Abstract

The Reynolds-averaged Navier–Stokes (RANS) models depend on empirical constants to close the Reynolds stress terms. The empirical constants were obtained using experiments conducted at low Reynolds numbers several decades ago. In this paper, we revisit the turbulent viscosity parameter Cμ, based on the stress–intensity ratio c2 = |uw|/k. Here, |uw| and k are the absolute values of the Reynolds stress and turbulent kinetic energy, respectively. Through a priori comparisons, we find that the currently accepted value of Cμ = 0.09 does not agree with the latest direct numerical simulation (DNS) and experimental datasets of wall-bounded turbulent planar flows. Therefore, a new value is suggested by averaging c2 in the equilibrium region, where the production (P) of k is within 10 % of the dissipation rate (ε), and consequently, c4 ≈ Cμ. We evaluate flows up to friction Reynolds number ReΓ ≈ 10 000 and find that with increasing ReΓ, Cμ approaches a value of 0.06, which is almost 50 % lower than the prevalent value of 0.09. Finally, we perform an a priori test with the new (proposed) value of Cμ = 0.06 to show that the estimated turbulent viscosity νT for wall-bounded flows is in much closer agreement with the exact (DNS) values than when νT is estimated using Cμ = 0.09.

Department(s)

Civil, Architectural and Environmental Engineering

Publication Status

Open Access

Keywords and Phrases

CFD; k–ε model; RANS; Turbulence modelling; Turbulence simulation; Turbulent viscosity

International Standard Serial Number (ISSN)

2633-4259

Document Type

Article - Journal

Document Version

Final Version

File Type

text

Language(s)

English

Rights

© 2025 Cambridge University Press, All rights reserved.

Creative Commons Licensing

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.

Publication Date

10 Oct 2024

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