Session D37: Particle-Laden Flows: Particle-Resolved Simulations

Particle-laden flow past a cylinder resolved with IBM and overset grids

Two different computational methods are used to resolve a bluff body in a cross flow, by using The Pencil Code software. The bluff body representations in this high-order finite-difference code for compressible DNS are: an immersed boundary method and an overset grid implementation. Strengths and weaknesses of the two methods are assessed, where computational cost and precision are of particular interest. Both methods are applied to a two-dimensional particle-laden flow simulation, where particles are convected towards and (possibly) past a circular cylinder at Reynolds numbers in the 2D vortex shedding regime. Particles impacting the cylinder are assumed to stick to the surface, and are removed from the simulation. The ratio of impacted to inserted particles is a measure of impaction efficiency, where particle Stokes number is a governing parameter. Both bluff body representations yield accurate impaction efficiencies, but the computational cost can be notably reduced by optimal choice of bluff body representation.   

A correction procedure for thermally two-way coupled point-particles

Development of a robust procedure for the simulation of two-way coupled particle-laden flows remains a challenge. Such systems are characterized by O(1) or greater mass of particles relative to the fluid. The coupling of fluid and particle motion via a drag model means the undisturbed fluid velocity evaluated at the particle location (which is needed in the drag model) is no longer equal to the interpolated fluid velocity at the particle location. The same issue arises in problems of dispersed flows in the presence of heat transfer. The heat transfer rate to each particle depends on the difference between the particle's temperature and the undisturbed fluid temperature. We borrow ideas from the correction scheme we have developed for particle-fluid momentum coupling [1] by developing a procedure to estimate the undisturbed fluid temperature given the disturbed temperature field created by a point-particle. The procedure is verified for the case of a particle settling under gravity and subject to radiation. The procedure is developed in the low Peclet, low Boussinesq number limit, but we will discuss the applicability of the same correction procedure outside of this regime when augmented by appropriate drag and heat exchange correlations.   

Numerical study of the particle motion with 6 degree of freedom in a flow

Traditionally solid-fluid simulations used an incomplete physics model, with only a one-way coupling between the solid and fluid domains. The basis for our work is Gerris, an open-source fluid solver, (Popinet et al, 2003). Its adaptive Cartesian mesh scores over traditional algorithms in convergence. We augmented Gerris with a fully-coupled solver for fluid-solid interaction with 6 degrees-of-freedom (6DOF). This was done by using the immersed boundary method, which allows the solid boundary to move or deform while requiring few mesh adaptations. Our new solver, Gerris Immersed Solid Solver (GISS), accounts for collisions with a novel composite contact model (Ness {\&} Sun, 2016) for solid-solid interactions. We have validated our methodology against published experimental data. We are thus enabled to reveal some deep correlations between the hydrodynamic force and particle motion in inviscid flow. (Aref, 1993) had shown that the dynamics should be chaotic under certain conditions and our inviscid results agree with these findings. Our analysis includes analytic solutions and recurrence quantification (Marwan et al, 2007), to quantify the chaos and to evaluate the nature of that behaviour.   

Analysis of the dynamics of porous particles settling in a stratified fluid

We study the settling of a porous sphere in a density-stratified ambient fluid. Simulations are compared to two mathematical models. We quantify the delay in settling due to lighter fluid becoming denser through diffusion and that due to ambient fluid entrainment. We study the effects of the Reynolds, P\'eclet, and Darcy numbers, as well as the thickness of the transition layer, and the ratio of the density difference between the lower and upper fluid layer to the density difference between the particle and the upper layer. Dominant effects are identified and a simple fitting formula is presented to describe the settling time delay as a function of each of those five non-dimensional parameters.   

