Particle-laden Channel Flow Research Articles

A comprehensive study of large eddy simulation models in capturing the dynamics of gas-particle turbulent suspensions

The particle phase attenuates the fluid fluctuations with an increase in volume fraction, and a sudden collapse in the turbulence is observed at a particular particle volume fraction, called critical particle volume loading (CPVL) [P. Muramulla et al. J. Fluid Mech. 889, A28 (2020)]. The present study reports the capability of two different classes of large eddy simulation (LES), viz. anisotropic and eddy viscosity-based, models to capture the turbulence modulation and the sudden disruption of the fluid fluctuations in the particle-laden vertical channel flows. The simulations are performed at two bulk Reynolds numbers of 3300 and 5600 based on the channel width and the bulk averaged fluid velocity. Our study on different LES models shows that approximate deconvolution (ADM) and scale similarity (SS) models accurately predict the critical loading for the Reynolds number of 3300. However, these models predict the critical loading qualitatively only for the Reynolds number of 5600 in the sense that they fail to predict the discontinuity as shown by the direct numerical simulation (DNS) study. The coherent structure model (CSM) predicts the critical loading with an 80% accuracy at both Reynolds numbers. The energy spectral density, production, and particle-induced dissipation spectra are plotted to analyze the distribution across wavenumbers. For all the LES models, a decrease in more than one order of magnitude is observed in the energy spectrum density at the critical loading compared to the unladen flow. The energy density decreases more in the channel center than in the near-wall region for the same particle volume loading. The mean component of particle-induced dissipation is almost two orders of magnitude larger than the particle dissipation spectra of fluctuating energy. The magnitude of streamwise and spanwise dissipation spectra of fluctuating components is higher in the near-wall region than the channel center. However, the magnitude of wall-normal dissipation spectra is higher in the channel center than near the wall region.

Mixed convection in turbulent particle-laden channel flow at Re τ = 180

A numerical investigation of mixed convection in a turbulent particle-laden channel flow is presented. Using Eulerian-Lagrangian Direct Numerical Simulations (DNSs) within the point-particle approach, the interaction between wall turbulence, particle inertia and thermal inertia, and buoyancy in the two-way coupling regime has been studied. The flow dynamics is controlled by the friction Reynolds number, Richardson number, particle Stokes and thermal Stokes numbers, and the Prandtl number. The effects of particle inertia and buoyancy on fluid and particle statistics are shown for a friction Reynolds number of 180, Stokes numbers ranging from 0.6 to 120, Richardson numbers ranging from 2.72 × 10−4 to 27.2 at a single Prandtl number, 0.71. The results indicate that the effect of particle inertia is significant on particle statistics, but not as pronounced on fluid statistics at the relatively low volume fraction considered. Particle inertia modulates the overall heat flux in a non-monotonic way.

Models of interphase drag force from direct numerical simulations of upward turbulent particle-laden channel flows

Data from the interfaced-resolved direct numerical simulations (IR-DNSs) of upward turbulent channel flow laden with finite-size heavy particles at particle concentration ranging from 0.84% to 2.36% are used to develop improved drag correlations which account for the effect of turbulence on drag enhancement. First, the contribution of drag nonlinearity to drag enhancement for the turbulent flow over a fixed sphere is analyzed with the consideration of velocity fluctuation anisotropy. The nonlinear drag enhancement is generally smaller than the actual drag enhancement in our numerical simulations. Second, several models for turbulence correction are presented with different choice of model parameters, and it is found that the turbulent intensity normalized by the mean slip velocity and the particle size normalized by the Kolmogorov scale are most important for modeling the effect of turbulence on particle drag, while the anisotropy of fluctuating velocity and the particle Reynolds number are less important.

