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Improvement of the Mixing Length Model and Numerical Calculation of the Flow over a Backward-Facing Step

Author(s): Huang Shehua; Zhuang Keyun; Lv Tianshu; Fu Xiangqian

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Keywords: Turbulence scale; Mixed turbulence model; Reynolds stress; Flow over a backward-facing flow; Numerical calculation

Abstract: Among turbulence models for closure of Reynolds averaged equation based on Boussinesq eddy viscosity hypothesis, the standard k-epsilon model has been widely applied in engineering. However, the model mainly considers the effects of turbulence transport and dissipation on Reynolds stress in small-scale structure, which leads to low accuracy in the calculation of flows such as rotational flow, adverse pressure gradient and back flow. Prandtl mixing length model is the simplest algebraic equation model, but it contains the velocity gradient, which in some sense corresponds to the large-scale structure of turbulence. In this paper, based on the comparative study of the two models, an improved mixed turbulence model is firstly proposed by means of dimensional analysis, in which the calculation formula of eddy viscosity coefficient includes not only turbulent kinetic energy k and its dissipation rate ε, but also the velocity gradient of the mean field. Then the model is applied to the numerical simulation of the flow over a backward-facing step. And the calculated longitudinal velocity profile, turbulent kinetic energy k and dissipation rate ε distribution of separation zone are analyzed. Meanwhile, by comparing with some measured data and the calculation results under the standard k-ε model, it is fortunately found that in the range of Reynolds number (Re) from 5×103-1×105, the improved mixed turbulence model with velocity gradient can predict this type of turbulent flow more accurately.

DOI:

Year: 2020

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