Bayesian inference of mean velocity fields and turbulence models from flow MRI

TL;DR

This paper presents a Bayesian approach to infer mean velocity fields and turbulence model parameters from flow MRI data, successfully reconstructing flow and learning model parameters with uncertainty quantification.

Contribution

It introduces an algorithm that jointly reconstructs flow fields and learns turbulence model parameters from MRI data, applicable to various turbulence models and unsteady flows.

Findings

Successfully reconstructed mean flow in a turbulent jet

Learned turbulence model parameters with quantified uncertainties

Extended methodology to unsteady turbulent flows

Abstract

We solve a Bayesian inverse Reynolds-averaged Navier-Stokes (RANS) problem that assimilates mean flow data by jointly reconstructing the mean flow field and learning its unknown RANS parameters. We devise an algorithm that learns the most likely parameters of an algebraic effective viscosity model, and estimates their uncertainties, from mean flow data of a turbulent flow. We conduct a flow MRI experiment to obtain mean flow data of a confined turbulent jet in an idealized medical device known as the FDA (Food and Drug Administration) nozzle. The algorithm successfully reconstructs the mean flow field and learns the most likely turbulence model parameters without overfitting. The methodology accepts any turbulence model, be it algebraic (explicit) or multi-equation (implicit), as long as the model is differentiable, and naturally extends to unsteady turbulent flows.