Numerical Modeling of Particle Dynamics in a Cylindrical Chamber Containing a Rotating Disk

Numerical modeling was performed to study the submicron particle dynamics in a confined flow field containing a rotating disk, temperature gradient, and various inlet gas flow rates. The Lagrangian model was employed to compute particle trajectories under the temperature gradient, disk rotation speed, and inlet gas flow rate effects. The trajectories of particles with diameters of 1 μm, 0.1 μm, and 0.01 μm were examined in this study. When the inlet gas temperature was lower than that of the disk, particle-free zones were created due to upward thermophoretic force for 1 μm and 0.1 μm particles. Disk rotation was found to depress the size of the particle-free zone. Particle deposition onto the disk for 0.01 μm particles was possible because of the Brownian motion effect. A detailed evaluation of the particle-free zone size as a function of the temperature gradient, disk rotation speed, and inlet gas flow rate was performed. When the inlet gas temperature was higher than the disk temperature, particle deposition onto the disk was enhanced due to the downward thermophoretic force for 1 μm and 0.1 μm particles. Disk rotation was found to increase the deposition rate. For 0.01 μm particles, Brownian motion was more important than thermophoretic force in controlling particle behavior. The particle deposition rates as a function of the temperature gradient, disk rotation speed, and inlet gas flow rate were performed.     

可吸入颗粒物在管内湍流流动时的动力学特性及热泳沉积

The kinematical characteristics and thermophoretic deposition of inhalable particles with the diameters of 0-2.5μm （hereafter referred to as PM2.5） suspended in turbulent air flow in a rectangular duct with temperature distribution were experimentally studied. Particle dynamics analyzer （PDA） was used for the on-line measurement of particle motion and particle concentration distribution in the cross-sections of the duct. The influences of the parameters such as the ratio of the bulk air temperature to the cold wall temperature and the air flow rate in the duct on the kinematical characteristics and the deposition efficiencies of PM2.5 were investigated. The experimental re- sults show that the deposition efficiencies of PM2.5 mainly depend on the temperature difference between the air and the cold wail, wffile the air flow rate and the particlecon~centration almost affect hardly tile clep0si-tion-effi ciency. The radial force thermophoresis to push PM2.5 to the cold wail is found the key factor for PM2.5 deposition.Based on the experimental results, an empirical modified Romay correlation for the calculation of thermophoretic deposition efficiency of PM2.5 is presenlext. The empirical correlation agrees reasonably well with the experimental data.     

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.     

Experiments Measuring Particle Deposition from Fully Developed Turbulent Flow in Ventilation Ducts

Particle deposition in ventilation ducts influences particle exposures of building occupants and may lead to a variety of indoor air quality concerns. Experiments have been performed in a laboratory to study the effects of particle size and air speed on deposition rates of particles from turbulent air flows in galvanized steel and internally insulated ducts with hydraulic diameters of 15.2 cm. The duct systems were constructed of materials typically found in commercial heating, ventilating, and air conditioning (HVAC) systems. In the steel duct system, experiments with nominal particle sizes of 1, 3, 5, 9, and 16 μm were conducted at each of three nominal air speeds: 2.2, 5.3, and 9.0 m/s. In the insulated duct system, deposition rates of particles with nominal sizes of 1, 3, 5, 8, and 13 μm were measured at nominal air speeds of 2.2, 5.3, and 8.8 m/s. Fluorescent techniques were used to directly measure the deposition velocities of monodisperse fluorescent particles to duct surfaces (floor, wall, and ceiling) at two straight duct sections where the turbulent flow profile was fully developed.

In steel ducts, deposition rates were higher to the duct floor than to the wall, which in turn were greater than to the ceiling. In insulated ducts, deposition was nearly the same to the duct floor, wall, and ceiling for a given particle size and air speed. Deposition to duct walls and ceilings was greatly enhanced in insulated ducts compared to steel ducts. Deposition velocities to each of the three duct surface orientations in both systems were found to increase with increasing particle size or air velocity over the ranges studies. Deposition rates measured in the current experiments were in general agreement with the limited observations of similar systems by previous researchers.     

