ОБТЕКАНИЕ ЦИЛИНДРА И АЭРОДИНАМИЧЕСКОГО ПРОФИЛЯ С УЧЕТОМ ЛАМИНАРНО-ТУРБУЛЕНТНОГО ПЕРЕХОДА

Abstract

A simulation of the flow around a cylinder and a NACA 4412 airfoil was carried out using the γγ-Reθ laminar-turbulent transition model and without it. Numerical simulation was performed on the basis of the Reynolds-averaged Navier-Stokes equations (URANS), using the Spalart-Allmaras differential one-parameter turbulence model. The system of initial equations was written with respect to an arbitrary curvilinear coordinate system. The coordination of the pressure and velocity fields was carried out using the method of artificial compressibility modified to calculate non-stationary problems. The integration of the system of initial equations was carried out numerically using the control volume method. For convective flows, a countercurrent Rogers-Kwak approximation was used based on the third-order Roe scheme. In turbulence models, the TVD scheme with a third-order ISNAS flow limiter was used to approximate convective terms. Comparison of the calculation results for a flow past a cylinder is carried out using the laminar-turbulent transition model and without it. It is shown that at low Reynolds numbers, when the flow around a cylinder is laminar, and the track isturbulent use of the Spalart-Allmaras turbulence model leads to the development of a turbulent boundary layer on the cylinder and, consequently, to a change in the position of the separation point. The incorrect position of the separation point affects the pressure distribution in the bottom of the cylinder and, as a result, the integral aerodynamic characteristics. The use of the transition model allows one to adequately reconstruct the laminar separation near the leading edge of the airfoil with its subsequent reattachment. The use of the Spalart-Allmaras model alone leads to excessive generation of turbulent viscosity. It is shown that the use of the γ-Reθ laminar-turbulent transition model the qualitatively and quantitatively improves the results of numerical simulation. The results of numerical simulation of the flow around a circular cylinder and the NACA 4412 aerodynamic airfoil agree well with experimental data in a wide range of Reynolds numbers.