Session S18: Particle-laden Flows V

Lagrangian statistics of light particles in turbulence

We study the Lagrangian velocity and acceleration statistics of light particles (bubbles in water) in homogeneous and isotropic turbulence. Bubbles of size comparable to the Kolmogorov length scale (Stokes numbers $\approx$ O(0.01)) are dispersed in a turbulent water tunnel operated at Taylor Reynolds numbers $Re_{\lambda}$ ranging from 130 to 260. The bubble trajectories are experimentally captured using the three-dimensional Lagrangian Particle Tracking technique. The bubble acceleration PDFs are found to be highly intermittent with flatness values around 23-30. We study the dependence of the velocity and acceleration statistics (PDFs and autocorrelation functions) on $Re_{\lambda}$ and compare our results to those from point-particle DNS and other experiments. We also present our latest results on the Lagrangian statistics of finite-size inertial bubbles (size $\approx$ 2-4 mm and St $\approx$ O(1)).   

Interpolation error in DNS simulations of turbulence: consequences for particle tracking

An important aspect in numerical simulations of particle-laden turbulent flows is the interpolation of the flow field. Interpolations are needed in many applications, for example, simulations of turbulent aerosol transport, transport of bed load sediments and marine species. For the interpolation different approaches are used. Where some studies use low-order linear interpolation, others use high-order spline methods. This study focuses on estimating the interpolation error and compares it with the discretisation error of the flow field. In this way one can balance the errors in order to achieve an optimal result. Algorithms have been developed for the approximation of the interpolation error. As a spin-off of the theoretical analysis a practical method is proposed which enables direct estimation of the interpolation error from the energy spectrum of the flow. Furthermore it is shown how this energy spectrum is affected by the interpolation. Our results suggest that a coherent choice of the interpolation method and the value of $k_{max}\eta$ should be made in order to balance the errors. Our approach may provide a quantitative indicator for this purpose.   

Rotation rate of rods in turbulent flow

We study the motion of single small rod-like particles in turbulent flow. The orientation and position of rods are measured experimentally using Lagrangian particle tracking with images from multiple cameras in a flow between two oscillating grids. We also have performed numerical simulations of rod motion in homogeneous isotropic turbulence. The probability distribution of the rotation rate of the rods has extended tails indicating rare events with large rotation rate. Rods rotation rate is determined by the velocity gradient of the flow, so measurements of the rotation rate provides indirect access to statistics of the velocity gradient of the flow. However, tracer rods preferentially sample the flow since their orientation becomes correlated with the local axes of the velocity gradient tensor. The result is that the typical rotation rate of rods is much smaller than it would be if they were randomly oriented. The numerical simulations allow us to quantify the preferential alignment, including its dependence on rod aspect ratio. This allows measurements of the second moment of the rod rotation rate to be used to measure the energy dissipation rate in the turbulent flow.   

Subgrid scale flux of heavy particle concentration in coarse grained Eulerian fields as deduced from DNS of 2D homogeneous isotropic turbulence

Properties of preferential concentration of heavy particles in 2D homogeneous isotropic turbulence are investigated in an Eulerian framework. Particle motion is simulated in a Lagrangian framework, which is then used to derive the Eulerian particle concentration and velocity fields. Eulerian fields are coarse grained at several filter widths within the turbulence inertial subrange and statistics are analyzed. Focus is placed on the development of models to represent the subgrid scale (SGS) particle flux in large eddy simulation using the Eulerian equilibrium approach. It is argued that the SGS particle flux has two independent components that represent different physical processes: turbulent mixing due to SGS turbulence and clustering due to particle inertial response to SGS acceleration. These processes are completely independent and must be modeled separately. Phenomenological models based on centrifuging and the sweep-stick mechanisms are proposed for the inertial component.   

Lateral migration and orientation of ellipsoidal particles in Poiseuille flow

Inertial migration is widely used for separating microparticles in microfluidics. We use a hybrid numerical method that combine the lattice Boltzmann model and lattice spring model to investigate the dynamics of neutrally buoyant ellipsoidal particles in a Poiseuille flow with a finite Reynolds number. We find distinctive behaviors of particles depending on the particle shape, initial orientations and ratio of the particle size to channel width. Due to nonlinear flow effects, the particles equilibrate at off-center trajectories depending on particle geometry. Two possible equilibrium modes of motion are found. Particles either tumble with the main ellipsoid axis in the plane parallel to the flow direction or rotate along the main axis oriented perpendicular to the flow direction. We present a phase diagram showing the transitions between these two modes. The results indicate the possibility of particle separation by shape using microchannel flows.   

Effects of Polarization and Charging on the Deposition of Fine Particles on a Cylindrical Fiber: Simulation and Experiments

In this work, the particle deposition on a cylindrical fiber is investigated using a novel particle-level approach--discrete element method (DEM). The electrostatic effects, including both pre-charging and pre-polarization of fine particles, on the deposition patterns are discussed. Particularly, by this kind of method, a microscopic view on the depositions of neutral, polarized or charged particles is built, in which some basic finding are drawn. First, we find pre-polarization of fine particles enhances the deposition at nearly an order of magnitude; secondly, the charge of particle initially increases the deposition but finally inhibit it because of the repulsion between incident particles and deposited particles. A bench-scale set-up consisting of single fiber filtration system, particle charger, particle polarization unit and digital microscopy unit is built. The validation of DEM by experimental results is conducted.   

Intrinsic filtering errors of Lagrangian particle tracking in LES flow fields

Large-Eddy Simulations (LES) of two-phase turbulent flows exhibit quantitative differences in fluid and particle statistics if compared to Direct Numerical Simulations (DNS) which are considered here the exact reference case. Differences are due to filtering, a fundamental intrinsic feature of LES. In this paper, we quantify a lower bound for the filtering error using a DNS database of inertial particles dispersion in turbulent channel flow. Through ad hoc a-priori tests we single out the error purely due to filtering by removing error accumulation effects, which would lead to progressive divergence between DNS and LES particle trajectories. By applying filters of different type and width at varying particle inertia, we characterize the statistical properties of the filtering error. Results show that filtering error is stochastic and has a non-Gaussian distribution. In addition, the distribution of the filtering error depends strongly on the wall-normal coordinate being maximum in the buffer region. These findings provide insight on the effect of subgrid-scale velocity field on the force driving the particles, and establish the requirements which a LES model must satisfy to predict correctly particle segregation and preferential concentration.   

Lateral wall effects on the immersed pendulum dynamics and its interaction with a downstream target

The unsteady motion of a solid sphere in an incompressible viscous liquid and its interaction with solid boundaries has been examined and most existing knowledge concerns sphere motion in creeping flow regime or sphere collision dynamics. Much less investigated is when the solid sphere exhibits unsteady lateral motion relative to one or two planes. Thus, this work studies the dynamics of a fully immersed spherical pendulum when it moves midways between two lateral walls via systematic experiments. By changing the release angle and the liquid viscosity, a wide range of maximal particle Reynolds number, Re* from 3 to 295, were achieved without the presence of lateral walls. The same release was repeated with lateral walls imposed at various gaps, with a gap-to-diameter ratios W/D =1.2$\sim $5.0, and the resulting maximum Re* were measured. We also estimated the coupling distance, Xc, when a downstream target sphere was set into motion by the impact sphere. If head-on collision was observed, the ratio of the relative sphere velocities after and before the collision were used to calculate the coefficient of restitution, e. The measured Re*, Xc, and e will be presented as a function of W/D along with some preliminary analysis.