Exact aerodynamic force decomposition and dynamic force derivatives in non linear flows

An unconventional expression of the aerodynamic force in unsteady viscous flow is pre- sented. It is based on the computation of the Lamb vector field, and it allows for a physical breakdown of the force. The unsteady aerodynamic force acting on an oscillating flat plate in incompressible viscous regime is discussed and the key role of the Lamb vector, and more generally of vorticity, on the aerodynamic force generation, is enlightened. It allows for an innovative method to exactly compute dynamic force derivatives in strongly non linear two-dimensional flows has been derived thanks to the present decomposition. The results have been confirmed analysing and post processing numerical solutions of the flow around a pitching plate and a pitching airfoil at low and high Reynolds numbers. A breakdown between thrust and drag contributions is also obtained, evidencing, for instance, the flow regions were the thrust force is generated. The obtained decomposition is compared with the classical analytical linear inviscid theories of Theodorsen & Mutchler and von Karman & Sears. Finally, a new mixed inertial-non inertial formula is proposed, more accurate when dealing with high Reynolds numbers flows.