Effect of drag force modeling on the flow of electrostatically charged particles

In CFD simulations of two-phase flows, accurate drag force modeling is essential for predicting particle dynamics. However, a generally valid formulation is lacking, as all available drag force correlations have been established for specific flow situations. In particular, these correlations have not been evaluated for particle-laden flows subjected to electrostatic forces. The paper reports the effect of drag force modeling on the flow of electrically charged particles. To this end, we implemented different drag force correlations to the open-source CFD tool pafiX. Then, we performed highly-resolved Direct Numerical Simulations (DNS) using the Eulerian–Lagrangian approach of a particle-laden channel flow with the friction Reynolds number of 180. The simulations generally revealed a strong influence of the precise drag correlation on particles in the near-wall region and a minor effect on the particles far from the walls. Due to their turbophoretic drift, particles accumulate close to the channel walls. For uncharged particles, the simulations show large deviations of the particle concentration profile in the near-wall region depending on the drag force correlation. Therefore, the disturbance of the flow surrounding a particle by a nearby wall or other particles is important for its drag. Driven by electrostatic forces, charged particles accumulate even closer to the wall. Contrary to the uncharged cases, when the particles carry a high charge (in our case one femto-coulomb), we found minor effects of drag force modeling on particle concentration profiles. In conclusion, for the investigated conditions, we propose to account for the effect of nearby particles and walls on the drag of low- or uncharged particles.

Effect of Stokes number on energy modulation of the fluid in turbulent particle-laden channel flows

Effect of Stokes number on energy modulation of the fluid in turbulent particle-laden channel flows

Applicability of large eddy simulations to capture turbulence attenuation in particle-laden channel flows

The applicability of large eddy simulation (LES) (Smagorinksy and dynamic Smagorinsky) models in predicting turbulence modulation is investigated. The LES models capture the turbulence modulation/fluctuations accurately at low volume fractions. However, at high volume loading, the LES models underpredict the turbulent kinetic energy production, which results in an underprediction of the particle volume loading where complete turbulence collapse is observed. The study highlights that modeling error in LES models is more significant at high particle volume loading than the filtering error and inaccuracy in feedback force.

A direct numerical simulation study of flow modulation and turbulent sedimentation in particle-laden downward channel flows

Fully resolved direct numerical simulations of turbulent downward channel flow laden with finite-size spherical particles are performed using the lattice Boltzmann method. Unlike upward particle-laden channel flows, the potential energy of settling particles serves as the driving force in the downward channel flows. Furthermore, the particles have an overall positive slip velocity at the center which causes the lateral hydrodynamic force to drive particles away from the center region. Both changes in the flow driving mechanism and the particle distribution affect the details of turbulence modulation in the downward channel, when compared to the upward channel flow. In this study, we focus on the effect of different particle terminal velocities, i.e., different particle settling Reynolds numbers, on the turbulent modulation of particle-laden downward channel flows. Indeed, the simulation results for downward channel flow show larger local particle concentration in the near-wall region, relative to the upward channel. It is also found that the level of particle near-wall accumulation increases with the particle terminal velocity. Opposite to the upward channel flows, the fluid-phase mean velocity in the downward channel flows is increased by heavy particles in the channel center, but reduced in the buffer layer. The reduction of mean velocity in the buffer layer is caused by the particle accumulation in low-speed streak regions. For the largest particle settling Reynolds number case (ReT = 30) investigated, strong accumulation of particles in the buffer layer interrupts the near-wall turbulence structures and thus leads to the reductions of fluid turbulence intensity and Reynolds stress.

The effect of gravity on turbulence modulation in particle-laden horizontal open channel flow

Two-way coupled direct numerical simulation of turbulence in a horizontal open channel with Lagrangian tracking of heavy particles is performed to study the joint influence of particle inertia and wall-normal gravity on turbulence modulation. The Stokes numbers based on the wall units considered in the study are St+= 1 (low inertia), 31 (moderate inertia), and 202 (high inertia) and the gravitational accelerations are g+= 0, 0.0068, 0.068, and 0.2221, varying from case to case. It is found that heavy particles (gravity involved in simulation) with low inertia subtly increase or have little significant influence on turbulence modulation, regardless of gravitational acceleration. Particles with high inertia and large gravitational acceleration significantly reduce the mean streamwise fluid velocity and the scales of turbulence structure near the wall, and vice versa in the outer layer. In this case, turbulence fluctuations are notably suppressed and the turbulence structures tend to be two-dimensional and laminar due to the strong rebound and trajectory-crossing effect. Moderate-inertia particles probably cause anisotropic turbulence modulation due to the competition between particle inertia and gravity settling. In the parameter range studied in this work, particles have indistinctive modification on turbulence when τp+g+ (=St+g+)<0.2 but suppress turbulence when τp+g+>0.2.

