Particle-laden Turbulent Channel Flow Research Articles

Direct numerical simulation of turbulent flow and heat transfer in a particle-laden turbulent channel flow

Direct numerical simulation (DNS) is conducted to investigate the impact of solid particles on heat transfer in a plane channel flow. For comparison, two corresponding DNSs of unladen channel flow are also performed. The numerical simulation of the particle-laden case employs a two-way coupled Eulerian–Lagrangian computational model, which allows for the consideration of momentum transfer between the two phases: discrete particles and the continuous fluid phase. The presence of particles results in an increase in the mean temperature, the root mean square (rms) of temperature fluctuations, and the streamwise turbulent heat flux within the core region. Furthermore, particles exert a more significant influence on these characteristics at higher solid volume fractions. Additionally, the correlation between velocity and temperature is affected by the presence of particles. When comparing heat transfer in particle-laden channel flow to that in the corresponding unladen channel flow, it is observed that the difference in heat flux arises from changes in the rms of the wall-normal velocity and temperature fluctuations. The impact of particles on turbulent heat flux transport is significant in the vicinity of the wall, while their influence within the core region is relatively small.

Preferential accumulation of finite-size particles in near-wall streaks

The preference for particles to accumulate at specific regions in the near-wall part is a widely observed phenomenon in wall-bounded turbulence. Unlike small particles more frequently found in low-speed streaks, finite-size particles can accumulate in either low-speed or high-speed streaks. However, mechanisms and influencing factors leading to the different preferential concentration locations still need to be clarified. The present study conducts particle-resolved direct numerical simulations of particle-laden turbulent channel flows to provide a better understanding of this seemingly puzzling behaviour of preferential accumulation. These simulations cover different particle-to-fluid density ratios, particle volume fractions, particle sizes and degrees of sedimentation intensity. We find that the large particle size is the crucial factor that results in particles accumulating in high-speed streaks. Large particles not only are difficult to be conveyed by the quasi-streamwise vortices to low-speed streaks but also can escape from the near-wall region before moving spanwisely out from high-speed streaks. The sedimentation effect allows particles to gather closer to the channel wall and stay longer in the near-wall regions, reinforcing the sweeping mechanism of quasi-streamwise vortices that transport particles from high- to low-speed streaks. As a result, sedimenting particles tend to accumulate in the low-speed streaks.

The influence of particle density and diameter on the interactions between the finite-size particles and the turbulent channel flow

Understanding the influence of different particle parameters on the two-way interactions between the particles and wall-bounded turbulence is important in many natural phenomena and engineering applications. In this work, particle-resolved direct simulation of particle-laden turbulent channel flow is performed based on the mesoscopic lattice Boltzmann method (LBM), and the particle–fluid interface is treated using the interpolated bounce back scheme. The friction Reynolds number (Reτ) of the single phase turbulent channel flow is 180, and the particle volume fraction is fixed at 1%. Three particle–fluid density ratios and three particle diameters are considered, and five particle-laden simulations are performed to investigate the influence of particle density and diameter on the interactions between the particles and the carrier turbulence. Results show that the streamwise velocity of the solid phase is larger than that of the fluid phase in the near-wall region, and the velocity difference between the two phases decreases with increasing particle density, but increases with increasing particle diameter. The probability density functions (PDFs) of particle velocity and angular velocity depend on the distance between the particles and the wall, but the PDFs of particle acceleration and angular acceleration are not spatially dependent. The distribution of particle Reynolds number follows the Gamma distribution within the buffer region and viscous sublayer. The solid phase concentration is high in the near-wall region, and the largest solid-phase concentration in this region occurs in the case with particles of intermediate density. Particles with different parameters would lead to different modulation to the carrier flow. Then, two aspects of the turbulence modulation are explored, i.e., the streamwise velocity and the turbulent kinetic energy (TKE). The presence of finite-size particles typically increases the streamwise velocity in the near-wall region and reduce the streamwise velocity outside this region. The trend is similar for TKE, but the TKE attenuation mainly occurs in the buffer region. The modulation to the streamwise velocity is analyzed using the streamwise momentum balance equation. It is found that the streamwise velocity modulation is dominated by the weighted Reynolds stress, but the different modulation in the near-wall region is due to the difference in weighted particle-induced stress, whereas the different modulation outside the near-wall region is due to the change in weighted Reynolds stress. Through TKE budget analysis, it is found that the enhancement of the total TKE source in the viscous sublayer increases with increasing particle density and diameter and the attenuation of total TKE source in the buffer region increases with increasing particle density and diameter, which is consistent with the TKE modulation for different cases.

