Effect of Sub-Grid Scales on Large Eddy Simulation of Particle Deposition in a Turbulent Channel Flow

Large-eddy simulations (LES) of particle transport and deposition in turbulent channel flow were presented. Particular attention was given to the effect of subgrid scales on particle dispersion and deposition processes. A computational scheme for simulating the effect of subgrid scales (SGS) turbulence fluctuation on particle motion was developed and tested. Large-eddy simulation of Navier-Stokes equations using a finite volume method was used for finding instantaneous filtered fluid velocity fields of the continuous phase in the channel. Selective structure function model was used to account for the subgrid-scale Reynolds stresses. It was shown that the LES was capable of capturing the turbulence near wall coherent eddy structures.

The Lagrangian particle tracking approach was used and the transport and deposition of particles in the channel were analyzed. The drag, lift, Brownian, and gravity forces were included in the particle equation of motion. The Brownian force was simulated using a white noise stochastic process model. Effects of SGS of turbulence fluctuations on deposition rate of different size particles were studied. It was shown that the inclusion of the SGS turbulence fluctuations improves the model predictions for particle deposition rate especially for small particles. Effect of gravity on particle deposition was also investigated and it was shown that the gravity force in the stream wise direction increases the deposition rate of large particles.     

Reynolds number dependence of gas-phase turbulence in particle-laden flows: Effects of particle inertia and particle loading

A gas-particle flow experiment at a low particle loading (m = 0.4) in a vertical downward pipe is conducted at three different Reynolds numbers (Re = 6000, 10,000, and 13,000) to investigate the Re influence on the gas-phase turbulence modulation. The mean and fluctuating velocity data of both phases are acquired using a two-component LDV/PDA system. Two particles of varying degrees of inertia (i.e. high-density 70 µm glass beads and low-density 60 µm cenospheres) are used as the model particles to examine the effect of particle inertia on the trend in the turbulence modulation as a function of Re. An experiment at a higher particle loading (m = 4.0) using the glass beads is also conducted to examine the effect of particle concentration. In the presence of high inertia particles (St_T > 500) at a low particle loading, the gas-phase turbulence intensity in the pipe core is increased with increasing Re resulting in turbulence enhancement relative to the unladen flow. The turbulence enhancement is attributed to 1) a modification of the turbulence production by the Reynolds stress due to interparticle collision and/or 2) a reduction in the fluctuating drag force due to a change in the radial profile of the particle concentration. In contrast, the gas-phase turbulence intensity in the presence of low inertia particles (St_T < 500) is found to decrease with increasing Re similar to the trend in the unladen flow. Lastly, the turbulence enhancement at high Re is not observed at a high particle loading where the turbulent energy dissipation by the fluctuating drag force is dominant.     

Charged Particle Trajectory Statistics and Deposition in a Turbulent Channel Flow

The statistical properties of charged particles and their wall deposition in a turbulent channel flow in the presence of an electrostatic field is studied in this paper. For a dilute concentration, the influence of small particles on the fluid motion is neglected. The instantaneous velocity field is generated by a direct numerical simulation of the Navier-Stokes equation via a pseudospectral method. The case in which each particle carries a single unit of charge and the case in which the particles have a saturation charge distribution are analyzed. Ensembles of 8192 particle trajectories are used for evaluating various statistics. Effects of size and electric field intensity on particle trajectory statistics and wall deposition rate are studied. RMS particle velocities and particle concentrations at different distances from the wall are evaluated and discussed. The results for deposition rates are compared with those obtained from empirical equations.     

Modelling of heavy and buoyant particle dispersion in a two-dimensional turbulent mixing layer

Heavy and buoyant particle dispersion in the turbulent mixing layer was investigated numerically using a two-phase flow discrete vortex modelling. It was revealed from the modelling that inclusion of two-way momentum coupling is essential for properly modelling heavy particle dispersive transport in turbulent free shear flows. For heavy particles with small Stokes numbers, the dispersion is predominated by the large-scale vortex structures and they exert small influence on the carrier fluid flow. Heavy particles with large St directionally align along the braid region between the neighbouring vortices. However, the lateral dispersion of particles of large St is smaller than that of particles of small St.For buoyant particles with the density being slightly greater than that of the carrier fluid, numerical simulation revealed that the buoyant particles scatter over the whole vortex core rather than collect along the fringes of the vortex. The Lagrangian statistics calculation of buoyant particle dispersion showed that both the inertial and crossing-trajectory effects affect the particle dispersion behaviour and particle eddy diffusivity. The dispersion behaviour of buoyant particles is highly associated with the particle Stokes number. Large St buoyant particles exhibit a larger dispersion. It was also indicated from the numerical simulation that buoyant particles might disperse larger than the fluid tracers. The correlation between the buoyant particle and fluid tracer velocities was affected by including the coupling effect.     