Particle Deposition in Museums: Comparison of Modeling and Measurement Results

Deposition of airborne particles may lead to soiling and /or chemical damage of objects kept indoors, including works of art in museums. Measurements recently were made of the deposition velocity of fine particles (diameter range: 0.05–2.1 μm) onto surfaces in five Southern California museums. In this paper, theoretical predictions of particle deposition velocities onto vertical surfaces are developed for comparison against the experimental results. Deposition velocities are calculated from data on surface-air temperature difference and near-wall air velocity using idealized representations of the air flow field near the wall. For the five sites studied, the wall-air temperature differences were generally in the range of a few tenths to a few degrees Kelvin. Average air velocities measured at 1 cm from the wall were in the range 0.08–0.19 m s^?1. Based on a combination of modeling predictions and measurement results, the best estimate values of deposition velocity for the wall studied at each site are obtained. These values are in the range (1.3–20) × 10^?6 m s^?1 for particles with 0.05–μm diameter and (0.1–3.3) × 10^?6 for particles with 1-μm diameter. The range of 15–30 in deposition velocity for a given particle size is due primarily to differences among sites in the near-wall air flow regime, with the low and high values associated with forced laminar flow and homogeneous turbulence in the core of the room, respectively.     

温度梯度场内可吸入颗粒物运动特性及热泳沉积

对温度梯度场内垂直管中可吸入颗粒物在湍流工况下的运动特性和热泳沉积规律进行了实验研究,使用颗粒动态分析仪（PDA）在线测量了颗粒物在管道截面上的速度和浓度分布。重点研究了主流与水冷壁面的温差对粒径范围0～2.5 μm颗粒（PM2.5）的运动和沉积的影响,得到其沉积效率。结果表明,湍流扩散作用使颗粒在近壁面富集,而热泳力是PM2.5在冷壁面上发生沉积的最主要因素。得到了PM2.5热泳沉积的半经验公式,计算值与实验结果较为接近。     

Thermophoretic Deposition of Particles in Laminar and Turbulent Tube Flows

Thermophoretic deposition of aerosol particles (particle diameter ranges from 0.038 to 0.498 μm) was measured in a tube (1.18 m long, 0.43 cm inner diameter, stainless steel tube) using monodisperse NaCl test particles under laminar and turbulent flow conditions. In the previous study by Romay et al., theoretical thermophoretic deposition efficiencies in turbulent flow regime do not agree well with the experimental data. In this study, particle deposition efficiencies due to other deposition mechanisms such as electrostatic deposition for particles in Boltzmann charge equilibrium and laminar and turbulent diffusions were carefully assessed so that the deposition due to thermophoresis alone could be measured accurately. As a result, the semiempirical equation developed by Lin and Tsai in laminar flow regime and the theoretical equation of Romay et al. in turbulent flow regime are found to fit the experimental data of thermophoretic deposition efficiency very well with the differences of less than 1.0% in both flow regimes. It is also found that Talbot's formula for the thermophoretic coefficient is accurate while Waldmann's free molecular formula is only applicable when Kn is greater than about 3.0.     

Thermophoretic acceleration of particle deposition from laminar air streams

A preliminary study is reported of the use of temperature gradients to accelerate the deposition of small particles from laminar air streams. It is shown that appreciable effects can be obtained even with small temperature gradients and particles as large as 30 μm. An empirical correlation is proposed for the thermophoretic force based on the present results and those published previously for smaller particles.     

Particle Deposition in Ventilation Ducts: Connectors,Bends and Developing Turbulent Flow

