Probabilistic Constrained Bayesion Inversion for Transpiration Cooling

TL;DR

This paper introduces a probabilistic approach using Bayesian inversion and Polynomial Chaos to estimate coolant requirements in transpiration cooling, ensuring safety under uncertain conditions in rocket applications.

Contribution

It presents a novel Bayesian inversion method with chance constraints for modeling transpiration cooling, incorporating Polynomial Chaos and MCMC techniques.

Findings

Effective posterior distribution estimation under uncertainties.

Successful application to 2D transpiration cooling models.

Enhanced safety margin predictions for cooling systems.

Abstract

To enable safe operations in applications such as rocket combustion chambers, the materials require cooling to avoid material damage. Here, transpiration cooling is a promising cooling technique. Numerous studies investigate possibilities to simulate and evaluate the complex cooling mechanism. One naturally arising question is the amount of coolant required to ensure a safe operation. To study this, we introduce an approach that determines the posterior probability distribution of the Reynolds number using an inverse problem and constraining the maximum temperature of the system under parameter uncertainties. Mathematically, this chance inequality constraint is dealt with by a generalized Polynomial Chaos expansion of the system. The posterior distribution will be evaluated by different Markov Chain Monte Carlo based methods. A novel method for the constrained case is proposed and tested among others on two-dimensional transpiration cooling models.