Effect of Stokes number and particle-to-fluid density ratio on turbulence modification in channel flows

Two-way momentum-coupled direct numerical simulations of a particle-laden turbulent channel flow are addressed to investigate the effect of the particle Stokes number and of the particle-to-fluid density ratio on the turbulence modification. The exact regularised point-particle method is used to model the interphase momentum exchange in presence of solid boundaries, allowing the exploration of an extensive region of the parameter space. Results show that the particles increase the friction drag in the parameter space region considered, namely the Stokes number $St_+ \in [2,80]$ , and the particle-to-fluid density ratio $\rho _p/\rho _f \in [90,5760]$ at a fixed mass loading $\phi =0.4$ . It is noteworthy that the highest drag occurs for small Stokes number particles. A measurable drag increase occurs for all particle-to-fluid density ratios, the effect being reduced significantly only at the highest value of $\rho _p/\rho _f$ . The modified stress budget and turbulent kinetic energy equation provide the rationale behind the observed behaviour. The particles’ extra stress causes an additional momentum flux towards the wall that modifies the structure of the buffer and of the viscous sublayer where the streamwise and wall-normal velocity fluctuations are increased. Indeed, in the viscous sublayer, additional turbulent kinetic energy is produced by the particles’ back-reaction, resulting in a strong augmentation of the spatial energy flux towards the wall where the energy is ultimately dissipated. This behaviour explains the increase of friction drag in particle-laden wall-bounded flows.

Assessment of local isotropy, energetics, and modified eddy-viscosity based modelling for particle-laden turbulent channel flows

A large number of turbulence models (stochastic and large-eddy simulation (LES) models) developed to describe the dynamics of particle-laden turbulent flows are based on the assumption of local isotropy and use the Kolmogorov constant that correlates the spectral distribution of turbulent kinetic energy with the turbulent dissipation rate. Compilation of a large number of experimental data for different flow configurations has revealed that the Kolmogorov constant is independent of Reynolds number in the limit of high Reynolds number (Sreenivasan, Phys. Fluids, vol. 7, no. 11, 1995, pp. 2778–2784). However, several numerical studies, majorly in the area of multiphase flows at low and intermediate Reynolds numbers, consider that the Kolmogorov constant remains unchanged irrespective of whether the flow is single phase or multiphase. In this article, we assess the variation of local isotropy of the fluid fluctuations with the increase in particle loading in particle-laden turbulent channel flows. We also estimate the Kolmogorov constant using second-order velocity structure functions and compensated spectra in the case of low-Reynolds-number turbulent flows. Our study reveals that the Kolmogorov constant decreases in the channel centre with an increase in the particle volume fraction for the range of Reynolds numbers investigated here. The estimated variation of the Kolmogorov constant is used to express the Smagorinsky coefficient as a function of solid loading in particle-laden flows. Then, a new modelling technique is adopted using the large-eddy simulation (LES) to predict the fluid phase statistics without solving simultaneous particle phase equations. The new methodology also helps to qualitatively understand the phenomena of drastic collapse in turbulence intensity.

