A comprehensive approach in modeling Lagrangian particle deposition in turbulent boundary layers

Modeling of particle deposition on adjacent walls is a key issue in various applications like separation or transport processes. The present paper focuses on the modeling of turbophoretic deposition of particles in the micron size range. The first step is to evaluate the important range where turbophoresis plays an important role in comparison to other mechanisms e.g. gravity or electrostatic separation. The disadvantages of commonly used models will be analyzed and overcome by implementing a more sophisticated approach considering damping of turbulent fluctuations in the wall-boundary layer. In contrast to previous work, commonly used turbulence models are applied to solve the mean flow field of the examples under consideration. The results will show a good prediction of particle deposition in comparison to experimental values [B.Y.H. Liu, J.K. Agarwal, Experimental observation of aerosol deposition in turbulent flow, Aerosol. Sci. 5 (1974) 145-155.] by using the advanced model.     

Mechanisms of aerosol deposition in a nasal model

Total and regional aerosol deposition were investigated in a model of a normal human nasal airway. Contributions of fluid turbulence and particle inertia were evaluated using monodisperse aerosols. At fixed turbulent flow conditions, deposition percentage increased with particle size greater than 1 μm, suggesting that turbulent inertial deposition is a primary mechanism.

With same size aerosol, deposition increased with increasing fluid turbulence but its contribution was less with larger size aerosol. Turbulent diffusion was the dominant transport mechanism for particles less than 1 μm, where deposition decreased with particle size. Two major deposition sites were visualized with radio-aerosol in the anterior region of the nasal airway. One is close to the ostium internum where turbulent eddies are well developed, and the other is the anterior region of the middle turbinate where direction of airflow changes from upward to horizontal.     

Effects of air temperature and humidity on particle deposition

Particle deposition in a fully developed turbulent duct flow was studied. The random walk model of Lagrangian approach was used to predict the trajectories of 3000 particles with a density of 900 kg/m³. The effects of thermophoretic force and air humidity were also considered. The results were compared with the previous studies with a particle size range of 0.01–50 μm and air flow velocity of 5 m/s. The profile of dimensionless deposition velocity with relaxation time presents a V-shaped curve and the results are in good agreement with the previous studies.The effects of air temperature and humidity on particle deposition with a particle size of 1 μm were also investigated. The results show that thermophoretic force accelerates particle deposition onto the duct walls with increasing temperature difference between air flow and the duct wall surface. Meanwhile, it was found that particle deposition velocity increases with air humidity.     

Finite element modeling of ultra fine particle filtration by a membrane filter

Theoretical work has been carried out to investigate the filtration of ultra fine aerosol particles in a membrane filter. The analysis was done using a finite element method with a Newtonian fluid model for the carrier medium. Both inertial filtration and diffusional filtration were considered. Prior to the main analysis, our numerical scheme was tested with the analytical results for the diffusion of particles in the cylinder and showed good agreement, which confirms the importance of axial diffusion occurring in a short cylinder like a very thin membrane filter. Particle size, porosity, pressure drop, and flow velocity are found to be main variables that determine the filter efficiency. Two important mechanisms of filtration have opposite effects on the efficiency, depending on the variables. Increases in particle size, pressure drop, and flow velocity cause increases in the efficiency for intertial deposition, while decreases in those variables cause increases in the diffusional efficiency. The existence of a minimum value of total filtration efficiency (sum of inertial efficiency and diffusional efficiency) was indicated for intermediate values of the variables. Lower porosity is found to favor inertial deposition more than diffusion. Some other effects of filtration conditions on the total efficiency are also discussed.     

Effect of thermophoresis on sub-micron particle deposition from a laminar forced convection boundary layer flow onto an isothermal cylinder

Sub-micron deposition from a laminar forced convection boundary layer developing on a heated isothermal vertical cylinder has been investigated. Pseudo-similarity solutions, as proposed by Sparrow et al. (1970, AIAA J. 8, 1936), have been used to calculate the local cumulative particle deposition theoretically; with the thermophoretic velocity being that proposed by Talbot et al. (1980, J. Fluid Mech. 101, 737). It was demonstrated that the effect of thermophoresis can decrease particle transfer by about two orders of magnitude and that the effect increases with particle size and distance along the cylinder. Experiments were also conducted using mono-disperse fluorescent uranin particles with mean diameters of 0.05–0.25 μm. A calibrated fluorimeter was used to measure the mass of the particles deposited at different axial locations along the cylinder. Results showed similar trends to the theoretical model, but absolute values of the deposits were greater than theoretical predictions. On the other hand, good agreement was obtained for the percentage change in deposition relative to that obtained under isothermal conditions.     

