Effect of Knudsen Layer on the heat transfer in hypersonic rarefied gas flows

Abstract

Effect of the Knudsen layer on the surface heat transfer is investigated for the hypersonic flow applications in the slip and early transition flow regime. Knudsen Layer formulation is incorporated within an open source computational fluid dynamics framework, OpenFOAM. Navier-Stokes-Fourier constitutive relations, and first order slip and jump boundary conditions are modified based on the effective mean free path, which is dependent on the geometry of an obstacle and local flow gradients. The modified solver is validated against benchmark cases of low-speed Couette gas flow and hypersonic flow over a flat plate. Investigation is further extended to the high speed flow over a wedge and a circular cylinder covering a wide range of Knudsen numbers within the slip and early transition flow regime. Effect of Knudsen layer on the surface heat transfer is examined, and maximum improvement of 27% is achieved for a wedge case. Moreover, results show excellent agreement with the DSMC data, especially for the cylinder cases with high Knudsen numbers, Kn = 0.05 and 0.25. The simulation results convey that our approach greatly improves the predictive capabilities of the compressible N-S-F solver up to early transition flow regime (Kn ∼ 1). The current work is significant from the perspective of accurate thermal design of hypersonic vehicles.