Preferential Concentration Of Particles Research Articles

Spectral characteristics of particle preferential concentration in turbulence computed by Eulerian and Lagrangian methods

This study conducts a comprehensive analysis of the Fourier spectra characteristics of particle preferential concentration in turbulent flows obtained by Eulerian and Lagrangian modelling approaches for different Stokes numbers. Particle preferential concentration is characterized by clusters and voids in the spatial particle distributions formed in turbulent flows and can significantly influence processes such as droplet coalescence, evaporation, and gas-particle reactions. The research primarily focuses on comparing the performance of two Eulerian models—one with and one without second-order velocity moments—and one Lagrangian model, which are used to predict particle dispersion. Key findings include the impact of artificial diffusion in Eulerian methods, the superiority of methods incorporating second-order velocity moments contributions at higher Stokes numbers, and the sensitivity of the Lagrangian method to Poisson statistics. Notably, the study reveals minimal variation in mean velocity spectra across different Stokes numbers, as opposed to the marked variations in particle concentration, momentum, and energy spectra. Grid resolution emerges as a crucial factor in enhancing spectral energy predictions in Eulerian methods. The research underscores the nuanced distinctions between Eulerian and Lagrangian methods in modelling preferential concentration, providing a detailed spectral comparison of particle concentration, velocity, momentum, and energy, highlighting the importance of method selection based on specific modelling needs.

On the Preferential Concentration of Particles in Turbulent Channel Flow: The Effect of the Added-Mass Factor

Preferential concentration, observed in turbulent flows when particle response times are of the same order of the flow’s characteristic timescales, manifests as non-uniform particle distributions in space. Unraveling its governing mechanisms holds crucial implications for both natural and industrial processes reliant on particle-laden flows. Focusing on particles with small inertia, this study employs Direct Numerical Simulations coupled with Lagrangian particle tracking to investigate the influence of the added-mass factor on the preferential concentration of particles denser than the fluid in the one-way coupling regime. It is shown how the added-mass factor β affects particle distribution within the channel through the statistical correlations between particle concentration and typical descriptors of the flow topology. The results suggest that increasing values of β (corresponding to lighter particles) significantly reduce the effectiveness of turbophoresis in producing particle accumulation in the near-wall region. Resulting in a gradual decorrelation between particle concentration and both the strain-rate and the vorticity tensors, higher values of β lead to a more uniform particle distribution, regardless of the Stokes number.

Energization of Charged Test Particles in Magnetohydrodynamic Fields: Waves versus Turbulence Picture

Direct numerical simulations of three-dimensional compressible magnetohydrodynamic (MHD) turbulence have been performed in order to study the relation between wave modes and coherent structures and the consequent energization of test particles. Moreover, the question of which is the main mechanism of this particle energization is rigorously discussed. In particular, using the same initial conditions, we analyzed the nonlinear and linear evolution of a turbulent state along with the case of randomized phases. Then, the behaviors of the linear and nonlinear simulations were compared through the study of the time evolution of particle kinetic energy and preferential concentration. Also, spatiotemporal spectra were used to identify the presence of wave modes and quantify the fraction of energy around the MHD modes in linear and nonlinear simulations. Finally, the variation of the correlation time of the external forcing is studied in detail along with the effect on the particle energization (and clustering) and the presence of wave modes. More specifically, particle energization tends to decrease when the fraction of linear energy increases, supporting the idea that energization by structures is the dominant mechanism for particle energization instead of resonance with wave modes as suggested by Fermi energization theory.

A DNS study of pulverized coal combustion in a hot turbulent environment: Effects of particle size, mass loading and preferential concentration

In the present study, pulverized coal combustion in a hot turbulent environment is investigated using direct numerical simulation (DNS). The coal particles are tracked in the Lagrangian framework while the flow is solved in an Eulerian way. A model involving two competing reactions is used for describing the process of coal devolatilization. The volatile matter is treated as a postulated substance (CaHbOc) and a two-step global reaction mechanism for volatile combustion is adopted. The char combustion is modeled using a one-step global reaction model. The effects of various factors, such as particle size, mass loading and preferential concentration, on the combustion process of coal particles were explored. It was found that, the location of reaction zones appears more upstream and the volatile matter concentration is higher for the cases with smaller particles. The combustion modes were examined. It was shown that the contribution of premixed combustion decreases with increasing particle size while non-premixed combustion prevails in all cases. The increase of particle mass loading results in an increase of volatile matter mass fraction, which leads to higher heat release rate and combustion temperature. Through Voronoï analysis, the preferential concentration of particles was examined. It was found that the preferential concentration behavior of particles is more prominent when the particle Stokes number (St) is close to unity. The volatile matter concentration is higher when particles are preferentially concentrated, facilitating coal particles to ignite.

