Particle-laden Turbulent Flow Research Articles

Particle transport and turbulence modification in unstably stratified mixed convection within a horizontal channel

Particle transport and turbulence modification in an unstably stratified, particle-laden turbulent flow within a horizontal channel is studied via direct numerical simulations combined with Lagrangian point‒particle tracking techniques. Two-way coupling in momentum and energy is considered in dilute gas‒solid flows under mixed convection (synergistic effects of shear and buoyancy). For comparison, simulations of neutral turbulence are also conducted with equivalent parameters. The study reveals that large-scale longitudinal vortical structures induce significant spatial heterogeneity in the spanwise distribution of inertial particles. This heterogeneity is characterized by an increase in the particle concentration on the side of the cold plume and a corresponding decrease on the side of the hot plume. In the context of unstably stratified turbulence, particles reduce the fluid streamwise velocity and promote its profile toward symmetry. This phenomenon contrasts with that observed in neutral flows, where particles induce velocity asymmetry by dragging the upper flow and accelerating the lower flow. A quantitative analysis of the heat flux indicates that particles absorb heat as they settle, thereby reducing the average temperature of the flow. Buoyancy effects slow the settling and reinjection of particles, which in turn diminishes thermal energy absorption. Particles with higher inertia preferentially settle on the cooler plume side, minimizing their participation in heat exchange due to prolonged durations of repeated wall collisions.

Effect of secondary flow and wall collisions on particle-laden flows in 90° pipe bends

Fully developed, statistically stationary particle-laden turbulent flows in a 90° pipe bend at a moderate Reynolds number are studied using direct numerical simulation coupled to a Lagrangian particle tracking technique. Three populations of particles are studied which are two-way coupled with the carrier phase. The focus is the investigation of the effect of strong curvature on particle transport dynamics across a range of particle inertias. A validation of the carrier phase predictions is performed, with good agreement found with available experimental data. It is demonstrated that the presence of particles notably affects the turbulence statistics of the carrier phase, decreasing the mean fluid velocity in the outer bend while slightly increasing it in the inner bend. Two intriguing phenomena emerge: the presence of a particle void near the inner bend and reflection layers near the outer bend. Centrifugal forces are responsible for driving particles to the outer wall, with some rebounding back into the main body of the flow, and others, influenced by the secondary flow in the plane of the pipe cross-section, converging towards the inner wall before re-entering the central pipe region. These effects dictate the size and shape of the particle void region and the formation of reflection layers due to particle-wall collisions. These two phenomena have a significant influence on the particle distribution in the pipe bend, as well as on the first- and second-order moments of the velocity and acceleration of the particulate phase. Finally, a heat map of particle-wall collision statistics indicates that the effect of the secondary flow on particle distribution and particle-wall collisions is not negligible.

Numerical and experimental approach for dust dispersion and deposition behavior for safe decommissioning activities

ABSTRACT The use of high-fidelity modeling is a promising technique for studying the mechanisms of dust dispersion and deposition in safe decommissioning operations. Detailed multiphysics models for poly-dispersed turbulent flow, particle-laden flow, and particle surface interaction were coupled with a Reynolds Averaged Navier Stokes method for numerical simulation of dust dispersion and deposition. A model that considered the critical viscosity was utilized to estimate the interaction between particles and substrate. The deposition behavior of particles was a result of the competition between adhesion and rebound probabilities during the impact process, and only when the critical viscosity exceeded that of the impacting particles could they attach to the surfaces. To validate the accuracy of the simulation results, deposition experiments using zirconia particles were conducted. The experimental setup included a 3.2 m polycarbonate pipe, a fan regulated by an inverter to control the flow, an ultra-low penetration air filter capable of capturing particles with a minimum diameter of 120 nanometers. An air pump connected to a particle tank and a mixing tank was used for homogenizing the injection of particles. Particle concentration was measured during the experiments using a light scattering spectrometer system, WELASⓇ 2000, from the manufacturer PalasⓇ. This optical measurement technique functioned with a white light source and scattered light detection. The scattered light was collected via optical fibers, which led to the control and evaluation point, and results were displayed through special software. The numerical simulation results were compared with the experimental data and used to validate the numerical approach for flow with zirconia particles deposited on various material surfaces, including iron, titanium, stainless steel 304, and stainless steel 316, for airflow rates ranging from 54 L/min to 124 L/min.

