Unsteady panel method for two-dimensional airfoils

Potential Flow Theory based methods present advantages in terms of time saving and simplicity of problem formulation, compared to approaches like Computation Fluid Dynamics, if the assumption of inviscid and incom- pressible flow is not too restrictive. As the application of Potential Flow Theory, in the given conditions and forms, is not dependent upon finding a solution for the entire flow field, it is considerably more time efficient than Finite Difference Methods, which are, on the other hand. Finite Dif- ference Methods are used for cases in which viscosity and compressibility are factors that have to be taken into account and therefore produce much more precise results. The overall aim of this study is to produce the basic structure of a computer program which can solve the potential flow problem for two- dimensional airfoils, initially in basic steady conditions, and subsequently in more complex and unsteady flows, like in the specific case of helicopter harmonically moving blades. This will entail, in future enhancements to the code, the investigation of specific phenomena such as, among others, dynamic stall and blade vortex interaction, as they are a cause of instabil- ity and therefore need to be taken into account in many cases, especially in helicopter rotor design. This study seeks to bridge the gap between the analytical solution developed by Theodorsen for the harmonic moving plate and the solutions for unsteady flight conditions obtained by Computational Fluid Dyniamic calculations. Within this framework the method proposed here aims to achieve a compromise between time efficiency and accuracy of results, in the knowledge that in today’s industrial world there is a great demand for tools that can reconcile the need for quality with the pressures of time.