Numerical investigation of euler equations for the rigid and flexible wings in arbitrary motion

The work presented here shows the unsteady invisoid results obtained for the different wings which are in rigid and flexible oscillations. The results are generated by solving the unsteady Euler equations in a body–fitted coordinate system. It is based on the four–stage Runge–Kutta time stepping scheme developed by Jameson et al. To increase the time step, the implicit residual smoothing which is modified by using variable coefficients to prevent the loss of flow physics for the unsteady flow is engaged in the calculations. With this unconditional stable solver the unsteady flows about the wings in arbitrary motion can be solved efficiently. In this paper, the rectangular wing with NACA–0012 airfoil which is in rigid and flexible oscillation in the transonic flow is investigated. Then the unsteady transoic flow about the ONERA–M6 wing which is in rigid pitching oscillation is researched. Some of the computational results are compared with the experimental data. All the results given here arc reasonable.