An Improved Finite Element Formulation for Potential Flow Problems Using a Kutta Condition

The purpose of the present article is to develop a Finite Element Method (FEM) for steady potential flows over a range of bluff bodies like cylinders to streamlined profiles such as airfoils. In contrast to conventional panel methods, Laplace’s equation describing the potential flow is solved here for the velocity-potential function using the Galerkin method. A brief discussion on edge singularities in potential flows has also been presented using a half-cylinder case study. A novel method for implementing Kutta condition over airfoils to have lifting flow is explained. Compared with other techniques such as Finite Difference Method (FDM) and Finite Volume Method (FVM), the present methodology has proven to be computationally faster for airfoils with both a finite angle trailing edge and cusped trailing edge. The results obtained have demonstrated excellent accuracy compared to analytical and panel methods. The present method has also overcome edge singularity for airfoils, which ANSYS Fluent predicted inappropriately using the inviscid model.