Further developments in unsteady compressible vortex lattice method in two dimensional motion. - Marcos da Silva e Souza (2007)
Unsteady phenomena like flutter, buffeting, rapid maneuvers in flight and gust entry are usually modeled and studied by a theoretical treatment involving potential flow methods. The resulting equation from this approach is the governing differential equation for general non-steady, non-viscous, potential flow known as convected wave equation. The disturbance, represented in this equation by the velocity potential, is propagated as wave which spreads at a rate equal to the local speed of sound. Linearization on the basis of small disturbances in a uniform stream of compressible fluid is made upon the equation by the procedure of retaining first order terms. Elementary solutions for this simplified equation recognized as primary extension of the concepts of source, sink, vortex and doublet, used together with boundary conditions associated with the governing equation, enables proper treatment for understanding and tackling non-steady aerodynamic problems. This thesis presents a numerical solution for the aerodynamics lift coefficient of a thin airfoil in arbitrary motion in a uniform, compressible, subsonic flow field. Distribution of vortex type elementary solutions of the convected wave equation is used together with a time function that schedules the vortex strength in time to represent in effect the arbitrary vortex moving along a chosen path. A field point is then influenced by the continuous disturbances generated by the vortex with a delay relative to the time of action of the same vortex. A fixed coordinate system in space relative to the body is chosen. So the body is fixed in a moving flow. The analytical vortex solution is presented together with the appropriate transformation variables needed to treat the problem.