Study on Unsteady Aerodynamic Force of Morphing Joukowski Airfoil

Assuming that the normal deformation velocity on the wing surface is much smaller than free stream velocity,the unsteady flow field and aerodynamic lift for the morphing Joukowski airfoil were calculated by combining the analytical solution and the discrete vortex method together.The error sources of quasi-steady assumption were analyzed rigorously and correspondingly the error correction method was proposed.The numerical calculations show that the vortex wake of morphing airfoil has almost no effect on the lift coefficient and the circulation around the airfoil.The additional unsteady aerodynamic lift caused by the virtual mass force is the main error source of quasi-steady solution for the aerodynamic lift of morphing airfoil.It is also shown that the flight attitude,the airfoil profiles and the deformation velocity determine the unsteady additional lift coefficient,which has little relation with the evolutionary history of deformation.It is proposed that the lift of morphing airfoil is approximately equal to the lift of quasi-steady solution adding the corresponding virtual mass force.