Publisher's Note: “A Lagrangian probability-density-function model for turbulent particle-laden channel flow in the dense regime” [Phys. Fluids 33, 053308 (2021)

Publisher's Note: “A Lagrangian probability-density-function model for turbulent particle-laden channel flow in the dense regime” [Phys. Fluids <b>33</b>, 053308 (2021)

A Lagrangian probability-density-function model for turbulent particle-laden channel flow in the dense regime

Modeling particle-laden turbulent flows at high volume fractions requires accounting for the coupling between phases. The latter is often a sensitive point, and proper closure of the exchange and production terms due to the presence of particles is not straightforward. In the present work, a Lagrangian probability-density-function model developed for homogeneous cluster-induced turbulence is extended to a channel flow. The key features are consistent two-way coupling and the decomposition of the particle velocity into spatially correlated and uncorrelated components, which is crucial for dense flows and which allows dealing with collisions from a statistical point of view. A numerical scheme for the coupled solution of the stochastic differential equations for the particles and a Reynolds-stress model for the fluid is developed. Tests with tracer particles without two-way coupling are done to assess the validity and the consistency of the numerical scheme. Finally, two sets of numerical simulations with particles with different diameters in a turbulent channel flow at a shear Reynolds of Reτ=300 are reported. The effect of two-way coupling by varying the mass loading of the dispersed phase in the mass-loading range φ= 0–2 is analyzed, and the results are compared to previous Eulerian–Lagrangian and Eulerian–Eulerian direct-numerical simulation (DNS) studies. Mean velocities and turbulent kinetic energy show good agreement with DNS, especially regarding the trend with respect to mass loading. Consistent with prior work, increased mass loading causes a drastic reduction of turbulent kinetic energy in the range φ= 0–2.

Direct numerical simulation of bidisperse inertial particles settling in turbulent channel flow

The behavior of settling velocity and clustering of bidisperse inertial particles in a turbulent channel flow is investigated through direct numerical simulation. The particle-laden planar channel flow has a friction Reynolds number at Reτ = 180. Eulerian–Lagrangian method is used to study the dynamic properties of bidisperse and monodisperse inertial particles with 16 different simulation sets, which are distinguished by Stokes numbers ranging from St+ = 1.31 to 52.58 and particle number ratio from 1:1 to 1:8. Momentum exchange between fluid and particle phases is considered in the simulation as the chosen initial volume fraction at 5 × 10−5 is in the two-way coupling regime. The gravity is set at the direction normal to both the wall normal direction and the streamwise direction. We observe that in the bidisperse cases the turbophoresis effect of inertial particles with the smaller diameter is significant even though it is very weak in the corresponding monodisperse cases. We use radial distribution function (RDF) to investigate the degree of clustering and turbophoresis. The results indicate that RDF is larger in the bidisperse cases for both large and small particles and it is greatly affected by the bulk particle number ratio and the Stokes number ratio. Unlike clustering, the terminal settling velocities of inertial particles in the bidisperse cases are affected by the final volume fraction at the dynamic equilibrium state. When their final volume fractions are lower than those in the corresponding monodisperse cases, the settling velocity of either particle becomes reduced from the monodisperse value. We also investigate the relationship between settling velocity and vortex strength. The results show that the preferential sweeping mechanism is strengthened with Stokes number decreasing and the mechanism can be quantified by the slope of the curve of settling velocity variation with vortex strength.

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.

Reynolds-stress modeling of cluster-induced turbulence in particle-laden vertical channel flow

We simulated particle-laden flow in a vertical channel with a Reynolds-averaged Navier--Stokes (RANS) two-fluid model including a Reynolds-stress model (RSM). Primary and turbulent statistics from counterpart Eulerian--Lagrangian (EL) and Eulerian--Eulerian Anisotropic-Gaussian (EE-AG) simulations were used to inform parameters and closures in the RSM. Flow in the channel center, including transitions, compared well with other simulations as mass loading increased. For small-Stokes particles, the RSM at greater mass loadings reproduced the transient clustering observed in the other models.

Direct numerical simulation of wall-to-liquid heat transfer in turbulent particle-laden channel flow

Direct numerical simulation on the turbulent flow between two parallel walls under constant heat flux reveals that, adding neutrally buoyant finite-size particles at volume fractions of 0.1 and 0.3 and bulk Reynolds numbers of 3800 and 5600 in general reduces the Nusselt number on average but enhances it near the walls. The enhancement is contributed by the near-wall streamwise vortex intensification, which is more significant for spheres than for prolates and oblates. These findings are helpful to intensify the wall-to-liquid heat transfer in particle-laden turbulent flow.

