UNSTEADY SUPERSONIC-FLOW OVER AN OSCILLATORY AEROFOIL USING A 2ND-ORDER TVD SCHEME

The unsteady flow over an oscillatory NACA0012 aerofoil has been simulated by the calculation with Euler equations. The equations are discretized by an implicit Euler in time, and a second-order space-accurate TVD scheme based on flux vector splitting with van Leer's limiter. Modified eigenvalues are proposed to overcome the slope discontinuities of split eigenvalues at Mach = 0.0 and +/- 1.0, and to generate a bow shock in front of the aerofoil. A moving grid system around the aerofoil is generated by Sorenson's boundary fitted co-ordinates for each time step. The calculations have been done for two angles of attack theta = 5.0-degrees sin (omegat) and theta = 3.0-degrees + 3.0-degrees sin(omegat) for the free-stream Mach numbers 2.0 and 3.0. The results show that pressure and Mach cells flow along characteristic lines. To examine unsteady effects, the responses of wall pressure and normal force coefficients are analysed by a Fourier series expansion.