Probabilistic constrained Bayesian inversion for transpiration cooling

International Journal for Numerical Methods in Fluids, vol. 94, pp. 2020–2039

Abstract

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.

Authors 4

1. Ella Steins corresponding Aachen IRTG Modern Inverse Problems

   RWTH Aachen University

   Affiliation as printed

   IRTG Modern Inverse Problems RWTH Aachen University Aachen Germany

   IRTG Modern Inverse Problems, RWTH Aachen University, Aachen, Germany

2. Tan Bui–Thanh
   Affiliation as printed

   Department of Aerospace Engineering & Engineering Mechanics The Oden Institute for Computational Engineering & Sciences Austin Texas USA

   Department of Aerospace Engineering & Engineering Mechanics The Oden Institute for Computational Engineering & Sciences Austin Texas USA

3. Michaël Herty Aachen Institute for Geometry and Practical Mathematics

   RWTH Aachen University

   Affiliation as printed

   Institute for Geometry and Practical Mathematics (IGPM) RWTH Aachen University Aachen Germany

   Institute for Geometry and Practical Mathematics (IGPM), RWTH Aachen University, Aachen, Germany

4. Siegfried Müller Aachen Institute for Geometry and Practical Mathematics

   RWTH Aachen University

   Affiliation as printed

   Institute for Geometry and Practical Mathematics (IGPM) RWTH Aachen University Aachen Germany

   Institute for Geometry and Practical Mathematics (IGPM), RWTH Aachen University, Aachen, Germany