Simulation of separated flow past an inclined and normal plates by a discrete vortex method

Abstract

Abstract Unsteady separated flow past a normal or an inclined flat plate is simulated using the discrete vortex method. The plate is replaced by attached discrete vortices and the separated flow motion behind the plate is modeled by free discrete vortices moving with a local velocity. The intensities of attached vortices at each moment of time are determined from the condition of impermeability of the streamlined body surface, as well as the condition that the total intensity of the attached and free vortices is equal to zero. A formula is introduced for determining the pressure coefficient in the position of the attached vortices, and it is obtained from the pressure in an unsteady-state flow by Cauchy-Lagrange function. The forces exerted on the plate at each instant of time determined from the generalized Blasius theorem. The calculations have shown, that by choosing an integration step and a quantity of the plate breakdowns, it is possible to obtain a satisfactory convergence with the experimental results on the normal force coefficient. But this results in some discrepancy in the Strouhal number of vortex shedding, especially at the small angles of attack. Replacement of the plate by the attached vortices leads to a passage of the free vortices through it, which leads to a discontinuous change in its aerodynamic characteristics. To avoid the latter, it is necessary to introduce a condition, for example, to exclude a normal velocity component of the free vortex near the plate. The introduction of the initial disturbance affects to some extent a subsequent development of the vortices and, thus, the dependence of the normal force coefficient on a time period.