Density ratio effects on the topology of coherent turbulent structures in two-way coupled particle-laden channel flows

This investigation considers the effect of density ratio on the modification of coherent turbulent structures in particle-laden channel flows at a shear Reynolds number of Reτ = 180. Direct numerical simulation and Lagrangian particle tracking are used to accurately predict the motion of particles dispersed within the flow at three Stokes numbers, St+ = 0.1, 50, and 92. Particle–fluid coupling is achieved through a local element-based force feedback field in the Navier–Stokes equations, which are solved using a seventh-order accurate spectral element method. After an initial transitory period wherein the effects of particle–fluid interaction are emphasized, the low density ratio particles are found to enhance the turbulence field, increasing the frequency of Q-criterion satisfying regions, while the inertial particles suppress the turbulence, reducing the number of quasistreamwise vortices. Results indicate that the topology of the quasistreamwise vortices is altered by the presence of the particles in the viscous sublayer, the buffer layer, and the log-law region such that the distribution of the third invariant of the deviatoric tensor, R, is widened by the presence of tracer-like particles and made thinner by the inertial particles. This effect reduces the amount of unstable focus/compressing regions and stable focus/stretching regions, which account for the streamwise vortical structures observed in these types of flow. Investigating the instantaneous coupling force field surrounding turbulent structures and low speed streaks shows that particles exert their greatest influence on the fluid in the regions noted, and mechanisms by which the particulate phase interacts with turbulent vortices are analyzed

Solid Particle Interaction Dynamics at Critical Stokes Number in Isotropic Turbulence

Binary solid spherical particle-particle interactions are studied in forced isotropic turbulence at = 29 and 197 using direct numerical simulation and an immersed boundary method. Isotropic turbulence in a periodic box is forced using a linear forcing method to maintain statistically stationary turbulence, with inter-particle interaction modelled using DLVO interaction forces which include attraction and repulsion due to van der Waals and electric double layer potential forces, respectively. Particle collisions are modelled using the inelastic hard sphere model with a coefficient of restitution of 0.4. The DLVO parameters are chosen to be representative of calcite particles, a simulant of nuclear waste material found in storage ponds in the UK. The Reynolds numbers chosen for the boxes are equivalent to typical values of that are found in the bulk flow and viscous sub-layer regions of a turbulent channel flow at =180. The techniques described are used to study the dynamics of critical Stokes number particles in turbulence by analysing probability density functions (PDFs) of collision statistics such as particle displacement and the particles’ relative velocities to determine the likelihood of agglomeration. The results indicate that agglomeration can occur in both the turbulent boxes considered. However, the occurrence is much more likely at lower values due to the higher dispersion of kinetic energy after impact

Prediction of polymer extension, drag reduction, and vortex interaction in direct numerical simulation of turbulent channel flows

Hydrodynamic and viscoelastic interactions between the turbulent fluid within a channel at Reₓ = 180 and a polymeric phase are investigated numerically using a multiscale hybrid approach. Direct numerical simulations are performed to predict the continuous phase and Brownian dynamics simulations using the finitely extensible nonlinear elastic dumbbell approach are carried out to model the trajectories of polymer extension vectors within the flow, using parallel computations to achieve reasonable computation timeframes on large-scale flows. Upon validating the polymeric configuration solver against theoretical predictions in equilibrium conditions, with excellent agreement observed, the distributions of velocity gradient tensor components are analyzed throughout the channel flow wall-normal regions. Impact on polymer stretching is discussed, with streamwise extension dominant close to the wall, and wall-normal extension driven by high streamwise gradients of wall-normal velocity. In this case, it is shown that chains already possessing high wall-normal extensions may attempt to orientate more in the streamwise direction, causing a curling effect. These effects are observed in instantaneous snapshots of polymer extension, and the effects of the bulk Weissenberg number show that increased WeB leads to more stretched configurations and more streamwise orientated conformities close to the wall, whereas, in the bulk flow and log-law regions, the polymers tend to trace fluid turbulence structures. Chain orientation angles are also considered, with WeB demonstrating little influence on the isotropic distributions in the log-law and bulk flow regions. Polymer–fluid coupling is implemented through a polymer contribution to the viscoelastic stress tensor. The effect of the polymer relaxation time on the turbulent drag reduction is discussed, with greater Weissenberg numbers leading to more impactful reduction. Finally, the velocity gradient tensor invariants are calculated for the drag-reduced flows, with polymers having a significant impact on the Q–R phase diagrams, with the presence of polymers narrowing the range of R values in the wall regions and causing flow structures to become more two-dimensional

