Nonlinear transport of rarefied Couette flows from low speed to high speed

Abstract

The nonlinear transport properties and macroscopic flow features of rarefied plane Couette flows from low speed to high speed for a monatomic gas are investigated in detail using the direct simulation Monte Carlo (DSMC) method. The effective viscosity and thermal conductivity are directly computed from the DSMC results according to the linear constitutive relations. The detailed structure of the Knudsen layer (KL) and the functional dependence of the effective transport coefficients on local Knudsen numbers in the whole system are presented and compared with existing theoretical models. The results show that the effective viscosity and thermal conductivity distributions in the KL for different Mach number flows can be recast into the same profile (i.e., isothermal scaling function) in terms of a scaled wall distance η=∫0y1/λ(y)dy, though the local flow is nonisothermal. For all cases, the shear-stress Knudsen number distributions across the channel show a well opposite trend to the effective transport coefficient profiles. The functional dependence between them in the bulk region always coincides with the normal solution that is derived from the Boltzmann model equations for unbounded shear flows, while that in the KL for low-speed cases shows a large difference with the normal solution. As the Mach number increases, the DSMC data in the KL can also agree approximately with the normal solution at a large shear-stress Knudsen number. These results can be very useful for developing phenomenological models to describe a wall-bounded rarefied shear flow, showing a good prospect in both microflow and high-altitude applications.

A constitutive relation generalizing the Navier–Stokes theory to high-rate regimes

“…Here is also referred to as the local shear-stress Knudsen number in the literature. Ou & Chen (2020) conducted DSMC analysis of wall-bounded rarefied shear flows and also showed that a shear-stress Knudsen number is the only parameter which is needed to characterize the macroscopic flow profile and nonlinear momentum transport in the bulk. This is in accordance with the finding presented here.…”

DSMC Study of Strong Shear Nonequilibrium Phenomenon in Hypersonic Knudsen-Layer Flows

“…Experiments conducted by Smoluchowski [1] and Knudsen [2] revealed some nonequilibrium phenomena (e.g., velocity slip and temperature jump) in the near-wall region of several mean free paths (λ) [3], and this region is usually called the Knudsen layer. The aerodynamic/aerothermal prediction of hypersonic vehicle relies on the momentum/energy transfer between the gas and wall, which involves the rarefied flow in the Knudsen layer, thus, some former works have been conducted to research the hypersonic Knudsen-layer flow [4][5][6][7][8][9][10].…”

Numerical study of strong shear nonequilibrium phenomenon and its relaxation mechanism in hypersonic Knudsen layer flows based on the direct simulation Monte Carlo method

“…Many physical problems involve the rare ed ow within the Knudsen layer, e.g., vaporization [4,5], adsorption/desorption [6,7], ablation [8,9], and micro/nano ows concerning slip effect and momentum/energy transfer between gas and solid [10][11][12][13][14]. Considering that the aerodynamic/aerothermal prediction of hypersonic vehicle depends on the gas-solid momentum/energy transfer, some works have been made to study the hypersonic Knudsen layer ow [14][15][16][17][18][19]. Gijare, Bhagat, and Dongari [14,15] studied the effect of the Knudsen layer on hypersonic ows using a computational uid dynamics (CFD) solver modi ed based on the effective mean free path.…”

“…Ou and Chen [17] investigated the nonlinear transport properties and macroscopic quantities of rare ed Couette ows at different velocities and found that transport properties are sensitive to the grid size. Chen and Zhou [18] analyzed several hypersonic ows over sharp bodies and blunt bodies and showed some special phenomena of velocity distributions in strong shear Couette ow.…”

“…In this case, λ needs to be corrected based on the numerical simulation results [18]. Furthermore, according to the computational experience in numerical simulation, there is always grid sensitivity when calculating the ow parameters in extremely nonequilibrium ow [17], and λ is no exception. Therefore, it may bring some uncertainty into the analysis of nonequilibrium relaxation based on the traditionally de ned λ [24].…”