Temperature statistics of settling particles in homogeneous isotropic turbulence

Heat transfer of settling particles in homogeneous isotropic turbulence is investigated in one-way coupled Eulerian–Lagrangian direct numerical simulations. In the absence of gravity, our observations highlight that there was a correlation between particles concentration and temperature fronts, which are characterized by high-temperature gradients. The particle clustering is mainly influenced by the preferential concentration and the non-local effect, the latter being the memory of their interaction with the flow along their trajectories. Nevertheless, gravity significantly affects the clustering of particles, which further influence the heat transfer of particles with the fluid. We find that the heat transfer of particles is intricately related to particle dynamic inertia and thermal inertia, which can be quantified by the particle Stokes number St and particle thermal Stokes number Stθ, respectively. In this study, we observe that the variance of particle temperature rate of change is independent of Stθ at small thermal inertia but inversely proportional to Stθ2 for large thermal inertia. In the presence of gravity, the variance converges to Stθ−1 for particles with negligible thermal inertia. Our findings reveal that the second-order structure function of the particle temperature, indicating the enhancement of Lagrangian scalar intermittency, adheres to a power-law behavior with limited thermal inertial particles in the dissipation region, denoted as r2. However, as Stθ increases, the power law of the structure function of the particle temperature is disrupted leading to ‘thermal caustics’. The present findings of the heat transfer behavior of settling particles advance the understanding of gravity effect, and are valuable for the modeling of heat transfer in particle-laden turbulent flows.

A fully-resolved LBM-LES-DEM numerical scheme for adhesive and cohesive particle-laden turbulent flows in three dimensions

Adhesive and cohesive particle-laden turbulent flows play a crucial role in numerous natural and industrial processes. Herein, a fully-resolved LBM-LES-DEM numerical scheme is developed for a better understanding of these flows in three dimensions. This numerical scheme is four-way coupling, where the adhesive and cohesive forces, such as van der Waals force, capillary force and viscous force, are embedded into DEM to simulate adhesive and cohesive particle-particle interactions, and the MRT-D3Q19 LBM is combined with LES based on the Smagorinsky model to simulate turbulent fluid flows, and the fluid-particle interactions are solved by momentum exchange method. Several benchmarks, such as 3D duct flow, single particle settling, and DKT processes, are validated, and the dynamics of particle pair in turbulent structures are further discussed. All the results indicate that this numerical scheme provides a promising method for the simulation of adhesive and cohesive particle-laden turbulent flows.

Numerical study of turbulent heat transfer and particle deposition in enhanced pipes with helical roughness

Large-eddy simulations of turbulent heat transfer and solid particle deposition in helically rib-roughened pipe flows have been performed for different Reynolds numbers Re and various particle diameters Dp. An Euler–Lagrange approach, using cyclic boundary conditions for the continuous and the dispersed phase, have been applied to achieve a fully developed turbulent flow. An adhesion and removal model have been added to the multiphase large-eddy simulations to take into account the physical effect of particle re-entrainment. The complex interactions between particle-laden turbulent flow and the structured pipe wall in multiple-started helically ribbed pipes are numerically investigated with regard to heat transfer, pressure loss, and particulate deposition. The results of the Nusselt numbers Nu, friction factors fd, and particle deposition rates Ṅd are presented for each geometry variant. For same Reynolds numbers Re, significant differences of those values have been observed for the differently structured pipes.

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 Role of Particle Inertia and Thermal Inertia in Heat Transfer in a Non-Isothermal Particle-Laden Turbulent Flow

We present an analysis of the effect of particle inertia and thermal inertia on the heat transfer in a turbulent shearless flow, where an inhomogeneous passive temperature field is advected along with inertial point particles by a homogeneous isotropic velocity field. Eulerian–Lagrangian direct numerical simulations are carried out in both one- and two-way coupling regimes and analyzed through single-point statistics. The role of particle inertia and thermal inertia is discussed by introducing a new decomposition of particle second-order moments in terms of correlations involving Lagrangian acceleration and time derivative of particles. We present how particle relaxation times mediate the level of particle velocity–temperature correlation, which gives particle contribution to the overall heat transfer. For each thermal Stokes number, a critical Stokes number is individuated. The effect of particle feedback on the attenuation or enhancement of fluid temperature variance is presented. We show that particle feedback enhances fluid temperature variance for Stokes numbers less than one and damps is for larger than one Stokes number, regardless of the thermal Stokes number, even if this effect is amplified by an increasing thermal inertia.

