Modeling oscillatory flows in the transition regime using a high-order moment method

Abstract

We present results using three different continuum-based models to study oscillatory flow in the transition regime. Data obtained from numerical solutions of the Boltzmann equation and the direct simulation Monte Carlo method, are used to assess the ability of the continuum models to capture important rarefaction effects. We further highlight the need to consider two Knudsen numbers: one based upon the length scale and the other upon the time scale. It is found that the regularized 26 moment model can follow kinetic theory in the early transition regime in terms of both Knudsen numbers but the regularized 13 moment equations can only be used up to the upper limit of the hydrodynamic regime. However, the subtle interplay of the length and time scales on oscillatory non-equilibrium flow causes the Navier-Stokes equations to fail even in the hydrodynamic regime. In addition, the effect of modifying the accommodation coefficient is also considered. It is found that reducing the accommodation coefficient on the stationary wall alone will increase the motion of the gas. However, gaseous movement will be reduced by changing both walls from diffusive to specular reflection.

Oscillatory rarefied gas flow inside rectangular cavities

“…In the past decade, in order to investigate the damping due to the normal pressure, the propagation of sound waves (Hadjiconstantinou 2002;Sharipov & Kalempa 2008a;Kalempa & Sharipov 2009;Gu & Emerson 2011;Struchtrup 2011;Desvillettes & Lorenzani 2012;Kalempa & Sharipov 2012) between two parallel plates or in a semi-infinite space has been extensively studied; to investigate the damping caused by the shear force, oscillatory Couette flows both in planar (Park, Bahukudumbi & Beskok 2004;Tang et al 2008;Sharipov & Kalempa 2008b;Doi 2009;Taheri et al 2009;Yap & Sader 2012) and cylindrical geometries (Emerson et al 2007;Shi & Sader 2010;Gospodinov, Roussinov & Stefan 2012) have been studied. For these investigations the adopted methods have included the direct simulation Monte Carlo (DSMC) method (Bird 1994), the discrete velocity method for the linearized Bhatnagar-Gross-Krook (BGK), ellipsoidal statistical BGK, and Shakhov kinetic model equations (Bhatnagar, Gross & Krook 1954;Holway 1966;Shakhov 1968), the numerical kernel method for the linearized Boltzmann equation of hard-sphere gases (Doi 2009), the regularized 13-and 26-moment equations (Struchtrup 2005;Gu & Emerson 2011), and the lattice Boltzmann method (Tang et al 2008;Meng & Zhang 2011).…”

Linearized-moment analysis of the temperature jump and temperature defect in the Knudsen layer of a rarefied gas

“…With a finite number of moments, such as 13 or 26 moments in three-dimensional applications (the number of moments in one-or two-dimensional problems is much reduced), recent studies have shown that both the regularized 13 (R13) and 26 (R26) moment equations are able to capture several well known nonequilibrium phenomena, such as the bimodal temperature profile in force-driven Poiseuille flow, nongradient heat flux in Couette flow, and the Knudsen minimum [5][6][7][8][9]. They have also been used to study oscillatory flow with some success [10].…”

Sound propagation through a rarefied gas in rectangular channels

“…In the past decade, oscillatory gas flows have been extensively studied [11][12][13][14][15][16][17][18][19][20], most of which, however, are for flows between two parallel plates. While the viscous damping is dominate at low oscillation frequencies, at relatively high oscillation frequencies, inertial force leads to the interference of sound waves along the oscillating direction of the plate, so that the magnitude of the damping force on the oscillating plate oscillates when the oscillation frequency varies [18].…”