Session D24: Particle-laden Flows I

Physical perspectives on the investigation of two-way interaction in particle-laden isotropic turbulence

The two-way coupling interaction in an isotropic turbulence has been investigated in both decaying and stationary turbulence to examine the effect of artificial forcing for the maintenance of stationary turbulence, on turbulence modulation mechanism. Direct numerical simulations (DNS) for stationary and decaying isotropic turbulence have been carried out using $128^3$ grids with the Taylor micro-scale, $R_{\lambda} \simeq 70$, in the presence of $10^6$ solid sphere particles whose diameter is smaller than the Kolmogorov length scale. The particles which were released with different Stokes number ($0 < St < 5$), are implemented as a point force approximation in Navier-Stokes equation. Turbulence kinetic energy, acceleration, enstrophy and their spectra have been examined to display the distinctions between decaying and stationary turbulence. A mathematical analysis is provided to support our physical perspectives, where we argued that the stationary turbulence is not appropriate for the study of turbulence modulation by particles with $St < 1$. Furthermore, it is shown that the injection perturbation of the particle, due to coupling, has a significant effect on the turbulence modulation in decaying turbulence. An investigation of correlation between turbulence field zones and the two-way interaction energy has been conducted for a better understanding of the modulation mechanism.   

Acceleration modification of near-wall turbulence by heavy particles

By conducting direct numerical simulation combined with Lagrangian particle tracking, we examine modifications of the near-wall turbulence by heavy particles. For simplicity, only spherical and rigid particles are considered in our study and particles are idealized as point-sources in our spectral simulation of turbulent channel flow laden with heavy particles. To assess the effect of particles on the flow field, we use the Particle-Source In Cell (PSIC) model proposed by Crowe et al (1977). Because particles suspended in wall-bounded turbulence can modify the near-wall turbulent structures depending on Stokes number, and these structures are associated with the intermittent, strong acceleration of fluid, particles are expected to modify the turbulence acceleration statistics in the near-wall region. Therefore, in the present study, we especially focus on the modification of the acceleration statistics of turbulence by particles in turbulent channel flow for various Stokes numbers. Detailed statistical changes of acceleration of turbulence by particles and plausible physical explanations will be presented in the meeting.   

The effect of particle size on the dynamics of a solid particle in a turbulent carrier flow

When the particle size is much smaller than the Kolmogorov scale of the carrier flow, the motion of the particle can be described by a point-particle model. Currently, it is not clear how to treat the motion of a solid particle when its size is comparable or larger than the Kolmogorov scale. Here we address this by using a numerical solution from a particle-resolved simulation code for a freely-moving finite-size particle suspended in a turbulent background flow. The code is based on the multiple-relaxation-time lattice Boltzmann equation. The no-slip boundary condition on the moving particle boundary is handled by a second-order interpolated bounce-back scheme. The populations at a newly converted fluid node are constructed by the equilibrium distribution with non-equilibrium correction. The main purpose here is to extend some recent advances made regarding the finite size effects on a buoyant particle to finite-size heavy or light particles where both inertial effect and finite-size effect are important. We will present results for different particle sizes relative to the Kolmogorov (or Taylor) microscale and different particle to fluid density ratios. The force acting on the particle and particle velocity and acceleration statistics will be discussed.   

Highly-scalable simulation of turbulent and particle-laden flows using the lattice Boltzmann approach

Particle-laden turbulent flows are found in many applications such as sediment transport, pollutant dispersion, interaction of cloud droplets, and chemical processing. Recently, we have developed a particle-resolved direct simulation of particle-laden turbulent flow using the mesoscopic lattice Boltzmann approach. Here we explore the parallel scalability of this approach by comparing the parallel efficiencies of the code using one, two, and three dimensional domain decompositions. First, we compare the scalability data of the turbulent flow simulation without particles and show that the communication overhead in the approach is negligible due to the local nature of data communication. Then, we discuss parallel implementation issues related to the interaction of solid particles with the carrier turbulent flow. The new results based on multiple dimensional decompositions will be compared to the previous results using one dimensional domain decomposition. Results from high-resolution particle-resolved multiphase flow simulations will be used to address flow modulation by finite-size solid particles when the size of the particles is comparable to or larger than the flow Kolmogorov scale.   

Development of modified body-force type immersed boundary method

Particulate flows occur frequently in nature and engineering applications. Examples include fluidized bed, transportation of aerosols, blood flow and so on. The behavior of flows is highly complex and it is still difficult to obtain reliable information experimentally and a computational prediction is required especially for the microscopic flows in the particle-level. In recent years, a number of CFD technique for fluid-solid interaction problems have been proposed. Some examples are immersed boundary method, lattice Boltzman and fictitions domain method. ``Body-force type immersed boundary method'' originally developed by Kajishima et al. (2001) is a simple scheme and have been applied to several problems. The method is based on a fixed Cartesian grid and solid body is represented by its volume fraction at each calculation cell. The method is quite efficient while it has intrinsic problems such as $\Delta $t-dependency of calculation results and the violation of divergence-free condition. In the present study, these problems are revealed and a modified method is proposed. Computations based on the present method are performed for a number of fluid-particle interaction problems and results are compared with the original one.   

