Зарождение вихреобразования на границе кругового цилиндра при его обтекании потоком вязкой жидкости

Abstract

The paper considers the problem of the generation of vortex formation on the surface of a circular cylinder placed in a flow of incompressible viscous fluid. To study this process, a new time-iterative approach is formu-lated for solving the 2D problem of flow around the circle based on the BIE method with Green's functions for the outer part of the cylinder with the Dirichlet boundary condition on its surface. A new approach, based on the transient Navier-Stokes equation in the variables stream function - vortex, using classical methods of potential theory and the boundary element method, allows us to obtain a complete system of three integral equations that determine the fields of stream functions and vorticity at a new time step, if these fields are known from the previous step. The assumption about the initial unexcited state of the flow (the vorticity function in the entire flow region is zero) allows us to obtain an analytical solution at the first time iteration step. The analysis of the obtained solution depending on the time step allows us to formulate a hypothesis about the nature of the generation of vortex formation on the surface of the circular cylinder in a flow of incompressible viscous fluid. The results obtained describe the appearance on the surface of the cylinder of two generalized vortices, having infinitely high intensity and infinitely small localization near the surface of the cylinder, which “instantly” break away from the surface of the cylinder, with a significant decrease in intensity, but with a large coverage of the flow around the cylinder.