Implementation and verification of the resolved Reynolds stress transport equations in OpenFOAM

TL;DR

This paper introduces and validates an open-source tool in OpenFOAM for computing the complete Reynolds Stress Transport Equation in LES, enabling detailed turbulence analysis and model development.

Contribution

The work implements and validates a comprehensive RSTE calculation library in OpenFOAM, filling a gap in open-source CFD tools for turbulence research.

Findings

The library accurately captures all RSTE budget terms.

Results converge towards DNS reference data with mesh refinement.

Validated on wall-bounded turbulent flows at Re_τ=180.

Abstract

The analysis of the Reynolds Stress Transport Equation (RSTE) provides fundamental physical insights that are essential for the development and validation of advanced turbulence models. However, a comprehensive and validated tool for computing the complete RSTE budget is absent in the widely-used open-source Computational Fluid Dynamics (CFD) framework, OpenFOAM. This work addresses this gap by presenting the implementation and a posteriori validation of a function object library for calculating all terms of the resolved RSTE budget in Large-Eddy Simulations (LES). The library is applied to simulate two canonical wall-bounded turbulent flows: a channel flow and a pipe flow, both at a friction Reynolds number of Re$_{\tau}=180$. The implementation is validated through a mesh refinement study where the results from the LES simulations are systematically compared against high-fidelity Direct Numerical Simulation (DNS) data. The computed budget terms are observed to converge systematically towards the DNS reference data. This validation demonstrates that the implemented library accurately captures the intricate balance of all budget terms. This contribution provides the open-source CFD community with a powerful utility for detailed turbulence analysis, thereby facilitating deeper physical understanding and accelerating the development of next-generation turbulence models.