Parametric solutions of turbulent incompressible flows in OpenFOAM via the proper generalised decomposition

TL;DR

This paper introduces a novel reduced order method using the proper generalised decomposition (PGD) for efficiently computing parametric turbulent incompressible flows in industrial applications with OpenFOAM, achieving high accuracy and efficiency.

Contribution

It is the first application of PGD to turbulent incompressible Navier-Stokes equations, enabling explicit parametric solutions within OpenFOAM for industrial flow problems.

Findings

Achieves qualitative and quantitative agreement with full-order solutions.

Handles Reynolds numbers up to one million.

Provides efficient parametric flow control solutions.

Abstract

An a priori reduced order method based on the proper generalised decomposition (PGD) is proposed to compute parametric solutions involving turbulent incompressible flows of interest in an industrial context, using OpenFOAM. The PGD framework is applied for the first time to the incompressible Navier-Stokes equations in the turbulent regime, to compute a generalised solution for velocity, pressure and turbulent viscosity, explicitly depending on the design parameters of the problem. In order to simulate flows of industrial interest, a minimally intrusive implementation based on OpenFOAM SIMPLE algorithm applied to the Reynolds-averaged Navier-Stokes equations with the Spalart-Allmaras turbulence model is devised. The resulting PGD strategy is applied to parametric flow control problems and achieves both qualitative and quantitative agreement with the full order OpenFOAM solution for convection-dominated fully-developed turbulent incompressible flows, with Reynolds number up to one million.