Bulletin of the American Physical Society
2006 59th Annual Meeting of the APS Division of Fluid Dynamics
Sunday–Tuesday, November 19–21, 2006; Tampa Bay, Florida
Session LE: Multiphase and Particle-Laden Flows VI |
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Chair: Lennon O'Naraigh, Imperial College, London Room: Tampa Marriott Waterside Hotel and Marina Florida Salon 123 |
Tuesday, November 21, 2006 8:00AM - 8:13AM |
LE.00001: Accuracy In Numerical Prediction Of Cavity Length and Vapor Cloud Shedding Frequency Of Cavitating Flows Over Various Geometries. Arvind Jayaprakash, Kathikeya Mahalatkar Standard two-equation turbulence models have been found to be incapable of predicting cavitating flow due to high compressibility in the vapor region. In order to predict the dynamics of vapor cloud shedding, Courtier-Delgosha (J. of Fluid Eng, 125, 2003) suggested a modification for the eddy viscosity for k-epsilon turbulence model. Though the modification works in capturing the dynamic behavior of cavitation sheet, the accuracy of cavity length and frequency is not achieved for a wide range of cavitation numbers. This is due to the complex flow features present during a cavitating flow and the incapability of Couitier-Delgosh's turbulence modification to account for these factors. A tuning factor is introduced in the turbulence modification of Coutier-Delgosha, which can be adjusted for different types of geometries. This modified form is then tuned and tested on prediction of cavitating flow over several geometries including NACA 0015 hydrofoil, Convergent-Divergent Nozzle, and Wedge. Good comparisons for both cavity length and frequency of vapor cloud shedding were obtained for wide range of cavitation numbers in all the geometries. The commercial CFD software Fluent has been used for this analysis. Comparisons of cavity length and vapor cloud shedding frequency as predicted by the present turbulence modification and those observed in experimental studies will be presented. [Preview Abstract] |
Tuesday, November 21, 2006 8:13AM - 8:26AM |
LE.00002: Beyond the Point Particle: LES-Style Filtering of Finite-Sized Particles. Brooks Moses, Chris Edwards Multiphase LES-style spatial filtering provides a rigorous means of modeling flow over computationally-unresolved particles and droplets, without recourse to the point-particle limit. As such, it can be used to investigate the validity of point-particle models for particles of finite sizes, and to provide refinements to point-particle models. We present results for the specific case of solid spherical particles, illustrating that the significant deviations from the point-particle assumption occur even for quite small particles, and that the addition of a dipole component to the standard single-point force provides a substantially improved model. [Preview Abstract] |
Tuesday, November 21, 2006 8:26AM - 8:39AM |
LE.00003: A hybrid Lagrangian-Eulerian scheme for two-phase flows Sourabh Apte A hybrid Lagrangian-Eulerian scheme combining a particle-based mesh-free technique with finite-volume method is being developed for direct simulations of two-phase flows. This merges the {\it locally adaptive} nature of the particle-based approach for efficient representation of the interface between two media with the {\it relative flexibility offered by grid-based solvers} for complex flows. The pure mesh-free Lagrangian technique developed by Hieber and Koumoutsakos (JCP 2005) is first integrated with an unstructured grid-based finite volume solver. The novelty here is to make use of the background-mesh connectivity and parallel partitioning to efficiently locate and transport the Lagrangian points (LP). Once the interface location is identified on the LPs, the jump conditions across the interface are enforced by following the techniques used in level-set methods, and the resultant governing equations are solved on the background mesh. The accuracy and efficiency of the method for standard test problems commonly used in interface tracking will be presented. Direct simulations of rigid particles, droplets or bubbles dispersed in a continuum fluid of different phase are being performed. Application and extension of the scheme to problems involving fluid-particle interactions will be discussed. [Preview Abstract] |
Tuesday, November 21, 2006 8:39AM - 8:52AM |
LE.00004: Numerical simulation of gravity-driven mixing of two fluids in an inclined tube Yannick Hallez, Jacques Magnaudet The concentration distribution in the mixing zone of interpenetrating light and heavy fluids in an inclined tube is studied using direct numerical simulation as a function of the tilt angle $\theta$ from the vertical. Two-dimensional computations first show evidence of the concentration contrast-driven velocity of the front at any $\theta$. However three-dimensional computations carried out in a circular tube reveal how crucial the geometry is. In these simulations,and for small $\theta$, mixing is very efficient and the observed pattern is similar to the 2D one. Increasing $\theta$, a concentration gradient appears across the tube section due to the transverse component of gravity and the concentration contrast at the front can reach that of the pure fluids. At still higher tilt angle, the transverse component of gravity becomes strong enough to set up a stable counterflow driven by viscous dissipation. The difference of behaviour between 2D and 3D cases appears to be due to the structure of the vorticity field, since the 2D vortices are found to be much more coherent than the 3D ones. Hence the pure fluid channel supplying the front is more easily broken by 2D vortices than by 3D ones, which leads to a smaller concentration contrast at the front in the former case. [Preview Abstract] |
