Hydrodynamic interaction between two polygonal cylinders in uniform potential flow

The analytical solution for uniform potential flow around two similar or dissimilar polygonal cylinders is obtained by using complex potential function for a doublet trapped in an annulus. The annulus of two circles is mapped conformally to the pair of polygonal cylinders by unique combination of bilinear and hypotrochoidal transformation and mathematical formulas to get velocity, pressure and hydrodynamic force distribution around two polygonal cylinders are presented. The effects of center distance between the cylinders, shape, orientation and corner radii of cylinders, and flow angle on the hydrodynamic interaction between the cylinders are also investigated and presented. The comparison of some of the numerical results obtained using present method is done with the results obtained from commercial CFD software package and results from literature.

Automated summary

The analytical solution for uniform potential flow around two similar or dissimilar polygonal cylinders is obtained using a complex potential function and conformal mapping method. Mathematical formulas for velocity, pressure and hydrodynamic force distribution are derived, and the effects of various parameters on the hydrodynamic interaction between the cylinders are investigated. The numerical results obtained from the present method are compared with those from commercial CFD software package and literature.