EULERIAN AND LAGRANGIAN SIMULATIONS OF PARTICLE DEPOSITION FROM A POINT SOURCE IN A TURBULENT CHANNEL FLOW

Results comparing Eulerian and Lagrangian simulations of particle deposition from a point source in a channel are presented. The mean turbulent flow field is simulated using a two-equation k-ε turbulence model. In the first, approach, diffusion of aerosol particles is studied by solving the corresponding advection-diffusion equation. Deposition of particles in the intermediate size range are analyzed by considering both the turbulent eddy diffusion and the eddy impaction processes, as well as the Brownian diffusion effects. In the second approach, the turbulence fluctuating velocity field are numerically simulated as a Gaussian random process. The Lagrangian trajectories of aerosol particles in the channel are then evaluated by solving the corresponding particle equation of motion. Effects of Brownian diffusion on particle motions are also included. A series of digital simulations for particles of various sizes which are released at different locations across the channel are carried out. Depositions of different size particles on the wall under a variety of conditions are analyzed. The relative significance of turbulence and Brownian effects are also discussed.     

EULERIAN AND LAGRANGIAN SIMULATIONS OF PARTICLE DEPOSITION FROM A POINT SOURCE IN A TURBULENT CHANNEL FLOW

ABSTRACT

Results comparing Eulerian and Lagrangian simulations of particle deposition from a point source in a channel are presented. The mean turbulent flow field is simulated using a two-equation k-? turbulence model. In the first, approach, diffusion of aerosol particles is studied by solving the corresponding advection-diffusion equation. Deposition of particles in the intermediate size range are analyzed by considering both the turbulent eddy diffusion and the eddy impaction processes, as well as the Brownian diffusion effects. In the second approach, the turbulence fluctuating velocity field are numerically simulated as a Gaussian random process. The Lagrangian trajectories of aerosol particles in the channel are then evaluated by solving the corresponding particle equation of motion. Effects of Brownian diffusion on particle motions are also included. A series of digital simulations for particles of various sizes which are released at different locations across the channel are carried out. Depositions of different size particles on the wall under a variety of conditions are analyzed. The relative significance of turbulence and Brownian effects are also discussed.     

Numerical study to predict the particle deposition under the influence of operating forces on a tilted surface in the turbulent flow

This study uses a v2-f turbulence model with a two-phase Eulerian approach. The v2-f model can accurately calculate the near wall fluctuations in y-direction, which mainly represent the anisotropic nature of turbulent flow. The model performance is 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 effects of lift, turbophoretic, electrostatic and Brownian forces together with turbulent diffusion are examined on the particle deposition rate. The influence of the tilt angle and surface roughness on the particle deposition rate were investigated. The results show that, using the v2-f model predicts the rate of deposition with reasonable accuracy. It is observed that in high relaxation time the effect of lift force on the particle deposition is very important. It is also indicated that decreasing the tilt angle from 90° to 0° enhances the deposition rate especially for large size particles. Furthermore, the results show that increasing the Reynolds number at a specific tilt angle decreases the rate of particle deposition and the tilt angle has insignificant impact on the particle deposition rate in high shear velocity or high Reynolds number.     

Predicting the Particle Deposition Characteristics Using a Modified Eulerian Method on a Tilted Surface in the Turbulent Flow

This study uses a v2-f turbulence model with a two phase Eulerian approach. The v2-f model can accurately calculate the near wall fluctuationsm which mainly represent the nonisotropic nature of turbulent flow near the walls. The Eulerian method was modified based on considering the most important mechanisms in the particle deposition rate when compared to the experimental data. The model performance is 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 takes into account the effects of lift, turbophoretic, electrostatic, gravitational, and Brownian forces together with turbulent diffusion on the particle deposition rate. Electrostatic forces due to mirror charging and due to charged particles under the influence of an electric field were considered. The influence of the tilt angle on the particle deposition rate was investigated. The results show that, using the modified model with v2-f model predicts the rate of deposition with reasonable accuracy. It is shown that considering the turbophoretic force as the only inertia force and neglecting the lift force, leads to reasonable accuracy in predicting particle deposition rate. It is also observed that when the mirror charging and electric field are present, the electrostatic force has the dominant effect in a wider range of particles’ size. Furthermore, the results show that increasing the Reynolds number at a given tilt angle decreases the rate of particle deposition and the tilt angle has insignificant impact on the particle deposition rate in high shear velocity or high Reynolds number.     

