Bulletin of the American Physical Society
68th Annual Meeting of the APS Division of Fluid Dynamics
Volume 60, Number 21
Sunday–Tuesday, November 22–24, 2015; Boston, Massachusetts
Session H40: Rarefied Flows and DSMC |
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Chair: Sergey Averkin, Worcester Polytechnic Institute Room: Sheraton Back Bay D |
Monday, November 23, 2015 10:35AM - 10:48AM |
H40.00001: Janus-Particles in a rarefied gas: thermophoresis and orientation Tobias Baier, Samir Shrestha, Sudarshan Tiwari, Steffen Hardt, Axel Klar Thermophoresis, the motion of a particle along a thermal gradient, has been used both for preventing and inducing the deposition of aerosols on heated or cooled surfaces. In the latter case it may be advantageous to induce the deposition with a preferred orientation of the particle, for example by utilizing non-uniform reflective properties on the particle surface. As a model system we investigate a spherical Janus particle on which gas molecules are reflected diffusively from one hemisphere and specularly from the other. In the limit of large Knudsen number this is studied analytically, focusing on the interplay between thermophoretic motion and alignment of the particle. Without motion, a torque orients the particle with its diffuse side towards the colder gas. However, any motion of the particle relative to the gas results in a preferred alignment with the specular side in direction of the particle velocity. Thus the thermophoretic motion, which is towards the colder side, results in a weakening of the particle alignment. The results are supported by Monte-Carlo simulations to extend the range of validity towards finite Knudsen numbers. These findings shed light on the efficiency of aligned deposition of nanoparticles from a gas stream on a cooled surface. [Preview Abstract] |
Monday, November 23, 2015 10:48AM - 11:01AM |
H40.00002: ABSTRACT WITHDRAWN |
Monday, November 23, 2015 11:01AM - 11:14AM |
H40.00003: Slow flow of a rarefied gas past a sphere: Numerical analysis of fundamental problem Satoshi Taguchi, Toshihiro Suzuki A slow flow of a rarefied gas past a sphere with a uniform temperature is considered with a special interest in the drag exerted on the sphere. It was shown previously [S. Taguchi, J. Fluid Mech. \textbf{774}, 363--394 (2015)] that the drag up to the second order of the Mach number is expressed in terms of two fundamental functions depending on the Knudsen number, which are obtained by solving the corresponding linearized problem. The present study aims to obtain these functions on the basis of the ellipsoidal-statistical (ES) model of the Boltzmann equation under the diffuse reflection boundary condition. [Preview Abstract] |
Monday, November 23, 2015 11:14AM - 11:27AM |
H40.00004: Aerothermodynamics of compressible flow past a flat plate in the slip-flow regime Chi-Yang Cheng, Yi Dai, Genong Li, Yitao Hu, Ming-Chia Lai Compressible flow past a flat plate in the slip-flow regime features a very simple geometry and flow field, but it retains the most relevant and interesting physics in high-speed rarefied gas dynamics. In the slip-flow regime, the aerothermodynamic issues, especially the recovery factors and the convection heat transfer correlation, are the focus of this presentation. We first present the detailed similarity equations, especially the transformed Maxwell's slip and jump boundary conditions, and the equations for the Chapman-Rubesin parameter as well as how we incorporate the variable gas properties and the constitutive scaling model for the Knudsen layer in the similarity equations. The similarity solutions are compared with results published by E.\ R.\ van Driest [NACA Technical Note 2597, 1952]. We point out that van Driest's solutions were computed by using no-slip and no-jump boundary conditions. The recovery factor and Nusselt number of the plate are shown as functions of the Reynolds number and the Mach number. Finally, the similarity solutions are also compared with simulations of a two-dimensional computational fluid dynamics model solving the full Navier-Stokes-Fourier equations with slip and jump boundary conditions. [Preview Abstract] |
Monday, November 23, 2015 11:27AM - 11:40AM |
H40.00005: Numerical solution of Boltzmann equation using discrete velocity grids Prakash Vedula An importance sampling based approach for numerical solution of the (single species) Boltzmann equation using discrete velocity grids is proposed. This approach involves a stochastic method for evaluation of the collision integral based on sampling of depleting/replenishing collisions and is designed to preserve important symmetries of the collision operator, including collision invariants. The underlying particle distribution function is represented as a collection of delta functions with associated weights that are non-negative. A key feature in the construction of the proposed method is that it ensures that the weights associated with the distribution function remain non-negative during collisional relaxation, thereby satisfying an important realizability condition. Performance of the proposed approach will be studied using test problems involving spatially homogeneous collisional relaxation flow and microchannel flows. Results obtained from the proposed method will be compared with those obtained from the (deterministic) collisional Lattice Boltzmann Method (cLBM) and the traditional direct simulation Monte Carlo (DSMC) method for solution of Boltzmann equation. Extension of the proposed method using discrete velocity grids for multicomponent mixtures will also be discussed. [Preview Abstract] |
Monday, November 23, 2015 11:40AM - 11:53AM |
H40.00006: A Kinetic 13-Moment Boundary Conditions Method for Particle Simulations of Viscous Rarefied Flows Sergey Averkin, Nikolaos Gatsonis The kinetic 13-moment (Navier-Stokes-Fourrier) boundary condition method is developed for direct simulation Monte Carlo (DSMC) simulations of rarefied gas flows. The particles are injected into the computational domain from the inlet and outlet following the first-order Chapman-Enskog distribution function. The unknown parameters of the Chapman-Enskog distribution function are reconstructed from the full 13-moment (Navier-Stokes-Fourier) equations discretized on the boundaries with the wave amplitudes calculated by the local one dimensional inviscid (LODI) formulation used in compressible (continuous) flow computations. The kinetic-moment boundary conditions are implemented in an unstructured 3D DSMC (U3DSMC) code and are supplemented with a neighboring-cell sampling approach and a time-average smoothing techniques to speed up convergence and reduce fluctuations. Simulations of a pressure-driven viscous subsonic flow in a circular tube are used for verification and validation of the boundary conditions. In addition, the present method is compared to the previously developed kinetic-moment boundary conditions derived from the five-moment (Euler) equations. [Preview Abstract] |
