Bulletin of the American Physical Society
2005 58th Annual Meeting of the Division of Fluid Dynamics
Sunday–Tuesday, November 20–22, 2005; Chicago, IL
Session GM: Rarefied Gas Dynamics |
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Chair: Michael Gallis, Sandia National Laboraory Room: Hilton Chicago PDR 1 |
Monday, November 21, 2005 10:34AM - 10:47AM |
GM.00001: Noncontinuum Effects in Gas-Phase Heat Transfer in Microdevices M.A. Gallis, J.R. Torczynski, D.J. Rader, B.L. Bainbridge Noncontinuum gas-phase heat transfer is simulated for two microscale geometries using two methods. Microscale thermal actuation from heating-induced expansion of a microbeam adjacent to the substrate and surrounded by air is the motivation. The first geometry is a \mbox{1-$\mu$m} gas-filled microgap bounded by parallel solid slabs. The second geometry is a heated \mbox{I-shaped} microbeam \mbox{2 $\mu$m} from the adjacent substrate, with gas in between. Two computational methods are used. The Navier-Stokes slip-jump method approximates noncontinuum effects with continuum heat transfer in the bulk gas and temperature jumps at boundaries. The Direct Simulation Monte Carlo method treats noncontinuum gas behavior more accurately by using computational molecules. The heat fluxes from both methods for the microgap agree closely for all pressures and accommodation coefficients. For the microbeam, there is good agreement except for low-pressure cases with near-unity accommodation coefficients. The causes of this discrepancy are discussed. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000. [Preview Abstract] |
Monday, November 21, 2005 10:47AM - 11:00AM |
GM.00002: Normal Solutions of the Boltzmann Equation for Fourier and Couette Flow J.R. Torczynski, M.A. Gallis, D.J. Rader Bird's Direct Simulation Monte Carlo (DSMC) method is used to simulate Fourier flow (uniform heat flux) and Couette flow (uniform shear stress) for highly nonequilibrium conditions. The gas is confined between two parallel, fully-accommodating walls at unequal temperatures with opposite tangential velocities. For small system Knudsen numbers, the solution is normal in the central region of the domain (outside the Knudsen layers). For small heat-flux Knudsen numbers, the normal solution exhibits Chapman-Enskog (CE) behavior. More specifically, excellent agreement is observed between the DSMC and CE thermal conductivity, viscosity, and Sonine-polynomial coefficients of the molecular velocity distribution function. At larger heat-flux Knudsen numbers, the normal solution systematically departs from the CE solution. Under these conditions, the DSMC results for Maxwell molecules are in excellent agreement with the exact solution of Santos and co-workers, and the DSMC results for hard-sphere molecules exhibit similar trends. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000. [Preview Abstract] |
Monday, November 21, 2005 11:00AM - 11:13AM |
GM.00003: Analysis of Rarefied Parallel Interacting Sonic Jets Wenhai Li, Foluso Ladeinde In this study, a DSMC procedure has been developed and used to investigate rarefied parallel interacting sonic free jets. The molecular penetration between the two jets has been studied in this paper and a modified Penetration Knudsen Number has been introduced to evaluate the effects of an interaction shock wave. It is shown that the existence of the interaction shock wave produces additional effects that decrease molecular penetration and create a displacement of molecular penetration in the jet exhaust direction. These effects can be observed in the density profiles from the DSMC calculation. We also analyzed the scaling law for the density profile along the symmetry axis, with the results that the scaling law is not suitable for small values of the separation distance between the two orifices or small values of the stagnation Knudsen number (Kn$_{s})$. [Preview Abstract] |
Monday, November 21, 2005 11:13AM - 11:26AM |
GM.00004: Flow of gases in isothermal prismatic channels at arbitrary Knudsen-numbers Andreas G. Class, Gottfried Class In rarefied gas flow in ducts of prismatic cross section a minimum of the flow resistance, which was first noted in 1909, is observed for Knudsen Numbers ranging from 1 to 10. We propose a closed correlation for the flow resistance and determine all the parameters from physical considerations. The relation is applicable to arbitrary Knudsen numbers and ducts of arbitrary length. Employing recent experimental data from the literature the correlation is verified for a wide range of parameters. The present study provides a phenomenological explanation of the Knudsen-minimum and can be used to extend results obtained for round channels to other prismatic cross sections. The proposed correlation allows for improved computations of channel flow in vacuum technology applications. [Preview Abstract] |
Monday, November 21, 2005 11:26AM - 11:39AM |
GM.00005: Nanowire experiments for cylinder drag in the transition regime of rarefied flows Rustom Bhiladvala, Mingwei Li, Theresa Mayer The ability to measure drag forces on vibrating silicon and metal nanowires with different surface structure or chemistry will enable a convenient tabletop testbed to study the effect of boundary conditions in different regimes of rarefied gas flows. Silicon nanowires, with a thin native oxide coating, vibrating in pure dry nitrogen from high vacuum (2 $\times$ 10$^{-10 }$atm) to atmospheric pressure have been used to measure drag on cylinders in rarefied flow. Knudsen numbers (\textbf{\textit{Kn}}) based on wire diameter are 0.2 $<$ \textbf{\textit{Kn}} $<$ 200 (transition and free molecular flow regimes) in the pressure range 10$^{-3} <$ \textbf{\textit{P }}$<$ 1 atmospheres, of importance to sensing applications. In the transition regime, analytical results [Yamamoto K. and Sera K., \textit{Physics of Fluids}, \textbf{28}, 1286, (1985)] for drag on a cylinder using a matched Boltzmann-BGK (near-field) / Stokes-Oseen (far-field) solution show good agreement with the nanowire data, while free molecular and unsteady continuum solutions extrapolated into the transition region both predict higher damping. The data show departure from free molecular behavior beginning at \textbf{\textit{Kn}} =10, if \textbf{\textit{Kn}} is based on wire diameter. [Preview Abstract] |
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