Hybrid Rocket Nozzle Geometry Modelling Using Level Set Method

Kurzfassung

Nozzle erosion remains a significant challenge for the technology readiness level of hybrid rocket engines. To assess the effects of erosion, it is essential to describe the three-dimensional, transient nozzle geometry during engine operation. Using this data, a comprehensive flow analysis within the nozzle and a general performance characterization can be performed. This study will demonstrate a novel method for simulating the time-resolved nozzle geometry, utilising an implicit surface definition, the level set method, and a common erosion rate model for ablative graphite. The heating of the nozzle structure is calculated using empirical heat transfer formulations for the nozzle flow and one-dimensional transient heat conduction in the solid. Subsequently, the erosion rate of the nozzle surface is determined through the application of a chemical reaction rate model, incorporating empirical coefficients. These erosion rates are employed to deform the geometry via a three-dimensional level set method. The surface is defined implicitly by a signed distance function in both the flow field and the structure. The movement of the surface in response to the erosion rates is calculated using the level set method. By doing so, the signed distance function is modified by means of a partial differential equation. This level set equation is discretised using finite differences in time and discontinuous Galerkin tetrahedron finite elements in space. This study presents an implementation of the level set method using the open-source FEniCSx FEM environment. Finally, it presents the results of the grid refinement studies, which demonstrate the effectiveness of the numerical methods employed. Furthermore, it compares the final nozzle shape obtained through the simulation with computed tomography scans from experiments. Thereby validating the method for geometric modelling of nozzle erosion in hybrid rocket engines.