Bulletin of the American Physical Society
60th Annual Meeting of the Divison of Fluid Dynamics
Volume 52, Number 12
Sunday–Tuesday, November 18–20, 2007; Salt Lake City, Utah
Session AP: Particle-Laden Flows I |
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Chair: Rodney Fox, Iowa State University Room: Salt Palace Convention Center 251D |
Sunday, November 18, 2007 8:30AM - 8:43AM |
AP.00001: Lattice Boltzmann Simulation of the Sedimentation of Elliptic Particles Kevin Connington, Zhenhua Xia, Shiyi Chen, Qinjun Kang The Lattice Boltzmann Method (LBM) has recently become a popular tool for simulating solid particle suspensions. Due to the method's affinity for handling complex boundary conditions on a stationary Cartesian grid, the LBM presents a promising alternative to more computationally expensive methods. We analyze the effectiveness of this method by comparing the LBM results to those of a finite element method for the case of elliptic particle sedimentation. Due to the moving geometry, the finite element method necessitates mesh regeneration, and projection of fluid variables from the old mesh to the new one at each time step. The LBM avoids these complications by virtue of its fixed grid. We examine several methods to implement the boundary conditions on the surface of the moving complex geometry. We also investigate the benefits and detriments of two methods to calculate the total force exerted by the fluid on the particle, i.e., the method of Momentum Exchange, unique to the LBM, and the method of Stress Integration. Then we implement the LBM to study some interesting phenomena associated with elliptic particle sedimentation. We analyze settling orientation, terminal Reynolds number, and frequency effects associated with shed vortices. [Preview Abstract] |
Sunday, November 18, 2007 8:43AM - 8:56AM |
AP.00002: A quadrature-based kinetic equation solver for arbitrary Knudsen numbers Rodney O. Fox, Prakash Vedula The Boltzmann kinetic equation can be applied to a wide range of flow phenomena including rarefied gas dynamics, gaseous flows in micro devices, and dilute gas-solids flows. While each application differs in the details, a fundamental problem is the treatment of cases far from equilibrium. Such flows are usually treated by (1) direct simulation Monte Carlo (DSMC) or (2) direct solvers for the velocity distribution function $f (\mathbf{r}, \mathbf{c},t)$. While each method has its advantages and disadvantages, both are computationally expensive relative to moment methods (e.g., hydrodynamic equations.) However, current implementations of moment methods fail when free molecular flow creates non-equilibrium velocity distributions (i.e.\ finite Knudsen numbers.) Here we propose a quadrature-based moment method for solving the kinetic equation for all $\mathrm{Kn}$. The method solves the transport equations for velocity moments by kinetic methods based on a finite set of velocities found by inverting the moments using quadrature. A particle mixing layer (equivalent at infinite Stokes to a Riemann shock tube) is used to illustrate the method for selected Mach and Stokes numbers, and for $0 \le \mathrm{Kn} \le \infty$. The results compare very favorably to published results using (1) and/or (2), but are computed at a fraction of the cost. Limitations of the approach and extensions to other flows (e.g.\ particle-laden channel flow) will also be discussed. [Preview Abstract] |
Sunday, November 18, 2007 8:56AM - 9:09AM |
AP.00003: Nanoparticle Knudsen Layers in Gases J.R. Torczynski, M.A. Gallis, D.J. Rader When diffusing toward a wall bounding an air-filled microscale region, nanoparticles form a particle Knudsen layer similar to the molecule Knudsen layer formed by a gas. At the wall, the particle number density has a nonzero value proportional to the particle flux. An approximate theory based on the generalized Fokker-Planck equation is developed for the nondimensional ``particle-flux coefficient'' of the proportionality, which depends on the reflection process and the drift velocity. Massively parallel Langevin particle simulations are performed to assess the accuracy of the theory. The particle-flux boundary condition can be used in advection-diffusion simulations of gas-phase nanoparticle transport in the same way that the velocity-slip and temperature-jump boundary conditions are used in fluid-dynamics and heat-transport simulations. This approach agrees well with Langevin simulations of particles injected into the gas-filled gap between two parallel plates. 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] |
Sunday, November 18, 2007 9:09AM - 9:22AM |
AP.00004: The motion of an ellipsoid particle in Hagen-Poiseuille flow Antoine Dechaume, Peter Minev, Warren Finlay The motion of solid particles in shear flows is crucially important in many situations, here we focus on an ellipsoid particle in Hagen-Poiseuille flow. The coupled motion of the fluid and particle is solved numerically with a non-Lagrange multiplier version of the fictitious domain method. The key idea of these methods is to fill the particle with fluid and impose rigid body as a side constraint, thus avoiding the remeshing of the fluid domain at each time-step. The motion of the particle depends on several parameters, such as the initial position and orientation, Reynolds number, relative density, orientation of gravity, aspect ratio and size of the particle. Different kind of motions are encountered, from tumbling and oscillating, to Segre-Silberberg migration, which are compared to the spherical particle case as well. [Preview Abstract] |
Sunday, November 18, 2007 9:22AM - 9:35AM |