Grid-generated turbulence in two-phase flow: The effect of parameters of the carrier medium and particles

Results are given of an experimental investigation of the initial region of decay of grid-generated turbulence in a downward two-phase flow of the “gas-solid particles” type. Optical diagnostic methods are used to obtain the distributions of the dynamic parameters of two-phase flow, namely, averaged and fluctuation velocities of gas, and the curves of decay of turbulence along the flow axis are constructed for grids with square meshes sized 4.8, 10, and 16 mm. The investigation results demonstrate that solid particles 700 μm in size have varying effect on the degree of decay of turbulence. In the case of grids with small mesh sizes of 4.8 and 10 mm, the presence of such particles leads to additional generation of turbulence; in the case of a grid with mesh size of 16 mm, vice versa, the particles suppress the turbulence. Investigations reveal that these tendencies become still more pronounced with increasing concentration of particles. In addition, the investigation of the effect of velocity phase slip reveals that the generation of turbulence increases with the difference between phase velocities. In so doing, variation of the pattern of the effect of particles on turbulence is observed for a grid with large meshes, namely, the suppression of turbulence at low values of velocity slip and generation of turbulence with increasing slip. Based on the results of analysis of experimental data, a criterional parameter is suggested, which defines the effect of particles on the turbulence of two-phase flow, i.e., the ratio of the Reynolds number of particle to the turbulence Reynolds number for gas.     

Large eddy simulation of particle deposition and resuspension in turbulent duct flows

Particle deposition and resuspension in a horizontal, fully developed turbulent square duct flow at four flow bulk Reynolds numbers (10,320, 83k, 215k and 250k) is simulated by applying large eddy simulation coupled with Lagrangian particle tracking technique. Forces acting on particles includes drag, lift, buoyancy and gravity. Four particle sizes are considered with the diameters of 5?μm, 50?μm, 100?μm and 500?μm. Results obtained for the fluid phase are in good agreement with the available experimental and numerical data. Predictions for particles show that particle size, flow Reynolds number and the duct (celling, floor and vertical) walls play important roles in near-wall particle deposition and resuspension. For the smallest particle (5?μm), the particle deposition rates in duct ceiling, floor and vertical walls are found to be similar with each other and all increase with the flow Reynolds number, while the particle resuspension tends to occur in the middle wall regions and corners of the duct with less influenced by the flow Reynolds number. The ceiling deposition rate gradually decreases with particle size while the floor and vertical wall deposition rates both increase with particle size. The ceiling particle deposition rate increases with Reynolds number while the floor deposition rate decreases with it. The vertical deposition rate for the small particles (5–50?μm) increases with the flow Reynolds number obviously, while for the large particles (100–500?μm) that becomes insensitive. In addition, the flow Reynolds number is found to have an obvious effect on particle resuspension while the effect of particle size on particle resuspension decreases with Reynolds number. Eventually, a dynamic analysis was conducted for particles deposition and resuspension in turbulent duct flows.     

Time behavior of heat fluxes in thermally coupled turbulent dispersed particle flows

The effect on heat transfer produced by injection of solid microparticles with high thermal capacity in turbulent channel flow is analyzed. Convection is forced by letting the fluid flow between a hot plate and a cold plate under zero-gravity conditions. An Eulerian?CLagrangian approach based on direct numerical simulation of turbulence (shear Reynolds number Re*?=?150 and molecular Prandtl number Pr?=?3) and on point-particle tracking is used. Full momentum and energy coupling between fluid and particles is considered. Different particle sizes and different particle concentrations are examined.     

Thermophoretic effects on submicron particle deposition in turbulent flow

Summary. Based on the model of surface renew and penetration the local cumulative sub-micron particle deposition from a turbulent flow onto a tube wall has been theoretically predicted. The conjoint effects of eddy diffusion, Brownian diffusion, and thermophoresis are considered in the deposition process. The quantitative predictions of mean particle deposition velocity coupled with appropriate estimates of the mean residence time are evaluated by comparison with previous models and experimental measurements. The thermophoretic effect can decrease particle transfer by about two orders of magnitude and fluctuates with particle size, Reynolds number and temperature gradient. Results show similar trends to the previous predictions and good agreement for the percentage change in deposition relative to that obtained under the isothermal conditions.     

