Rarefaction Effects in Low Reynolds Number Subsonic and Transonic Aerodynamics
The quantification of rarefaction effects for low Reynolds number (Re<10,000) transonic (M=0.8) flows is essential for the aerodynamic design of vehicles moving in vacuum environments approaching slip regime. Potential future applications in these conditions include low-pressure 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 the traditional Navier-Stokes equations in the low-Reynolds transonic regime. The results were compared to the deterministic solution of the ES-BGK type Boltzmann equation with the Runge-Kutta Discontinuous Galerkin Method (RKDG). Numerical simulations using these computational methods were compared to the electron beam fluorescence experiments at a Re=73 and a M=0.8, and it was observed that the numerical solution of the ES-BGK model using the RKDG method with 3rd order accuracy is computationally the most efficient. It was also shown that when the Reynolds number of the flow decreased from 10,000 to 1,000, slip effects become dominant. The flow becomes fully rarefied at Re=10. Furthermore, rarefaction effects were quantified for the NACA 0007 and the NACA 2407 at 0 and 10 degrees of angle of attack to investigate the effects of thickness, camber, and the angle of attack. It was observed that flow separation due to increase in thickness resulted in higher rarefaction effects. It was concluded that thin airfoils with very smooth shape changes minimize continuum breakdown / rarefaction effects. Rarefied gas phenomena that only appear in low pressures (such as thermal effects) can be exploited for performance enhancement of applications in slightly rarefied aerodynamics. In this study, feasibility and advantages of using thermal control to reduce drag and mitigate vortex shedding for airfoils are studied. NACA 0012 airfoil with a temperature difference applied between the upper and the lower surface is simulated in the continuum regime with a Navier-Stokes solver and compared to experimental data for verification of parameters and turbulence modelling. At lower pressures, an elevated temperature on the bottom surface of the airfoil is investigated to create lift and understand the rarefaction effects. Continuum NS results were compared to the rarefied ES-BGK solver for the rarefaction effects. It was shown that an elevated temperature enhances the lift by 25 % and reduces the drag at high angles of attack. In the second part, a temperature gradient on the upper surface is applied and it was seen that drag is reduced by 4 % and vortex shedding frequency is reduced due to gradients introduced in the flow by thermal transpiration.
Alexeenko, Purdue University.
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