A numerical study of particle wall-deposition in a turbulent square duct flow

The deposition of dense solid particles in a downward, fully developed turbulent square duct flow at Re_τ = 360, based on the mean friction velocity and the duct width, is studied using large eddy simulations of the fluid flow. The fluid and the particulate phases are treated using Eulerian and Lagrangian approaches, respectively. A finite-volume based, second-order accurate fractional step scheme is used to integrate the incompressible form of the unsteady, three-dimensional, filtered Navier-Stokes equations on an 80 × 80 × 128 grid. A dynamic subgrid kinetic energy model is used to account for the unresolved scales. The Lagrangian particle equation of motion includes the drag, lift, and gravity forces and is integrated using the fourth-order accurate Runge-Kutta scheme. Two values of particle to fluid density ratio (ρ_p/ρ_f = 1000 and 8900) and five values of dimensionless particle diameter (d_p/δ × 10⁶ = 100, 250, 500, 1000 and 2000, δ is the duct width) are studied. Two particle number densities, consisting of 10⁵ and 1.5 × 10⁶ particles initially in the domain, are examined.Variations in the probability distribution function (PDF) of the particle deposition location with dimensionless particle response time, i.e. Stokes number, are presented. The deposition is seen to occur with greater probability near the center of the duct walls, than at the corners. The average streamwise and wall-normal deposition velocities of the particles increase with Stokes number, with their maxima occurring near the center of the duct wall. The computed deposition rates are compared to previously reported results for a circular pipe flow. It is observed that the deposition rates in a square duct are greater than those in a pipe flow, especially for the low Stokes number particles. Also, wall-deposition of the low Stokes number particles increases significantly by including the subgrid velocity fluctuations in computing the fluid forces on the particles. Two-way coupling and, to a greater extent, four-way coupling are seen to increase the deposition rates.     

Laminar suspension flow with diffusive,gravitational deposition in the entrance of a converging and diverging channel

The simultaneous development of the fluid and particle phases was solved numerically to effect deposition rate results in converging and diverging straight wall channels with significant gravity effects. The flow was laminar and two-dimensional with non-reacting dilute suspensions in an incompressible carrier. Deposition rate was found to be higher in a favorable pressure field (i.e. converging channel) than that in an adverse pressure field (i.e. diverging channel) when diffusion was the predominant force involved. However, in a gravity field, bottom deposition rates were found to increase in adverse pressure fields, whereas favorable pressure fields effected less deposition rates. Moreover, top deposition rates were found to decrease with both increasing convergence and divergence angles. Finally, the bottom deposition rates were found to increase to very high proportions (near separation points) for high N_β in diverging channels due to the large magnitude of the particle density on the bottom wall.     

稀疏气固两相湍流边界层拟序结构变动特性

应用PIV两相同时测量方法,对壁面Reynolds数为430的水平槽道稀疏气固两相湍流边界层拟序结构变动特性进行了研究。选取质量载荷为10^-4~10^-3的110 μm聚乙烯颗粒作为离散相。结果表明,低载荷颗粒仍能显著改变湍流拟序结构,进而影响宏观湍流属性。颗粒重力沉降形成的粗糙壁面增强了壁面附近湍流猝发行为,导致黏性底层中的气相法向脉动速度和雷诺剪切应力显著增大。颗粒与壁面的碰撞加强了低速流体上抛、削弱了高速流体下扫,同时增强了轨道交叉效应,从而抑制了湍流拟序结构发展,显著减小了黏性底层以上区域的法向脉动速度和雷诺剪切应力。此外,颗粒惯性还减小了黏性底层厚度、增大了流向速度梯度,导致气相流向脉动速度峰值增大,且其对应位置也更加靠近壁面。     

Numerical study of particle dispersion in the wake of gas-particle flows past a circular cylinder using discrete vortex method

