Consistently formulated eddy-viscosity coefficient for k-equation model

• Published in: Journal of turbulence Vol. 19; no. 11-12; pp. 959 - 994
• Main Authors: Rahman, M. M., Keskinen, K., Vuorinen, V., Larmi, M., Siikonen, T.
• Format: Journal Article
• Language: English
• Published: Taylor & Francis 02.12.2018
• Subjects: coefficient of eddy-viscosity; cubic equation; k-equation model; production-to-dissipation ratio; turbulence anisotropy
• ISSN: 1468-5248; 1468-5248
• DOI: 10.1080/14685248.2019.1567926

An approach to devising a consistency formulation for (production-to-dissipation ratio) is proposed to obtain a non-singular (coefficient of eddy-viscosity) embedded in the one-equation model based on the turbulent kinetic energy k. The dissipation rate ε is evaluated with an algebraically prescribed length scale having only one adjustable coefficient, accompanied by an anisotropic function enhancing the dissipation in non-equilibrium flow regions. The model accounts for the distinct effects of low Reynolds number (LRN) and wall proximity. The stress-intensity ratio is formulated as a function of local variables without resorting to a constant . The parameters and entering the turbulence production prevents presumably the overestimation of in flow regions where non-equilibrium effects could result in a misalignment between turbulent stress and mean strain rate with a linear eddy-viscosity model. A comparative assessment of the present model with the Spalart-Allmaras (SA) one-equation model and the shear stress transport (SST) k-ω model is provided for well-documented simple and non-equilibrium turbulent flows. Finally, the current model provides a proposal to compute free shear flows.