Dynamics of Fully Resolved Binary Particle Interactions in Isotropic Turbulence

Binary particle-particle interaction events in turbulence are simulated using the spectral elementbased DNS solver, Nek5000 and an immersed boundaries method. Particle-fluid coupling is achieved using the ghost-cell approach. Two periodic boxes of isotropic turbulence are obtained via linear forcing with Taylor microscale Reynolds numbers, ܴ݁Reλ = 29 and ܴ݁Reλ = 197. These have been selected to match those typical in the bulk and viscous sublayer regions of a ܴ݁Reₓ = 180 turbulent channel flow respectively. Both solid and fluid phase material and chemical properties are chosen to represent 100μm calcite particles in a 0.02݉m half-height channel flow. Simulations are initialised based on the most frequently occurring particle-particle collision events sampled from a four-way coupled DNS-LPT simulation. Particle interaction is modelled using interparticle forces based on DLVO theory and the hard sphere collision model. Results indicate that particles in regions of increased turbulence are less likely to agglomerate, since their motion is dominated by the viscous and pressure forces on the particle, whereas in the bulk of the channel, forces transverse to streamwise motion allow pairs of particles travelling together to undergo agglomeration. Further variables of motion are monitored, such as angular velocity, in order to elucidate the effect of turbulence on a sphere’s rotational behaviour. It is to be determined in future work how the chemical and material properties of both phases affect these trajectories and potential for agglomeration

Effect of Reynolds Number on Critical Stokes Number Particle Collision Statistics in Multiphase Turbulent Channel Flows

Spherical particle collision statistics in multiphase turbulent channel flows are obtained using a Lagrangian particle tracking algorithm four-way coupled to direct numerical simulations. Two channel flows are simulated at Reτ=180 and Reτ=590 with particles of the Kolmogorov Stokes number StK=1. Particle collision velocities and angles within four regions of the channel flows (viscous sublayer, buffer layer, log-law region and bulk flow) are analysed to elucidate the dynamics of particle interactions in the various regions of the turbulent flows. The results indicate that the most significant contribution to collision velocities arises in the streamwise direction, with particles in the viscous sublayer region colliding with lower streamwise velocities compared to those in other regions of the flow. Furthermore, the spread in the distribution of collision angles is found to be highest in the viscous sublayer, and lowest in the bulk flow region

Near-wall interparticle collision dynamics in multi-phase turbulent channel flows

Interparticle collision statistics in a turbulent channel flow are obtained using direct numerical simulation coupled to Lagrangian particle tracking. The particle motion solver considers drag, lift, pressure gradient and added mass force contributions. Fluid momentum coupling and hard-sphere deterministic interparticle collisions are also accounted for. Collision behaviour for particle Stokes numbers outside of the range usually considered in similar investigations is discussed in detail. The analysis focuses on separating the turbulent channel flow into four regions of varying turbulence intensity. Collision velocities are analysed for each region and discussion as to how particles obtain those velocities is offered. The mean value of the collision angle is observed to scale with both Stokes number and wall proximity, with the former having the greatest effect. The greatest collision rate is found to be in the viscous sublayer and for the higher Stokes number

Simulation of Fully Resolved Particle-Particle Interactions in Turbulence with Behavioural Modification

Fully resolved particle-particle interaction events in turbulence are studied using high fidelity simulation. The continuous phase uses a spectral element-based direct numerical simulation and the discrete phase is modelled using the immersed boundary method. The ghost-cell technique is used to achieve particle-fluid coupling and the method is validated against empirically determined drag coefficients with strong agreement for high resolution particle meshes. The interactions take place in an isotropic box of turbulence at Reynolds number (based on the Taylor microscale), = 51 . This value is selected to closely resemble those typical of the buffer layer in a turbulent channel flow at shear Reynolds number, = 180. Particulate phase properties are chosen to represent 100 diameter calcite particles in water, but the chemical and dynamic properties of both phases are varied to determine the extent of behavioural modification through alteration of these parameters. Results indicate that the restitution coefficient has the greatest effect on collision dynamics, with an increase leading to fewer particle agglomerations. Reducing the Hamaker constant has a lesser effect on the resulting interaction but does lower the mean speed of the particles undergoing collision. The electric double layer potential has very little effect on any of the agglomeration dynamics, since its strength and effective range is much lower than that of the van der Waals component. Suggestions are offered for behavioural modification techniques based on the present results

Near-wall dynamics of inertial particles in dilute turbulent channel flows

This investigation considers the effect of the Stokes number on the near-wall particle dynamics of two-phase (solid-fluid) turbulent channel flows. The spectral element method-based direct numerical simulation code Nek5000 is used to model the fluid phase at a shear Reynolds number, Reτ = 180. Dispersed particles are tracked using a Lagrangian approach with one-way coupling. Eulerian fluid and particle statistics are gathered and analyzed to determine the effect of the Stokes number, first on macroscopic statistics. Previous work of this nature indicates that mean streamwise particle velocities and root-mean-square velocity fluctuations are reduced in the bulk and increased very close to the wall, an effect which is stronger with increased particle Stokes number or inertial particles. This phenomenon has important consequences for mechanisms such as particle deposition and preferential concentration, and so for the first time, this work aims to elucidate the dynamics of this effect through rigorous analysis on various scales. An in-depth force analysis indicates the importance of the lift force, even at increased Stokes numbers, in predicting particle motion in the buffer layer and log-law regions. It is also observed that pressure gradient and virtual mass forces are significant close to the wall. Alongside bulk velocity and acceleration statistics, microscopic behavior is analyzed by considering region-based particle dynamics. Probability density functions are used to determine the effect of the Stokes number on particle motion in three near-wall regions, as well as within the bulk flow. It is observed that at higher Stokes numbers, the viscous sublayer contains particles with dynamic properties similar to those present in the buffer layer. This suggests rapid interlayer migration in the wall direction, causing increased particle turbulence intensities in near-wall regions. A local flow topology classification method is also used to correlate particle behavior with near-wall coherent turbulent structures, and a mechanism for particle sweep toward the wall is suggested. Finally, low-speed streak accumulation and interlayer particle fluxes are considered and the extent of mixing for low and high Stokes numbers is discussed