How electrostatic forces affect particle behaviour in turbulent channel flows

In dispersed two-phase flows, particle electrification is a prevalent phenomenon that plays a crucial role in particle transport. However, the influences of electrostatic forces on particle behaviour in wall-bounded turbulent flows, especially in bidisperse cases, is not well understood. In this study, using direct numerical simulations based on a coupled Eulerian–Lagrangian point-particle approach at friction Reynolds number $Re_\tau =550$ , we demonstrate that when the electrostatic Stokes number is of the order of $O(10^{-1})$ , electrostatic forces could considerably alter particle behaviour in both monodisperse and bidisperse particle-laden turbulent channel flows. Specifically, the wall-normal profiles of the particle concentration are determined by the competition of turbophoresis, biased sampling and electrostatic effects. The electrostatic forces are found to reduce the concentrations of lighter particles by electrostatic drift directly, whereas they alter those of heavier particles by strengthening turbophoresis indirectly. With increasing electrical charge, the dynamics of the lighter particles remains approximately unchanged, but that of the heavier particles is modulated significantly due to their relatively strong particle–electrostatic interaction. In the near-wall region, electrostatic forces tend to homogenize the distribution of lighter particles in the spanwise direction by inhibiting the formation and destruction of particle clusterings and voids, thereby maintaining the anisotropic streaky clusterings. Furthermore, even though the clustering dynamics remains unchanged, the spatial extents of the clusterings at the channel centreline are suppressed (enhanced) by a factor of two, probably due to the remarkable reduction (increase) of particle concentration in this layer.

Effect of channel dimensions and Reynolds numbers on the turbulence modulation for particle-laden turbulent channel flows

The addition of particles to turbulent flows changes the underlying mechanism of turbulence and leads to turbulence modulation. The important parameters are particle Stokes number, mass loading, particle Reynolds number, fluid bulk Reynolds number, etc., that act together and affect the fluid phase turbulence intensities. In the present study, simulations are carried out for different system sizes (2δ/dp=54,81, and 117) and fluid bulk Reynolds numbers (Reb = 5600 and 13 750) to quantify the extent of turbulence attenuation. Here, δ is the half-channel width, dp is the particle diameter, and Reb is the fluid Reynolds number based on the fluid bulk velocity and channel width. Our study shows that system size and fluid bulk Reynolds number are the two crucial parameters that affect the particle feedback force and turbulence modulation more significantly than the other. The extent of turbulence attenuation increases with an increase in system size for the same volume fraction while keeping the Reynolds number fixed. However, for the same volume fraction and fixed channel dimension, the extent of attenuation is low at a higher Reynolds number. The streamwise turbulent structures are observed to become lengthier and fewer with an increase in system size for the same volume fraction and fixed bulk Reynolds number. However, the streamwise high-speed streaks are smaller, thinner, and closely spaced for higher Reynolds numbers than the lower ones for the same volume fraction. Particle phase velocity statistics for different cases have also been reported.

Analysis and Discussion of Two-Way Coupling Effects in Particle-Laden Turbulent Channel Flow

This paper studies the turbulence modification caused by the presence of solid particles in fully developed channel flow by means of the point particle Direct Numerical Simulations (DNS) approach. Inertial particles much smaller than the smallest vortical flow structures are considered, maintaining a volume fraction of the order , where inter-particle collisions are rare and have nearly no influence on flow development. To avoid concurrent effects that could mask the analysis of fluid turbulence interaction, gravity is not included in the study, and particle-smooth wall collisions are modelled as ideal reflections. The alteration of fluid turbulence dynamics by the particles is illustrated and discussed, providing an overview of the fluid-particle interaction phenomena occurring at both microscopic and macroscopic flow levels. Finally, the relation of such phenomena with drag-reducing effects by particles is demonstrated.

