Thesis title: Modeling of Conjugate Heat Transfer Including Ablation and Pyrolysis for Propulsive Applications
A crucial component of space transportation systems is the propulsive nozzle assembly. Here, due to the high temperature and velocity of the exhaust gases, harsh conditions in terms of heat fluxes are faced, leading to the requirement of a proper Thermal Protection System (TPS). Regarding Solid Rocket Motors (SRM) and Hybrid Rocket Engines (HRE), a common solution employed by the aerospace industries worldwide is to use a carbon-based ablative passive TPS. Different types of ablative materials can be employed to this scope, ranging from non-pyrolyzing ablators (e.g., graphite, carbon-carbon (C/C)) to pyrolyzing ablators (e.g., carbon-phenolic (CPh)). Anyway, regardless to the particular carbon-based ablative material selected, the ablative TPS carbon-based surface recedes because of its chemical interaction with the oxidizing species present in rocket engine combustion products, increasing the nozzle throat area and resulting in a engine performance loss. Moreover, it is important to ensure a proper sizing of the ablative TPS, leading to lightweight (i.e., minimum thickness) structures and preventing at the same time an excessive heating of the metallic nozzle back-wall beneath. In this context, reliable numerical models are required to accurately predict the thermochemical and thermophysical behavior of ablative TPS in terms of both surface erosion and in-depth heating.
In this context, the aim of the present thesis is to propose and study different modeling solutions, ranging from high-fidelity to low-order models, to predict nozzle heating, ablation, and pyrolysis as typically faced by ablative TPS in propulsive nozzle applications. In particular, the first part of the present thesis is devoted to the presentation and development of high-fidelity models for both steady-state and transient flow-material in-depth heating, ablation, and pyrolysis simulations. The second part is instead focused on the derivation of low-order models for nozzle throat erosion predictions, to be used in engine preliminary design and parametric analysis.
Regarding the first part, dedicated to high-fidelity models, a numerical framework for the investigation of nozzle ablation and its thermophysical in-depth material response has been established. In particular, axisymmetric Computational Fluid Dynamics (CFD) simulations including finite-rate ablative boundary conditions and pyrolysis gas species injection in the boundary layer, as well as eventual multi-phase flow effects on thermochemical erosion (the latter, a factor which has never received enough attention in the open literature) have been coupled to simulations obtained with the recently developed Porous material Analysis Toolbox based on Open-FOAM (PATO), a transient material response code with specific applications to ablative materials. The present thesis represents the first application of PATO in the open literature to propulsive nozzle ablative analysis. A novel numerical procedure for the generation of finite-rate thermochemical ablation tables for propulsive applications is proposed and described, overcoming the limitation of the classic equilibrium approach employed in state-of-art ablative material response codes. The results obtained by coupling CFD and material response simulations using three different coupling strategy and employing the calculated finite-rate ablation tables are validated by comparison with firing tests data for both SRM and HRE applications. In particular, concerning SRM, two different sub-scale versions of the Space Shuttle solid propellant booster employing a carbon-phenolic nozzle have been analyzed. On the other hand, regarding HRE, the experimental data from a group of 2kN-thrust class CAMUI-type hybrid rocket firing tests performed at the Hokkaido University have been employed for validation. The capabilities of the CFD-material response coupled approach in predicting the erosion onset time and the in-depth heating/pyrolysis of nozzle ablative TPS are stressed by comparing the obtained results with state-of-art steady-state CFD simulations, as well as with the available experimental data.
Moving to the second and final part of the thesis, devoted to low-order models for nozzle erosion prediction, two different class of models (i.e., closed-form regression laws and and a reduced-order physic-based model) have been proposed, developed, and finally implemented in the European Space Propulsion System Simulation (ESPSS) platform. Models implementation allowed to improve the overall predictive capabilities of the solid/hybrid thrust chamber components available in the ESPSS framework by including nozzle erosion effects on engine performances. Models have been validated by means of comparison with a large number of CFD simulations and experimental data available in the literature.