A numerical investigation on the particle dispersion in the wake of particle-laden gas flows past a circular cylinder at Reynolds number of 10⁵ is presented. In the numerical method, the Discrete Vortex Method with the diffusion velocity model is employed to calculate the unsteady gas flow fields and a Lagrangian approach is applied to track individual particles. A dispersion function is defined to represent the dispersion scale of the particle. The distributions of gas velocities and vortex blobs, the trajectories and dispersion functions as well as distributions for particles with various Stokes numbers ranging from 0.01 to 1000 are obtained. The numerical results show that: (1) very small sized particles with St = 0.01 can distribute both in the vortex core and around the vortex periphery, whereas intermediate sized particles with St = 1.0, 10 are distributed around the vortex periphery, and very large sized particles with St = 1000 do not feel the gas flow; (2) only at small Stokes number (St = 0.01, 0.1) the particles do not impact with the cylinder; (3) the particle's dispersion intensity decreases precipitously as St is increased from 0.01 to 10.     

Coupled CFD–DEM of particle-laden flows in a turning flow with a moving wall

The nature of the particle–solid interactions and particle–fluid interactions in rectangular duct bend geometry with/without a moving wall is studied, taking into account particle collision, colloidal, and hydrodynamic forces, and four way coupling between the fluid flow and particles. The focus is on systems where particles and fluid phase have similar length scales, fluid Reynolds number (Re_f) ∼ 1, and particle's Stokes number (St) ∼ 1. Particles move toward the walls of the channel near the bend, and have long residence times in these regions. Buoyancy force has negligible effect on particle motion, where adhesion and drag forces lead to particle motion and agglomeration patterns. The effect of a free surface on agglomeration sites in the turning flow is elucidated.     

Analysis of non‐Brownian particle deposition from turbulent liquid‐flow

The deposition of non‐Brownian particles from turbulent liquid‐flow onto channel walls is numerically analyzed. The approach combines Lagrangian particle tracking with a kinematic model of the near‐wall shear layer. For nonbuoyant particles, direct interception is the main deposition mechanism and the deposition velocity scales as the particle diameter (in wall units) to the power of 1.7. When wall/particle hydrodynamic interactions are taken into account, the deposition velocity is significantly reduced and the correction factor scales as the cubic root of the wall roughness to particle diameter ratio. For buoyant particles, sedimentation is usually the predominant deposition mechanism and the hydrodynamic interactions significantly affect the deposition velocity when the drainage characteristic time driven by buoyancy is of the order of the particle residence time close to the wall. Last, a wall‐function for the suspended particles is proposed. © 2015 American Institute of Chemical Engineers AIChE J, 62: 891–904, 2016     

Numerical simulation for the collision between a vortex ring and solid particles

This study is concerned with the numerical simulation for the collision between a vortex ring and an ensemble of small glass particles. The vortex ring, convecting with its self-induced velocity in a quiescent air, collides with the particles. The Reynolds number for the vortex ring is 2600, and the particle diameters are 50 and 200 μm. The Stokes number St for the 50 μm particle is 0.74, while the St for the 200 μm particle is 11.4. Immediately after the collision with the vortex ring, the 50 μm particles surround the vortex ring, forming a dome. It is parallel with the preferential distribution for the particle with St ? 1 around large-scale eddies, which has been measured experimentally and simulated numerically in various free turbulent flows. The 200 μm particles disperse more due to the collision with the vortex ring. This is attributable to the centrifugal effect of large-scale eddy, which has been reported by the numerical simulation for the motion of the particle with St = 10 in a wake flow. The collision between the vortex ring and the particles induces an organized three-dimensional vortical structure. It also reduces the strength and convective velocity of the vortex ring.     

DEM simulation of gas-solid flow behaviors in spout-fluid bed

Three-dimensional gas and particle turbulent motions in a rectangular spout-fluid bed were simulated. The particle motion was modeled by discrete element method and the gas motion was modeled by k-ε two-equation turbulent model. Shear induced Saffman lift force, rotation induced Magnus lift force as well as drag force, contract force and gravitational force acting on individual particles were considered when establishing the mathematics models. A two-way coupling numerical iterative scheme was used to incorporate the effects of gas-particle interactions in volume fraction, momentum and kinetic energy. The gas-solid flow patterns, forces acting on particles, the particles mean velocities, jet penetration depths, gas turbulent intensities and particle turbulent intensities were discussed. Selected stimulation results were compared to some published experimental and simulation results.     

Aerosol Particle Deposition in a Recirculation Region

Digital simulation results concerning aerosol particle transport and deposition in a recirculation region are presented. It is assumed that the particles are shed from sources near the back face of a block in a turbulent duct flow. The results show that a large number of particles may be captured by the block and the upper wall of the channel due to impaction and interception. The capture efficiencies increase as the source distance from the wall decreases. The gravitational effects on the particle deposition rate are also studied.     