Preferential Concentration of Particles in Forced Turbulent Flows: Effects of Gravity

The impact of gravity on the particle preferential concentration is investigated by direct numerical simulations in an Eulerian–Lagrangian framework for a large range of Stokes numbers Stη=0.01∼4. For particles with small Stokes numbers such as Stη=0.01, the gravity has minor effects on the particle spatial distribution in the turbulence. With increasing Stη, stripped structures of the high number density of particles appear and expand along the gravity direction. Different evaluation methods of particle preferential concentration are discussed such as the spatial distribution, the box index, and the probability density function. The number density of particles in the accumulating regions reduced under the influence of gravity. The reduction becomes prominent for the particle cloud at Stokes number Stη≈1, especially in the clusters of high particle number density. For large Stokes number Stη, the slip velocity significantly increases due to the particle gravity. Due to the gravity, the particle concentration reduces globally, particularly in the low vorticity regions. For the Stokes number range explored in this paper, gravity has a considerable impact on the particle-turbulence interaction.

Role of density ratio on particle dispersion in a turbulent jet

The behavior of dispersed particles in a turbulent round jet is experimentally investigated. The role of particle-to-fluid density ratio ρp/ρf is analyzed by inspecting particle velocity fields and preferential concentration at four different ratios, from 0.7 to 19.3. The jet near-field region, i.e., up to X/D=11, is analyzed and compared to the unladen case. Particle-to-fluid density ratio is reported to have a strong impact on particle velocity field structure, in terms of jet transition and self-similar region as well as on turbulent fluctuations. Concentrations of particles show that increasing particle density corresponds to larger departure from uniformity. This occurrence is limited to the region X/D<5, where also the largest differences of average and fluctuating velocities with respect to the unladen case are measured.

Wall-bounded thermal turbulent convection driven by heat-releasing point particles

In this work we investigate the thermal convection driven by heat-releasing point particles. Three-dimensional direct numerical simulations are conducted for$1\times 10^7\le {\textit {Ra}} \le 1\times 10^{10}$and$0.01\le {\textit {St}} \le 10$, where the Rayleigh number${\textit {Ra}}$and Stokes number${\textit {St}}$measure the strengths of the heat releasing rate and the Stokes drag, respectively. A regime at intermediate Stokes numbers is identified with most particles accumulating into the top boundary layer region, while for other cases particles are constantly advected over the entire domain. For the latter state, the flow motions are stronger at the upper part of the domain. The thicknesses of both momentum and thermal boundary layers at the top plate follow the same scaling law with${\textit {Ra}}$and show minor dependences on${\textit {St}}$. The volume-averaged temperature and convective flux exhibit non-monotonic variations as${\textit {St}}$increases and reach their minimums at intermediate${\textit {St}}$. The fraction coefficient of heat flux, i.e. the ratio between the heat flux through the bottom plate and the total flux through both plates, shares the similar dependence on${\textit {St}}$as the convective flux. The relation between these scaling laws can be explained by using the global balance between the dissipation and convective flux. The scaling laws for the transition between different flow regimes are also proposed and agree with the numerical results. The preferential concentration of particles is observed for all cases and is strongest at intermediate Stokes numbers, for which multiscale clustering emerges with small clusters forming larger ones.

A Short Review on the Preferential Concentration of Particles in Fluid Flow

Particle laden fluid flows are important in many fields of application such as environmental, chemical, astrophysical, and biological flows. They are examples of multicomponent fluid flow where the dispersed component is transported within a carrier fluid, and the dynamics of the flow are mostly dictated by the carrier fluid. The dispersed phase generally consists of particles such as droplets, bubbles, sediments, or nanoparticles while the carrier phase is typically water, oil, and chemical and biological liquids. Preferential concentration is an important characteristic of such multicomponent fluid flow which is defined by a higher density of particles in local regions of flow based on local acceleration, vorticity, strain, and pressure. Due to the intrinsic challenges of dealing with turbulence, mixing, particle tracking, and inter-and intra-component interactions, these flows are complicated to model. Based on the mass ratio of the particles to the fluid, the particles exhibit different preferential concentration patterns. In this article, experimental and numerical works on the preferential concentration of dispersed particles in different fluid flow problems are reviewed and discussed.

