Rarefaction Effects for Transonic Airfoil Flows at Low Reynolds Numbers

Abstract

The quantification of rarefaction effects for low-Reynolds-number () transonic () flows is essential for the aerodynamic design of vehicles moving in vacuum environments approaching the slip regime. Potential future applications include evacuated-tube high-speed ground transportation, high-altitude unmanned aerial vehicles, Martian aircraft, and rotorcraft. For the quantification of rarefaction effects, the NACA 0012 airfoil was analyzed using continuum Navier–Stokes equations in the low Reynolds transonic regime. The results were compared to the deterministic solution of the ellipsoidal statistical Bhatnagar–Gross–Krook model Boltzmann kinetic equation with the Runge–Kutta discontinuous Galerkin method. Numerical simulations using these methods were compared to the electron beam fluorescence experiments at a Reynolds number of 73 and a Mach number of 0.8. It was observed that the numerical solution of ellipsoidal statistical Bhatnagar–Gross–Krook model using the Runge–Kutta discontinuous Galerkin method with third-order accuracy is the most computationally efficient. It was also shown that, when the Reynolds number of the flow decreased from 10,000 to 1000, slip effects become dominant. The flow becomes fully rarefied at . Furthermore, rarefaction effects were quantified for the NACA 0007 and the NACA 2407 at 0 and 10 deg of angles of attack to investigate the effects of thickness, camber, and the angle of attack. It was observed that flow separation due to an increase in thickness resulted in higher rarefaction effects. It was concluded that thin airfoils with very smooth shape changes minimize the continuum breakdown and rarefaction effects.