Tuesday, November 21, 2006 8:52AM - 9:05AM |
LE.00005: On the advective Cahn-Hilliard Equation Lennon O'Naraigh, Jean-Luc Thiffeault The advective Cahn-Hilliard equation describes the chef's problem of stirring olive oil and soy sauce. An efficient way of doing this is to choose a chaotic mixing protocol. Intuition suggests that bubbles of oil and soy will form on a certain scale, and previous studies of Cahn-Hilliard dynamics indicate the presence of one dominant length scale. See, for example, Berthier et al., 2001. The Cahn-Hilliard demixing mechanism however, contains a hyperdiffusion term and in this study we show how, by stirring the mixture at sufficiently large amplitude, we may excite the diffusion and overwhelm the demixing to create a homogeneous liquid. At intermediate amplitudes we see regions with oil and soy bubbles, and regions with hyperdiffusive filaments, implying that the problem in fact possesses two length scales. In this state, the system is in dynamical equilibrium and this is surprising, given that the homogenous state is unstable in the unstirred case. We compare our results with the case for a variable mobility, in which coarsening (growth of bubble size) is dominated by interfacial, rather than bulk, effects. The no-flow equivalent of this situation was considered by Zhu et al. (1999). We discuss the possibility that these results point in fact to the real-world limitations of the binary fluid model. [Preview Abstract] |
Tuesday, November 21, 2006 9:05AM - 9:18AM |
LE.00006: Stochastic modeling of the subgrid fluid velocity fluctuations along inertial particle trajectories. Pascal Fede, Philippe Villedieu, Olivier Simonin, Kyle Squires Large Eddy Simulation (LES) coupled with Discrete Particle Simulation (DPS) is a powerful approach for the prediction of particle behavior in turbulent flows. To further advance the technique, several issues should be clarified for the fluid phase (such as the effect of the particles on modeling the subgrid fluid turbulence) and for the particulate phase (such as the effect of the subgrid fluid turbulence on particle dispersion and inter-particle collision rates). The present study focuses on the modeling of the subgrid fluid velocity fluctuation along solid inertial particle trajectories with relaxation times close to the fluid subgrid turbulent time scale. A Langevin model has been derived which ensures that the resulting equation for the variance of the subgrid velocity along the particle path is coherent with the subgrid mean kinetic energy equation derived from the filtered Navier-Stokes system. To assess the model, one- and two-point statistics measured using fluid velocity fields computed using DNS of homogenous, isotropic turbulence and Lagrangian particle tracking for the dispersed phase have been compared with results obtained using filtered velocity fields (issued from the DNS case) and the stochastic Langevin equation for the subgrid velocity reconstruction. [Preview Abstract] |
Tuesday, November 21, 2006 9:18AM - 9:31AM |
LE.00007: Large-eddy Simulation of Particle Concentration by Equilibrium Eulerian Approach Babak Shotorban, S. Balachandar A Large-eddy Simulation (LES) formulation is developed for particle concentration in turbulent flows using equilibrium assumption in which the velocity of particle can be expressed in terms of the velocity and acceleration of fluid for small Stokes numbers (Maxey, JFM, 1987). Filtered particle concentration defined in this formulation is solved in the Eulerian frame using a transport equation with a closure problem in the form of subgrid-scale particle flux term. A Smagorinsky type of model is proposed to close this term. The model is implemented in a particle-laden forced isotropic turbulent flow and the LES results assessed against the results obtained by Direct Numerical Simulation (DNS). Good agreement is observed between them. [Preview Abstract] |
Tuesday, November 21, 2006 9:31AM - 9:44AM |
LE.00008: A 3D Explicit Finite-Difference Scheme for Particulate Flows with Boundary Conditions based on Stokes Flow Solutions A. Perrin, H. Hu We have extended previous work on an 2D explicit finite-difference code for direct simulation of the motion of solid particles in a fluid to 3D. It is challenging to enforce the no-slip condition on the surface of spherical particles in a uniform Cartesian grid. We have implemented a treatment of the boundary condition similar to that in the PHYSALIS method of Takagi et. al. (2003), which is based on matching the Stokes flow solutions next to the particle surface with a numerical solution away from it. The original PHYSALIS method was developed for implicit flow solvers, and required an iterative process to match the Stokes flow solutions with the numerical solution. However, it was easily adapted to work with the present explicit scheme, and found to be more efficient since no iterative process is required in the matching. The method proceeds by approximating the flow next to the particle surface as a Stokes flow in the particleâ€™s local coordinates, which is then matched to the numerically computed external flow on a ``cage'' of grid points near the particle surface. Advantages of the method include superior accuracy of the scheme on a relatively coarse grid for intermediate Reynolds numbers, ease of implementation, and the elimination of the need to track the particle surface. Several examples are presented, including flow over a stationary sphere in a square tube, sedimentation of a particle, and dropping, kissing, and tumbling of two particles. This research is supported by a GAANN fellowship from the U.S. Dept. of Education. [Preview Abstract] |