Mechanisms of particle preferential concentration induced by secondary motions in a dilute turbulent square duct flow

Particle-laden turbulent square duct flows at Reτ = 300 (based on the duct half-width and the mean friction velocity) are investigated using direct numerical simulation with one-way coupled Lagrangian particle tracking. Four particle-to-fluid density ratios are considered with the corresponding shear Stokes number St+ = 0.31, 25, 125, and 260. Particle motion is governed by drag, lift, added-mass, and pressure gradient forces. The main purpose of this work is to examine the effect of the turbulence-driven secondary flows on particle preferential accumulation and their dependence on the Stokes number. Results obtained indicate that the cross-stream secondary motions encourage inertial particles to accumulate preferentially in the duct corners, where the maximum of the cross-sectional particle concentration occurs. The extent of accumulation here is strongly dependent on the Stokes number, with the greatest accumulation found at St+ = 25. Interestingly, the maximum of the intensity of the secondary particle velocity along the corner bisector is also achieved at St+ = 25, whereas in the region adjacent to the wall, it is found to decrease with a particle Stokes number. Additionally, it is observed that the higher inertia particles are more easily trapped in the stagnation zone of secondary flows with low turbulence intensity in the corner region. In the near-wall region, the heavier particles (St+ ≥ 25) are prone to reside and form elongated clusters along the low-speed streamwise velocity streaks, with this trend less pronounced with the increasing Stokes number. Along the wall, away from the corner where the secondary motion is attenuated, particle accumulation is dominated by the near-wall coherent vortices. This phenomenon is further discussed using a region-based correlation analysis between the particle spatial distribution and local flow topology. An in-depth particle dynamic analysis determines that the average cross-sectional drag force resulting from the secondary flow is mainly responsible for the particle motion throughout the duct cross section, which tends to push particles away from the walls in the near-wall region but shows the exact opposite trend in the bulk flow region. Moreover, the pressure gradient force also plays an important role for low-inertia particles. As the Stokes number is increased, the lift force becomes progressively dominant in the viscous sublayer, acting to pull particles toward the corners and walls of the duct

Turbulent Heat Transfer In Nanoparticulate Multiphase Channel Flows With A High Prandtl Number Molten Salt Fluid

The growing interest in energy efficient and sustainable technologies has created significant demand for novel heat transfer and thermal energy storage materials, such as nanofluids. The importance of nanoparticle science cannot be underestimated, since the motivation for the manipulation, through nanoparticle addition, of the properties of existing thermofluids (e.g. molten salt) arises from their poor thermal properties which represent a major limitation to the development of more energy-efficient processes. In this work, consideration is given to investigating the role of heat transfer in nanofluids in three-dimensional flows using an advanced computational modelling approach to simulate such flows. In the present work, we use direct numerical simulation coupled with a Lagrangian particle tracking technique. The heat transfer behaviour of a nanofluid within a turbulent wall-bounded flow is investigated, with the fluid phase properties chosen to represent a solar molten salt (NaNO3-KNO3, 60:40 weight ratio) thermofluid typical of those present in solar thermal power plants. The configuration is a fully developed channel flow with uniform heating/cooling from both walls. The continuous phase is modelled using the open source spectral element-based solver, Nek5000. Predictions of a statistically steady turbulent channel flow at shear Reynolds number Reτ = 180 and high turbulent Prandtl number Prt = 5.0 are first obtained and validated. A particle tracking routine is implemented to simulate the dispersed phase which can accommodate one-, two- and four-way coupling between the fluid and discrete phases. To investigate the effect of particles on the turbulent heat flux and temperature field, the nanoparticle concentration response to temperature variations and turbulence is obtained across the channel, with the associated first and second-order flow and temperature field statistics presented. The advantage of the model developed is its ability to study in detail phenomena such as interparticle collisions, agglomeration, turbophoresis and thermophoresis, with the approach also being of value in investigations of the heat transfer performance and long-term thermal stability of nanoparticle dispersions which as yet have not been considered in detail. The outcome of this study allows conclusions to be reached regarding the implications of nanoparticle-seeded molten salts for solar thermal energy storage systems