Calculation of the Potential Flow Past Multi-Component Airfoils using a Vortex Panel Method in the Complex Plane (Calcul dans le Plan Complexe de l'Ecoulement a Potentiel Autour de Profils a Composants Multiples par la Methode des Petits Paves a Tourbillons).

摘要

An efficient algorithm for a vortex panel method in the complex plane is developed to compute the potential flow past multi-component airfoils in free air and a porous-wall wind tunnel. The theoretical foundations of the method-the properties of the source and vortex density functions, the relationship between the exterior and interior flows, and the general Kutta-Joukowski condition for a trailing edge with crossflow - are derived from the theory of the Cauchy type integral. The method utilizes flat panels with linear vortex and source densities, the latter being used to simulate the displacement effect of boundary layers. The airfoil boundary condition is satisfied at all panel midpoints and the overdetermined system of linear algebraic equations solved as a least squares problem, in the L sub 1 norm, or in the L sub infinity norm. The wind tunnel wall interference problem is treated using the concept of the Green's function in the complex plane. Examples are worked out for some theoretical airfoils and extensive tables of exact and computed pressure distributions are given. (Author)