Reduced-order modeling of reactive flows interacting with uncertain porous media using a hybrid physics-based and data-driven approach

Accurately capturing coupled physical processes under uncertainty is essential for reliable modeling and design in performance-critical applications such as combustion systems. Ablative heat shield design, as a specific example of this class, involves modeling multi-physics interactions between reacting flows and the porous material. These models can involve multiple uncertain parameters, including the transport properties of the porous heat shield material. Since new low-density ablative materials are highly porous, the flow at the interface between the surrounding gas and the porous material can exhibit a variety of behaviors, depending on the flow regime. Despite advancements in this field, the interaction between porous heat shields and the surrounding complex flow remains poorly understood. On the other hand, repeated evaluations of the models to quantify parametric uncertainties are computationally expensive. In this work, we combine physics-based modeling using a single-domain approach with reduced-order modeling via the operator inference method. In a previous study, we demonstrated that a single-domain modeling approach is effective for capturing these interfacial processes in the problem of solid fuel combustion and near-field flow dynamics. In this approach, transport phenomena are captured through spatially averaged equations, enabling a uniform representation across the entire domain. Results from the physics-based simulations show that the model can reproduce the surface temperature of an object exposed to high-enthalpy flow in a plasma wind tunnel experiment within 2%. We further use the model to demonstrate the effect of fluctuations in the surrounding flow on the heat fluxes at the interface. The parametric reduced-order model, built on physics-based simulation data, captures variations in quantities of interest resulting from changes in the permeability and heat transfer coefficient of the porous material in two separate studies: solid fuel combustion in quiescent air and ablation in a wind tunnel.