Consistently formulated eddy-viscosity coefficient for k-equation model

ABSTRACT

An approach to devising a consistency formulation for $P_k/\epsilon$$P_k/\epsilon$ (production-to-dissipation ratio) is proposed to obtain a non-singular $C_{\mu }$$C_{\mu }$ (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 $q_{\epsilon }$$q_{\epsilon }$ enhancing the dissipation in non-equilibrium flow regions. The model accounts for the distinct effects of low Reynolds number (LRN) and wall proximity. The stress-intensity ratio $R_{\mathrm{b}}=\overline{u_1{u}_2}/k$$R_{\mathrm{b}}=\overline{u_1{u}_2}/k$ is formulated as a function of local variables without resorting to a constant $\sqrt{C_{\mu }^{\ast }}=0.3$$\sqrt{C_{\mu }^{\ast }}=0.3$. The parameters $R_{\mathrm{b}}$$R_{\mathrm{b}}$ and $P_k/\epsilon$$P_k/\epsilon$ entering the turbulence production $P_k$$P_k$ prevents presumably the overestimation of $P_k$$P_k$ 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.

KEYWORDS:

• k-equation model
• turbulence anisotropy
• cubic equation
• production-to-dissipation ratio
• coefficient of eddy-viscosity

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

We are grateful to the National Natural Science Foundation of China (No. 51709070), Natural Science Foundation of Zhejiang Province (LQ17E090007), Key R& D Program of Zhejiang Province (2018C04002).