Dynamics of particle-laden turbulent Couette flow: Turbulence modulation by inertial particles

In particle-laden turbulent flows, it is established that the turbulence in the carrier fluid phase gets affected by the dispersed particle phase for volume fractions above 10−4. Hence, reverse coupling or two-way coupling becomes relevant in that volume fraction regime. Due to their greater inertia, larger particles change either the mean flow or the intensity of fluid-phase fluctuations. In a recent study [Muramulla et al., “Disruption of turbulence due to particle loading in a dilute gas–particle suspension,” J. Fluid Mech. 889, A28 (2020)], a discontinuous decrease of turbulence intensity is observed in a vertical particle-laden turbulent channel flow for a critical volume fraction O(10−3) for particles with varying Stokes numbers (St) in the range of 1−420 based on the fluid-integral time scales. The collapse of turbulent intensity is found out to be the result of a “catastrophic reduction of turbulent energy production rate.” Mechanistically, a turbulent Couette flow differs from a pressure-driven channel flow in many ways, such as fluid-phase mean-velocity profile and turbulent coherent structures. In the particle-laden Couette flow, particles are treated as neutrally buoyant. Therefore, it is worth investigating the mechanism of turbulence modulation by inertial particles in the particle-laden turbulent Couette flow. In this article, the turbulence modulation in the fluid phase in the presence of inertial particles is investigated using two-way coupled direct numerical simulations of a particle-laden sheared turbulent suspension. The particle volume fraction (ϕ) is varied from 1.75×10−4 to 1.05×10−3 and the Reynolds number based on the half-channel width (δ) and the wall velocity (U) (Reδ) is 750. The particles are of high inertia with St∼367 based on a fluid integral timescale represented by δ/U. A discontinuous decrease in turbulence intensity and Reynolds stress is observed beyond a critical volume fraction ϕcr∼7.875×10−4. The drastic reduction of shear production of turbulence leads to the collapse of fluid-phase turbulence. The stepwise particle injection and stepwise removal study confirm the role of critical volume loading in the discontinuous transition. Additionally, the effect of the nature of particle–particle and particle–wall collisions has been investigated. It is observed that the inelastic collisions increase the ϕcr marginally although the nature of turbulence modulation remains similar. The explicit role of the inter-particle collisions has also been investigated by switching off the particle–particle collisions. In this case, ϕcr increases more than in the case of an inelastic collision. The turbulence modulation carries the signatures of transition from sheared turbulence to particle-driven fluid fluctuation at higher volume loading.

On the existence and formation of multi-scale particle streaks in turbulent channel flows

Direct numerical simulations of particle-laden turbulent channel flows at friction Reynolds number $Re_\tau$ from $600$ to $2000$ have been performed to examine the near-wall particle streaks. Different from the well-observed small-scale particle streaks in near-wall turbulence of low $Re_\tau$ , the present results show large-scale particle streaks through the computational domain formed for relatively high-inertia particles at high $Re_\tau$ . Transferred by large-scale sweep and ejection events ( $Q^-$ ), these high-inertia particles preferentially accumulate in near-wall regions beneath the large-scale low-speed flow streaks observed in the logarithmic region. The corresponding Stokes numbers are associated with the lifetime of large-scale $Q^-$ structures, which increases as the Reynolds number grows. The small-scale particle streaks with a typical Stokes number $St_\nu \approx 30$ are mainly driven by the $Q^-$ structures in the buffer layer, whose lifetime is approximately $30$ in viscous time unit. Therefore, we propose a new structure-based Stokes number normalized by the lifetime of $Q^-$ structures of different scales. The relevant flow scales that control the formation of the large-scale particle streaks are parameterized by the structure-based Stokes number. The small-scale (large-scale) particle streaks are most prominent when the buffer-layer (large-scale) structure-based Stokes number approaches unity. The present findings reveal that formation of near-wall particle streaks is governed by the $Q^-$ structures of different scales, and the particles with different inertia respond efficiently to the $Q^-$ structures of corresponding scales with respect to the particle translational motion.