Scale-dependent particle clustering in transitional wake flow

Dispersion and mixing of inertial point particles in the unsteady and three-dimensional wake of a circular cylinder at$Re=200$are investigated via one-way coupled simulations. The presence of streamwise-oriented vortical braids originating from the mode A instability in the transition regime has a profound impact on the particle dynamics and preferential concentration in the near wake. Particles trapped between the Kármán rollers and the streamwise braids form an inner layer of densely concentrated particles, while discrete particle clumps on the otherwise thin ribbon-like clusters between two consecutive Kármán rollers are another manifestation of the streamwise braids. The effect of particle inertia on the size of clusters and voids ascribed to centrifugal ejection is examined by volume-averaged Voronoï analysis. A distinct dependence on Stokes number ($Sk$) is seen at the cluster scale, whereas the void scale exhibits self-similarity. New physics-based threshold values of clusters and voids are distinctly different from the probability-distribution-based threshold at cluster scale. Increasing inertia is found to suppress particle acceleration more than deceleration. The particle velocity is further suppressed by the presence of the streamwise vortical braids. The effects of particle inertia vary non-monotonically in$Sk$with the strongest effect at$Sk=1$when most particles tend to reside in high-strain/low-vorticity regions.

Dynamic coupling between carrier and dispersed phases in Rayleigh–Bénard convection laden with inertial isothermal particles

We investigate the dynamic couplings between particles and fluid in turbulent Rayleigh–Bénard (RB) convection laden with isothermal inertial particles. Direct numerical simulations combined with the Lagrangian point-particle mode were carried out in the range of Rayleigh number $1\times 10^6 \le {Ra}\le 1 \times 10^8$ at Prandtl number ${Pr}=0.678$ for three Stokes numbers ${St_f}=1 \times 10^{-3}$ , $8 \times 10^{-3}$ and $2.5 \times 10^{-2}$ . It is found that the global heat transfer and the strength of turbulent momentum transfer are altered a small amount for the small Stokes number and large Stokes number as the coupling between the two phases is weak, whereas they are enhanced a large amount for the medium Stokes number due to strong coupling of the two phases. We then derived the exact relation of kinetic energy dissipation in the particle-laden RB convection to study the budget balance of induced and dissipated kinetic energy. The strength of the dynamic coupling can be clearly revealed from the percentage of particle-induced kinetic energy over the total induced kinetic energy. We further derived the power law relation of the averaged particles settling rate versus the Rayleigh number, i.e. $S_p/(d_p/H)^2{\sim} Ra^{1/2}$ , which is in remarkable agreement with our simulation. We found that the settling and preferential concentration of particles are strongly correlated with the coupling mechanisms.

Influence of particle-fluid density ratio on the dynamics of finite-size particles in homogeneous isotropic turbulent flows.

In this paper, direct numerical simulations of particle-laden homogeneous isotropic turbulence are performed using lattice Boltzmann method incorporating interpolated bounce-back scheme. Four different particle-fluid density ratios are considered to explore how particles with different particle-fluid density ratios respond to the turbulence. Overall particle dynamics in the homogeneous isotropic turbulence such as the Lagrangian statistics of single particle and the preferential concentration of particles are investigated. Results show that particle acceleration and angular acceleration are more intermittent than velocity and angular velocity for finite-size particles with different particle-fluid density ratios. The preferential concentration of particles is investigated using radial distribution function and Voronoï tessellation, and the preferential concentration is more profound for particles with two intermediate particle-fluid density ratios. The Voronoï analysis indicates that the distribution of Voronoï cells satisfy the log-normal distribution better than the gamma distribution. The mechanism of preferential concentration is analyzed using the sweep-stick mechanism and drift mechanism. Results show that although a higher probability of having particles located near the sticky points is found, the sticky mechanism is very weak for large density ratios. The particle clustering is then found to be better qualitatively described by the drift mechanism.

