Session FE: Multiphase Particle-Laden Flows III

LES-Style Filtering and Partly-Resolved Particles

By applying LES-style spatial filtering to detailed multiphase- flow equations, we derive a set of immersed-interface equations that rigorously account for imprecise resolution of the interfaces, and are consistent with LES turbulence modeling. These equations are applicable over the entire range of atomization phenomena from nearly-fully-resolved primary breakup to evaporating near-point particles. As a demonstration, we apply the equations to partly-resolved (filter-scale) solid circular particles in 2D flow, and illustrate that these can be accurately modeled using low-order parameterizations that build on standard point-particle models, yet appropriately account for the nonzero particle diameter. From these results, we draw conclusions about the range of validity of point-particle models in turbulent LES calculations, and suggest methods of extending those models to larger non-point particles.   

Fully-coupled compressible multiphase formulation using the Equilibrium Eulerian method

In the Equilibrium Eulerian method of Ferry and Balachandar (IJMF 27:1199, 2001), the particle velocity is expressed as a perturbation of the local fluid velocity. The main advantages of the method compared to conventional Eulerian approaches are that the stiffness for small particles is removed and that polydisperse systems can be solved very efficiently. The Equilibrium Eulerian method has been carefully validated for incompressible flows. The goal of the present work is to develop a fully-coupled multiphase formulation for compressible flows based on the Equilibrium Eulerian method. We address the fundamental question about the accuracy of the Equilibrium Eulerian method relative to Lagrangian tracking for expansion fans and shock waves. This allows the quantification of errors for a given particle size. The fully-coupled formulation is applied to several compressible flow problems.   

The role of particle-fluid velocity correlation in single-point statistical closures of dispersed turbulent two-phase flows

The evolution equation for the dispersed--phase turbulent kinetic energy in the standard continuum model for turbulent two--phase flow contains an unclosed term-- the Eulerian particle velocity--acceleration covariance---which is a two--point statistic. A widely-used Lagrangian linear slip-- velocity model for the particle acceleration implies a model for this quantity, which depends on the Eulerian {\em single--point} covariance of velocity between carrier fluid and dispersed-- phase particles. However, earlier Eulerian formulations have shown that the particle--fluid velocity covariance in a two--phase flow is a two--point statistic, which is always zero in the single--point limit, because the presence of one phase disallows the simultaneous presence of the other at the same space--time location. This paradox is resolved in this work, where it is shown that this Eulerian single--point covariance of carrier fluid velocity with dispersed--phase velocity is correctly interpreted as a single--point surrogate for the particle-- fluid velocity covariance. It is shown that in zero mean--slip homogeneous flows, this surrogate is nothing but the two-phase mixture velocity covariance, which can be expressed as a weighted sum of the velocity covariance in the fluid--phase and the velocity covariance in the dispersed-phase. Therefore, this single-- point surrogate for the particle--fluid velocity covariance should not form a part of the set of independent equations in {\em single-point} closures of turbulent two-phase flow.   

Study of Aerosol Particle Clustering in Isotropic Turbulence Using DNS and Holographic PIV

DNS shows that aerosol particles, owing to their inertial mismatch with the lighter surrounding gas, will cluster in regions of high strain in turbulent flows. Particle radial distribution function (RDF) has been identified as a key variable used in the clustering theory. Due to the difficulties in 3D measurement of particulate flows and DNS at high Reynolds numbers, the dependence of RDF on the turbulence and particle parameters are not fully quantified. Our aim is to test the particle preferential concentration in an isotropic turbulent flow field using digital holographic PIV technique (DHPIV) and DNS at comparable conditions. The dependence of RDF on system parameters (e.g. particle size and response time) is explored using DNS. With the DHPIV, Particle 3D positions and velocities are measured directly via reconstructions from digital holographic recording. Good agreement between the experimentally obtained RDF and the simulations confirmed the existence of particle clustering, and quantified the dependence of RDF on the Stokes number. The results also confirm the capability to extend the exploration to a broader range of Reynolds number.   

Turbulence Modification by Solid Particles Measured by a High Resolution Particle Image Velocimetry.

Previous studies show that fine solid particles can strongly attenuate the turbulence of a gaseous flow, but the mechanisms of the reduction in turbulence kinetic energy (TKE) are not understood. Obviously, high TKE dissipation rates caused by a high strain around particles must play a role. In order to accurately measure the high dissipation rate surrounding particles, spatial resolution smaller than the particle size is necessary. Since most of the particle-laden research did not achieve such resolution, we believe that the TKE dissipation rate has been underestimated on the whole. The goal of the present research is to accurately estimate the distribution of TKE dissipation rate in a particle-laden air flow using a high resolution PIV system whose vector spacing (70 \textit{$\mu $}m) is about half of the Kolmogorov length scale. The experiments are conducted in a homogeneous-isotropic turbulence chamber with a set of eight synthetic jets. The Reynolds number based on Taylor micro scale is approximately 200. The particles are 250 \textit{$\mu $}m polystyrene spheres at a mass loading ratio around 20{\%}. The TKE dissipation rate increases in the presence of particles, which is opposite of the previous findings. This results from strong shear strains in the vicinity of each particle, producing local regions of very high dissipation rate.   

