After investigating the various thin airfoil theories that are all set up for harmonic motion of. Specifically, Isaacs surging airfoil theory assumes a two-dimensional thin flat plate at small angles of attack under a sinusoidally-oscillating freestream in. We will assume that we have potential flow such that the governing equation for the flow field is the Laplace of the velocity potential. The limitations and assumptions of existing theories. More complicated models exist but they all are based on the simplified form presented here.

But here we are just introducing the method to get a feel for its usefulness in external flows, so we will use a simply geometry with a simply distribution of flow elements. There are a number of books and papers written that describe the method in very general terms and even the inclusion of viscous forces to some degree. The formation of the circulation and generation of lift are discussed based on numerical simulations of a viscous starting flow over an airfoil, and the evolution of the flow topology near the. The interaction of the elements are accounted for and must also satisfy the condition that far from the object the flow should be equal to the free stream velocity approaching the object. : In this report analytical expressions for the unsteady 2D force distribution on a variable geometry airfoil undergoing arbitrary motion are derived under the assumption of incompressible, irrotational, inviscid flow. The panel method is basically a numerical approximation that relies on using discrete elements on the surface of an object and then prescribing a flow element (such as a vortex or doublet or source or sink) on each element that will satisfy certain boundary conditions (like no flow crosses the surface of the object). The method, as we present it here, is based on inviscid flow analysis, so it is limited to the resultant pressure forces over the surface.

The panel method is an analysis method that can be used to arrive at an approximate solution for the forces acting on an object in a flow.

Assumptions for thin airfoil theory