Nonuniqueness of the “physical” acceleration for the Lorentz-Dirac equation

The Lorentz-Dirac equation is analyzed for the case of a charged particle injected into a step-function electric field of finite extent. It is shown that for small exit velocities, the relation between entrance and exit velocities is inverted in the sense that the larger the entrance velocity, the smaller the exit velocity. As a consequence, some entrance velocities can yield at least two distinct exit velocities. Numerical evidence bearing on the possibility of experimentally detecting this dichotomy is presented.     

Real-time measurement of bubbling phenomena in a three-dimensional gas-fluidized bed using ultrafast magnetic resonance imaging

Ultrafast magnetic resonance imaging has been applied for the first time to measure simultaneously both the rise velocities and coalescence of bubbles, and the dynamics of the solid phase in a gas-solid two-phase flow. Here, we consider the hydrodynamics within a gas-fluidized bed of particles of diameter 0.5 mm contained within a column of internal diameter 50 mm; gas velocities in the range of 0.18-0.54 m/s were studied. The data are of sufficient temporal and spatial resolution that bubble size and the evolution of bubble size and velocity following coalescence events are determined.     

Diffusion of a single particle in a 3D random packing of spheres

We report an experimental study of the dispersion properties of individual spherical particles of size d, moving under gravity in a dry random packing of large spheres of size D. The diameter ratio d/D is below the critical value 0.1547 above which beads get pinned inside the packing . They move in this regime at a constant mean velocity decreasing with the ratio d/D. We analyse dispersion parallel and transverse to the mean velocity by studying the bead distribution in the x-y plane at the exit of the packing (radial dispersion) and the transit time distribution (longitudinal dispersion) while varying the height H of the bed. Diffusion in both directions is found to be governed essentially by the diameter D of packed spheres and not by the size d of the small beads. A dispersivity length characterising the spreading amplitude is determined. Comparisons between transverse and longitudinal dispersion demonstrate that both processes have similar properties. A key parameter is the diameter D which controls the path length of the particles. Received 5 November 1999 and Received in final form 30 March 2000     

Theoretical evaluation of a shadow Doppler velocimeter

The shadow Doppler velocimeter (SDV) allows one to measure the velocity and size of non-spherical and optically non-homogeneous particles with high temporal and spatial resolution. The technique is based on coherent, near forward off-axis imaging of the particles. This paper is devoted to the rigorous evaluation of the image formation of a spherical particle illuminated by two continuous laser beams and to define the theoretical limits and the sizing accuracy of the SDV approach.     

Simultaneous measurement of particle size, velocity, andtemperature in thermal plasmas

The in-flight measurement of particle parameters (size, velocity, temperature, and local number density) can prove insight into the plasma processing of solid materials. A measurement technique for simultaneously obtaining the size, velocity, and temperature of particles entrained in high-temperature flow fields is described. Particle size and velocity are obtained from a combination laser-particle-sizing system and laser Doppler velocimeter. The particle temperature is determined by a two-color pyrometry technique and the data rate is a measure of relative particle number density. Typical measured temperatures and velocities for the 5-100 μm particles used in plasma spraying are 1600-3500 K and 100-300 m/s, respectively. Since particle size, velocity, and temperature are measured simultaneously, cold particles (<1600 K) are identified and their relative number density can be quantified. Data from two plasma spray systems, a metal one (Ni-Al) and a metal oxide one (Al₂O₃), are presented and their application to understanding the plasma spray-coating process is illustrated     

Effect of surrounding gas temperature on the morphological evolution of TiO2 nanoparticles generated by laser ablation in tubular furnace

Titanium oxide nanoparticles are synthesized by laser ablation of Ti target in oxygen atmosphere under well-controlled temperature profiles in a tubular furnace. The size and the shape of generated nanoparticles are varied by changing the temperature of furnace. The mobility-based size distributions of generated air-borne nanoparticles are measured using a scanning mobility particle sizer, and the size distributions of primary particles are analyzed by a scanning electron microscope. When the particles are generated by laser ablation at the room temperature, the particles are agglomerates in gas phase with the average mobility diameter of 117 nm and the mean diameter of primary particles of 11 nm. The primary particle diameter increases from 11 to 24 nm by raising the furnace temperature up to 800 °C. Since the mass of Ti vapor ablated from a target is found to be constant regardless of the furnace temperature, this particle growth may be attributed to the reduction in nuclei number as a result of mild quenching at higher temperatures. As the temperature reaches higher than 1,000 °C, the mobility diameter suddenly drops and the primary particle diameter increases due to sintering, and at 1,200 °C the mobility diameter coincides with the primary particle diameter. Since the laser oven method offers an independent control of vapor concentration and the temperature of surrounding atmosphere, it is an effective tool to study the formation process of nanoparticles from primary particles with a given size.     

