On Problems in 2D Viscous Flows Simulation at Higher Values of the Reynolds Numbers by Vortex Methods Using the VM2D Code

Abstract

Vortex methods of computational fluid dynamics are an efficient tool in engineering practice for estimating hydrodynamic loads acting on bodies placed in a flow. Their usage allows for solving of coupled hydroelastic problems with relatively small computational cost. In many applications, the cross flow around structural elements with large elongation is considered, that allows one to use the flat cross-sections method providing the acceptable accuracy. Thus, flat flows simulation around airfoils is required. Modern modifications of vortex particle methods make it possible to simulate flows of a viscous incompressible medium. Based on the method of viscous vortex domains in 2017-2022 the VM2D code have been developed in Bauman University and Ivannikov Institute for System Programming. This code allows for flow simulating around airfoils with acceptable accuracy at low Reynolds numbers, while for higher Reynolds numbers, correct results are observed only for airfoils with sharp edges and corner points, and only in regimes where the most intensive flow separation takes place at these points. The reason for the error in the results for other regimes is seen in incorrect modeling of the flow separation on smooth airfoil surface line at high Reynolds numbers, which, in turn, is a consequence of incorrect modeling of vorticity evolution in the vicinity of separation points (zones). Some results of flow simulations around different airfoils at different values of the Reynolds number are presented and a hypothesis explaining the reason for the discrepancy between numerical results and experimental data is proposed. It is shown that the kinetic energy spectrum of turbulence corresponds to “two-dimensional turbulence”.