A Preliminary Research On Two-dimensional Unsteady Vorticity Aerodynamics Model

Vorticity dynamics is a good break point when researching unsteady aerodynamics. In the history, there have been different kinds of unsteady vorticty aerodynamics model simplifying flow field into vortex system. In need of theoretical research and practical application, the study of unsteady aerodynamics model has become particularly important.The purpose of this paper is to explore and establish a model for two-dimensional unsteady vorticity aerodynamics, so as to simulate the unsteady flow field around rigid wing sections, and to calculate aerodynamic force. Based on vorticity dynamics theory, a two-dimensional simplified model for unsteady aerodynamics in inviscous incompressible flow has been established in single-connected domain. And the mechanism of unsteady aerodynamic has been researched preliminarily.First of all, the impact of diffusion has been neglected, and a two-dimensional unsteady vortex system model has been built. Simulating of free-falling motions of plates of different curvature in the air has been conducted. The result showed that: supposing that the separation took place at the left and the right edges only, and that the flow fields were symmetrical, during the preliminary stage and the later period of falling, virtual mass force and wake induced force was the major aerodynamic force respectively; when the far vortex moved at the same speed as the flow far away, the aerodynamic force totally came from wake near the plate; the greater curvature the plate was of, the smaller velocity would it move at finally, which had something to do with the velocity of the newly shedding vortex; in the later period of falling, the fluctuation of aerodynamic force, velocity and the vortex shedding were related with the irregularity of the wakes.Secondly, based on the conservation of vortex sheet before and after conformal mapping,an iteration-free conformal mapping method was designed, with which single-airfoil could be transformed into an unit circle. This method has showed high efficiency and accuracy while transforming a variety of airfoils to an unit circle, and calculating virtual masses of several simple shapes.Finally, in view of vortex sheet, the formula of virtual mass has been re-derived.