T-Schemes for Mathematical Simulation of Vorticity Generation on Airfoils with Corner Points in Vortex Particle Methods

Abstract

The boundary integral equation is considered which arises when modeling flow around airfoils using vortex methods. Numerical schemes for solving this equation previously developed by the authors (T-schemes) provide a higher order of accuracy only for smooth airfoils. At the same time, in many engineering applications, airfoils have corners and/or sharp trailing edge. From a mathematical point of view, this means that the kernel of the integral equation is unbounded and its solution has singularity. A type of singularity is known, this allowed us to propose a T-scheme of higher order of accuracy with a piecewise linear representation of the solution, which is applicable to calculating the flow past arbitrary airfoils with corner points and sharp trailing edge. Experiments show that the developed schemes correctly reproduce the velocity field of the flow near the corner points. It is important for the correct modeling of vorticity generation. All the formulae for calculating a discrete analogue of the integral equation are given. The results of the a posteriori accuracy analysis for the intensity of the vortex sheet on the airfoil and components of the added mass tensor are presented for model problems with a known solution

Please cite this article in English as:

Marchevskii I.K., Sokol K.S., Izmailova Yu.A. T-schemes for mathematical simulation of vorticity generation on airfoils with corner points in vortex particle methods. Herald of the Bauman Moscow State Technical University, Series Natural Sciences, 2025, no. 4 (121), pp. 56--77 (in Russ.). EDN: QHKLXC

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