Influence of Particle Mass Fraction over the Turbulent Behaviour of an Incompressible Particle-Laden Flow

The presence of spherical solid particles immersed in an incompressible turbulent flow was numerically investigated from the perspective of the particle mass fraction (PMF or ϕm), a measure of the particle-to-fluid mass ratio. Although a number of different changes have been reported to be obtained by the presence of solid particles in incompressible turbulent flows, the present study reports the findings of varying ϕm in the the turbulent behaviour of the flow, including aspects such as: turbulent statistics, skin-friction coefficient, and the general dynamics of a particle-laden flow. For this purpose, a particle-laden turbulent channel flow transporting solid particles at three different friction Reynolds numbers, namely Reτ=180, 365, and 950, with a fixed particle volume fraction of ϕv=10−3, was employed as conceptual flow model and simulated using large eddy simulations. The value adopted for ϕv allowed the use of a two-way coupling approach between the particles and the flow or carrier phase. Three different values of ϕm were explored in this work ϕm≈1,2.96, and 12.4. Assessment of the effect of ϕm was performed by examining changes of mean velocity profiles, velocity fluctuation profiles, and a number of other relevant turbulence statistics. Our results show that attenuation of turbulence activity of the carrier phase is attained, and that such attenuation increases with ϕm at fixed Reynolds numbers and ϕv. For the smallest Reynolds number case considered, flows carrying particles with higher ϕm exhibited lower energy requirements to sustain constant fluid mass flow rate conditions. By examining the flow velocity field, as well as instantaneous velocity components contours, it is shown that the attenuation acts even on the largest scales of the flow dynamics, and not only at the smaller levels. These findings reinforce the concept of a selective stabilising effect induced by the solid particles, particularly enhanced by high values of ϕm, which could eventually be exploited for improvement of energetic efficiency of piping or equivalent particles transport systems.

Turbulence modulation by finite-size heavy particles in a downward turbulent channel flow

Interface-resolved direct numerical simulations of downward particle-laden turbulent channel flows are performed by using a direct-forcing fictitious domain method. The effects of the particle settling coefficient, the density ratio (2, 10, and 100), and the particle size on fluid-turbulence interactions are investigated at a bulk Reynolds number of 5746 and a particle volume fraction of 2.36%. Our results indicate that the significant particle-induced reduction in the turbulence intensity does not take place for the downflow at a low density ratio of 2, and the turbulence intensity generally increases with an increasing particle Reynolds number at the same other control parameters, unlike the upflow case. The total turbulent kinetic energy (TKE) in the channel is larger for the downflow than for the upflow at the same particle Reynolds number, whereas the TKE at the channel center is roughly independent of the flow direction when the particle inertia is very large. For a density ratio of 2, the particles aggregate and are preferentially located in the low-speed streaks in the near-wall region, whereas for a density ratio of 10, the particles migrate toward the channel center, similar to the zero-gravity case. The flow friction increases with an increasing settling coefficient for the same density ratio and particle size, and the friction at the density ratio of order (10) is smallest. The pair distribution function shows the transition from the turbulence-dominated feature to the sedimentation-dominated feature, as the settling coefficient increases.

Effects of the quiescent core in turbulent channel flow on transport and clustering of inertial particles

The existence of a quiescent core (QC) in the center of turbulent channel flows was demonstrated in recent experimental and numerical studies. The QC-region, which is characterized by relatively uniform velocity magnitude and weak turbulence levels, occupies about 40% of the cross-section at Reynolds numbers Reτ ranging from 1000 to 4000. The influence of the QC region and its boundaries on transport and accumulation of inertial particles has never been investigated before. Here, we first demonstrate that a QC is unidentifiable at Reτ=180, before an in-depth exploration of particle-laden turbulent channel flow at Reτ=600 is performed. The inertial spheres exhibited a tendency to accumulate preferentially in high-speed regions within the QC, i.e. contrary to the well-known concentration in low-speed streaks in the near-wall region. The particle wall-normal distribution, quantified by means of Voronoï volumes and particle number concentrations, varied abruptly across the QC-boundary and vortical flow structures appeared as void areas due to the centrifugal mechanism. The QC-boundary, characterized by a localized strong shear layer, appeared as a barrier, across which transport of inertial particles is hindered. Nevertheless, the statistics conditioned in the QC-frame show that the mean velocity of particles outside of the QC was towards the core, whereas particles within the QC tended to migrate towards the wall. Such upward and downward particle motions are driven by similar motions of fluid parcels. The present results show that the QC exerts a substantial influence on transport and accumulation of inertial particles, which is of practical relevance in high-Reynolds number channel flow.

