Evaluation of nonequilibrium boundary conditions for hypersonic rarefied gas flows

Abstract

A new Computational Fluid Dynamics (CFD) solver for high-speed viscous §ows in the OpenFOAM code is validated against published experimental data and Direct Simulation Monte Carlo (DSMC) results. The laminar §at plate and circular cylinder cases are studied for Mach numbers, Ma, ranging from 6 to 12.7, and with argon and nitrogen as working gases. Simulation results for the laminar §at plate cases show that the combination of accommodation coe©cient values σ u = 0.7 and σ T = 1.0 in the Maxwell/Smoluchowski conditions, and the coe©cient values A 1 = 1.5 and A 2 = 1.0 in the second-order velocity slip condition, give best agreement with experimental data of surface pressure. The values σ u = 0.7 and σ T = 1.0 also give good agreement with DSMC data of surface pressure at the stagnation point in the circular cylinder case at Kn = 0.25. The Langmuir surface adsorption condition is also tested for the laminar §at plate case, but initial results were not as good as the Maxwell/Smoluchowski boundary conditions.

New slip boundary condition in high-speed rarefied gas flow simulations

“…For the sharp-leading-edge flat plate, a rectangular mesh is used for the plate case with final cell sizes, Δ x = 0.15 mm, Δ y = 0.30 mm, are adopted in the studies by Le et al. 9,10 The mesh 256 × 256 of the biconic case in the study by Le et al. 18 (i.e.…”

“…Its value might be evaluated either a mean free path away from the surface or in the freestream. The Langmuir slip condition was also tested for hypersonic rarefied gas flows in the study by Le et al, 10 and it did not give good prediction for the slip velocity. Le et al 9 developed a hybrid slip condition, which is called as ''the Langmuir-Maxwell slip condition.''…”

“…Computational meshes are constructed to wrap around the oblique and bow shocks. For the sharpleading-edge flat plate, a rectangular mesh is used for the plate case with final cell sizes, Áx ¼ 0.15 mm, Áy ¼ 0.30 mm, are adopted in the studies by Le et al 9,10 The mesh 256 Â 256 of the biconic case in the study by Le et al 18 (i.e. 256 cells in the axial streamwise direction and 256 cells in the radial, surface normal direction) is adopted for the CFD biconic simulations.…”

“…Slip velocity BC were studied in the literature. [1][2][3][4][5][6][7][8][9][10][11] They are designed to work with the N-S-F governing equations in the CFD method. The first-order conventional slip condition was developed by Maxwell in 1890 for a flat plate based on his earlier work on the theory of viscosity in gases.…”

Thermal Rarefied Gas Flow Investigations Through Micro-/Nano-Backward-Facing Step: Comparison of DSMC and CFD Subject to Hybrid Slip and Jump Boundary Conditions

“…where is an equilibrium constant relating to the surface temperature, given by: (10) where A m is either measured or calculated approximately by N A d 2 /4 for gases [3,29]; d is Covalent diameter of the molecule: for nitrogen gas d = 0.142 nm [25]; D e is the measured value of the heat of adsorption (J/mol): for argon and nitrogen gases D e = 5255 (J/mol) given in references [3,29]. These conditions were implemented into the solver rhoCentralFoam in OpenFOAM for simulating rarefied gas flows [25,30].…”