Monday, November 23, 2015 11:53AM - 12:06PM |
H40.00007: DSMC-LBM hybrid scheme for flows with variable rarefaction conditions Gianluca Di Staso, Sauro Succi, Federico Toschi, Herman Clercx The kinetic description of gases, based on the Boltzmann equation, allows to cover flow regimes ranging from the rarefied to the continuum limit. The two limits are traditionally studied by numerically approximating the Boltzmann equation via Direct Simulation Monte Carlo (DSMC) method or the Lattice Boltzmann Equation method (LBM). While DSMC is suitable for rarefied flows, its computational cost makes it unpractical to study hydrodynamic flows. The LBM has instead proved itself to be an efficient and accurate method in the hydrodynamic limit even though simulation of rarefied flows requires additional modeling. Here, results on the development of a hybrid scheme capable of coupling the LBM and the DSMC methods and able to efficiently simulate flows with variable rarefaction conditions are presented. The coupling scheme is based on Grad's moment method approach and the local single particle distribution function at a given order of truncation is built by using the Hermite polynomials expansion approach and Gauss-Hermite quadratures. The capabilities of the hybrid approach for simulating flows in the transition regime are illustrated in the case of planar Couette and Poiseuille flows. [Preview Abstract] |
Monday, November 23, 2015 12:06PM - 12:19PM |
H40.00008: Relaxation rates for inverse power law particle interactions and their variable hard sphere surrogates Robert Rubinstein It is well known that collision models based on an assumed intermolecular potential (IPL, LJ, ...) can be successfully replaced by simplified surrogates (VHS, VSS, VS, ...) in DSMC calculations. But these surrogates only reproduce certain gross properties of the molecular model, for example, the temperature dependence of the viscosity; they do not approximate, and even mis-state, the details of the particle interactions. The success of the simplified models in problems at finite Knudsen number, where the Navier-Stokes approximation is not valid, may therefore seem surprising. To understand this success in a very special case, we showed that the first seven relaxation rates of the linearized Boltzmann equation for Maxwellian molecules are well approximated by the corresponding relaxation rates of its VHS surrogate. We will show that this analysis can be extended in somewhat less generality to IPL interactions, and to some extent to more realistic models including LJ. We believe that this analysis can help address the more general problem of identifying the properties of the collision model that dominate the predictions of the Boltzmann equation. [Preview Abstract] |
Monday, November 23, 2015 12:19PM - 12:32PM |
H40.00009: DSMC Simulation of Microstructure Actuation by Knudsen Thermal Force Aaron Pikus, Israel Sebastiao, Andrew Strongrich, Alina Alexeenko Compact, low-power and highly accurate vacuum sensors are needed for emerging applications such as high-altitude communication platforms, small satellites and in-vacuum manufacturing processes. A novel MEMS-based pressure and gas sensor -- Microelectromechanical In-plane Knudsen Radiometric Actuator (MIKRA) -- has been developed at Purdue. MIKRA is based on Knudsen thermal force generated by rarefied flow driven by thermal gradients within the microstructure. The goal of this work is to model the rarefied gas flow in the MIKRA sensor to validate the numerical modeling of rarefied thermally-driven flows and gain insights for sensor design. The Direct Simulation Monte Carlo (DSMC) solver SPARTA is employed to numerically calculate the distribution of the flowfield and surface properties. The resulting forces on the colder shuttle beam are calculated and compared to the available experimental data as well as other numerical solvers. Both DSMC and experimental results suggest that the maximum forces occur at a Knudsen number of approximately 1. The streamlines indicate the presence of two small vortexes between the heated beam and the colder shuttle beam, and a larger one above these two beams. The DSMCsimulations, validated by experimental measurements, help understand the unique flow behaviors encountered in rarefied thermally-driven flows. [Preview Abstract] |
Monday, November 23, 2015 12:32PM - 12:45PM |
H40.00010: Analytical and Numerical Modeling of Strongly Rotating Rarefied Gas Flows Sahadev Pradhan, Viswanathan Kumaran Centrifugal gas separation processes effect separation by utilizing the difference in the mole fraction in a high speed rotating cylinder caused by the difference in molecular mass, and consequently the centrifugal force density. These have been widely used in isotope separation because chemical separation methods cannot be used to separate isotopes of the same chemical species. More recently, centrifugal separation has also been explored for the separation of gases such as carbon dioxide and methane. The efficiency of separation is critically dependent on the secondary flow generated due to temperature gradients at the cylinder wall or due to inserts, and it is important to formulate accurate models for this secondary flow. The widely used Onsager model for secondary flow is restricted to very long cylinders where the length is large compared to the diameter, the limit of high stratification parameter, where the gas is restricted to a thin layer near the wall of the cylinder, and it assumes that there is no mass difference in the two species while calculating the secondary flow. There are two objectives of the present analysis of the rarefied gas flow in a rotating cylinder. The first is to remove the restriction of high stratification parameter, and to generalize the solutions to low rotation speeds where the stratification parameter may be \textit{O(1)}, and to apply for dissimilar gases considering the difference in molecular mass of the two species. Secondly, we would like to compare the predictions with molecular simulations based on the direct simulation Monte Carlo (DSMC) method for rarefied gas flows, in order to quantify the errors resulting from the approximations at different aspect ratios, Reynolds number and stratification parameter. [Preview Abstract] |
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