Bulletin of the American Physical Society
64th Annual Meeting of the APS Division of Fluid Dynamics
Volume 56, Number 18
Sunday–Tuesday, November 20–22, 2011; Baltimore, Maryland
Session A23: Rarefied Gases and DSMC |
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Chair: Steffan Hardt, Technical University of Darmstadt Room: 326 |
Sunday, November 20, 2011 8:00AM - 8:13AM |
A23.00001: A thermally driven ratchet for the separation of gas molecules Steffen Hardt, Sudarshan Tiwari, Axel Klar If a gas is confined between two suitably structured surfaces, the application of a temperature gradient between the surfaces gives rise to nontrivial phase-space distributions inside the gas if the Knudsen number is larger than one. In such non-equilibrium situations a nonzero momentum and mass flux can be created in a direction parallel to the surfaces. We study a situation of comparatively large molecules of low concentration moving in a background gas of small molecules. It is assumed that the Knudsen number of the small molecules is much larger than one. Therefore, the small molecules dominantly collide with the wall boundaries, whereas the large molecules undergo collisions with the walls as well as the small molecules. Such a scenario is analyzed using Monte-Carlo simulation techniques based on a hard-sphere collision model. It is shown that while the small molecules show no net motion, the large molecules are driven parallel to the surfaces with a velocity that depends on their size. Larger molecules are transported faster than smaller ones. In consequence we have demonstrated a novel scheme of gas dynamics that may find applications in the size separation of molecules. [Preview Abstract] |
Sunday, November 20, 2011 8:13AM - 8:26AM |
A23.00002: Quadrature--based moment closures for non--equilibrium flows: hard--spheres collisions and approach to equilibrium Matteo Icardi, Pietro Asinari, Daniele Marchisio, Salvador Izquierdo, Rodney Fox Recently the Quadrature Method of Moments (QMOM) has been extended to solve several kinetic equations, in particular for gas--particle flows and rarefied gases. This method is usually coupled with simplified linear models for particle collisions. In this work QMOM is tested as a closure for the dynamics of high--order moments with a more realistic collision model namely the hard--spheres model in the Homogeneous Isotropic Boltzmann Equation. The behavior of QMOM far away and approaching the equilibrium is studied. Results are compared to other techniques such as the Lattice--Boltzmann (LBM) and the Grad's expansion (GM) methods. Comparison with a more accurate and computationally expensive model, based on the Discrete Velocity Method (DVM), is also carried out. Our results show that QMOM describes very well the evolution when it is far away from equilibrium, without the drawbacks of the GM and LBM or the computational costs of DVM but it is not able to accurately reproduce the equilibrium and the dynamics close to it. Corrections to cure this behavior are proposed and tested. [Preview Abstract] |
Sunday, November 20, 2011 8:26AM - 8:39AM |
A23.00003: DSMC Simulations Assessing the ES-BGK Kinetic Model for Gas-Phase Transport between Parallel Walls M.A. Gallis, J.R. Torczynski Bird's Direct Simulation Monte Carlo (DSMC) method is used to simulate gas-phase diffusive transport at near-continuum conditions. The molecules collide using either the Boltzmann collision term or the ellipsoidal-statistical Bhatnagar-Gross-Krook (ES-BGK) kinetic model. Momentum, heat, and mass transport between parallel walls (i.e., Couette, Fourier, and Fickian flows) are investigated. The ES-BGK model produces values of the viscosity and the thermal conductivity outside the Knudsen layers that agree closely with the corresponding values from the Boltzmann collision term (also implemented in DSMC). However, the ES-BGK model produces less accurate values for the mass self-diffusivity, with a modest difference for the Maxwell interaction but a large difference for the hard-sphere interaction. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000. [Preview Abstract] |
Sunday, November 20, 2011 8:39AM - 8:52AM |
