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

TL;DR

This work addresses the lack of a validated tool for computing the full resolved Reynolds stress transport equation budget in OpenFOAM by implementing a function-object library within LES. The authors verify the approach against high-fidelity DNS for channel and pipe flows at friction Reynolds number 180, demonstrating term-by-term convergence of the budget toward DNS references as mesh resolution increases. The study provides detailed, open-source utilities to compute convection, production, turbulent transport, pressure diffusion, pressure-strain, viscous diffusion, dissipation, and SGS terms, enabling deeper physical insight and facilitating advanced turbulence model development. The open-source tool offers a robust framework for turbulence analysis in OpenFOAM, with potential to enhance model validation and accelerate closures, while future work aims to reduce memory usage and extend applicability to cylindrical and spherical geometries.

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$_τ=180$. 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.

Figures (12)

• Figure 1: Mesh topology for channel (Fig. \ref{['fig:chan_flow_mesh']}) and pipe flow (Fig. \ref{['fig:pipe_flow_mesh']}). The number of cells has been reduced in this figure for visualisation purposes.
• Figure 2: Velocity $\langle u \rangle$ and TKE $k$ profiles.
• Figure 3: Profiles of $R_{ij}$, specifically components $11$, $22$, $33$, and $12$.
• Figure 4: RSTE budget for the streamwise normal stress component $\langle u^{\prime}_1 u^{\prime}_1\rangle$.
• Figure 5: RSTE budget for the wall-normal stress component $\langle u^{\prime}_2 u^{\prime}_2 \rangle$.