SCP investigation. Our method improves upon previous models by integrating a thermal solver as the driving force of the PF regression model,
which increases the number of kinematic forces accounted for and allows for the study of thermal diffusivity in the system. Furthermore, our approach implements a strong form elasticity solver to compute the stress fields during the burn. Our method effectively reproduces experimental data by matching temperature, burn rate, stress, and thermal diffusivity profiles. In conclusion, our phase-field model offers a powerful tool for designing and predicting the behavior of SCPs, with the potential to improve future propulsion systems.