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

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

Direct numerical simulation of particle-laden turbulent boundary layers without and with combustion

In the present work, direct numerical simulations of non-reactive and reactive turbulent boundary layers laden with inert particles were performed to investigate the influences of combustion on particle motions in wall-bounded flows. It was found that the coherent vortical structures of turbulent boundary layers are significantly modified by combustion. The streamwise velocity of particles is enhanced, while the velocity fluctuation is reduced in the reactive case due to the relaminarization effects. The preferential concentration of particles in the reactive case was found to be attenuated based on both visualization and the Voronoi analysis. The particle concentration in the outer layer of the reactive case is reduced because of the thermal expansion effects. However, the concentration is increased in the near-wall regions. The quadrant analysis of the Reynolds stress component was applied to explain this behavior. It was revealed that the magnitude of the mean Reynolds stress component is attenuated as a result of relaminarization. The frequency of the sweep event is increased but that of the injection event is reduced in the near-wall regions, which is responsible for the high particle concentration near the wall of the reactive case. The present study improves fundamental understandings of particle behaviors in non-reactive and reactive turbulent boundary layers.

Effect of turbulence-driven secondary flow on particle preferential concentration and clustering in turbulent square duct flows

In this study, the preferential concentration and clustering of inertial particles in fully developed turbulent square duct flows are studied using large eddy simulations combined with Lagrangian approach, where the Reynolds number is equal to Reτ=600 (based on the mean friction velocity and duct full height), and the particle Stokes number ranges from 0.0007 to 1.16. The results obtained for duct flows are compared with those for channel flows under the same working conditions. Then, the effect of the secondary flow on the particle concentration in duct flows is investigated. The equation of particle motion is governed by the drag force, lift force, added mass force, pressure gradient force, and gravity. The inter-phase interaction that was considered includes one-way and two-way coupling. The simulations of a single phase are verified and in good agreement with the available literature data. For the discrete phase, particles in the duct flow are found to be more dispersed in the vertical direction compared with the channel flow. In near-wall regions, a small fraction of particles tends to accumulate in duct corners, forming stable particle streaks under the effect of the secondary flow. Meanwhile, most particles are likely to reside preferentially in the low-speed flow regions and form elongated particle streaks steadily in the middle region of duct or channel floors. The Voronoi diagram analysis shows that the near-wall secondary flows in the square duct could cause particle clusters to transfer from regions of high to low concentration, and this trend increases with particle size. In addition, two-way coupling is found to enhance the near-wall particle accumulation and to promote particles to form more elongated streaks than one-way coupling. Finally, the mechanism responsible for the particle preferential concentration in turbulent square duct flows is determined.

DNS of an Oblique Jet in a Particle-Laden Crossflow: Study of Solid Phase Preferential Concentration and Particle-Wall Interaction

A DNS study of the interaction between an oblique laminar jet and a particle-laden crossflow is presented. The delivery tube is included in the simulation and jet in crossflow blowing ratio is set equal to 0.5, typical for gas turbine film cooling applications. The solid phase is polydisperse and it is simulated by adopting a Lagrangian two-way coupling point-particle approach. Wall-particle interaction is also taken into account. The fluid flow in the jet outflow region was found to be dominated by a strong vorticity field and by hairpin shaped vortices that are shed periodically in the crossflow. Hairpin legs are associated to a counter-rotating vortex pair that persist in the far-field of the jet. The spatial distribution of the dispersed phase is strongly influenced by these large-scale coherent structures. A three-dimensional Voronoi analysis demonstrated a particle preferential concentration induced by hairpin vortices downstream from the jet exit. Volume fractions curves are presented as a function of the spanwise direction for different transversal sections of the crossflow region. A void particle region is induced by vortices in the central near-wall zone downstream of the jet exit. Particles tend to accumulate along two symmetric regions placed on the lateral side of the structures generated by the jet injection. By an analysis of particle impacts on the wall it was observed that particles characterized by lower values of the $${\textit{St}}$$ number, whose response time is comparable with the characteristic time of the hairpin vortices, tend to impact on the wall on two symmetric side of the jet exit in the proximity of hairpin legs. This demonstrated that the generated large-scale coherent structures play a major role in the not homogeneous dispersion of the solid phase.

