Numerical Simulation of a Flow in a Two-Dimensional Channel on the Basis of a Two-Liquid Turbulence Model

Abstract

The article presents the results of a numerical study of the flow structure in a two-dimensional channel at high Reynolds numbers. A feature of such flows is that the flow is turbulent. It is known that many turbulence models are based on the solution of systems of Navier-Stokes equations averaged over Reynolds. Such models are called RANS models. These models are based on the Boussinesq hypothesis, where turbulent stresses are assumed to be proportional to the strain rate of the averaged velocities. In addition, a hypothesis is made that turbulence is isotropic. However, studies of the turbulent flow structure have shown that turbulence is anisotropic. Therefore, to calculate anisotropic turbulent flows, models are used that do not use the Boussinesq hypothesis. One of such directions in turbulence modeling is Reynolds stress methods. These methods are complex and require rather large computational resources. Recently, another model of turbulence has been developed, which is based on a two-fluid approach. The essence of this approach is that a turbulent flow is represented as a heterogeneous mixture of two fluids that perform relative motion. In contrast to the Reynolds approach, the two-fluid approach makes it possible to obtain a closed system of turbulence equations using two-fluid dynamics. Therefore, while empirical equations are used for closure in RANS models, in the two-fluid model the equations used are exact equations of dynamics. One of the main advantages of the two-fluid model is that it is able to describe complex anisotropic turbulent flows. Therefore, in this paper, we used the two-fluid turbulence model for testing and the Reynolds stress method for comparison. In this work, numerical results are obtained for the longitudinal velocity profiles, turbulent stresses, as well as the coefficient of friction in a flat channel. The results are compared with known experimental data. In addition, the paper also presents the numerical results of the Reynolds stress method EARSM-WJ. The results are obtained for Reynolds numbers Re = 5600, Re = 13700 and Re = 13750.