Implementation of Knudsen Layer Phenomena in Rarefied High-Speed Gas Flows

Bhagat, Apurva and Gijare, Harshal and Dongari, Nishanth (2019) Implementation of Knudsen Layer Phenomena in Rarefied High-Speed Gas Flows. Journal of Aerospace Engineering, 32 (6). 04019100. ISSN 0893-1321

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Abstract

A numerical investigation of Knudsen layer effects in high-speed flows in a rarefied flow regime has been carried out. The conventional compressible flow computational fluid dynamics (CFD) solver is reformed based on the effective mean free path model to augment the validity of the Navier-Stokes-Fourier equations in the slip-transition flow regime. The mean free path is expressed as a function of the distance from the surface and local flow gradients, and has been used to modify linear constitutive relations, as well as slip and jump boundary conditions, to incorporate Knudsen layer correction. The improved solver has been validated against direct simulation Monte Carlo (DSMC) data of benchmark test cases of hypersonic flow (Mach number=6.1 and 12.7) over a flat plate in the slip-flow regime (Knudsen number=0.004), and Mach 10 flow over a circular cylinder in the transition flow regime (Knudsen number=0.25). The results show that the accuracy of the conventional CFD solver has been significantly improved due to the implementation of the Knudsen layer approach in the near-wall region and the bulk-flow region. Crucial nonlinear trends are captured in the nonequilibrium regions of high-speed flows, such as shock waves and the Knudsen layer. The location of an oblique shock around the flat plate is accurately captured and overall, the Knudsen layer incorporation has exhibited good agreement with the DSMC with deviations within 4% in the upstream region of the cylinder.

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