Particle-wall impacts in a confined extensional flow

Buoyant particles entrained in liquid flowing in confined geometries such as pipes and channels arise in a broad spectrum of areas including engineering and the natural and biological sciences. Understanding the particle behavior upon changes in flow direction is crucial in problems where particle inertia is important, such as the erosion process in pipe bends. We present results on the impact of particles in a T-shaped channel in the laminar-turbulent transitional regime. The impacting event for a given system regime is described in terms of the particle Stokes number and the Reynolds number, where for the model local extensional flow the latter also characterizes the ratio of particle size to thickness of the viscous boundary layer which forms in the region below the impingement. Experimental results for the impact are compared with the trajectories predicted by theoretical particle-tracing models for a range of configurations to determine the role of the viscous boundary layer in slowing down the particles and reducing the rate of collision with the substrate. The implications of our results on the erosion process in a piping system are discussed.   

Rotational Diffusion of Particles in Turbulence

We experimentally compare the rotation of spherical and ellipsoidal particles in homogeneous, isotropic turbulence. We find that the particle orientation is well described by a Gaussian diffusion process. This theoretical model would predict that the Lagrangian autocorrelation function for angular velocity is a negative exponential. We measure this Lagrangian autocorrelation function using stereoscopic particle image velocimetry (SPIV) applied to particles whose size is within the inertial subrange of the ambient turbulence. The SPIV resolves 3 velocity components in a nearly 2-dimensional planar volume, which we use as inputs for a nonlinear optimization to quantify the solid body rotation of the particles. This provides us the angular velocity timeseries for individual particles. Through ensemble statistics, we determine the Lagrangian autocorrelation function of angular velocity, from which we can quantify the turbulent rotational diffusivity and its behavior between the extremes of short-term non-Fickian transport and long-term Fickian diffusion.   

Dynamics of Arrays of Falling Cylinders and Modeling of Collisions Using the Lubrication Theory

Motivated by our interest in understanding collective behavior and self-organization resulting from hydrodynamic interactions, we investigate the dynamics of horizontal arrays of settling cylinders at intermediate $Re$. Here, we focus on pairwise interactions by quantifying the interaction force for a pair of cylinders and its dependence on the initial spacing $d_{0}$. We fiund that the pair initially experiences a repulsive force which varies as $1/d_{0}^{\alpha},~\alpha>0$. We then study the dynamics of a falling cylinder in presence of its left and right neighbors and compare them to those of an isolated cylinder and with results in Stokes flow. Our findings show that, unlike in Stokes flow, the middle cylinder experiences a higher drag force due to the presence of co-moving cylinders, resulting in a slower settling velocity. Additionally, the smaller $d_0$, the sooner wake asymmetries for the middle cylinder arise and the sooner it settles to steady-state. For small $d_0$ or for large collections of cylinders ($n>5$), collisions occur. Instead of using an {\it ad hoc} collision model, we derive the interstitial pressure field using the lubrication theory. The lubrication pressure and shear force are then used to compute the repulsive force during the approach phase between two particles. Results using this theory will be compared to those using a simple dry collision model.   

Monodisperse and Polydisperse Particle Flow over a Backward Facing Step Preceding a Porous Medium

Computational Fluid Dynamic predictions were performed for the flow of monodisperse and polydisperse particles over a backward facing step with and without a porous medium downstream. The carrier fluid was air and the particles had a density of 500 kg/m3. Monodisperse particles with diameters of 10 and 40 microns and polydispersed particles from 1 to 50 microns with a Rosin-Rammler size distribution were used. The step had an expansion ratio of 2 and the step Reynolds numbers were 6550 and 10000. The k-epsilon RNG model with standard wall functions was used with FLUENT's discrete phase model for the particles. Velocity and particle residence time tracks were examined. The placement of the medium at 4.25h from the step was found to control the velocity profiles and the length of the recirculation zone while placement at 6.75h had negligible effects. The particle tracks show that more particles with lower Stokes number enter the recirculation zone while the particles with higher Stokes number tend to bypass the recirculation zone and move directly to the filter. The results for the monodispersed and the polydispersed particles appear virtually the same at low particle concentrations, but the polydispersed results provide a very good view of the phenomena.   

Experimental investigation of free falling thin disks. Part I: The flow structures and the Reynolds number effects of zigzag motion

We present experimental investigations on the behaviors of free falling thin circular disk in still water. Flow patterns of the zigzag disk motion are studied with dye visualization and particle image velocimetry. Time-resolved disk motions with six degrees of freedom are obtained with a stereoscopic vision method. The flow separation and shedding vortices are found changing with free falling Reynolds number Re. At high Reynolds number, we found a new dipole vortices shedding from the disk besides the Karman-type vortices at low Reynolds numbers. The vortical structures are mainly composed of leading edge vortices, counter-rotating vortex pair and secondary trailing edge vortices. It was found that the dimensionless amplitude of horizontal oscillation was dependent on the Reynolds number Re. There existed a critical Reynolds number about 2000, oscillatory amplitude was proportional to Re when Re is below the critical value, but invariant with Re when Re is above this value. The onset of dipole vortices was directly related to the increasing Reynolds number and horizontal oscillations.