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Uncertainty quantification of reacting fluids interacting with porous media using a hybrid physics-based and data-driven approach

Diba Behnoudfar, Kyle E. Niemeyer

TL;DR

This work addresses uncertainty quantification for reacting flows interacting with porous media by marrying physics-based single-domain models with data-driven operator-inference reduced-order models. It preserves a polynomial structure and employs an affine parametric decomposition to enable efficient uncertainty propagation, validated on solid-fuel combustion and ablation in a plasma wind tunnel. The approach achieves accurate surface-temperature predictions (within 5% of data) and quantifies how uncertain parameters like permeability and heat-transfer coefficients affect key quantities, while delivering substantial computational speedups (up to ~380×). The framework provides a practical pathway to rapid, reliable UQ in complex, coupled PDE systems involving porous materials, with open-source tooling and clear avenues for extending beyond affine parameterizations.

Abstract

Accurately simulating 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 a porous material. Repeatedly evaluating these models to quantify parametric uncertainties would be prohibitively computationally expensive. In this work, we combine physics-based modeling using a single-domain approach with data-driven reduced-order modeling to quantify uncertainty via the operator inference method. The detailed physics-based simulations reproduce the measured surface temperature of an object exposed to high-enthalpy flow in a plasma wind tunnel experiment within 5%. We further use the model to demonstrate the effect of complex flow situations on the dynamic interactions between the porous heat shield material and the surrounding gas. The parametric reduced-order model, built on physics-based simulation data, successfully 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 and emission of buoyant reacting plumes in quiescent air and ablation in a wind tunnel.

Uncertainty quantification of reacting fluids interacting with porous media using a hybrid physics-based and data-driven approach

TL;DR

This work addresses uncertainty quantification for reacting flows interacting with porous media by marrying physics-based single-domain models with data-driven operator-inference reduced-order models. It preserves a polynomial structure and employs an affine parametric decomposition to enable efficient uncertainty propagation, validated on solid-fuel combustion and ablation in a plasma wind tunnel. The approach achieves accurate surface-temperature predictions (within 5% of data) and quantifies how uncertain parameters like permeability and heat-transfer coefficients affect key quantities, while delivering substantial computational speedups (up to ~380×). The framework provides a practical pathway to rapid, reliable UQ in complex, coupled PDE systems involving porous materials, with open-source tooling and clear avenues for extending beyond affine parameterizations.

Abstract

Accurately simulating 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 a porous material. Repeatedly evaluating these models to quantify parametric uncertainties would be prohibitively computationally expensive. In this work, we combine physics-based modeling using a single-domain approach with data-driven reduced-order modeling to quantify uncertainty via the operator inference method. The detailed physics-based simulations reproduce the measured surface temperature of an object exposed to high-enthalpy flow in a plasma wind tunnel experiment within 5%. We further use the model to demonstrate the effect of complex flow situations on the dynamic interactions between the porous heat shield material and the surrounding gas. The parametric reduced-order model, built on physics-based simulation data, successfully 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 and emission of buoyant reacting plumes in quiescent air and ablation in a wind tunnel.

Paper Structure

This paper contains 15 sections, 24 equations, 13 figures.

Table of Contents

  1. Introduction
  2. Methodology
  3. Governing equations with a single domain approach
  4. Operator inference for learning reduced order models
  5. Low-dimensional state representation
  6. Learning the operators by solving a least-squares problem
  7. Affine parametric model
  8. Results and discussion
  9. Solid-fuel combustion in quiescent air
  10. Non-parametric model performance
  11. Parametric model performance
  12. Ablation in plasma wind tunnel
  13. Physics-based model performance
  14. ROM performance and quantifying uncertainty due to variability in $h_{fs}$
  15. Conclusions

Figures (13)

  • Figure 1: Computational domain for the buoyant reacting plumes simulation. The portion of the domain used for reduced-order modeling is indicated by the orange dashed line and has dimensions of $14.4H$ by $10H$.
  • Figure 2: Relative ROM error versus time for the non-parametric reduced-order model for the reacting buoyant plume.
  • Figure 3: Evolution of quantities of interest at the center point on the interface in the reacting buoyant plume, with $r=40$ and $\lambda = 10^{-4}$. The dashed line indicates the end of the training data.
  • Figure 4: Non-parametric model predictions at the last time step of training data for the reacting buoyant plume.
  • Figure 5: Sensitivity of the ROM to the number and location of parameter samples
  • ...and 8 more figures