Thermophoretic deposition of aerosol particles in laminar mixed-convection flow in a channel with two heated built-in square cylinders

The thermophoretic deposition of aerosol particles in laminar mixed-convection flow in a channel with two heated built-in square cylinders was studied numerically. The objective of this research was to study the effect of free convection and the distance between cylinders, on deposition of particles. Continuity, momentum and energy equations were solved to determine the velocity and temperature profiles in the channel. The particle trajectories were evaluated by solving the Lagrangian equation of motion that included the drag, Brownian diffusion and thermophoresis forces. It was found that the temperature gradient near the channel wall, in mixed flow regime, is higher than the temperature gradient in forced convection regime. Increasing the temperature gradient increased the effect of thermophoresis on deposition of particles. It was observed that the deposition was increased with the Richardson number. The distance between cylinders is a parameter that influences the deposition of particles. Temperature gradient decreases with increasing the cylinders’ distance; on the other hand, the length of the high temperature gradient zone, which is located in the region between the cylinders where the most deposition occurs, will be increased. These two opposite phenomena cause the fact that at a distance which is four times longer than the cylinders’ length, a maximum cumulative deposition fraction occurs. It was eventually concluded that the thermophoresis and the inertial impaction are dominant deposition mechanisms of particles on the channel wall.     

The movement law and orientation control of rectangular particles in the viscous fluid domain based on IS-FEM

Understanding the movement law and orientation control mechanism of non-spherical particles are significant for industrial applications. In this work, the flow characteristics of rectangular particles, in the uniform and wedge viscous fluid domain, are simulated by the immersed smoothed finite element method (IS-FEM). The influences of mesh resolution and time-step on particle velocity are analyzed, and the numerical procedure is validated by the published model and sedimentation experiments. The operating parameters that affect the particle flow are systematically studied, including Reynolds number, initial angle, channel offset distance, and aspect ratio. Moreover, the particle angles are adjusted by the velocity gradient of fluid domains. The result indicates that the velocities, angle, and drag of rectangular particles are closely related to the working conditions. The long axis of rectangular particles is consistent with the flow direction in shrinking fluid domains and is perpendicular to the flow direction in expanding fluid domains. The angle distribution law of rectangular particles in moving wedge fluid domains is determined. These findings provide a theoretical foundation for particle sedimentation and suspension flow, which is helpful for the further separation and orientation control of mixed particles.     

Computer Simulation of Pollutant Transport and Deposition Near Peace Bridge

Using computer simulations, transport, dispersion, and deposition of particulate pollutants near the Peace Bridge in the city of Buffalo, New York, are studied. An unstructured computational grid of Peace Bridge and its vicinity is generated, and the wind flow in the area is simulated. The Reynolds stress transport (RST) and the k-ε models of FLUENT code are used for simulating the mean airflow condition. The instantaneous turbulence fluctuating velocity is simulated by a discrete random walk (DRW) model. A Lagrangian particle-tracking model is used, and dispersion and deposition of particulate emissions from the motor vehicle exhaust on the bridge and in the Peace Bridge Plaza (customs area) are analyzed. The pollutant transport model accounts for the drag and Brownian forces acting on the particles, in addition to the gravitational sedimentation effects. For the case of a northwesterly wind of 7.7 m/s and particulate emissions in the size range of 0.01 to 50 μm, the corresponding deposition rates on various surfaces are studied. The importance of wind turbulence and gravity on particle deposition are evaluated. It is found that the Peace Bridge Plaza provides for a large fraction of the pollutants.     