Measurements of pollen grain dispersal in still air and stationary, near homogeneous, isotropic turbulence

The dispersal of ragweed, pine and corn pollen as well as polystyrene spheres in still air and stationary, near homogeneous, isotropic turbulence (HIT) was investigated using high-speed, digital inline holographic cinematography enabling Lagrangian tracking of the particles. Mean still air settling velocities were similar as reported literature values. Small discrepancies were most likely related to species/size differences and water content of the grains. Near-HIT was generated by loudspeakers mounted on the corners of a 40 cm³ chamber and the turbulent flow field at the center of the chamber was validated using stereoscopic Particle Image Velocimetry (PIV). Results showed near homogeneity and near isotropy with mean velocities 5–10 times smaller than the corresponding rms values of velocity fluctuations. The turbulent kinetic energy dissipation rate was determined from the PIV data sets and used to calculate the Kolmogorov scales and Taylor microscales. Experiments were carried out for two different loudspeaker amplifications corresponding to Taylor microscale Reynolds numbers, R_λ=144 and 162, respectively. The mean settling velocity in turbulent conditions was in all cases higher than the corresponding still air value, the difference becoming smaller as particle Stokes numbers increased. For the present conditions, the still air particle settling velocity was lower than the rms values of air fluctuating velocities. As a result, dispersion was dominated by inertia and for a given R_λ, particle fluctuating velocity autocorrelations fell more rapidly as the particle Stokes number decreased; corresponding particle diffusion coefficients also decreased. Transverse particle diffusion coefficients were lower than those in the direction of gravity in agreement with the continuity effect. Under the present range of experimental parameters, results showed that inertial particles (0.6<St<11) in highly turbulent conditions disperse more effectively than the air.     

Application of a modified Eulerian model to study the particle deposition on a vertical surface in turbulent flow

In this study the v2-f model was used with the two-phase Eulerian approach to predict the particle deposition rate on a vertical surface in a turbulent flow. The standard Eulerian particle model was adopted from the literature and modified, considering the majority of particle transport mechanisms in the particle deposition rate. The performance of the modified model was examined by comparing the rate of particle deposition on a vertical surface with the experimental and numerical data in a turbulent channel flow available in the literature. The model took into account the effects of drag force, lift force, turbophoretic force, electrostatic force, inertia force and Brownian/turbulent diffusion on the particle deposition rate. Electrostatic forces due to mirror charging and charged particles under the influence of an electric field were considered. The predictions of the modified particle model were in good agreement with the experimental data. It was observed that when both electrostatic forces are present they are the dominant factor in the deposition rate in a wider range of particle sizes.     

Prediction of Particle Deposition Using a Simplified Particle Model in Fully Developed Channel Flow

In this study the Eulerian particle model was modified to predict the particle deposition rate in fully developed channel flow. The modified model is less complicated and has much lower computation time. The performance of the simplified model was examined by comparing the particle deposition rate in a vertical channel with the experimental data for fully developed channel flow available in the literature. The effects of turbophoretic force, thermophoretic force, electrostatic force, gravitational force, Brownian/turbulent diffusion, and the wall roughness on the particle deposition rate were examined. The predictions of the modified particle model were in agreement with the experimental data.     

Relative importance of the lift force on heavy particles due to turbulence driven secondary flows

Saffman lift forces on dense particles due to gradients in both streamwise and cross-stream velocities in a downward, fully developed turbulent square duct flow at Re_τ = 360 are studied using large eddy simulations. Volume fraction of the dispersed phase is low enough (≤ 10^− 5) that the one-way coupling approach is reasonable, i.e., two-way coupling and particle-particle collisions are not considered. Eulerian and Lagrangian approaches are used to treat the continuous and dispersed phases, respectively. Subgrid stresses are modeled with the dynamic subgrid kinetic energy model of Kim and Menon [W.W. Kim and S. Menon. Application of the localized dynamic subgrid-scale model to turbulent wall-bounded flows, AIAA 97-0210, 1997.]. The particle equation of motion includes drag, lift forces due to both the streamwise and cross-stream velocity gradients, gravity, and is integrated using the fourth-order accurate Runge-Kutta scheme. Dependence of particle drag and lift forces on duct cross-sectional location and particle response time is demonstrated using the mean value contours and probability density functions (PDFs) of particle forces. It is shown that the streamwise component of the mean drag force experienced by particles of all response times is a deceleration force, i.e. on average, fluid streamwise velocity lags the particle streamwise velocity. Secondly, the two wall-normal (or lateral) components of the mean drag force are oriented such that the particles experience a net mean force toward the duct corners. PDFs of particle drag force components show that smaller response time particles experience a wider range of drag force about the mean value, as compared to the more inertial particles. Contours of mean wall-normal lift forces due to streamwise velocity gradients show that this force predominantly acts toward the duct walls and that the maximum lift force occurs close to the walls. PDFs of lift force due to streamwise velocity gradients show that the range of fluctuations increases with particle response time, but the dependence on particle response time is weaker compared to drag force. Lift forces due to cross-stream velocity gradients are at least an order of magnitude smaller than lift forces due to streamwise velocity gradients and are found to decrease in their range of fluctuations with particle response time. It is demonstrated that lift forces due to secondary flow velocity gradients are not as important as those due to streamwise velocity gradients in a square duct flow.     

