## Abstract

An approach to devising a consistency formulation for Pk/ϵ(production-to-dissipation ratio) is proposed to obtain a non-singular C_{μ}(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 qϵ 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_{b} = u1u2/k is formulated as a function of local variables without resorting to a constant √C^{*} _{μ}= 0.3. The parameters R_{b} and Pk/ϵ entering the turbulence production P_{k} prevents presumably the overestimation of 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.

Original language | English |
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Pages (from-to) | 959-994 |

Number of pages | 36 |

Journal | JOURNAL OF TURBULENCE |

Volume | 19 |

Issue number | 11-12 |

DOIs | |

Publication status | Published - 1 Jan 2019 |

MoE publication type | A1 Journal article-refereed |

## Keywords

- coefficient of eddy-viscosity
- cubic equation
- k-equation model
- production-to-dissipation ratio
- turbulence anisotropy
- REYNOLDS-STRESS
- ARTIFICIAL COMPRESSIBILITY METHOD
- TURBULENCE
- FLOWS
- EXPLICIT
- HOT-WIRE
- EPSILON