A mixed-time-scale low-Reynolds-number one-equation turbulence model

Abstract

In this paper, a new low-Reynolds-number (LRN) one-equation turbulence model for eddy viscosity is proposed. A mixed time scale, representing a combination of three time scales: two time scales made of strain-rate parameter S and vorticity parameter Ω and the turbulent time scale k/ϵ, is introduced into this model. The proposed model is derived from an LRN k−ϵ two-equation model where the mixed time scale has been proved to be very effective for predicting local flows over complex terrains. In the transport equation of the model, the mixed time scale is included in the production and the dissipation terms. The new model is evaluated in channel flows at various Reynolds numbers, boundary layer flows with or without pressure gradient and backward-facing step flows with different expansion ratios and Reynolds numbers. Then the grid convergence of the model is investigated. Finally, the model performance for different values of the weighting constant C_s in the mixed time scale is assessed. The results show that the proposed model reproduces the correct wall-limiting behaviour of turbulent quantities and performs well in the near-wall region of turbulent flows. The model could be expected to be adopted in hybrid Reynolds averaged Navier–Stokes/large eddy simulation methodology for complex wall-bounded flows at high Reynolds numbers.

Keywords:

• near-wall turbulence modelling
• eddy viscosity
• mixed time scale
• computational fluid dynamics

Acknowledgements

This work was partially supported by the National Natural Science Foundation of China (Grant No. 51190102).