Bulletin of the American Physical Society
67th Annual Meeting of the APS Division of Fluid Dynamics
Volume 59, Number 20
Sunday–Tuesday, November 23–25, 2014; San Francisco, California
Session D36: Rarefied Flows |
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Chair: Venkatraman Ayaswamy Room: Alcove A |
Sunday, November 23, 2014 2:15PM - 2:28PM |
D36.00001: Plane Poiseuille flow of a highly rarefied gas between the two walls of Maxwell-type boundaries with different accommodation coefficients: Effect of a weak external force Toshiyuki Doi Plane Poiseuille flow of a highly rarefied gas between the two walls of Maxwell-type boundaries with different accommodation coefficients is studied based on kinetic theory when the gas is subject to a weak external force perpendicular to the walls. The flow behavior is studied numerically based on the spatially one-dimensional Boltzmann equation for a hard-sphere gas derived by the asymptotic analysis for a slow variation in the longitudinal direction. Due to the effect of a weak external force, there is an appreciable difference in the mass-flow rate between the flows in which the two walls are interchanged when the mean free path is sufficiently large. If both of the accommodation coefficients are close to unity, the mass-flow rate is reduced due to the effect of the external force. In contrast, if the accommodation coefficient of one wall is considerably smaller than unity, the mass-flow rate of the gas can be enhanced when this wall is placed on the side to which the external force points. [Preview Abstract] |
Sunday, November 23, 2014 2:28PM - 2:41PM |
D36.00002: Frequency-Domain DSMC Method for Oscillatory Gas Flows Daniel Ladiges, John Sader Gas flows generated by resonating nanoscale devices inherently occur in the non-continuum, low Mach number regime. Numerical simulation of such flows presents a tremendous challenge, which has motivated the development of several direct simulation Monte Carlo (DSMC) methods for low Mach number flows. We present a frequency-domain DSMC method for oscillatory low Mach number gas flows, based on the linearized Boltzmann equation. This circumvents the need for temporal simulations, providing direct access to both amplitude and phase information using a pseudo-steady algorithm. The proposed method is demonstrated with several examples, and good agreement is found with both existing time-domain DSMC methods and accurate numerical solutions of the Boltzmann-BGK equation. Analysis of these simulations, using a rigorous statistical approach, shows that this frequency-domain method provides a significant improvement in computational speed compared to existing time-domain DSMC methods. [Preview Abstract] |
Sunday, November 23, 2014 2:41PM - 2:54PM |
D36.00003: Relaxation rates in the Maxwellian collision model and its variable hard sphere surrogate Robert Rubinstein The variable hard sphere and related models have proven to be accurate and computationally convenient replacements for the inverse power law model of classical kinetic theory in DSMC calculations. We provide theoretical support for this success by comparing the relaxation rates in the linearized Boltzmann equation for the Maxwellian model with those of its variable hard sphere surrogate. We demonstrate that the linearized collision operators for these two models agree closely under well defined and broadly applicable conditions and show some implications of this agreement for time dependent solutions of the linearized Boltzmann equation. [Preview Abstract] |
Sunday, November 23, 2014 2:54PM - 3:07PM |
D36.00004: Hybrid DSMC-LBM scheme for pressure-driven flows Gianluca Di Staso, Federico Toschi, Herman J.H. Clercx Lattice Boltzmann Method (LBM) is a standard numerical methodology that, in principle, can be used to simulate flows ranging from hydrodynamic to rarefied gas as it is based on a discretisation of the Boltzmann equation. However at increasing rarefaction the number of needed speeds may become very large making the scheme prohibitively expensive under very rarefied conditions. Another classical technique, also based on the discretisation of the Boltzmann equation, and effective under rarified conditions is the Direct Simulation Monte Carlo (DSMC). We present results on the development of a hybrid scheme able to combine both numerical techniques to efficiently and accurately study flows with varying rarefaction. Details of the implementation and validation against few representative flows will be presented. [Preview Abstract] |
Sunday, November 23, 2014 3:07PM - 3:20PM |
