Numerical solution of Navier-Stokes equations for flow over a flapping wing

A three-dimensional (3-D) moving grid adapting to simulation of viscous flow over flapping wing based on the transfinite interpolation is developed, and the 3-D compressible unsteady Navier-Stokes equations transformed by preconditioning method are employed by finite volume method and dual-time stepping method. As the computational results are in good agreement with reference data, the method given in this paper is correct and reliable. The flow over a flapping wing in the motion of plunging combined with pitching is complicated due to the change of some key parameters such as reduced frequency, flapping amplitudes and attack angle. Through careful computations, the influence of reduced frequency, flapping amplitudes and attack angle on lift, thrust and lift/drag ratio is determined. Reduced frequency is a quadratic function relation of thrust; as reduced frequency increases, the lift will rise rapidly. Flapping amplitude mainly influences the peak value of lift coefficient; as flapping amplitude increases, the peak value of lift coefficient will increase speedily, but the average of lift will decrease. Attack angle mainly influences the average of lift and lift/drag ratio; as attack angle increases, lift/drag ratio will decrease rapidly, but the average of lift will increase.