A Robust and Simple Low-Mach Number Solver for Flapping-Wing Simulations

In the current study, a very simple preconditioned Navier-Stokes solver based on Roe type numerical fluxes is developed to investigate the unsteady aerodynamics around the flapping wings. A modified Osher-Chakravarthy (MOC) upwind finite-volume scheme is used for space discrete. To evaluate unsteady accuracy, a dual-time stepping strategy including the second-order Euler implicit method and diagonal dominant alternating direction implicit scheme (DDADI) are selected for the physical time and pseudo time stepping implements. In the test cases, two-dimensional airfoil in pure plunging and pitching motion are computed for validation of purpose scheme, respectively. The present numerical results are in good agreement with other’s numerical results. Then, the simulation is carried out on a NACA0012 wing oscillating in heave motion. As a result, the frequency of thrust coefficient is twice the plunging frequency since the maximum thrust is occurred as the airfoil passes the neutral position twice in one period and the frequency of the lift coefficient is the same. By testing the aerodynamic force varying with the reduce frequency of pure heave motion airfoil, the results indicate that the mean thrust output increasing and propulsion efficiency decreasing while reduce frequency is increasing.