AP.00005: DNS of Sheared Particulate Flows with a 3D Explicit Finite-Difference Scheme Andrew Perrin, Howard Hu A 3D explicit finite-difference code for direct simulation of the motion of solid particulates in fluids has been developed, and a periodic boundary condition implemented to study the effective viscosity of suspensions in shear. The code enforces the no-slip condition on the surface of spherical particles in a uniform Cartesian grid with a special particle boundary condition based on matching the Stokes flow solutions next to the particle surface with a numerical solution away from it. The method proceeds by approximating the flow next to the particle surface as a Stokes flow in the particle's local coordinates, which is then matched to the finite difference update in the bulk fluid on a ``cage'' of grid points near the particle surface. (The boundary condition is related to the PHYSALIS method (2003), but modified for explicit schemes and with an iterative process removed.) Advantages of the method include superior accuracy of the scheme on a relatively coarse grid for intermediate particle Reynolds numbers, ease of implementation, and the elimination of the need to track the particle surface. For the sheared suspension, the effects of fluid and solid inertia and solid volume fraction on effective viscosity at moderate particle Reynolds numbers and concentrated suspensions will be discussed. [Preview Abstract] |
Sunday, November 18, 2007 9:35AM - 9:48AM |
AP.00006: Gravity driven effect in flowing particle laden thin films Robert Glidden, Christopher Fox, Thomas Ward, Andrea Bertozzi The flow characteristics of an anisopycnic particle-laden thin film flowing down an inclined plane is analyzed experimentally near the maximum packing limit for polydisperse hard spheres. The mutliphase fluid is a mixture of silicone oil and polydisperse heavy glass beads of varying viscosities and bead diameter, respectively. For the high volume concentrations studied, $50\% < \phi < 56\%$, we observe that the elapsed time, $t$, versus average front position, $x_N$, still scales with the Huppert solution where $C_N=x_N^3/t$ is a constant [Nature 300(2), 1982]. For very high background fluid viscosities, the particle settling velocity is very slow with respect to the fluid and $C_N$ decreases with increasing concentration. As the background fluid viscosity is decreased $C_N$ remains relatively constant as the particle density approaches the maximum. We propose that the latter effect may be the result of a transition from viscous fluid flow to that of a lubricated sliding solid body. Experiments are performed to test an empirical correlation for the data in this parameter regime based on this hypothesis. [Preview Abstract] |
Sunday, November 18, 2007 9:48AM - 10:01AM |
AP.00007: An efficient representation of hydrodynamic interaction of cloud droplets and its application to collision efficiency Bogdan Rosa, Lian-Ping Wang, Wojciech Grabowski An efficient method for treating the hydrodynamic interaction of two spherical particles settling under gravity is developed in order to evaluate the collision efficiency. An effort is made to ensure accuracy of the method for any inter-particle separation by considering three separation ranges. The first is the long- range interaction where a second-order multipole method is applied. The second range concerns the short-range interaction where leading-order lubrication expansions are employed. Finally, for the intermediate range, a third-order polynomial fitting is proposed to bridge the long-range and short-range interactions. This integrated representation is found to be highly accurate when compared with the exact two-body solution of Stokes flows. Using this efficient method, accurate collision efficiencies for the case of gravitational interaction have been calculated. Extension of the method to many-body interactions and to a turbulent background flow will also be discussed. [Preview Abstract] |
Sunday, November 18, 2007 10:01AM - 10:14AM |
AP.00008: Particle-laden boundary layers and singularities M.R. Foster The dusty-gas model for flow in dilute particle suspensions generates a singularity in particle volume fraction in a variety of viscous boundary layer problems. Such a singularity, at say $x=x_s$ along the wall, makes it impossible to continue the solution to the equations. Previously, we have found that computation of the Blasius boundary layer, with a modified equation set that permits fluid volume fraction significantly different from $1$, still leads to a velocity singularity at a slightly modified location.\footnote{{\it Foster, Duck \& Hewitt}, Bull. Amer. Phys. Soc., November, 2006} Contrary to some published work, the Saffman force has not been found to mitigate the singularity for the conventional equation set, and again here, though the Saffman force does become comparable to the Stokes drag near the singularity, it alters the structure only slightly, and does not remove it. If $\alpha_o$ is the particle volume fraction of the fluid in which the boundary layer is embedded, then in certain re-scaled coordinates, the singularity occurs in a region $\alpha_o\times \alpha_o/|\log\alpha_o|$ about $x_s$, where a reduced set of equations applies. Within this region, there is a downstream-running ray from the origin on which $\alpha \equiv 1$. However, the vertical fluid and particle velocity components are unbounded on that line. On replacing the line with a solid surface of particle material, a narrow boundary layer may be inserted, in which velocity singularities are removed. [Preview Abstract] |
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