In ventilation ducts the turbulent flow profile is commonly disturbed or not fully developed, and these conditions are likely to influence particle deposition to duct surfaces. Particle deposition rates at eight S-connectors, in two 90° duct bends and in two ducts where the turbulent flow profile was not fully developed were measured in a laboratory duct system with both bare steel and internally insulated ducts with hydraulic diameters of 15.2 cm. In the bare-steel duct system, experiments with nominal particle diameters of 1, 3, 5, 9, and 16 μm were conducted at each of three nominal air speeds: 2.2, 5.3, and 9.0 m/s. In the insulated duct system, deposition of particles with nominal diameters of 1, 3, 5, 8, and 13 μm was measured at nominal air speeds of 2.2, 5.3 and 8.8 m/s. Fluorescent techniques were used to measure directly the deposition velocities of monodisperse fluorescent particles to duct surfaces. Deposition at S-connectors, in bends, and in straight ducts with developing turbulence was often greater than deposition in straight ducts with fully developed turbulence for equal particle sizes, air speeds, and duct surface orientations. Deposition rates at all locations were found to increase with an increase in particle size or air speed. High deposition rates at S-connectors resulted from impaction, and these rates were nearly independent of the orientation of the S-connector. Deposition rates in the two 90° bends differed by more than an order of magnitude in some cases, probably because of the difference in turbulence conditions at the bend inlets. In straight sections of bare steel ducts where the turbulent flow profile was developing, the deposition enhancement relative to fully developed turbulence generally increased with air speed and decreased with downstream distance from the duct inlet. This enhancement was greater at the duct ceiling and wall than at the duct floor. In insulated ducts, deposition enhancement was less pronounced overall than in bare steel ducts. Trends that were observed in bare steel ducts were present, but weaker, in insulated ducts.     

Thermophoresis in Rarefied Gas Flows

Numerical calculations are presented for the thermophoretic force acting on a free-molecular, motionless, spherical particle suspended in a rarefied gas flow between parallel plates of unequal temperature. The rarefied gas flow is calculated with the direct simulation Monte Carlo (DSMC) method, which provides a time-averaged approximation to the local molecular velocity distribution at discrete locations between the plates. A force Green's function is used to calculate the thermophoretic force directly from the DSMC simulations for the molecular velocity distribution, with the under-lying assumption that the particle does not influence the molecular velocity distribution. Perfect accommodation of energy and momentum is assumed at all solid/gas boundaries. Earlier work for monatomic gases (helium and argon) is reviewed, and new calculations for a diatomic gas (nitrogen) are presented. Gas heat flux and particle thermophoretic forces for argon, helium, and nitrogen are given for a 0.01 m spacing between plates held at 263 and 283 K over a pressure range from 0.1 to 1000 mTorr (0.01333- 133.3 Pa). A simple, approximate expression is introduced that can be used to correlate the thermophoretic force calculations accurately over a wide range of pressures, corresponding to a wide range of Knudsen numbers (ratio of the gas mean free path to the interplate separation).     

Annular flow configuration with high deposition efficiency for the experimental determination of thermophoretic diffusion coefficients

An experimental study was carried out to produce reliable data for the determination of the thermophoretic diffusion coefficient K_th of suspended oil particles in air, in the transition regime. An original device was used for the thermophoretic deposition efficiency measurement, involving a turbulent flow through a concentric tube annulus, with the inner tube cooled (5 °C) and the outer heated. Experimental parameters varied in particle diameter (0.039–5.13 μm), flow rate (150, 200, and 250 Nl min⁻¹, corresponding to Reynolds number in the range 5000–10 000) and hot wall temperature (65–125 °C). This configuration, based on three controlled temperatures (gas inlet, cold wall, hot wall), the so-called “3T”, permits an overall deposition efficiency enhancement compared to conventional “2T” penetration devices (hot gas flow in a cooled tube). In the 3T configuration, significant thermophoretic deposition efficiencies have been obtained (up to 27%), together with limited gas temperature axial variations, thus permitting a reliable determination of the thermophoretic diffusion coefficient K_th.An analytical model was developed for the prediction of the thermophoretic deposition efficiency, for a given value of the thermophoretic diffusion coefficient K_th. This model has been used, together with our measurement results, to derive the K_th experimental values, for a Knudsen number ranging from 0.01 to 3. These K_th values were compared with evaluations based on various models available in the literature. Although widely used, Talbot's model always provides K_th values higher than our experimental results in the transition regime. The most relevant model appears to be the one proposed by Beresnev and Chernyak, particularly for an energy accommodation slightly lower than one.     

