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.     

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.     

Numerical investigation of electrostatic effect on particle behavior in a 90 degrees bend

Particle behavior in a turbulent circular-sectioned 90° bend under electrostatic field at three air flow rates (1600 L/min, 1100 L/min and 950 L/min, the corresponding bulk Reynolds numbers are 58,000, 40,000, 34,000) is simulated by a Large Eddy Simulation-Lagrangian particle tracking technique (LES-LPT) method coupled with electrostatic field model by Coulomb’s law. This numerical simulation is dedicated to study the electrostatic effect on particle behavior and erosion occurred in the dilute particle-laden bend flow. Forces considered acting on particles includes drag, lift, gravity and electrostatic force. Results obtained for the fluid phase are in good agreement with experimental and numerical data. Predictions show that electrostatic field does affect the particle motion in the pipe bend. At higher air flow rate with higher electrostatics at the inner arc the increasement of impact angle is lower than that at lower flow rate with lower electrostatics. The same conclusion can be found at the outer arc. In addition, electrostatic effect does increase particle-wall impact velocity while such trend decreases with flow rate. Erosion rate increases with increasing air flow rate, which is independent of electrostatics. However, given the same flow rate, the electrostatics reduces the occurrence of erosion at the bend. The erosion rate under electrostatic effect is found to approach that without electrostatics as the flow rate increases. Therefore, the effect of electrostatics on erosion decreases with the air flow rate.     

WALL DEPOSITION OF SMALL SUSPENDED PARTICLES IN A TURBULENT CHANNEL FLOW

The diffusion of small suspended particles in a turbulent channel flow is studied by solving the transport advection-diffusion equation. The mean flowfield in the channel is simulated using a two-equation k-ε turbulence model. Deposition velocity is evaluated at different sections in the channel for different particle sizes and flow Reynolds numbers. The effects of turbulence dispersion and Brownian diffusion on particle deposition velocity are discussed. The variation of particle deposition velocity with particle diameter, density and flow Reynolds number are analyzed. The wall deposition velocities for different size particles are compared with those obtained by other models.     

Numerical simulation of solid-liquid mixing characteristics in a stirred tank with fractal impellers

The hydrodynamics of solid-liquid mixing process in a stirred tank with four pitched-blade impellers, fractal 1 impellers, and fractal 2 impellers were investigated using computational fluid dynamics (CFD) simulation. An Eulerian-Eulerian approach, standard k-ε turbulence model, and multiple reference frames (MRF) technique were employed to simulate the solid-liquid two-phase flow, turbulent flow, and impeller rotation, respectively. The effects of impeller speed, impeller type, impeller spacing, impeller blade tilt angle, impeller blade shape, solid particle size and initial solid particle loading on the solid particle suspension quality were investigated. Results showed that the homogenous degree of solid-liquid system increased with the increase of impeller speed. The impeller spacing of T5/6 and T and impeller blade tilt angle of 60° and 45° were appropriate for the solid-liquid suspension process. Fractal shape impeller was more efficient than jagged shape impeller in solid-liquid mixing process. Larger particle diameter and higher initial solid particle loading resulted in less homogenous distribution of solid particles. It was found that fractal impeller could improve the solid particle suspension quality compared with four pitched-blade impeller under the same power consumption, increasingly so with the fractal iteration number of fractal impeller. Moreover, fractal impeller reduced the size of impeller trailing vortex and consumed less power consumption compared with four pitched-blade impeller at the same impeller speed, and the more the number of fractal iteration, the higher the impeller energy utilization rate of fractal impeller.     

FRICTION LOSSES FOR FLOW OF SLURRIES IN PIPELINE BENDS,FITTINGS, AND VALVES

ABSTRACT

Resistance coefficients for flow of suspensions of well defined glass beads of narrow size fractions in 1-inch and 2-inch straight pipes, in standard 45^°, 90^° and 180^° bends, in 90^° smooth bends of various curvature radii, and also in gate and globe valves were measured. The measurements were made for two sizes of fine glass beads, -325 mesh and -200-325 mesh, covering wide ranges of turbulent Reynolds number and solids concentrations from 0 to 50 weight percent.