Kinetic energy balance in turbulent particle-laden channel flow

The present study investigates the influence of particle additives on the transfer, conversion, and dissipation of kinetic energy (KE) of a turbulent gas–solid channel flow. We derived the equations of KE, mean-flow KE, and turbulent KE (TKE) of the particle-laden flow and further performed two-way coupled direct numerical simulations of channel flow laden with four-million particles with Stokes number St = 30 (corresponding to a mass loading ratio of around one) with an Eulerian–Lagrangian approach. We found that, in the unladen flow, more than half of the input energy is directly dissipated in the mean flow, whereas the rest is converted to maintain the turbulence. By contrast, in the laden flow, both mean dissipation and energy supply are comparable with the unladen flow. However, the turbulence production is greatly reduced in the particle-laden flow. Another sink term due to the presence of the particle–fluid interactions corresponds to the rest loss of the total energy supply. The results reveal the particle-induced redistribution of mean KE, which is transferred from the mean flow to particles in the channel core, whereas the flow gains energy from particles in the near-wall region. In total, there is a loss of the mean-flow energy due to the presence of the inertial particles. Regarding TKE balance, the particles, gaining energy from the mean flow, transfer the energy to the fluid across the channel, which contributes around one third of the TKE source. The present results provide a general picture of KE balance of a particle-laden channel flow.

Non-monotonic effect of mass loading on turbulence modulations in particle-laden channel flow

The effect of mass loading on turbulence modulation in channel flows is investigated in two-way coupled direct numerical simulations with the Lagrangian point-particle method. We carried out the simulations of turbulent channel flows at Reτ = 180, and the particle mass loading ranges from 0 to 0.96 with a fixed Stokes number St = 30. The statistics show that the intensity of the streamwise velocity fluctuation augmented non-monotonically with the increase in mass loading. The maximum enhancement of the streamwise turbulence intensity observed at a mass-loading of ϕm = 0.75 is 60% greater than that of the unladen flow. However, the velocity fluctuations in the spanwise and wall-normal direction as well as the Reynolds shear stress are attenuated monotonically with mass loading. To better interpret the non-monotonic effect of mass loading on the streamwise turbulence intensity, we further examined the near-wall vortices and streaks and proposed two competitive mechanisms. First, we found that the near-wall vortices become fewer and weaker and the spacing between streaks become wider as ϕm increases, which results in the damping effect on the fluctuation of the streamwise velocity. Second, the vortex structures and the streaks become more organized and straightly aligned in the streamwise direction with an increase in the streak strength, which enhances the streamwise velocity fluctuations. In addition, we observed a non-monotonic change in turbulent kinetic energy transfer between particle and fluid phases. The statistics of energy budgets show that particles extract energy from the fluid phase at ϕm &amp;lt; 0.6 but transfers energy back to the fluid phase at ϕm &amp;gt; 0.75 in the stream-wise direction.

Agglomeration dynamics in liquid–solid particle-laden turbulent channel flows using an energy-based deterministic approach

A deterministic particle–particle agglomeration technique is applied together with direct numerical simulation and four-way coupled Lagrangian particle tracking in order to accurately simulate and investigate fully coupled agglomerating particle-laden channel flows at a shear Reynolds number, Reτ = 180. The collision outcome determination (recoil or aggregate) is based on the balance between kinetic energy dispersed in the collision and the work required to overcome the van der Waals attractive potential. The influence of particle size (dP = 202 μm, 286 μm, and 405 μm), both at a fixed volume fraction (ϕP = 10−3) and a fixed primary injected particle number (NP = 109 313), on the resulting collision and agglomeration dynamics is investigated. Attention is also focused on how collision and agglomeration rates vary throughout the wall-normal regions of the channel flow. The results demonstrate that the normalized collision rates are similar for all particle sizes at the fixed volume fraction but increase with particle size at the fixed particle number, and a preference is observed for collisions to occur close to the walls. Despite this, in all cases considered here, agglomeration events are most frequent at the center of the channel, with agglomeration efficiencies also peaking in this region. In terms of particle diameter effects, the smallest particles exhibit the greatest preference to aggregate, given that a collision has already occurred. Furthermore, whereas normalized collision and agglomeration event counts show differing diameter-dependence based on whether the number of primary particles or the volume fraction is fixed, agglomeration rates show diameter-independence and as such are based solely on particle size and local dispersive properties. Analysis of the dynamic collision properties throughout the channel confirms that agglomeration is favored within the bulk flow region due to low relative particle velocities and small collision angles at this location. The temporal evolution of important interaction properties is investigated, all of which demonstrate stability over the course of the time simulated. Particle diameter is also shown to influence the long-term population of higher-order agglomerates, with (for a given volume fraction) smaller particles aggregating faster to form larger particles. The systems studied, which resemble those present in the processing of nuclear waste, all exhibit substantial agglomeration over the time considered. This reinforces the importance of accurately modeling agglomeration dynamics in flows where electrokinetic interactions are important in order to correctly predict multiphase flow properties over long timeframes.

