Applying potential-based panel method for steady flow analysis across a wing with finite span

Abstract

In the paper hereby, an incompressible irrotational steady flow across a submerged body with finite dimensions will be studied. For this purpose, it is necessary to solve Laplace’s differential equation about a potential function in order to obtain the conservative velocity vector field. A general solution to the problem utilizing the Green identity implies the double layer potential function at an arbitrary point not belonging to the boundary surface. The potential is expressed by source/sink and doublet singularities distributed over the body surface and a wake attached to the trailing edge. The wake ensures that the Kutta condition is fulfilled. The submerged body geometry is approximated further by quadrilateral panels in order to compute the surface integrals for each panel exactly. To form a linear non-homogenous algebraic system, it is essentially to compute each panel influence to a collocation point of interest. The obtained coefficient matrix is diagonally dominant. The system is solved iteratively by means of the Gauss-Seidel method. The goal is development of a non-proprietary source code in order to work out a solution to the stated problem. The developed source code is authentic. Auxiliary libraries have not been used. Validation case and numerical results are depicted and discussed in the paper.