These friction loss data were analyzed with regard to the effects of Reynolds number and suspended solids concentration, and the calculated resistance coefficients were compared with those estimated from available design procedures recommended for turbulent single-phase Newtonian flow. Within the range of particle sizes examined in this work no particle size effects could be discerned. The effects of Reynolds number and suspended solids concentration on the friction loss measurement were calculated.     

Numerical Simulation of Particle Saltation Process

A numerical model for simulation of particle single-step saltation was developed. The model includes drag force, shear lift force, rotational lift force, buoyancy force, added mass force, and torque. The governing equations were solved using the fourth-order Runge-Kutta scheme. The model was calibrated and verified using the experimental data. The computational results include particle trajectory, longitudinal velocity of particle and flow, relative velocity of particle and flow, dimensionless drag, and lift forces along the trajectory. Sensivity analysis was performed to determine the influence of various parameters. Saltation characteristics were also calculated for various Reynolds numbers in the range of 2.5 to 7.7. It was found that very close to the bed, drag force decreases as Reynolds number increases. An increase of about three times the Reynolds number has a decreasing effect of three times and two times on the drag and lift force, respectively. The influence of Reynolds number increase on the falling phase was less than that on the rising phase.     

直径30cm圆柱的气动力参数和绕流特性研究

为研究光滑圆柱的气动力系数和绕流特性,在均匀流中进行不同风速下的测压风洞试验,试验获得了阻力系数、升力系数、表面风压分布、风压相关性系数、斯托罗哈数等随雷诺数的变化特征,并将试验结果与以往结果进行比较。研究表明:升力系数的脉动值大于阻力系数的脉动值,说明涡脱造成的横风向激励比顺风向紊流激励剧烈;雷诺数位于临界区域时,圆柱表面风压分布呈现出对称-不对称-对称的变化过程,反映了由层流分离转化为湍流分离的全过程;在雷诺数为352000时呈现一侧为层流分离、另一侧为湍流分离的临界流态,风压呈现出左右不对称的单边泡形式;获得层流分离和湍流分离时的表面风压相关性分布特征,层流分离时圆柱同一侧的风压测点均呈较强的正相关,而湍流分离时在分离点前的区域相关性较强,分离点之后的区域相关性较弱;层流分离的升力系数谱有显著的峰值,表明尾流是规则的漩涡脱落,而湍流分离的升力系数谱没有明显峰值,表明尾流是随机的漩涡脱落。     

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.     

THE CALCULATION OF PARTICLE DEPOSITION FROM A TURBULENT FLOW IN A PARALLEL VERTICAL PLATE

The formation of ash deposits may cause slagging and fouling problems in furnaces. The difficulties of predicting particle depositions are caused by the complexity of two-phase flow, which includes the particle size effects in a turbulent flow and the interparticle force between particles. Although some models were proposed to predict the particle deposition, few attempts were made for larger particles in the region of the dimensionless relaxation time (τ⁺) greater than 20. Thus, a reliable deposition model experimental results are needed for model verification, In this study, the modified turbulent intensity and apparent turbulent viscosity of the fluid were used to describe particles in suspension flow. And, an isothermal flow model was developed for calculating particle deposition rate in a parallel vertical plate, and for comparison with the experimental data. The predicted particle deposition rates under selected conditions are found to be in good qualitative agreement with available experimental results.     

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.     

Measurement of the deposit formation during pneumatic transport of PMMA powder

Deposit formation poses severe hazards and negatively affects the functionality of pneumatic powder transport systems. A novel test-rig was developed for the measurement of the deposition of polymethylmethacrylate powder in a horizontal, turbulent flow through a duct of a square cross-section. The parameters under investigation are the particles’ size, shape, and mass flow rate, the conveying air’s Reynolds number, relative humidity, and temperature, and the duct material. A continuous weighing method is used to quantify the particle deposition and resuspension rate and a Faraday cup is positioned at the duct outlet to measure the specific powder charge. For the considered conditions, the air humidity exhibits a strong influence, especially on the smallest particles. For small particles, a high charge even leads to deposition at the ceiling of the PC duct. Larger particles tend to settle at the center of the duct and smaller ones preferably at its corner.     

Numerical investigation of the character of the lift on a cylindrical particle in Poiseuille flow of a plane channel

The character of the lift on a cylindrical (porous and solid) particle in Poiseuille flow of a plane channel has been investigated. The lift at various values of the Reynolds number, the particle size, and its position in the flow have been calculated.     

