VORTEX - Grupo de Mecânica dos Fluidos de Escoamentos Complexos

Métodos integrais de contorno aplicados à solução de escoamentos aerodinâmicos permanentes e transientes (2009)

Autor: Ricardo Caiado de Alvarenga

Orientador: Francisco Ricardo Cunha

In this dissertation we describe a boundary integral method for calculating the incom- pressible potential °ow around arbitrary, lifting, two-dimensional and three-dimensional bodies. By using Green theorems to the inner and outer regions of the body and com- bining the resulting expressions we obtain a general integral representation of the °ow. The body surface is divided into small quadrilateral and triangular elements and each element has a constant singularities distribution of sinks and dipoles. The applica- tion of Kutta's condition for the steady °ow is quite simple; no extra equation or trailing-edge velocity point extrapolation are required. The method is robust with a low computational cost even when it is extended to solve complex three-dimensional body geometries. The boundary integral code developed here is veri¯ed by comparing the numerical predictions with experimental measurements, analytical solutions and results of the lifting-line theory and vortex-lattice method. A two-dimensional integral boundary layer method, was incorporated into the two-dimensional boundary integral method and is intended to give a preliminary estimate of boundary layer properties over a con¯guration. The method comprises a laminar boundary layer analysis, a transition and a turbulent boundary analysis. Finally, an unsteady two-dimensional boundary integral method has been developed. The present approach treats the body as moving through the air and put the mathematical problem in terms of a moving coordinate system attached to it. The Kutta condition is applied by imposing the same pressure on the upper and lower surfaces at the trailing edge. For this end, the unsteady Bernoulli equation is used. The airfoil contour is replaced by straight-line elements and a small straight-line wake element is attached to the trailing edge. The circulation on this element is imposed in the way that the global circulation around the airfoil and the wake is constant. A downstream wake of concentrated vortices is formed from the vorticity shed at earlier times and is convected according to the local velocities. The basic set of equations is nonlinear and an iterative procedure is adopted for its solution.


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