一种新型受热面飞灰颗粒的沉积特性

以一种余热锅炉中新型的受热面为研究对象,采用实验研究和数值模拟的方法研究其飞灰沉积特性。建立了菱形受热面飞灰颗粒的沉积模型,对飞灰颗粒的反弹、黏附及脱落过程进行预测,并与叉排管束和顺排管束的含灰烟气流的速度场、温度场和飞灰颗粒沉积率进行比较。结果表明,菱形受热面在换热和飞灰沉积方面优势明显。沉积主要集中于受热面左上部,颗粒由于惯性碰撞在迎风侧沉积。相同速度下,随颗粒粒径增加沉积率先增大后减小,在3 m·s^-1的烟气流速下颗粒直径为5 μm时飞灰颗粒沉积率最高,为9.49%。保持粒径不变,随速度增大沉积率逐渐降低。     

颗粒撞击单颗粒覆层的数值计算

颗粒与壁面的惯性碰撞机制是换热管壁积灰的主要原因之一,且国内外对微米级颗粒撞击壁面过程的研究较少。本文对单颗粒撞击颗粒覆层的碰撞过程进行了数值计算。首先通过建立颗粒与壁面法向碰撞的动力学模型,对颗粒与壁面（或颗粒）之间的碰撞过程进行研究。对于颗粒与壁面（或颗粒）的碰撞过程,无阻尼耗散下,理论计算结果与数值计算结果一致。相对于仅考虑黏附剥离功的情况,阻尼耗散的存在使得临界捕集速度增加。在此基础上,研究了颗粒与颗粒覆层撞击后的颗粒运动情况。颗粒-颗粒（黏附）-壁面的法向碰撞过程由于黏附颗粒的加入变得更加复杂。计算发现,对于二氧化硅颗粒-二氧化硅颗粒（黏附）-不锈钢表面的碰撞过程,当入射速度大于0.7m/s时,黏附颗粒将从壁面脱离。     

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     

Pilot‐scale investigation and CFD modeling of particle deposition in low‐dust monolithic SCR DeNOx catalysts

Deposition of particles in selective catalytic reduction DeNO_x monolithic catalysts was studied by low‐dust pilot‐scale experiments. The experiments showed a total deposition efficiency of about 30%, and the deposition pattern was similar to that observed in full‐scale low‐dust applications. On extended exposure to the dust‐laden flue gas, complete blocking of channels was observed, showing that also in low‐dust applications soot blowing is necessary to keep the catalyst clean. A particle deposition model was developed in computational fluid dynamics, and simulations were carried out assuming either laminar or turbulent flow. Assuming laminar flow, the accumulated mass was underpredicted with a factor of about 17, whereas assuming turbulent flow overpredicted the experimental result with a factor of about 2. The simulations showed that turbulent diffusion in the monolith channels and inertial impaction and gravitational settling on the top of the monolith were the dominating mechanisms for particle deposition on the catalyst. © 2013 American Institute of Chemical Engineers AIChE J, 59: 1919–1933, 2013     

An improved model for particle deposition in porous foams

Porous foam provides an inexpensive, light-weight and effective medium to capture physiologically-relevant aerosol fractions. It can be manufactured to have a wide range of properties relevant to aerosol deposition. A series of laboratory experiments were conducted to measure particle penetration though porous foam media of varying pore size and foam length. Both solid and liquid aerosols (0.01–10 μm diameter) were tested using a Sequenzial Mobility Particle Sizer or Aerodynamic Particle Sizer to count and size particles penetrating the foam. With this data, an existing semi-empirical model was improved upon to predict particle penetration through a foam of a given fiber diameter, and thickness. The model is based on three dimensionless parameters (St, Ng, Pe) that account for inertial, gravitational, and diffusive modes of deposition, respectively.     