Investigation of erosion behavior in different pipe-fitting using Eulerian-Lagrangian approach

Erosion is a wear mechanism of piping system in which wall thinning occurs because of turbulent flow along with along with impact of solid particle on the pipe wall, because of this pipe ruptures causes costly repair of plant and personal injuries. In this study two way coupled Eulerian-Lagrangian approach is used to solve the liquid solid ( water-ferrous suspension) flow in the different pipe fitting namely elbow, t-junction, reducer, orifice and 50{\%} open gate valve. Simulations carried out using incomressible transient solver in OpenFOAM for different Reynolds's number( 10k, 25k,50k) and using WenYu drag model to find out possible higher erosion region in pipe fitting. Used transient solver is a hybrid in nature which is combination of Lagrangian library and pimpleFoam. Result obtained from simulation shows that exit region of elbow specially downstream of straight, extradose of the bend section more affected by erosion. Centrifugal force on solid particle at bend affect the erosion behavior. In case of t-junction erosion occurs below the locus of the projection of branch pipe on the wall. For the case of reducer, orifice and a gate valve reduction area as well as downstream is getting more affected by erosion because of increase in velocities.   

Hydrodynamic Impacts on Dissolution, Transport and Absorption from Thousands of Drug Particles Moving within the Intestines.

Following tablet disintegration, clouds of drug particles 5-200 $\mu m $in diameter pass through the intestines where drug molecules are absorbed into the blood. Release rate depends on particle size, drug solubility, local drug concentration and the hydrodynamic environment driven by patterned gut contractions. To analyze the dynamics underlying drug release and absorption, we use a 3D lattice Boltzmann model of the velocity and concentration fields driven by peristaltic contractions \textit{in vivo}, combined with a mathematical model of dissolution-rate from each drug particle transported through the grid. The model is empirically extended for hydrodynamic enhancements to release rate by local convection and shear-rate, and incorporates heterogeneity in bulk concentration. Drug dosage and solubility are systematically varied along with peristaltic wave speed and volume. We predict large hydrodynamic enhancements (35-65{\%}) from local shear-rate with minimal enhancement from convection. With high permeability boundary conditions, a quasi-equilibrium balance between release and absorption is established with volume and wave-speed dependent transport time scale, after an initial transient and before a final period of dissolution/absorption.   

Modeling of electrochemical flow capacitors using Stokesian dynamics

Electrochemical flow capacitors (EFCs) are supercapacitors designed to store electrical energy in the form of electrical double layer (EDL) near the surface of porous carbon particles. During its operation, a slurry of activated carbon beads and smaller carbon black particles is pumped between two flat and parallel electrodes. In the charging phase, ions in the electrolyte diffuse to the EDL, and electrical charges percolate through the dynamic network of particles from the flat electrodes; during the discharging phase, the process is reversed with the ions released to the bulk fluid and electrical charges percolating back through the network. In these processes, the relative motion and contact of particle of different sizes affect not only the rheology of the slurry but also charge transfer of the percolation network. In this study, we use Stoekesian dynamics simulation to investigate the role of hydrodynamic interactions of packed carbon particles in the charging/discharging behaviors of EFCs. We derived mobility functions for polydisperse spheres near a no-slip wall. A code is implemented and validated, and a simple charging model has been incorporated to represent charge transfer. Theoretical formulation and results demonstration will be presented in this talk.    

Cloud-In-Cell modeling of shocked particle-laden flows at a ``SPARSE'' cost

A common tool for enabling process-scale simulations of shocked particle-laden flows is Eulerian-Lagrangian Particle-Source-In-Cell (PSIC) modeling where each particle is traced in its Lagrangian frame and treated as a mathematical point. Its dynamics are governed by Stokes drag corrected for high Reynolds and Mach numbers. The computational burden is often reduced further through a ``Cloud-In-Cell'' (CIC) approach which amalgamates groups of physical particles into computational ``macro-particles''. CIC does not account for subgrid particle fluctuations, leading to erroneous predictions of cloud dynamics. A Subgrid Particle-Averaged Reynolds-Stress Equivalent (SPARSE) model is proposed that incorporates subgrid interphase velocity and temperature perturbations. A bivariate Gaussian source distribution, whose covariance captures the cloud's deformation to first order, accounts for the particles' momentum and energy influence on the carrier gas. SPARSE is validated by conducting tests on the interaction of a particle cloud with the accelerated flow behind a shock. The cloud's average dynamics and its deformation over time predicted with SPARSE converge to their counterparts computed with reference PSIC models as the number of Gaussians is increased from 1 to 16.