SIMULATION OF PARTICLE TRANSPORT AND DEPOSITION IN A COMBUSTOR

A computational model for Lagrangian particle tracking for studying dispersion and deposition of particles in a combustor with swirling flow and chemical reaction is developed. The model accounts for the effect of thermophoretic force, as well as the drag and lift forces acting on particles, in addition to the Brownian motion and gravitational sedimentation effects. The mean turbulent gas flow, temperature fields and chemical species concentration in the combustor are evaluated using the stress transport turbulent model of the FLUENT code. The instantaneous fluctuation velocity field is generated by a Gaussian filtered white noise model.

The simulated axial, radial and tangential mean gas velocities are compared with the existing experimental data. Ensembles of particle trajectories are generated and statistically analyzed. The effects of size and initial distribution on particle dispersion and deposition are studied. The particle concentration at different sections are also evaluated and discussed. The results shows that the turbulence dispersion effect is quite important, while the thermophoresis effect is small.     

Thermophoretic interactions of aerosol particles with constant temperatures

This paper presents an analytical study of the thermophoretic motion of two free aerosol spheres with constant temperatures by using a method of reflections. The particles are allowed to differ in radius, in temperature, and in surface properties. The Knudsen numbers are assumed small so that a continuum model describes the fluid flow with a thermal creep and a hydrodynamic slip at the particle surfaces. The method of reflections is based on an analysis of the thermal and hydrodynamic disturbances produced by a single sphere with constant temperature placed in an arbitrarily varying temperature field. The results for two-sphere interactions are correct to O(r₁₂⁻⁷), where r₁₂ is the distance between the particle centers. For the special situation of two identical spheres, the effect of particle interactions will drive the pair system approaching each other if the particle temperature is less than the temperature of the surrounding. While the temperature of the particles is higher than the surrounding temperature, the thermophoretic force obtains a repulsive effect between the particles. Based on a microscopic model the results for two-particle interactions are applied to find the effect of particle concentration on the average thermophoretic velocity in a bounded suspension. In general, the effect of interactions on thermophoretic coagulation of particles with constant temperatures can be stronger than that on sedimentation.     

沿同心环面层流流动的气体中颗粒的传热沉积物的预测:发展中的流动和已充分发展的流动的比较

Thermophoresis is an important mechanism of micro-particle transport due to temperature gradients in the surrounding medium. It has numerous applications, especially in the field of aerosol technology. This study has numerically investigated the thermophoretic deposition efficiency of particles in a laminar gas flow in a concentric annulus using the critical trajectory method. The governing equations are the momentum and energy equations for the gas and the particle equations of motion. The effects of the annulus size, particle diameter, the ratio of inner to outer radius of tube and wall temperature on the deposition efficiency were studied for both developing and fully-developed flows. Simulation results suggest that thermophoretic deposition increases by increasing thermal gradient, deposition distance, and the ratio of inner to outer radius, but decreases with increasing particle size. It has been found that by taking into account the effect of developing flow at the entrance region, higher deposition efficiency was obtained, than fully developed flow.     

A study of the deposition of silt onto the surface of type 304 stainless steel

The deposition rate of Lake Ontario silt onto type 304 stainless steel at a fluid velocity of 1.05 m/s is given by: N = 2.1 × 10^?5 exp (-E/RT) C_b p. where E = 25.3 kJ/mol. Both the magnitude and the temperature dependence of the deposition rate is consistent with deposition that is surface rather than transport limited. The release rates were small compared to the deposition rates and independent of the surface temperature. Only particles less than 5 μm were found in the deposits at 1.05 m/s, even though particles up to 25 μm were in the flowing silt suspension. The maximum particle size in the deposit decreased with increasing deposition velocity.     

Direct Numerical Simulation of Kinematics and Thermophoretic Deposition of Inhalable Particles in Turbulent Duct Flows

Three-dimensional, incompressible turbulent air-particle flows in a channel with a temperature gradient are simulated by direct numerical simulations (DNS). The calculations used the fractional projection method to directly solve the Navier-Stokes equations. For obtaining more accurate results, the Oberbeck-Boussinesq model was used for considering the convective heat transfer and applied two-way coupling between the particles and the air phase to accurately simulate flow field state. The particles motions including mutual collisions were calculated with the direct simulation Monte-Carlo method (DSMC). The particles agglomeration and deposition in the turbulent channel flow with a temperature gradient were simulated by the Dahneke model. The research focused on the effects of the Reynolds number, the temperature gradient and particle concentration which simultaneity affect particle kinematics, impacts, agglomerations, and deposition characteristics. The numerical results show that the thermophoresis dominates the particle deposition, which agrees well with the experimental data, the particle concentration determines the particle collision and agglomeration rate, the Reynolds number determines the particle distribution in the duct and the 2.5 μm particles do not obviously affect the air phase motion under comparatively low concentration referred in this research.     

