Mathematical Modeling of Potential Flow over a Rotating Cylinder (RESEARCH NOTE)

Authors

1 Mechanical Engineering Department, Amir Kabir University of Technology

2 School of Automotive Engineering, Iran University of Science and Technology (IUST)

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’sequation. Flow over the cylinder was considered non-viscous. Neumann and Dirichlet boundaryconditions 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 intotwo parts including free stream over a stationary cylinder and flow over a rotating cylinder with no freestream. Because of linearity of the governing equation, solutions of these flows were superposed toobtain velocity potential function from which velocity and pressure distribution was obtained. Pressureforces acting on the cylinder were obtained by integrating pressure distribution over the cylinder surfacethat was exactly the same as the results of the singularity method. Present work achieved the famousKutta-Joukowski theorem in the aerodynamics and fluid mechanics. In addition, the proposed analyticalmodel was validated by numerical solution.

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