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.

Particle transport in turbulent square duct flows with a free surface

Direct numerical simulation combined with a one-way coupled Lagrangian particle tracking technique is employed to investigate dilute particle-laden turbulent flows in open square ducts with a free surface. The focus is on examining the influence of the mean cross-stream secondary flow on particle transport near the wall, free surface, and across the duct cross section. Based on the duct half-width and mean friction velocity, a shear Reynolds number of Reτ = 300 is considered, with the corresponding particle Stokes numbers ranging from St+ = 0.31 to 260. The results reveal that particle concentration near the sidewalls is lower than that near the bottom wall, and the minimum particle concentration is observed at the free surface. Along the bottom wall centerline orientated upward, particle concentration gradually decreases. An exception to this is in the vicinity of the free surface where a slight increase is observed for the heavier particles (St+ ≥ 25), and the amplitude of this increase gradually declines as the Stokes number increases. In the streamwise direction near the free surface, heavier particles tend to preferentially concentrate in regions where the instantaneous transverse secondary flow velocity is negative. As the Stokes number increases, the position of the maximum streamwise velocity for heavier particles is closer to the free surface, and the rotation centers of inner and outer secondary particle motions gradually disappear. The streamwise root mean square velocity for the lightest St+ = 0.31 particles is higher than that for particles with higher inertia in the middle region of the free surface.

Heat transport in a non-homothermal turbulent particle-laden flow in the collisional regime

In this investigation, we explore the impact of particle collisions on turbulent heat flux within a temporally developing thermal mixing layer arising from the interaction of two homothermal regions driven by a statistically homogeneous and isotropic velocity field. Employing two-way thermally coupled Eulerian-Lagrangian Direct Numerical Simulations (DNSs) at a Taylor microscale Reynolds number up to 124, we examine the influence of particle collisions for a Stokes number from 0.2 to 3, maintaining a fixed thermal to kinetic relaxation times ratio of 4.43. Our study quantifies the reduction in average heat transport induced by particle-to-particle collisions, which disrupt the temperature-velocity correlation created by the initial temperature difference. Notably, while collisions diminish this correlation, our analysis reveals their overall impact remains minor, even at the highest simulated Stokes number. Additionally, we present statistics of the temperature difference among colliding particles across various flow conditions.

Experimentally trained hybrid machine learning algorithm for predicting turbulent particle-laden flows in pipes

A hybrid learning algorithm consisting of a preprocessor, a k-nearest neighbors regressor, a noise generator, and a particle–wall collision model is introduced for predicting features of turbulent single-phase and particle–liquid flows in a pipe. The hybrid learning algorithm has the ability to learn and predict the behavior of such complex fluid dynamic systems using experimental dynamic databases. Given a small amount of typical training data, the algorithm is able to reliably predict the local liquid and particle velocities as well as the spatial distribution of particle concentration within and without the limits of the range of training data. The algorithm requires an order of magnitude less training data than a typical full set of experimental measurements to give predictions on the same level of accuracy (typically, 20 cf. 100 trajectories for phase velocity distribution and 40 cf. 500 trajectories for phase concentration distribution), thus leading to huge reductions in experimentation and simulation. A feature importance analysis revealed the effects of the different experimental variables on the particle velocity field in a two-phase particulate flow, with particle–liquid density ratio and particle vertical radial position being the most influential and particle concentration the least. The algorithm is amenable to extension by using more complex databanks to address a much more comprehensive range of flow situations.

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.

