A numerical approach for assessing flow compressibility and transonic effect on airfoil aerodynamics

Abstract

For free Mach numbers M∞ < 0.65, the standard methods for subsonic potential flows break down when the flow becomes supersonic locally. The transition of the potential equation from elliptic to hyperbolic indicates that the flow changes from a diffusive character to a propagation behavior. The elliptic numerical operators for the subsonic flow will not be able to correctly simulate the propagation properties of supersonic flow regions, which are governed by the equation of hyperbolic type. The presence of local supersonic regions significantly influences the aerodynamic characteristics of airfoil when compared to the predicted results using the standard methods for subsonic flows. To evaluate this transonic effect, the paper presents a method of solving the full potential equation using central and backward finite difference schemes corresponding to the subsonic and supersonic regions. The rotated difference scheme consists in differencing all the derivatives in the normal direction centrally, while the derivatives in the local flow direction are upwind differenced at supersonic points. The transonic effects on airfoil aerodynamics depending on the free Mach number, incidence angle and airfoil geometry were evaluated.