Effects of the collision model in interface-resolved simulations of particle-laden turbulent channel flows

The effects of the particle collision model in a direct-forcing fictitious domain method on the fluid and particle statistics of a fully developed turbulent channel flow laden with finite-size neutrally buoyant particles are numerically investigated. The particle collisions are described by a combination of the discrete element method and the lubrication force correction model. We first validate our code via several benchmark tests, including the normal particle–wall collisions at different impact Stokes numbers and the oblique collisions with varied incidence angles. Subsequently, the effects of the lubrication correction and the particle stiffness on the fluid and particle statistics of the particle-laden turbulent flows are examined. The results show that the lubrication force correction has an important effect on the particle pair statistics at the near-contact regime. Both the lubrication force between the particles and the decrease in the particle stiffness result in the decrease in the flow friction mainly due to the increase in the fluid Reynolds stress. The flow friction is always larger for smaller particles at the same particle volume fraction irrespective of the lubrication correction. The particle–particle lubrication force decreases the near-wall particle concentration, whereas the particle–wall lubrication force has the opposite effect.

A correction scheme for wall-bounded two-way coupled point-particle simulations

The accuracy of Euler-Lagrange point-particle models employed in particle-laden fluid flow simulations depends on accurate estimation of the particle force through closure models. Typical force closure models require computation of the slip velocity at the particle location, which in turn requires accurate estimation of the undisturbed fluid velocity. Such an undisturbed velocity is not readily available when the fluid and particle phases are two-way coupled, due to the disturbance created by the particle's force in the nearby fluid velocity field. A common practice is to use the disturbed velocity to compute the particle force which can result in errors as much as 100% in predicting the particle dynamics. In this work, a correction scheme is developed that facilitates accurate estimation of the undisturbed fluid velocity in particle-laden fluid flows with and without no-slip walls. The model is generic and can handle particles of different size and density, arbitrary interpolation and projection functions, anisotropic grids with large aspect ratios, and wall-bounded flows. The present correction scheme is motivated by the recent work of Esmaily & Horwitz (JCP, 2018) on unbounded particle-laden flows. Modifications necessary for wall-bounded flows are developed such that the undisturbed fluid velocity at any wall distance is accurately recovered, asymptotically approaching the result of unbounded schemes for particles far away from walls. A detailed series of verification tests was conducted on settling velocity of a particle in parallel and perpendicular motions to a no-slip wall. A range of flow parameters and grid configurations; involving anisotropic rectilinear grids with aspect ratios typically encountered in particle-laden turbulent channel flows was considered in detail. When the wall effects are accounted for, the present correction scheme reduces the errors in predicting the near-wall particle motion by one order of magnitude smaller values compared to the unbounded correction schemes.

Interface-resolved numerical simulations of particle-laden turbulent channel flows with spanwise rotation

Interface-resolved simulations of particle-laden turbulent channel flows with spanwise rotation at a Reynolds number of 180 and different rotation numbers ranging from 0.1 to 1.0 are performed with a fictitious domain method. The difficulty of the centrifugal force on the particles not satisfying the periodic boundary condition is circumvented by the feature of the fictitious domain formulation for the neutrally buoyant case, where the centrifugal force in the particle motion equation vanishes, and by only considering a low rotation number of 0.1 and setting the rotation center to be far away from the channel for the non-unity density ratio case. Our results show that the heavy particles (i.e., the particle density being larger than the fluid density) migrate towards the pressure wall, whereas the light particles migrate towards the suction wall. For the density ratio being unity, the particle concentration is higher near the pressure wall than near the suction wall, and we attribute the reason to the effects of the mean secondary flow structure (i.e., the Taylor–Görtler vortices), since similar particle concentration distribution and secondary flow structure are observed in a rotating laminar channel flow. The mean velocities of heavy particles are smaller in the pressure-side half channel except the near-wall region, and larger in the suction-side half channel, compared to the fluid mean velocity; the opposite occurs for the light particle case. The addition of the finite-size particles increases the flow drag. The flow drag is not sensitive to the density ratio for the light particles and increases with increasing density ratio for the heavy particles. The effects of the particles on the fluid root-mean-square velocities of the rotating turbulent channel flow are generally similar to the non-rotating channel case, but become more complicated because of the asymmetric turbulence intensity and particle concentration distribution near two walls caused by the channel rotation.

