Моделирование турбулентных течений с использованием алгебраической модели рейнольдсовых напряжений с универсальными пристеночными функциями

The paper explores the application of an Explicit Algebraic Reynolds Stress Model (EARSM) to turbulent flow simulation using universal wall functions. With universal wall functions, friction coefficients and velocity derivatives on a solid wall can be predicted with good accuracy, but the correct application of these functions entails changes in the formulation of turbulence models. Despite the fact that the use of this approach has been well investigated for RANS turbulence models, the question of how to introduce these functions in the EARSM has not been adequately addressed. A detailed consideration shows that in the case of EARSM, application of a coarser near-wall resolution leads to an unsatisfactory accuracy of the Reynolds stress gradient in the areas of rapid change in the velocity field and, as a consequence, to the oscillations of physical quantities in the boundary layer. The present paper proposes a method for eliminating these oscillations modified by calculating the velocity gradients on the inner faces of computational grid cells. A numerical implementation algorithm for the EARSM model which provides stable computation in the interface and acceptable simulation results on arbitrary unstructured grids with various level of grid-spacing near the rigid surface is presented. The effectiveness of the proposed algorithm is illustrated by solving the problem of turbulent flow over a flat plate. The results show that the algorithm is able to eliminate the spatial oscillations in velocity inside the boundary layer at any type of a grid. The analysis of two problems considering the asymmetrical flow indicates that the application of the developed EARSM algorithm gives a noticeable improvement of simulation results compared with the basic RANS model even in the case of the unstructured grid with arbitrary grid-spacing near the rigid surface.