Particle Deposition in Laminar Curved Duct Flow

Deposition of particles in a duct of square cross-section and constant streamwise curvature is studied numerically. Fully elliptic two-dimensional calculations with three nonzero velocity components are performed on a highly resolved grid. The Reynolds number is varied to simulate typical conditions in laminar micro-mixer devices. The particle density is assumed to be much greater than the fluid density such that the drag term dominates the particle equation of motion. Particle concentrations are low such that the one-way coupling approach is valid. Particle deposition patterns are shown in terms of probability distribution functions of deposition location. The Dean number is varied such that both the classic two- and four-cell Dean vortex patterns are simulated. Deposition trends are presented as a function of particle response time.   

Fluctuating Immersed Material (FIMAT) Dynamics for the Direct Numerical Simulation of the Brownian Motion of Particles

A Direct Numerical Simulation (DNS) scheme, named Fluctuating Immersed MATerial (FIMAT) dynamics, for the Brownian motion of rigid particles will be presented. In this approach the thermal fluctuations are included in the fluid equations via random stress terms. Solving the fluctuating hydrodynamic equations coupled with the particle equations of motion result in the Brownian motion of the particles. There is no need to add a random force term in the particle equations. The particles acquire random motion through the hydrodynamic force acting on its surface from the surrounding fluctuating fluid. The random stress in the fluid equations is easy to compute unlike the random terms in the conventional Brownian dynamics type approaches. The approach is tested for a variety of cases including single spheres, single ellipsoids and many spheres by considering quasi-steady simulations in the long time limit. Translational and rotational diffusion of the particles are considered. Unsteady simulations are also performed to test the short time behavior of the velocity autocorrelations. The method correctly reproduces the algebraic velocity autocorrelation.   

Characterization of the distribution of microparticles in turbulent boundary layers

In this paper, we examine particle distribution in the wall region of turbulent boundary layers, considering specific flow conditions ($Re_{\tau}=150$) and spanning two orders of magnitude of particle inertial parameter, namely the particle timescale. First, we identify the flow timescales that govern particle distribution examining the degree of particle preferential concentration determining the optimum in connection with particle timescale. Second, we identify which of the flow variables may be used to control particle distribution. These are the streamwise and spanwise shear stress components at the wall, which correspond to the only non-vanishing elements of the fluctuating fluid velocity gradient tensor.   

Implementation of Defiltering Techniques in Large-eddy Simulation of Particle-laden Turbulent Flows

In most studies of particle-laden turbulent flows in which the carrier phase is simulated by LES and particles are individually tracked in the Lagrangian framework, the effect of sub-filter scales on particles is neglected. However, the error resulted from such neglect can be significant if the sub-filter energy is relatively large and/or particle time constant is small. It has been recently shown that the prediction of turbuphoresis in the wall-bounded turbulence (Kuerten {\&} Vreman, \textit{Phys. Fluids} \textbf{17}, 017011, 2005) and particle dispersion in the homogeneous turbulence (Shotorban {\&} Mashayek, \textit{Phys. Fluids }\textbf{17}, 081701, 2005) can be largely improved if the sub-filter scales are reconstructed for particles via defiltering. In this work, the formulation for the use of defiltering techniques in the LES of particle-laden turbulent flows is reviewed and recent results obtained for the particle-laden homogeneous isotropic and shear flows are presented.   

DNS of finite-size heavy particles in vertical turbulent channel flow

We consider the upward flow of an incompressible fluid in a vertical plane channel with suspended rigid spherical particles. In order to take into account finite-size effects, we perform ``true'' direct simulations, i.e.\ the particles are resolved by the grid, using the immersed boundary method of [Uhlmann, J.\ Comput.\ Phys.209(2):448-476, 2005]. The solid volume fraction is in the dilute regime ($\leq0.01$), which allows for a simplified treatment of collisions. Our simulations are run in turbulent conditions, with the friction-velocity-based Reynolds number measuring around 200. The particle diameter corresponds to 9 wall units, equivalent to 14 mesh widths of our uniform grid. We have accumulated statistics in a relatively small bi-periodic domain of approximately 4 minimal flow units, including 512 particles. The Reynolds number based upon the particle diameter and the difference between the mean velocities of the two phases is around 150 in the bulk of the flow. In this contribution we will discuss the averaged flow quantities with respect to modifications of the near-wall turbulence structure. Correlation data along particle paths as well as flow visualizations will be presented.