Direct numerical simulation of ellipsoidal particles in turbulent channel flow

This paper investigates the behaviour of elongated, axi-symmetric ellipsoidal particles, their interaction with turbulence, and the effects of the ellipsoids on turbulence in a turbulent channel flow with Re _τ = 150. The simulations are carried out with full four-way coupling using the point-source approach: the particles are affected by the fluid, the particles affect the fluid, and the particles can collide with each other or the wall using a realistic collision algorithm. The trajectories of the ellipsoids are tracked by solving the translational and rotational equations of motion in a Quaternion framework and are closed with hydrodynamic drag and torque laws. To specifically identify the effect of particle shape, simulations of single phase channel flow are compared to simulations with spherical particles and to simulations with ellipsoids. In all cases, the driving pressure drop, to establish a flow with Re _τ = 150, is kept constant. Both the spherical particles and the ellipsoidal particles have a Stokes number of 5. Although the volume fraction is very low, 0.00725 and 0.0219 % for the spheres and ellipsoids, respectively, there is some effect of the particles and the ellipsoids on the turbulence. Although the transport terms in the turbulent kinetic energy equation of the fluid are hardly affected, the turbulence kinetic energy itself decreases by 6.0 % for the flow laden with spherical particles and 4.8 % for the ellipsoidal particles. The homogeneous dissipation of turbulence kinetic energy by the fluid decreases due to the addition of particles, and the production also decreases. The particles dissipate turbulence kinetic energy of the fluid phase, predominantly in the near-wall region. Because there is a high average slip velocity in the stream-wise direction between the particles and the fluid in the near-wall region, the root mean square of the particle velocity is higher than that of the fluid velocity in this direction. In the other directions, the root mean square velocities of the particles are significantly lower than of the fluid. There is, however, a positive slip velocity between the particles and the fluid in the wall-normal direction, indicating that the particles move towards the wall with a higher momentum than that they return to the centre of the channel with. As a result, there is a 4–5 times higher concentration of particles near the wall than in the centre of the channel. As both the spherical and the ellipsoidal particles are very small, there is no major difference in their overall behaviour. However, in the near-wall region, there are some profound differences. The collision mechanism of ellipsoids with the walls is significantly different compared to spheres, the former predominantly inducing rotation resulting from a collision and the latter predominantly moving away from the wall after colliding. This is confirmed by the strong rotation as well as large root mean square of rotation of the ellipsoidal particles in the near-wall region. This results in a slight inward shift of the peak of the root mean square velocities of the fluid and the ellipsoidal particles as well as the peak in slip velocity, driving the momentum transfer, compared to the simulations with the spheres. Finally, the statistics of the orientation show that the ellipsoids align in the stream-wise direction in the near-wall region, because of the fluid boundary layer as well as the particle–wall collisions, but that there is no significant orientation of the ellipsoids outside of the near-wall region.     

Numerical study on particle deposition in rough channels with different structure parameters of rough elements

This paper presents a study of the characteristics of particle deposition in rib-roughened channels. The gas-particle flow was numerically investigated by Reynolds stress model (RSM) with the discrete particle model (DPM). The particle deposition velocity and deposition ratio at different positions were numerically investigated in a channel where the relative roughness factor, e/D, were between 0.02 and 0.1, and the ratios of rough-element spacing to its height, p/e, were between 7 and 20. It is found that the eddy structures behind the rough-elements are changed by the increase of e/D. The windward surfaces are the main deposition regions and the cavities between the rough-elements are the secondary deposition regions. e/D contributes more to the increase of particle deposition velocity than p/e.     

Influence of particles on the transition to turbulence in pipe flow

We investigate by experiment the influence of suspended solids upon the transition to turbulence in pipe flow. The particles are monodisperse and neutrally buoyant with the liquid. The role of the particles on the transition depends upon both the volume fraction, phi, and particle size. Below a critical particle diameter, particles alter the transition to larger critical Reynolds numbers for all phi. In contrast to this, larger particles move the transition to smaller Reynolds numbers for small phi, but they delay the transition at larger concentration.     

Numerical study of microscopic particle arrangement of suspension flow in a narrow channel for the estimation of macroscopic rheological properties

In a narrow channel, the apparent relative viscosity of a suspension with finite-size particles is strongly dependent on its microscopic particle arrangement. Relative viscosity increases when suspended particles flow near the channel wall; thus, a suspension in a narrow channel does not always exhibit the same rheological properties even if the concentration is the same. In this study, we focus on the inertia and concentration of particles in a narrow channel and consider their effects on the microscopic particle arrangement and macroscopic suspension rheology. Two-dimensional pressure-driven suspension flow simulations were performed using a two-way coupling scheme, and normalized particle density distribution (PDD) were implemented to consider their particle arrangements. The results demonstrated that the velocity profiles for the particle suspension were changed by the Reynolds number and particle concentration because of the interactions between particles according to the power-law index. These changes affected the particle equilibrium positions in the channel, and the subsequent changes in solvent layer thickness caused changes in the macroscopic apparent viscosity. The behavior of microscopic particles played important roles in determining macroscopic rheology. Thus, we have confirmed that a normalized PDD can be used to estimate and assess the macroscopic rheology of a suspension.     

Simulation of packed-bed chromatography utilizing high-resolution flow fields: comparison with models

A computer simulation of a section of the interior region of a liquid chromatographic column is performed. The detailed fluid flow profile is provided from a microscopic calculation of low Reynolds number flow through a random packed bed of nonporous spherical particles. The fluid mechanical calculations are performed on a parallel processor computer utilizing the lattice Boltzmann technique. Convection, diffusion, and retention in this flow field are calculated using a stochastic-based algorithm. This computational scheme provides for the ability to reproduce the essential dynamics of the chromatographic process from the fundamental considerations of particle geometry, particle size, flow velocity, solute diffusion coefficient, and solute retention parameters when retention is utilized. The simulation data are fit to semiempirical models. The best agreement is found for the "coupling" model of Giddings and the four-parameter Knox model. These models are verified over a wide range of particle sizes and flow velocities at both low and high velocity. The simulations appear to capture the essential dynamics of the chromatographic flow process for non-dimensional flow velocities (Péclet number) less than 500. Since the same packing geometry is utilized for different particle size studies, the interpretation of the parameter estimates from these models can be extended to the physical column model. The simulations reported here agree very well with a number of experiments reported previously.     

