A robust spectral element implementation of the $k - τ$ RANS model in Nek5000/NekRS
- Aristotle University of Thessaloniki (Greece)
- Argonne National Laboratory (ANL), Argonne, IL (United States)
- Argonne National Laboratory (ANL), Argonne, IL (United States); Pennsylvania State University, University Park, PA (United States)
- University of Illinois at Urbana-Champaign, IL (United States); Argonne National Laboratory (ANL), Argonne, IL (United States)
The $k - ω$ Reynolds Averaged Navier Stokes (RANS) model is one of the industry standard approaches for modeling of turbulent flows. It performs better than the $k - ϵ$ model for low Reynolds number flows and is also more suitable for boundary layers with adverse pressure gradients. Major drawback of the model, however, is that the asymptotic value of $$ω$$ at the walls is singular, necessitating the use of a contrived “sufficiently” large value for $$ω$$ as the boundary condition for its transport equation. Here, this invariably leads to the solution being sensitive to near wall grid spacing. While an acceptable solution for low order (finite volume) methods, the excessive near wall gradients lead to persistent numerical stability issues in high order codes. To alleviate the problem, specifically in the context of the high order spectral element code Nek5000, a regularized $k - ω$ approach was formulated in our prior work (Tomboulides et al., 2018). The formulation, however, relies on the use of wall distance and its gradients for modeling the closure terms and can pose problems for simulations in complex geometries. This work presents a novel implementation of the $k - τ$ RANS model in Nek5000, where $τ = 1/ω$, eliminating the need for regularization, owing to the asymptotically bounded behavior of the source terms in the $$τ$$ transport equation, and also eliminating dependence on wall distance. Robustness and stability of the $k - τ$ model is ensured through implicit treatment of the source terms and their careful numerical implementation and demonstrated through several cases aimed at verification and validation. Studies include both canonical and engineering relevant problems, viz., turbulent channel flow, pipe flow, backward facing step, flow over NACA 0012 airfoil and flow in a T-junction. Results from the $k - τ$ model are shown to be consistent with regularized $k - ω$ model and also with the $k - ω$ SST model in OpenFOAM (for select studies). Comparison with experimental data is also shown, where available, to bolster validation efforts for the $k - τ$ model implementation through prediction of key turbulent quantities of interest.
- Research Organization:
- Argonne National Laboratory (ANL), Argonne, IL (United States)
- Sponsoring Organization:
- USDOE Office of Nuclear Energy (NE), Nuclear Energy Advanced Modeling and Simulation (NEAMS)
- Grant/Contract Number:
- AC02-06CH11357
- OSTI ID:
- 2588840
- Journal Information:
- International Journal of Heat and Fluid Flow, Journal Name: International Journal of Heat and Fluid Flow Vol. 112; ISSN 0142-727X
- Publisher:
- Elsevier BVCopyright Statement
- Country of Publication:
- United States
- Language:
- English
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