Turbulent channel flow of dense suspensions of neutrally-buoyant spheres

Dense particle suspensions are widely encountered in many applications and in environmental flows. While many previous studies investigate their rheological properties in laminar flows, little is known on the behaviour of these suspensions in the turbulent/inertial regime. The present study aims to fill this gap by investigating the turbulent flow of a Newtonian fluid laden with solid neutrally-buoyant spheres at relatively high volume fractions in a plane channel. Direct Numerical Simulation are performed in the range of volume fractions Phi=0-0.2 with an Immersed Boundary Method used to account for the dispersed phase. The results show that the mean velocity profiles are significantly altered by the presence of a solid phase with a decrease of the von Karman constant in the log-law. The overall drag is found to increase with the volume fraction, more than one would expect just considering the increase of the system viscosity due to the presence of the particles. At the highest volume fraction here investigated, Phi=0.2, the velocity fluctuation intensities and the Reynolds shear stress are found to decrease. The analysis of the mean momentum balance shows that the particle-induced stresses govern the dynamics at high Phi and are the main responsible of the overall drag increase. In the dense limit, we therefore find a decrease of the turbulence activity and a growth of the particle induced stress, where the latter dominates for the Reynolds numbers considered here.Comment: Journal of Fluid Mechanics, 201

Channel flow of rigid sphere suspensions: particle dynamics in the inertial regime

We consider suspensions of neutrally-buoyant finite-size rigid spherical particles in channel flow and investigate the relation between the particle dynamics and the mean bulk behavior of the mixture for Reynolds numbers $500 \le Re \le 5000$ and particle volume fraction $0\le \Phi \le 0.3$, via fully resolved numerical simulations. Analysis of the momentum balance reveals the existence of three different regimes: laminar, turbulent and inertial shear-thickening depending on which of the stress terms, viscous, Reynolds or particle stress, is the major responsible for the momentum transfer across the channel. We show that both Reynolds and particle stress dominated flows fall into the Bagnoldian inertial regime and that the Bagnold number can predict the bulk behavior although this is due to two distinct physical mechanisms. A turbulent flow is characterized by larger particle dispersion and a more uniform particle distribution, whereas the particulate-dominated flows is associated with a significant particle migration towards the channel center where the flow is smooth laminar-like and dispersion low.Interestingly, the collision kernel shows similar values in the different regimes, although the relative particle velocity and clustering clearly vary with inertia and particle concentration.Comment: 36 Pages, 12 figure

Effects of the finite particle size in turbulent wall-bounded flows of dense suspensions

We use interface-resolved simulations to study finite-size effects in turbulent channel flow of neutrally-buoyant spheres. Two cases with particle sizes differing by a factor of 2, at the same solid volume fraction of 20% and bulk Reynolds number are considered. These are complemented with two reference single-phase flows: the unladen case, and the flow of a Newtonian fluid with the effective suspension viscosity of the same mixture in the laminar regime. As recently highlighted in Costa et al. (PRL 117, 134501), a particle-wall layer is responsible for deviations of the statistics from what is observed in the continuum limit where the suspension is modeled as a Newtonian fluid with an effective viscosity. Here we investigate the fluid and particle dynamics in this layer and in the bulk. In the particle-wall layer, the near wall inhomogeneity has an influence on the suspension micro-structure over a distance proportional to the particle size. In this layer, particles have a significant (apparent) slip velocity that is reflected in the distribution of wall shear stresses. This is characterized by extreme events (both much higher and much lower than the mean). Based on these observations we provide a scaling for the particle-to-fluid apparent slip velocity as a function of the flow parameters. We also extend the flow scaling laws in to second-order Eulerian statistics in the homogeneous suspension region away from the wall. Finite-size effects in the bulk of the channel become important for larger particles, while negligible for lower-order statistics and smaller particles. Finally, we study the particle dynamics along the wall-normal direction. Our results suggest that 1-point dispersion is dominated by particle-turbulence (and not particle-particle) interactions, while differences in 2-point dispersion and collisional dynamics are consistent with a picture of shear-driven interactions

Universal Scaling Laws for Dense Particle Suspensions in Turbulent Wall-Bounded Flows

The macroscopic behavior of dense suspensions of neutrally-buoyant spheres in turbulent plane channel flow is examined. We show that particles larger than the smallest turbulence scales cause the suspension to deviate from the continuum limit in which its dynamics is well described by an effective suspension viscosity. This deviation is caused by the formation of a particle layer close to the wall with significant slip velocity. By assuming two distinct transport mechanisms in the near-wall layer and the turbulence in the bulk, we define an effective wall location such that the flow in the bulk can still be accurately described by an effective suspension viscosity. We thus propose scaling laws for the mean velocity profile of the suspension flow, together with a master equation able to predict the increase in drag as function of the particle size and volume fraction.Comment: Accepted for publication in PRL. Supplemental material include

Modelling the Eddy Pattern in the harbour of Zeebrugge

Hydrodynamic

Local energy balance, specific heats and the Oberbeck-Boussinesq approximation

A thermodynamic argument is proposed in order to discuss the most appropriate form of the local energy balance equation within the Oberbeck-Boussinesq approximation. The study is devoted to establish the correct thermodynamic property to be used in order to express the relationship between the change of internal energy and the temperature change. It is noted that, if the fluid is a perfect gas, this property must be identified with the specific heat at constant volume. If the fluid is a liquid, a definitely reliable approximation identifies this thermodynamic property with the specific heat at constant pressure. No explicit pressure work term must be present in the energy balance. The reasoning is extended to the case of fluid saturated porous media.Comment: 14 pages, 2 figures, 1 table, submitted for publicatio

Monitoring spatially heterogeneous dynamics in a drying colloidal thin film

We report on a new type of experiment that enables us to monitor spatially and temporally heterogeneous dynamic properties in complex fluids. Our approach is based on the analysis of near-field speckles produced by light diffusely reflected from the superficial volume of a strongly scattering medium. By periodic modulation of an incident speckle beam we obtain pixel-wise ensemble averages of the structure function coefficient, a measure of the dynamic activity. To illustrate the application of our approach we follow the different stages in the drying process of a colloidal thin film. We show that we can access ensemble averaged dynamic properties on length scales as small as ten micrometers over the full field of view.Comment: To appear in Soft Material

Analysis of FPTASes for the Multi-Objective Shortest Path Problem

We propose a new FPTAS for the multi-objective shortest path problem. The algorithm uses elements from both an exact labeling algorithm and an FPTAS proposed by Tsaggouris and Zaroliagis (2009). We analyze the running times of these three algorithms both from a the- oretical and a computational point of view. Theoretically, we show that there are instances for which the new FPTAS runs an arbitrary times faster than the other two algorithms. Fur- thermore, for the bi-objective case, the number of approximate solutions generated by the proposed FPTAS is at most the number of Pareto-optimal solutions multiplied by the number of nodes. By performing a set of computational tests, we show that the new FPTAS performs best in terms of running ti