Particle Transport and Deposition in a Duct Flow with a Rectangular Obstruction

The airflow field and particle trajectory and deposition in a duct with a rectangular obstruction were studied. The governing conservation equations of mass and momentum were discretized using a finite volume method, and the corresponding velocity vector and pressure fields were evaluated. The particle trajectories were evaluated by solving the Lagrangian equation of motion that included the drag, Saffman's lift, and gravity forces. Effects of different forces as well as the blockage and the obstruction aspect ratios on particle trajectory and deposition were analyzed for a Reynolds number of 200. The simulation results showed that with the increase of Stokes number, particle deposition efficiency on the front side of the obstruction increased and also the presence of the gravitational force in the span-wise direction caused the particles to be deposited on the channel lower wall. The presence of gravity in the stream-wise direction increased the deposition efficiency and in the counter-stream-wise direction decreased the deposition efficiency. Changing the obstruction aspect ratio had no noticeable effect on the deposition but increasing the blockage ratio increased the deposition efficiency. The presence of a lift force had different effects for different blockage ratios and Stokes numbers. But the lift force generally increased the deposition rate, especially at large Stokes numbers and large blockage ratios.     

Effect of the inlet angle on the performance of a cyclone separator using CFD-DEM

Hydrodynamic characteristics in a cyclone separator are simulated by means of DEM-CFD. Reynolds stress turbulence model (RSM) is used to capture gas turbulence. By changing the inlet angle, the distributions of pressure drop, tangential and axial velocity of gas phase are obtained within the cyclone. Simulated results indicate that the flow pattern consists of two regions: loss-free vortex region and forced vortex region. The negative inlet angle brings about a larger pressure drop comparing to positive inlet angle. The separation efficiency and trajectory of particles from simulation are obtained. The effects of inlet angle and particle size on separation efficiency are quantified. The separation efficiency is increased with an increase of particle size, while the separation efficiency firstly increases and then declined as inlet angle changes from negative to positive. An agreement between the numerical simulation and experimental results has been achieved in a cyclone separator.     

Numerical Investigation of Phase Distribution and Liquid Turbulence Modulation in Dilute Particle-Laden Flow

Studies on the motion of particles in turbulence and interactions between particles and turbulence are extremely significant, which can help us to improve the efficiency of industrial processes. In this article, we investigated the particle distribution and particle-turbulence interaction in a solid-liquid channel flow with the Euler-Lagrange two-way model. The liquid phase was solved using direct numerical simulation (DNS), and the particle motion was tracked by Newtonian equations of motion considering effects of drag force, pressure gradient force, and gravity. Two-way coupling was used to explain the effect of particles on the turbulence structure. The results show that the local void fraction of particles indicates the wall-peaked profile, particles scatter uniformly in the spanwise direction, and the injection of particles suppresses the turbulence activities in the near wall region. Suppression of the liquid turbulence is mainly caused by vortexes decay of different sizes.     

Gas-particle turbulent flow of foursquare tangential jets in a simplified pulverized-coal firing boiler

An experimental cold-model of a simplified tangential firing boiler was established to investigate the mesoscale turbulent flow behaviors, including gas vortex structures, particle motions and interactions between two phases. A modified PIV technology, employing two pairs of lasers and cameras, was applied to measure the velocity and velocity gradient of turbulent flow in foursquare tangential jets alternatively. At a given initial gas velocity and particle mass loading, the interaction between gas and particles was studied at three different particle sizes. It was found that two main coherent vortex structures, circular eddy and hairpin eddy, distributed mainly in low speed area and heavy impingement area, respectively. The characteristics of particle motion in foursquare tangential jets correlated with gas turbulence dissipation, particle size, particle concentration and particle density. Small particles were easily entrained by gas vortex, so that they consumed more turbulence energy and attenuated the gas turbulence intensity. On the contrary, large particles had more inertia and led to heavier impingement in the chamber center, resulting in particle random distribution and complex momentum transfer between gas and particles. Moreover, large particles stretched the coherent vortex to be narrow and long, while small particles pulled down the vortices rotation intensity.