Pseudo real-time continuous measurements of particle preferential concentration in homogeneous isotropic turbulence

Preferential concentration is a phenomenon where particles in turbulent flow concentrate in regions of low vorticity and high strain rate, forming clusters. This phenomenon is prevalent in nature and various industrial environments. Previous measurement systems for detecting this phenomenon have been based mostly on discrete images, and is relatively slow because of the image post processing involved. We have developed a new fast-response continuous measurement system comprised of a photomultiplier tube (PMT), custom-designed lens tube, and a continuous wave Nd:YAG laser. Experiments were conducted in a chamber that creates homogeneous isotropic turbulence with no mean flow. Image-based Voronoi analysis and box counting analysis from a high-speed camera were compared against the new PMT-based method for three Stokes number cases of near 0, 2.2, and 10. As the Stokes number was varied, the new technique showed similar results compared to the conventional camera-based methods.

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

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

A dynamic spectrally enriched subgrid-scale model for preferential concentration in particle-laden turbulence

A new subgrid-scale (SGS) model for turbulent velocity fluctuations is proposed for large-eddy simulations (LES) of dispersed multi-phase flows. The modeled velocity contains scales smaller than the LES grid resolution, thereby enabling the prediction of small-scale phenomena such as the preferential concentration of particles in high-strain regions. The construction of the spectrally enriched velocity field in physical space is made dynamically, and is based on (1) modeling the smallest resolved eddies of sizes comparable to the LES grid size via approximate deconvolution, and (2) reconstructing the SGS fluctuations via non-linear generation of small-scale turbulence. The model does not contain tunable parameters, can be deployed in non-uniform grids, and is applicable to inhomogeneous flows subject to arbitrary boundary conditions. The performance of the model is assessed in LES of isotropic turbulence laden with inertial particles, where improved agreement with direct numerical simulation results is obtained for the statistics of preferential concentration.

Translational and rotational motions of small solid particles in a spatially developing turbulent boundary layer with heat transfer

Direct numerical simulations have been performed to investigate the translational and rotational motions of small solid particles in a spatially developing turbulent boundary layer with heat transfer and two-way coupling, using the Eulerian-Lagrangian point-particle approach. The particles are assumed to be smaller than the Kolmogorov length scale in the dilute gas-solid flow. The simulation results show that the motion of particles is affected by particle inertia, particle preferential concentration and two-way coupling. The mean particle angular velocity is slightly larger than the fluid one in the buffer layer since the small heavy particles preferentially accumulate in regions of high strain rate, whereas the particles rotate slower than the surrounding fluid in the close vicinity of the wall due to their high rotational inertia. In the streamwise direction, the fluid spin intensity exceeds the corresponding particle spin intensity, as a consequence of particle preferential concentration in regions of low streamwise fluid vorticity; while the opposite is true in the wall-normal and spanwise directions. In addition, the differences in the temperature, linear and angular velocities between different inertial particles can be explained in terms of the two-way interactions between dispersed particles and continuous fluid.

Effects of particle polydispersity on radiative heat transfer in particle-laden turbulent flows

This study considers the effects of polydispersity of particles on thermodynamic and hydrodynamic behaviour of solid particle solar receivers. To this end we consider a canonical setting of a semi-periodic domain and perform DNS of turbulent flows interacting with point particles subject to a heating source. The turbulent flow is seeded with polydisperse particles that have a specific cumulative distribution function of particle sizes that is tuned based on available measurements. A thermodynamically equivalent monodisperse particle size is calculated, in a sense that the mass loading ratio of particles to gas and the total frontal area of particles available for radiation absorption are matched between the polydisperse and monodisperse particles. Our results show that the effective heat transfer rate between the two phases is significantly impacted by both particle clustering and polydispersity. We compare our DNS results to the predictions of a semi-analytical 1D model that assumes uniform particle concentration and gas properties per streamwise cross-section. Gas and particle temperatures predicted by this 1D model show least agreement with DNS at a Stokes number close to unity, where particles are most preferentially concentrated. Capturing the quantitative effects of particle preferential concentration on the effective heat transfer leads to a closure problem in the context of the 1D model. Using the DNS data, we examine such closure models and assess whether closure corrections inferred from monodisperse DNS can be applied to polydisperse mixtures viewed as superposition of multiple monodisperse systems.