A23.00004: An Expression for the Gas Mass Flow Rate through a Tube from Free-Molecular to Continuum Conditions J.R. Torczynski, M.A. Gallis An expression for the steady isothermal gas mass flow rate through a long thin tube from free-molecular to continuum conditions with arbitrary accommodation is developed. This expression is based on the Navier-Stokes equations and a slip boundary condition developed with the philosophy that the mass flow rate is more important than the velocity field. Its form permits integration along the tube to obtain a closed-form expression. This expression contains three coefficients. The first and the second are known from free-molecular and near-continuum flow. The third is determined from Direct Simulation Monte Carlo (DSMC) simulations for flows in the transitional regime. A similar expression is developed for rectangular channels. These expressions agree well with recent experiments measuring mass flow rates through microscale tubes and channels. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000. [Preview Abstract] |
Sunday, November 20, 2011 8:52AM - 9:05AM |
A23.00005: Characteristics Based Boundary Conditions for 3D Unstructured DSMC Simulations Sergey Averkin, Nikolaos Gatsonis The theoretical and algorithmic framework of a characteristic-based method for subsonic boundary conditions suitable to the Direct Simulation Monte Carlo (DSMC) is presented. This method is based on the local one dimensional inviscid (LODI) formulation used in compressible (continuous) flow computations. The method is implemented in an unstructured 3D DSMC (U3DSMC) code and is supplemented with a neighboring-cell sampling approach and a time-average smoothing technique to speed convergence and reduce fluctuations. Simulations of a pressure-driven subsonic flow in a circular tube are used for verification and validation of the boundary condition method. The length and the radius of the tube are 0.02m and 0.001m respectively. The inlet surface is specified with a fixed pressure 300Pa and a number density 7.2464e+22 m$^{-3}$ and the outlet surface is specified with a fixed pressure 150Pa. The corresponding Knudsen number at the inlet is 0.1786 and at the exit 0.3572 covering the transitional rarefied flow regime. The sidewall is modeled as a diffuse surface with full accommodation to a temperature of 300K. The average inlet Mach number is 0.156. Local error estimates are compared with theoretical predictions. The numerical results are in good agreement with theoretical and experimental results. [Preview Abstract] |
Sunday, November 20, 2011 9:05AM - 9:18AM |
A23.00006: Effect of weak gravitation on the plane Poiseuille flow of a highly rarefied gas Toshiyuki Doi Plane Poiseuille flow of a highly rarefied gas that flows horizontally in the presence of weak gravitation is studied based on the Boltzmann equation for a hard sphere molecular gas. The behavior of the solution in the regime of large mean free path and small strength of gravity is studied numerically based on the one-dimensional Boltzmann equation derived by means of an asymptotic analysis for a slow variation in the flow direction. It is clarified that the effect of weak gravity on the flow is not negligible when the mean free path is so large that it is comparable to the maximum range of the parabolic molecular path within the channel. When the mean free path is much larger than this range, the effect of gravity that makes the molecules fall plays the dominant role in determining the distribution function, and thus the over-concentration in the distribution function as well as the flow velocity does not grow further even if the mean free path is increased. [Preview Abstract] |
Sunday, November 20, 2011 9:18AM - 9:31AM |
A23.00007: Continuous Stochastic Equations for Diatomic Rarefied Gas Flows Hossein Gorji, Patrick Jenny In this talk, we postulate a non-linear Fokker-Planck model for simulations of the rarefied gas flows whereas the gas molecules would possess the internal degrees of freedom (DoF). The main motivation of the proposed model is the computational efficiency which is obtained due to the fact that in this solution algorithm no collisions between notional particles have to be calculated. The model equation is based on the Fokker-Planck approximation of the Boltzmann equation which has already been used for the motion of monatomic gas molecules by authors. However, a new set of stochastic differential equations (SDEs) is proposed for internal modes of the diatomic molecules. Based on the proposed model the heat conductivity of nitrogen is calculated for the range of temperatures from 200 to 800 K and it is shown that excellent agreement with regard to experimental results is gained. [Preview Abstract] |
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