CVBEM Formulation for Multiple Profiles and Cascades

A numerical algorithm based on the CVBEM (from Complex Variable Boundary Element Method) for plane incompressible potential flow around aerofoils and cascades is described. The method is based on the representation of the complex disturbance velocity by means of a Cauchy-type integral around the foil. The Cauchy density function is approximated piecewise linearly and a linear system on the nodal values is obtained by collocation at the nodes. The Kutta condition is imposed via a Lagrange multiplier, in contrast with the least-squares formulation used in a previous work. For cascades, the problem is conformally mapped by a simple hyperbolic function (exponential or hyperbolic tangent) to a related problem with only one profile and one or two poles. Thus, the cascade problem is accurately solved with minor modifications to the single profile code and at the same cost of a single profile computation. Finally, several numerical examples are shown: single Joukowski and NACA profiles, interference coefficients for the flat plate cascade and a plane cascade at the external cylindrical section of an industrial fan.