Drag,lift and torque acting on a two-dimensional non-spherical particle near a wall

Gas-solid granular flows with non-spherical particles occur in many engineering applications such as fluidized beds. Such flows are usually contained by solid walls and always some particles move close to a wall. The proximity of a wall considerably affects the flow fields and changes the hydrodynamic forces and torque acting on particles moving near the wall. In this paper, we numerically investigate the drag, lift and torque acting on a non-spherical particle in the vicinity of a planar wall by means of lattice Boltzmann simulations. To gain an exhaustive understanding of the complex hydrodynamics and study the influence of various geometrical and flow parameters, a single 2D elliptical particle is selected as our case study. In the simulations, the effect of particle Reynolds number, distance to the wall, orientation angle and aspect ratio on drag, lift and torque is studied. Our study shows that the presence of a wall causes significant changes in hydrodynamic forces, with increasing or decreasing drag and lift forces, depending on the distance from the wall. Even the direction of lift and torque may change, depending on both the distance from the wall and particle orientation angle. Also, an ellipse with higher AR experiences larger hydrodynamic forces and torque whatever the gap size and orientation angle.     

Analysis of particle rotation in fluidized bed by use of discrete particle model

The particle rotation was found important in the fluidized bed when the heterogeneous structures appeared. Some researches show that Magnus lift force might play an pivotal role in fluid-solid system, especially when the particles have fast rotation speed. As the Magnus lift force is acted at the single particle level, a pseudo two-dimensional discrete particle model (DPM) was used to investigate the influence of Magnus lift force in fluidized bed. The rotational Reynolds number (Re_r) bases on the angular velocity and the diameter of the spheres is used to characterize the rotational movement of particles. We studied the influence of Magnus lift force for particles with rotational Reynolds number in the range of 1–100. Our results show that the influence of Magnus lift force is enhanced with a higher Re_r. Magnus lift force affects the movement of particles in both radial and axial directions while Re_r is high. However, in low Re_r case it can be neglected in computational simulation model. This indicates the introduction of Magnus lift force may improve the discrete particle model only in high Re_r case and Magnus effect should be considered in real gas-solid two phase system when the particle rotational speed is high.     

微椭圆形截面斜拉索临界雷诺数区气动特性试验研究

为了研究微椭圆形截面斜拉索临界雷诺数区的气动特性,以标准圆形截面斜拉索模型和微椭圆形截面斜拉索模型为研究对象,开展了考虑截面变形和风攻角变化的风洞试验,得到了不同情况下雷诺数对模型气动力系数的影响规律,同时通过对升力时程和升力频谱分析,得到了临界雷诺数及附近区域的标准圆形截面和微椭圆形截面模型尾流旋涡脱落的变化。结果表明:微椭圆形截面模型在雷诺数亚临界区时,升力系数基本不受雷诺数的影响;在临界区时,升力系数随雷诺数逐渐增大;风攻角0°~50°时,微椭圆形截面模型升力系数最大值对应的雷诺数随风攻角同步增大;微椭圆形截面模型的升力时程在TrBL0向TrBL1阶段和TrBL1向TrBL2阶段过渡中会出现双稳态现象;微椭圆形截面变形会影响斜拉索尾流区旋涡脱落情况,进而影响不同雷诺数下的St数值变化。     

PARTICLE DISPERSION IN ANISOTROPIC HOMOGENEOUS TURBULENCE

ABSTRACT

A numerical study of particle dispersion in anisotropic homogeneous turbulent flows is reported. The stochastic turbulent field is represented by a set of random numbers with a pre-set covariance simulating the Reynolds stress in a turbulent flow. The effects of turbulence intensity, aerodynamic response time and Reynolds stress on the particle dispersion are presented.     

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.     

PARTICLE DISPERSION IN ANISOTROPIC HOMOGENEOUS TURBULENCE

A numerical study of particle dispersion in anisotropic homogeneous turbulent flows is reported. The stochastic turbulent field is represented by a set of random numbers with a pre-set covariance simulating the Reynolds stress in a turbulent flow. The effects of turbulence intensity, aerodynamic response time and Reynolds stress on the particle dispersion are presented.