A Theoretical-Experimental Study of the Flapping Flight of a Membrane Ornithopter. Part 1

Within the framework of the improved method of discrete vortices (IMDV), generalized for viscous vortex media, a mathematical model was built fortheoretical and experimental studies of the aerodynamics of an elastic membrane ornithopter flapping its wings in the normal hovering flight modewith flow separation from the leading edges of the wings in still air. The peculiarity of the developed approach is the use of the results of high-speedvideo recording of ornithopter wing flaps. A quasi-three-dimensional problem of the dynamics of an incompressible viscous medium was considered:the solution of the three-dimensional problem was reduced to two-dimensional solutions for the cross-sections of the ornithopter wings. The Lamb –Oseen vortex, a fundamental solution of the generalized Helmholtz equation, was used as a partial (basic) solution of each two-dimensional problem. In this case, no restrictions were imposed on the Reynolds number, Strouhal number and angle of attack. The use of the Cauchy – Lagrange formula,generalized for vortex flows in viscous incompressible media, to find the pressure drop on the ornithopter surface allowed us to represent the normalforce coefficient as the sum of three components: the circulation one, which is an analogue of the quasi-stationary Zhukovsky force for the normalforce and is determined by the instantaneous value of the circulation along the contour adjacent to the calculated cross-section of the ornithopter surface(without taking into account the vortices that have entered the flow); the inertial one, which depends on the instantaneous added mass of the calculatedcross-section of the ornithopter surface and is determined by the acceleration circulation, and the vortical (inductive) component, which is determinedby the current magnitude and distribution of vorticity around the calculated cross-section of the ornithopter surface.