Modeling of Gas‐Particle Turbulent Flow in Spout‐Fluid Bed by Computational Fluid Dynamics with Discrete Element Method

Gas and solid turbulent flow in a cylindrical spout‐fluid bed with conical base were investigated by incorporating various gas‐particle interaction models for two‐way coupling simulation of discrete particle dynamics. The gas flow field was computed by a k‐ϵ two‐equation turbulent model, the motion of solid particles was modeled by the discrete element method. Drag force, contact force, Saffman lift force, Magnus lift force and gravitational force acting on individual particles were considered in the mathematical models. Calculations on the cylindrical spout‐fluid bed with an inside diameter of 152 mm, a height of 700 mm, a conical base of 60° and the ratio of void area of 3.2 % were carried out. Based on the simulation, the gas‐solid flow patterns at various spouting gas velocities are presented. Besides, the changes in particle velocity, particle concentration, collision energy, particle and gas turbulent intensities at different proportions of fluidizing gas to total gas flow are discussed.     

Influence of the lift force in direct numerical simulation of upward/downward turbulent channel flow laden with surfactant contaminated microbubbles

In this work, we employ direct numerical simulation of turbulence one-way coupled to Lagrangian tracking to investigate microbubble distribution in upward and downward channel flow. We consider a closed channel flow at Re_τ=150 and a dispersion of microbubbles characterized by a diameter of . Bubbles are assumed contaminated by surfactants (i.e., no-slip condition at bubble surface) and are subject to drag, gravity, pressure gradient forces, Basset history force and aerodynamic lift.Our results confirm previous findings and show that microbubble dispersion in the wall region is dominated by the action of gravity combined with the lift force. Specifically, in upward flow, bubble rising velocity in the wall region generates a lift force which pushes bubbles to the wall. In downward flow, bubble rising velocity against the fluid generates a lift force which prevents microbubbles from reaching the viscous sublayer.In the wall region, we observe bubble preferential segregation in high-speed regions in the downflow case, and non-preferential distribution in the upflow case. This phenomenon is related to the effect of the lift force. Compared to experiments, the current lift force model produces larger consequences, this effect being overemphasized in the upflow case in which a large number of bubbles is segregated near the wall. In this case, the resulting bubble wall-peak of concentration outranges experimental results.These results, so deeply related to the lift force, underline the crucial role of current understanding of the fluid forces acting on bubbles and help to formulate questions about available force models, bubble-bubble interactions and two-way coupling which can be crucial for accurate predictions in the region very near the wall.     

Experimental study on collision rates of inertial particles in particulate flows under the effect of gravity

To investigate the inter-particle collision frequency, the present experiment conducts two streams of particulate flow converging into a main flow in a junction. Each stream of particulate flow consists of inertial steel particles of 1 and 2 mm diameter, respectively. Particles glide down inside two branches of slanting glass rectangular ducting. We use a high-speed camera to record the trajectory of particle and a PTV technique for data processing. The correlation between the inter-particle collision frequency, particulate concentration, effective diameter and mean fluctuation velocity of inertial particles is explored experimentally. The effect of inter-particle collision frequency under the effect of gravity force is considered and analyzed. Due to the high inertia of steel particles, the turbulent effect of gas-phase is eliminated. A significant difference between the characteristics of the gravitational particulate flow and the homogeneous isotropic flow is found. The physical interpretation for it and the statistical correlation with inter-particle collision frequency are discussed. The results support the analogy of kinetic theory for inertial particles in gas-solid flow provided the gravity effect is excluded.