Supersonic low-density flow over airfoils

Two-dimensional, Reynolds-averaged, full Navier-Stokes equations for a perfect gas are solved for supersonic, low-density flow at Reynolds numbers ranging from 4 x 10-3.5 x 10. Slip-velocity boundary conditions based on various Knudsen numbers are introduced. This formulation is referred to as the extended NavierStokes method. Numerical results are obtained for three symmetric airfoils (NACA 0009, NACA 0012, and a 9%-thick, circular-arc airfoil) traveling at supersonic speeds at an angle of attack of 1.25 deg. The effect of the slip velocity becomes noticeable when the Knudsen number is greater than 0.01 and becomes important for Kn > 0.1. In a low-density atmosphere, the airfoil lift coefficients are low and drag coefficients are high because of strong viscous effects. The effect of the slip velocity tends to reduce both the lift and drag coefficients, but to a much smaller degree than the effect due to viscosity.