Underwater noise from submarine turbidity currents

Submarine landslides and associated turbidity currents can be orders of magnitude larger than their terrestrial equivalents. Their prevalence globally is hugely underrepresented by in situ observations. In addition to their importance in mass transport and morphologic change they can pose significant threat to coastal communities and subsea infrastructure. This presentation focusses on noise measurements from turbidity currents flowing down the face of a fjord delta and how they can inform the use of passive acoustics as a tool for future observations of these under sampled phenomena. Noise was measured underwater at frequencies from 1 to 1200 kHz. The noise spectra are consistent with sound generation by collisions among sand-sized particles within the turbidity current, also known as acoustic sediment-generated noise or SGN. The spectra from the leading head of the current extend to higher frequencies than those from the trailing body, indicating that collisions were between finer-grained particles in the head and coarser-grained particles in the body. Noise intensity increased 100-fold for a two-fold increase in current head speed, consistent with the expected collision rate for granular materials in the high-flow gas-like phase and highly turbulent particle-laden flows.

Simulation of multiphase flow in pipes with simplified models of deposited beds

Turbulent particle-laden flows in pipes can result in particle deposition leading to the formation of solid beds. The presence of such beds modifies the flow field, resulting in secondary motions in the plane of the pipe cross-section, which in turn impact particle transport. In this work turbulent pipe flows with equal mass flow rates and solid beds of height Hb = 0 (full pipe), 0.5R (three-quarter pipe), and R (half pipe) are predicted using direct numerical simulation, with the beds represented simplistically as flat surfaces. The particulate phase is one-way coupled to the flow at a volume fraction of 10−3 and particle motion is solved for using a Lagrangian point-particle approach. The Reynolds numbers computed based on bulk velocity and equivalent pipe diameter for the full, ¾ and, ½ pipes are 5,300, 5,909 and 7,494, respectively. The same particle size is used in all the simulations and their respective Stokes numbers, based on the shear timescale, are 0.5, 1.2 and 1.9, respectively. The results for flows with beds show that the fluid flow exhibits secondary vortices and an increase in the mean streamwise vorticity caused by corners in the cross-sectional plane of the pipes, with their intensity near the upper curved wall increasing with Hb. However, the upper vortices remain relative weak compared to those in lower regions of the pipes. The increase in mean streamwise vorticity in the half pipe is larger than that in the three-quarter pipe near the upper curved wall, while similar near the flat pipe floor due to the resistance of the curved wall to secondary motions. The movement of the particles in the cross-sectional plane is consistent with that of the secondary flows, but with slightly lower velocities. In regions near the wall away from the pipe corners, particle concentration in the half pipe is lower than in the three-quarter pipe, most likely due to its thinner boundary layer. This is reversed for concentration maxima near the pipe corners because of the magnitude of the secondary flows. Finally, the secondary flow changes the deposition or resuspension rate of the particles, particularly near the pipe corners, but these are always less than equivalent rates in the full pipe flow, which is likely caused by the magnitude of the wall unit.

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.

Insight into the particle-laden turbulent flow statistics in sharply bent channels

In canonical wall-bounded flows, point particle-laden turbulence exhibits a substantial interaction between scales with a variety of regimes, and the dynamics of the point particle-laden fluid are primarily identified by the Reynolds number. Such interactions are even more augmented in curved channels with variable curvature, and fixed Reynolds numbers demonstrate distinct flow behavior, as shown by Brethouwer [J. Fluid Mech. 931, A21 (2022)]. In this work, we demonstrate the characteristics of wall-bounded point particle-laden turbulent flows in sharply bent channels by evaluating the time-averaged velocity profiles at the straight section, at the bend, and in the inclined sections. The mean (time-averaged) normalized velocity profiles retain their well-known logarithmic features, with the von Kármán and additive constants taking different values depending on the acute inclination of the bend. Near-wall fluctuations at the bend are found to be intensified due to the bend that leads to increased turbulent activity. On examining the friction Reynolds number along the bent channel walls in the streamwise direction, a modulated behavior with an abrupt change at the bend is observed. Budgets of turbulent kinetic energy (TKE) are delineated for various inclinations of the bend at different sections of the channel and are compared with the unladen sharply bent turbulent channel flows, which illustrate that TKE is modulated at the bend and there is an overall attenuation of TKE on loading the channel with point particles.

Large eddy simulation model for two-way coupled particle-laden turbulent flows

Large eddy simulation model for two-way coupled particle-laden turbulent flows

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.