A Formulation of Unsteady Forces with a Three-dimensional Discrete Vortex Model

Abstract

A formulation of unsteady forces acting on bodies in three-dimensional, incompressible and inviscid flow is performed with a discrete vortex model. The flow field is determined by the number of discrete vortex filaments (vortex segment) as are the three-dimensional bodies. The total impulse acting on bodies in a certain time interval is calculated by applying the momentum theorem to control the volume which encloses the bodies and all vortex segments and which moves with the fluid. The forces are obtained by taking the time average of the total impulse and calculated by using the state of positions and the strengths of vortex segments at the beginning and the end of the time interval. This formula is applied to the calculation of the unsteady forces acting on a delta wing in uniform and nonuniform flow. As a result, it is found that this formula is very easy and effective to calculate unsteady forces with the three-dimensional discrete vortex model.