Transient growth in turbulent particle-laden channel flow

Linear transient growth of optimal perturbations in particle-laden turbulent channel flow is investigated in this work. The problem is formulated in the framework of a Eulerian–Eulerian approach, employing two-way coupling between fine particles and fluid flow. The model is first validated in laminar cases, after which the transient growth of coherent perturbations in turbulent channel flow is investigated, where the mean particle concentration distribution is obtained by direct numerical simulation. It is shown that the optimal small-scale structures for particles are streamwise streaks just below the optimal streamwise velocity streaks, as was previously found in numerical simulations of particle-laden channel flow. This indicates that the optimal growth of perturbations is a dominant mechanism for the distribution of particles in the near-wall region. The current study also considers the transient growth of small- and large-scale perturbations at relatively high Reynolds numbers, which reveals that the optimal large-scale structures for particles are in the near-wall region while the optimal large-scale structures for fluid enter the outer region.

Multiphase Eulerian–Lagrangian LES of particulate fouling on structured heat transfer surfaces

In this study, multiphase Eulerian–Lagrangian large-eddy simulation (LES) is used to analyze the interaction between local flow structures, convective heat transfer and particle depositions (fouling) for a turbulent channel flow with a dimpled surface. Thus, eddy-resolving LES is applied for calculation of the turbulent working fluid (carrier flow), combined with an efficient Lagrangian particle tracking (LPT) algorithm, suitable to predict the trajectories of the suspended foulant particles precisely in time and space. In order to decrease the computational effort and to enhance the applicability of the proposed approach, deposited particles are deactivated and converted into a second continuous phase (fouling layer), which is modeled as a porous medium and accounts for the hydraulic losses as well as for the additional thermal resistance due to the fouling deposits. Prior to the fouling simulations, the envisaged method is validated for a turbulent particle-laden channel flow at Reτ=150, based on DNS results available in the literature, which shows the capability of the Eulerian–Lagriangian LES of capturing the flow physics within turbulent particle-laden, wall-bounded flows. Based on this observations, fouling simulations were carried out for a turbulent particle-laden channel flow over a staggered arrangement of sharp-edged spherical dimples, whereby two different dimple depth-to-diameter ratios are considered (d/D=0.26 and 0.35). The thermo-hydraulic performance is analyzed for the clean and contaminated dimpled surfaces.

Direct numerical simulations of spanwise slope-induced turbidity currents in a fine sediment-laden steady turbulent channel: Role of suspended sediment concentration and settling velocity

Wave- and current-supported turbidity currents (WCSTCs) constitute a subclass of turbidity currents that ubiquitously participate in shaping the marine geomorphology. Rather than the turbulence generated by its forward motion, WCSTCs require boundary-layer turbulence generated by the surface waves and/or currents that are parallel or normal to the shore to keep the sediments suspended. This study focuses on the characteristics of WCSTCs due to shore parallel current only. Such flows can be approximated as particle-laden channel flows with a mild spanwise slope. Due to the spanwise slope, the submerged weight of the suspended sediments creates spanwise force and thus a spanwise current. The resultant flow is affected by two competing mechanisms: (i) additional turbulence generation by the spanwise turbidity current and (ii) turbulence suppression due to suspended sediment-induced stable density stratification. In this study, the role of sediment settling velocity and concentration on these competing processes is investigated by direct numerical simulations. The results of the conducted simulations suggest that turbulence production due to spanwise current is a quadratic function of the suspended sediment concentration, whereas buoyancy dissipation due to sediment-induced stably density stratification linearly varies with the suspended sediment concentration. Turbulent energy distribution among the fluctuating velocity components also suggests that spanwise velocity fluctuations rely less on the turbulence production due to streamwise current. Therefore, a high-concentration turbidity with fine sediment content tends to evolve into a self-sustaining turbidity current, whereas the low-concentration turbidity composed of relatively larger sediments require the current-induced turbulence to sustain its motion.