THE COLLISION RATE OF PARTICLES IN TURBULENT FLOW

A review of previous derivations of particle collision rates in turbulent fluid flow shows that these are applicable only to limited cases. A more general derivation is given, taking into account the effects of the inertia of the particles and the difference in densities of the fluid and the particles. A universal solution for the relative velocity of two particles due to turbulent accelerations in a gaseous or liquid system is presented. In gaseous systems the acceleration mechanism becomes predominant at particle sizes far below the Kolmogorov microscale of turbulence. In liquid systems, the particle inertial and added mass effects become important above the Kolmogorov microscale. Here the particle collision rate cannot be estimated from the fluid turbulent velocity fluctuations only.     

Computational study of particle in-flight behavior in the HVOF thermal spray process

A computational framework is developed for the multiphase flow in a high velocity oxygen-fuel (HVOF) thermal spray coating process with steel powders as the feedstock. The numerical model includes continuum-type differential equations that describe the evolution of gas dynamics and multi-dimensional tracking of particle trajectories and temperature histories in the turbulent reacting flow field. The numerical study shows that the particle temperature is strongly affected by the injection position while the particle velocity is less dependent on this parameter. Moreover, both particle velocity and temperature at impact are strongly dependent on particle size, although the spatial variation of these two variables on the substrate is minimal. It is also found that not all the particles are deposited on the substrate perpendicularly (even if the spray angle is 90°), due to substantial radial fluid velocities near the stagnation point. A statistical distribution of particle velocity, temperature, impinging angle and position on the substrate as well as particle residence time is obtained in this work through independent random tracking of numerous particles by accounting for the distributed nature of particle size in the feedstock and injection position as well as the fluctuations in the turbulent gas flow.     

Changes in large particle size distribution due to dry deposition processes

A dry deposition model is described that can simulate variations in the size-resolved mass size distribution of large ( diameter) atmospheric particles due to dry deposition processes. The model is unique because it is based on both gravitational and inertial effects in turbulent flow and includes deposition and suspension velocities for large, airborne particles. The model allows the integration of a large number of variables, covering a wide range of conditions (height of particle injection, meteorological conditions, and removal time). Changes in the size distributions that result from model simulations of deposition show the expected decrease in concentration with size since the deposition is greater for the larger particles. However, the size distribution does not decrease with size in a uniform manner as would be suggested by Stokes settling velocity due to the effect of inertial forces acting on the particles. Application of the model reveals a number of patterns, including the development of two peaks in the large particle mass size distribution, a persistent peak in the 1– size range, and a second peak in the 10– range that is strongly affected by meteorological conditions.     

Bubble evolution through submerged orifice using smoothed particle hydrodynamics: Basic formulation and model validation

Smoothed particle hydrodynamics is used to simulate the bubble evolution in liquid pool through a submerged orifice. Discontinuities in the physical properties along the interface are taken care using appropriate smoothening functions. Surface tension at the interfacial plane is also added in the momentum equation to track the evolution of the bubbles. To prevent abrupt intrusion of one fluid into the other no penetration force is applied for two closely situated particles of different properties. Solid walls are modelled with two layer of virtual particle along the boundary. Further, the use of corrective form of kernel approximation eradicates the inherent particle deficiency at the interface and solid boundary. The model is capable to simulate the growth of the bubble, neck formation and its detachment from the orifice along with the dynamic velocity field in both the phases. Comparison between the numerical bubble contour and published results shows excellent predictability of the model. The volume of the bubble at the detachment and the bubble frequency are compared satisfactorily with available experimental observations.     

气固流化床内射流穿透深度的CFD模拟及其实验验证

在经典的Gidaspow无黏性双流体模型中考虑离散颗粒对流体和固体动量守恒方程的影响后,建立了一个具有模拟大规模流化床内气固两相流体动力学特性潜在优势的简化数学模型。在CFX4.4商业化软件平台上通过增加用户自定义子程序考察了二维气固流化床(高2.00 m、宽0.30 m)内射流气速、喷嘴尺寸、环隙气速和静床高度对射流穿透深度的影响,并以树脂颗粒(粒径670 μm、密度1474 kg·m^-3)为研究对象在厚度为0.025 m的矩形床内进行了对比实验。结果表明,选取空隙率为0.8的等高线作为射流边界比较合适;射流穿透深度随射流气速或射流喷口尺寸的增加而增大;射流周围环隙气速由0变到最小流化速度时,射流穿透深度随环隙气速增加而增大,在最小流化速度时达到最大值,然后随环隙气速增加单调减小,当环隙气速大于2.5倍最小流化速度时,射流穿透深度减小程度变缓;在相同射流气速下射流穿透深度随着静床高度的增加而减小,静床高度对射流穿透深度的影响随着射流气速增加呈现扩大的趋势。     

