The effect of Knudsen layer on rarefied hypersonic gas flows

Abstract

Effect of the Knudsen layer (KL) on surface and bulk flow properties is investigated for the hypersonic flow applications in the slip flow regime. Knudsen Layer formulation is incorporated within an open source computational fluid dynamics framework, OpenFOAM. Navier-Stokes (N-S) 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. This new approach is evaluated for three configurations: (1) the flate plate with M = 6.1 and Kn = 0.004, (2) the sharp wedge, with M = 10 and Kn = 0.01, and (3) the cylinder, with M= 10 and Kn = 0.05, with argon and nitrogen as working gases. Simulation results are validated against published Direct Simulation Monte Carlo (DSMC) and experimental results. The surface velocity predicted by new formulation give good agreement with the DSMC data especially for the flat plate case. It has also shown maximum improvement of 47 % at θ = 90◦ for cylinder case over a conventional solver. Knudsen layer formulation have improved the results in the bulk flow region as well. Simulation results convey that our approach greatly improves the predictive capabilities of the compressible N-S-F solver upto early transition flow regime. The current work is significant from the perspective of accurate thermal design of hypersonic vehicles.