Tuesday, November 21, 2006 9:44AM - 9:57AM |
LE.00009: Distributed-Lagrange-Multiplier-based computational method for particulate flow with collisions Arezoo Ardekani, Roger Rangel A Distributed-Lagrange-Multiplier-based computational method is developed for colliding particles in a solid-fluid system. A numerical simulation is conducted in two dimensions using the finite volume method. The entire domain is treated as a fluid but the fluid in the particle domains satisfies a rigidity constraint. We present an efficient method for predicting the collision between particles. In earlier methods, a repulsive force was applied to the particles when their distance was less than a critical value. In this method, an impulsive force is computed. During the frictionless collision process between two particles, linear momentum is conserved while the tangential forces are zero. Thus, instead of satisfying a condition of rigid body motion for each particle separately, as done when particles are not in contact, both particles are rigidified together along their line of centers. Particles separate from each other when the impulsive force is less than zero and after this time, a rigidity constraint is satisfied for each particle separately. Grid independency is implemented to ensure the accuracy of the numerical simulation. A comparison between this method and previous collision strategies is presented and discussed. [Preview Abstract] |
Tuesday, November 21, 2006 9:57AM - 10:10AM |
LE.00010: Pressure and volume fraction calculation in particle-in-cell method for multiphase flows Duan Zhang, Qisu Zou, Brian VanderHeyden Particle-in-cell method, especially its later development, possesses significant advantages in solving problems with history dependent constitutive relations. This method avoids numerical diffusion problems of Eulerian methods and mesh distortion issues of Lagrangian methods. Recently we have combined this method with multiphase flow theories to study fluid-structure interactions. Numerical error associated with the method for volume fraction is of the first order in the spatial discretization. We will show that this error results in failure in pressure calculation if the traditional way, enforcing the sum of the volume fraction to be one, is used. An alternative method using evolution equations for the volume fraction is introduced. [Preview Abstract] |
Tuesday, November 21, 2006 10:10AM - 10:23AM |
LE.00011: Experimental and numerical observation of sediment suspension from ripple beds in oscillatory flow Philip Knowles, Ken Kiger, Alberto Scotti The University of Maryland Oscillatory Sediment Flume (UMOSF) is an experimental facility built to investigate sediment transport mechanics within an oscillatory turbulent boundary layer over a mobile sediment bed. The range of sediment characteristics and fluid timescales are selected in the current work to study flows which generate rippled bed forms. The measurement technique utilizes a simultaneous two-phase PIV method to examine fluid-particle interactions, focusing on the suspension mechanisms and to obtain statistics to describe the two-way coupling. Specifically, measurements will focus on the upslope face, crest and recirculation zone of the ripple, where previous simulations have shown the strongest regions of suspension, injection into the boundary region, and mixing with the outer flow to occur. Results of these experiments are closely coordinated with ongoing numerical simulations, and comparison of the results from both experiments and simulations will be discussed. [Preview Abstract] |
Tuesday, November 21, 2006 10:23AM - 10:36AM |
LE.00012: The Refined Level Set Grid Method for Simulating Liquid/Gas Interfaces Marcus Herrmann The Refined Level Set Grid (RLSG) method is a level set based interface tracking scheme that allows for grid converged simulations of the phase interface geometry. The Navier-Stokes equations describing the flow can be solved on a structured or unstructured grid, whereas all level set equations are solved on a separate, equidistant Cartesian grid that can be independently refined to ensure grid convergence of the phase interface geometry. Coupling of the two grids is performed using the parallel interpolation and volume integration infrastructure CHIMPS. Together with a recently proposed balanced force algorithm [Francois et al., JCP 2006] the resulting coupled scheme gives second order converging spurious currents in the canonical test of an inviscid stationary drop. Test cases highlighting the performance of the RLSG method as well as extensions of the method to simulate liquid jet atomization will be discussed. [Preview Abstract] |
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