Hybrid Approach to Uniform Flow Past Two Cylinders

Abstract

An approximate approach that transforms an analytical solution for uniform flow past two circular cylinders into a solution for uniform flow past two cylinders of arbitrary shape is proposed in this study. This approximate approach is a combination of the analytical solution, which is obtained in bipolar cylindrical coordinates, and the numerical pseudoconformal transformation. The method applied in this study is not only simpler than conventional numerical methods, but also considers the Kutta condition. The numerical transformation is examined by the Joukowski transformation. The streamlines of uniform flow past a symmetric Joukowski airfoil with an ellipse in front of it shows good agreement with the Hele-Shaw cell experiment. The lift force on the airfoil is also compared with the lift force of a single airfoil.