Thermophoretic particle deposition efficiency in turbulent tube flow

This study investigated the thermophoretic particle deposition efficiency numerically. The critical trajectory was used to calculate thermophoretic particle deposition in turbulent tube flow. The numerical results obtained in turbulent flow regime in this study were validated by particle deposition efficiency measurements with monodisperse particles (particle diameter ranges from 0.038 to 0.498 μm) in a tube (1.18 m long, 0.43 cm i.d., stainless-steel tube). The theoretical predictions are found to fit the experimental data of Tsai et al. [Tsai, C. J., J. S. Lin, S. G. Aggarwal, and D. R. Chen, “Thermophoretic Deposition of Particles in Laminar and Turbulent Tube Flows,” Aerosol Sci. Technol., 38, 131 (2004)] very well in turbulent flows. In addition, an empirical expression has been developed to predict the thermophoretic deposition efficiency in turbulent tube flow.     

A method for reducing the deposition of small particles from turbulent fluid by creating a thermal gradient at the surface

The present paper suggests the use of thermophoretic phenomena to decrease the rate of particle deposition onto pipe walls from a turbulent flow. When a tube is externally heated; the particles will be subjected to thermal force within the laminar sublayer in a direction away from the surface preventing or reducing their deposition. A theory proposed by EI-Shobokshy and Ismail (1980) has been used for estimating the deposition velocity. The thermal velocity component was calculated and the effective velocity of particles approaching the wall surface computed. The results present the relationship between particle penetration and particle size at different values of pipe wall temperature and Re. The experimental results showed a good agreement with theoretical results for particle sizes 6 -10 μm diameter, Re = 6000 – 8000 and pipe wall temperatures 50 – 150°C.     

Fine particle deposition in laminar and turbulent flows

The deposition of fine silica and polystyrene spheres was measured for conditions of laminar and turbulent flow (960 ≤ Re ≤ 16040) in a rectangular channel using image analysis. The plate glass deposition surfaces were rendered positively charged by coating them with a cationic copolymer while, under the water chemistry conditions employed, both types of particles were negatively charged. It was found that, contrary to the results for laminar flow, the initial depositon rates in turbulent flow decreased with increasing Re, indicating that deposition was no longer mass-transfer controlled and that particle attachment played an increasingly important role as Re was raised. Attachment was modelled as a rate process in series with mass transfer in which the attachment rate varies inversely as the square of the friction velocity. Under the conditions of the present experiments, no particle re-entrainment was observed, so that the declining rate of particle accumulation on the wall recorded in each run could only be attributed to a declining deposition rate. Even where asymptotic accumulations were reached, particle coverages never exceeded 3.5%.     

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.     

CHEMICALLY INDUCED MIGRATION OF PARTICLES ACROSS FLUID STREAMLINES

The velocity of a colloidal particle that moves because of a gradient of concentration of a molecular solute depends on the concentration field at the surface of the particle. Effects of macroscopic convection of the suspending fluid on two such transport phenomena, capillary-driven movement of fluid particles and diffusiophoresis of rigid particles, are considered here. In the case of fluid particles our results also apply to motion caused by a temperature gradient. If the particles are in a laminar flow with the solute gradient directed perpendicular to the direction of flow, as might arise in the boundary layer near a surface to which the particles are being deposited, the local solute concentration field around each particle is disturbed from that of pure diffusion of the solute. Using published results for these concentration disturbances in a simple-shear flow, we determine the effect of the imposed velocity gradient on the speed of the particles in the direction of the solute gradient. For both fluid and rigid particles, the correction due to macroscopic shear is 0(Pe^3/2:) where Pe is the Peclet number based on particle radius and fluid shear rate; this effect opposes the zero-shear particle velocity. A possible consequence of this result is that by increasing the shear rate in a laminar boundary layer in the hope of enhancing the rate of particle adsorption, one may actually be decreasing the rate.