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.     

Experimental Study of Particle Deposition on Semiconductor Wafers

A sensitive method for detecting particle deposition on semiconductor wafers has been developed. The method consisted of generating a monodisperse fluorescent aerosol, depositing the known-size monodisperse aerosol on a wafer in a laminar flow chamber, and analyzing the deposited particles using a fluorometric technique. For aerosol particles in the size range of 0.1–1.0 μm, the mobility classification-inertial impaction technique developed by Romay-Novas and Pui (1988) was used to generate the monodisperse test aerosols. Above a particle diameter of 1.0 μm, monodisperse uranine-tagged oleic acid aerosols were generated by a vibrating-orifice generator. The test wafer was a 3.8-cm diameter silicon wafer placed horizontally in a vertical laminar flow chamber which was maintained at a free stream velocity of 20 cm/s. A condensation nucleus counter and an optical particle counter were used to obtain the particle concentration profile in the test cross section and to monitor the stability of aerosol concentration during the experiment. The results show that the measured particle deposition velocities on the wafers agree well with the theory of Liu and Ahn (1987) in the particle size range between 0.15 and 8.0 μm. The deposition velocity shows a minimum around 0.25 μm in particle diameter and increases with both smaller and larger particle size owing to diffusional deposition and gravitational settling, respectively.     

Predicting the deposition spot radius and the nanoparticle concentration distribution in an electrostatic precipitator

Abstract

Deposition of aerosol nanoparticles using an electrostatic precipitator is widely used in the aerosol community. Despite this, basic knowledge regarding what governs the deposition has been missing. This concerns the prediction of the size of the particle collection zone, but also, perhaps more importantly, prediction of the nanoparticle concentration distribution on the substrate, both of which are necessary to achieve faster and more precise deposition. In this article, we have used COMSOL Multiphysics simulations, experimental depositions, and two analytical models to describe the deposition. Based on that, we propose a simple equation that can be used to predict the size of the deposition spot as well as the particle concentration on the substrate. The equation we derive concludes that the size of the deposition spot only depends on the gas flow rate into the precipitator, and on the constant drift velocity of a particle in an electric field. The equation also displays that the deposited particle concentration is independent of the gas flow rate. Our general mathematical analysis has great applicability, as it can be used to model different geometries and different types of deposition methods than the one described in this article. We can therefore also propose that the drift velocity in this model easily could be replaced by another velocity acting on the particles at other deposition conditions, for instance, the thermophoretic velocity during thermophoretic deposition. This would result in the same dependence as presented in this article. Finally, we demonstrate analytically and through experiment that the particle distribution inside the spot will be homogenous and follows a top hat profile.     

Eulerian Model for Prediction of Particle Transport and Deposition in Turbulent Duct Flows with Thermophoresis

The Reynolds-averaged equations for turbulent particle population/transport in an Eulerian framework must be closed by specifying models for several terms: a turbophoretic force; a turbulent thermophoretic force; and a turbulent particle-diffusion term. In this article, new models are proposed for the turbophoretic term, as a particle-size dependent extrapolation of the corresponding turbulent fluid-velocity correlation, and for the turbulent thermophoretic term as an eddy-viscosity-scaled multiple of the corresponding mean thermophoretic term, appropriate for small low-inertia particles with τ⁺_p < 10. When the turbophoresis model is incorporated in a system of equations that describes particle motion within the surrounding fluid, it predicts particle deposition velocities that are in good agreement with experimental data over a range of particle sizes. When this equation system is included in a computational model to predict particle transport in turbulent pipe flows, the efficiency of particle deposition in pipes with upstream heating and downstream cooling is found to be in fair agreement with experimental measurements at two different Reynolds numbers, and over a range of particle sizes and temperature differences.

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