New Type of Smoluchowski Temperature Jump Condition Considering the Viscous Heat Generation

Abstract

The effect of the sliding friction has been important in calculating the heat flux of gas flow from the surface because there is some slip over the surface. There is not any temperature jump condition including the sliding friction part (viscous heat generation) in its derivation so far. In this paper, the Smoluchowski temperature jump condition is modified by considering viscous heat generation. This new temperature jump condition will be evaluated for three configurations in high-speed rarefied gas flow simulations using the computational fluid dynamics method, which solves the Navier–Stokes equations within the OpenFOAM framework: 1) the flat plate, with Mach number 2) the NACA0012 microairfoil, with Mach number ; and 3) the sharp 25–55 deg biconic case, with Mach number . The working gases are air and nitrogen. The airfoil case is simulated with various Knudsen numbers from 0.026 to 0.26, and the angles of attack are from 10 to 20 deg. The surface gas temperatures predicted by the new temperature jump condition give good agreement with the direct simulation Monte Carlo data, especially the NACA0012 microairfoil cases with the high Knudsen numbers ( and ) with an angle of attack of 20 deg.