D36.00005: A continuum breakdown parameter based on the characteristic function of the molecular velocity distribution Arghavan Alamatsaz, Ayyaswamy Venkattraman Rarefied flows characterized by Knudsen numbers (Kn) greater than 0.1 are frequently encountered in several applications including low-pressure, high speed and microscale flows and require computationally expensive molecular approaches such as direct simulation Monte Carlo (DSMC) to accurately capture the physical phenomena unique to these flows. However, most of these flows also contain regions where traditional inexpensive continuum techniques such as the Navier-Stokes (NS) equations are sufficiently accurate making a hybrid NS-DSMC approach attractive and optimal. Such a hybrid method typically requires a robust continuum breakdown parameter (CBP) to determine regions where each method should be applied. Historically, hybrid methods have used CBPs based on the macroscopic properties which are lower order moments of the molecular velocity distribution function (VDF) and their gradients which can have significant inaccuracies. In this work, we propose a novel CBP that utilizes all moments of the VDF by computing the characteristic function with limited computational overhead. We also compare the performance of this CBP using standard benchmark problems including structure of a normal shock wave and Fourier-Couette flow for various Kn from continuum to free-molecular. [Preview Abstract] |
Sunday, November 23, 2014 3:20PM - 3:33PM |
D36.00006: An evaluation of collision models in the Method of Moments for rarefied gas problems David Emerson, Xiao-Jun Gu The Method of Moments offers an attractive approach for solving gaseous transport problems that are beyond the limit of validity of the Navier-Stokes-Fourier equations. Recent work has demonstrated the capability of the regularized 13 and 26 moment equations for solving problems when the Knudsen number, Kn (where Kn is the ratio of the mean free path of a gas to a typical length scale of interest), is in the range 0.1 and 1.0--the so-called transition regime. In comparison to numerical solutions of the Boltzmann equation, the Method of Moments has captured both qualitatively, and quantitatively, results of classical test problems in kinetic theory, e.g. velocity slip in Kramers' problem, temperature jump in Knudsen layers, the Knudsen minimum etc. However, most of these results have been obtained for Maxwell molecules, where molecules repel each other according to an inverse fifth-power rule. Recent work has incorporated more traditional collision models such as BGK, S-model, and ES-BGK, the latter being important for thermal problems where the Prandtl number can vary. We are currently investigating the impact of these collision models on fundamental low-speed problems of particular interest to micro-scale flows that will be discussed and evaluated in the presentation. [Preview Abstract] |
Sunday, November 23, 2014 3:33PM - 3:46PM |
D36.00007: Generalized slip-flow theory and its related Knudsen-layer analysis for a slightly rarefied gas I Masanari Hattori, Shigeru Takata A systematic asymptotic analysis of the Boltzmann equation shows that the overall behavior of a gas can be described by fluid-dynamic-type equations with the appropriate slip/jump boundary condition when the Knudsen number is small [the generalized slip-flow theory (Sone, Molecular Gas Dynamics, 2007)]. Near the boundary, a non-fluid-dynamic correction (the Knudsen-layer correction) to the overall solution is required. Although the generalized slip-flow theory has been established up to the second order of the Knudsen number expansion, the data of those corrections have been completed only for the BGK model. Completing the corresponding data for the original Boltzmann equation has been demanded. In the present work, partial results of completing the data for a hard-sphere gas under the diffuse reflection condition are reported. [Preview Abstract] |
Sunday, November 23, 2014 3:46PM - 3:59PM |
D36.00008: Dual-Wavelength Interferometry Plasma Electron Density Measurements Brian Neiswander, Eric Matlis, Thomas Corke Plasma is an optically controllable medium with potential for improving high-speed adaptive optics technology, particularly in aero-optical wavefront-control. The index of refraction of a plasma depends on the electron density and gas density. These two parameters are highly coupled and must be uniquely determined in order to assess the effectiveness of plasma as a high-speed adaptive optic medium. Presented here are time-resolved experimental measurements of plasma electron density and gas density for a low-pressure cylindrical dielectric barrier discharge (DBD). Optical measurements were obtained using a dual-wavelength Michelson interferometer system featuring visible (0.633 $\mu$m) and infrared (3.39 $\mu$m) HeNe lasers. Along with results, a method used to increase the accuracy of the measurement system by incorporating a piezoelectric actuated scanning mirror and phase-demodulation analysis will be discussed. [Preview Abstract] |
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