Mathematical Modeling of Potential Flow over a Rotating Cylinder

Abstract Potential flow over rotating cylinder is usually solved by the singularity method. However, in this paper a mathematical solution is presented for this problem by direct solution of the Laplace's equation. Flow over the cylinder was considered non-viscous. Neumann and Dirichlet boundary conditions were used on the solid surfaces and in the infinity, respectively. Because of non-viscous flow, the Laplace equation is the governing equation of the flow field. The entire flow field was divided into two parts including tree stream over a stationary cylinder and flow over a rotating cylinder with no free stream. Because of linearity of the govell}jng equation, solutions of these flows were superposed to obtain velocity potential function from whfch velocity and pressure distribution was obtained. Pressure forces acting on the cylinder were obtained by integrating pressure distribution over the cylinder surface that was exactly the same as the results of the singularity method. Present work achieved the famous Kutta-Joukowski theorem in the aerodynamics and fluid mechanics. In addition, the proposed analytical model was validated by numerical solution. " c~