Mitigation of turbophoresis in particle-laden turbulent channel flows by using incident electric fields

The influence of electric forces on inertial particles in turbulent channel flows is explored using direct numerical simulations. It is found that the near-wall buildup of particle concentration due to turbophoresis can be reduced up to 2 orders of magnitude by imposing an ac electric field.

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.

A direct numerical investigation of two-way interactions in a particle-laden turbulent channel flow

Understanding the two-way interactions between finite-size solid particles and a wall-bounded turbulent flow is crucial in a variety of natural and engineering applications. Previous experimental measurements and particle-resolved direct numerical simulations revealed some interesting phenomena related to particle distribution and turbulence modulation, but their in-depth analyses are largely missing. In this study, turbulent channel flows laden with neutrally buoyant finite-size spherical particles are simulated using the lattice Boltzmann method. Two particle sizes are considered, with diameters equal to 14.45 and 28.9 wall units. To understand the roles played by the particle rotation, two additional simulations with the same particle sizes but no particle rotation are also presented for comparison. Particles of both sizes are found to form clusters. Under the Stokes lubrication corrections, small particles are found to have a stronger preference to form clusters, and their clusters orientate more in the streamwise direction. As a result, small particles reduce the mean flow velocity less than large particles. Particles are also found to result in a more homogeneous distribution of turbulent kinetic energy (TKE) in the wall-normal direction, as well as a more isotropic distribution of TKE among different spatial directions. To understand these turbulence modulation phenomena, we analyse in detail the total and component-wise volume-averaged budget equations of TKE with the simulation data. This budget analysis reveals several mechanisms through which the particles modulate local and global TKE in the particle-laden turbulent channel flow.

Turbulent flow of finite-size spherical particles in channels with viscous hyper-elastic walls

We study single-phase and particle-laden turbulent channel flows bounded by two incompressible hyper-elastic walls with different deformability at bulk Reynolds number $5600$. The solid volume fraction of finite-size neutrally buoyant rigid spherical particles considered is $10\,\%$. The elastic walls are assumed to be of a neo-Hookean material. A fully Eulerian formulation is employed to model the elastic walls together with a direct-forcing immersed boundary method for the coupling between the fluid and the particles. The data show a significant drag increase and the enhancement of the turbulence activity with growing wall elasticity for both the single-phase and particle-laden flows when compared with the single-phase flow over rigid walls. Drag reduction and turbulence attenuation is obtained, on the other hand, with highly elastic walls when comparing the particle-laden flow with the single-phase flow for the same wall properties; the opposite effect, drag increase, is observed upon adding particles to the flow over less elastic walls. This is explained by investigating the near-wall turbulence, where the strong asymmetry in the magnitude of the wall-normal velocity fluctuations (favouring positive $v^{\prime }$), is found to push the particles towards the channel centre. The particle layer close to the wall contributes to turbulence production by increasing the wall-normal velocity fluctuations, so that in the absence of this layer, smaller wall deformations and in turn turbulence attenuation is observed. For a moderate wall elasticity, we increase the particle volume fraction up to $20\,\%$ and find that particle migration away from the wall is the cause of turbulence attenuation with respect to the flow over rigid walls. However, for this higher volume fractions, the particle induced stress compensates for the decreasing Reynolds shear stress, resulting in a higher overall drag for the case with elastic walls. The effect of the wall elasticity on the overall drag reduces significantly with increasing particle volume fraction.