The effects of powder properties on in-flight particle velocity and deposition process during low pressure cold spray process

In cold spray process, impacting velocity and critical velocity of particles dominate the deposition process and coating properties for given materials. The impacting velocity and critical velocity of particles depend on the powder properties and cold spray conditions. In the present study, the in-flight particle velocity of copper powder in low pressure cold spraying was measured using an imaging technique. The effects of particle size and particle morphology on in-flight particle velocity and deposition efficiency were investigated. The critical velocity of copper powder was estimated by combining the in-flight particle velocity and deposition efficiency. The effect of annealing of feedstock powder on deposition and critical velocity was also investigated. The results showed that the irregular shape particle presents higher in-flight velocity than the spherical shape particle under the same condition. For irregular shape particles, the in-flight velocity decreased from 390 to 282 m/s as the particle size increases from 20 to 60 μm. Critical velocities of about 425 m/s and more than 550 m/s were estimated for the feedstock copper powder with spherical and irregular shape morphology, respectively. For the irregular shape particles, the critical velocity decreased from more than 550 to 460 m/s after preheating at 390 °C for 1 h. It was also found that the larger size powder presents a lower critical velocity in this study.     

Experimental investigation of particle velocity distributions in windblown sand movement

With the PDPA (Phase Doppler Particle Analyzer) measurement technology, the probability distributions of particle impact and lift-off velocities on bed surface and the particle velocity distributions at different heights are detected in a wind tunnel. The results show that the probability distribution of impact and lift-off velocities of sand grains can be expressed by a log-normal function, and that of impact and lift-off angles complies with an exponential function. The mean impact angle is between 28° and 39°, and the mean lift-off angle ranges from 30° to 44°. The mean lift-off velocity is 0.81–0.9 times the mean impact velocity. The proportion of backward-impacting particles is 0.05–0.11, and that of backward-entrained particles ranges from 0.04 to 0.13. The probability distribution of particle horizontal velocity at 4 mm height is positive skew, the horizontal velocity of particles at 20 mm height varies widely, and the variation of the particle horizontal velocity at 80 mm height is less than that at 20 mm height. The probability distribution of particle vertical velocity at different heights can be described as a normal function. Supported by the National Natural Science Foundation of China (Grant No. 10532030) and the National Basic Research Program of China (Grant No. G2000048702)     

Noise from small air jets and a quiet valve

Noise measurements of air jets of from 0·0794 to 0·635 cm diameter, with jet exit velocity varying from 54 to 244 m/s, to frequencies of 100 kHz are presented. Results are compared to those previously obtained for larger nozzles; acoustical power spectral density curves are found to be similar to those for the larger nozzles at like velocities. Results of a noise survey conducted near a 0·127 m line size quiet vent valve having approximately 20 000 square jets, 0·127 cm on a side are presented and found to agree with the laboratory nozzle noise data. Noise above a jet velocity of 120 m/s was found to be quadrupole in nature, while below this velocity dipole surface sound was observed; this surface noise is the noise of quiet valves, which operate at low velocities. It is estimated that a quiet valve jet of 0·025 cm diameter, with a velocity near 60 m/s will exhibit a peak acoustical power spectral density at frequencies beyond the range of human audibility.     

高速数字全息测量乙醇喷雾火焰中液滴三维位置、粒径及蒸发率

喷雾蒸发燃烧的研究对指导发动机燃烧系统设计具有重要意义。本文搭建了高速数字全息系统,在线测量乙醇喷雾火焰中液滴的粒径、三维位置、速度及蒸发率。对喷雾火焰中的液滴进行了统计分析,得到液滴粒径及三维空间分布。燃烧喷雾场液滴的平均粒径为68μm;非燃烧火焰测试区液滴数量多且较密集,燃烧火焰测试区液滴数量少且稀疏.追踪单液滴并处理得到湍流火焰中液滴的运动轨迹及速度。通过研究粒径的平方D2随停留时间ts的变化,测得液滴平均蒸发率为-3.343×10-7 m2/s.     

Prediction of particle sticking efficiency for fly ash deposition at high temperatures

The tendency of ash particles to stick under high temperatures is dictated by the ash chemistry, particle physical properties, deposit surface properties and furnace operation conditions. A model has been developed in order to predict the particle sticking efficiency for fly ash deposition at high temperatures. The model incorporates the particle properties relevant to the ash chemistry, particle kinetic energy and furnace operation conditions and takes into consideration the partial sticking behaviour and the deposit layer. To test the model, the sticking behaviours of synthetic ash in a drop tube furnace are evaluated and the slagging formation from coal combustion in a down-fired furnace is modelled. Compared with the measurements, the proposed model presents reasonable prediction performance on the particle sticking behaviour and the ash deposition formation. Through a sensitivity analysis, furnace operation conditions (velocity and temperature), contact angle and particle size have been found to be the significant factors in controlling the sticking behaviours for the synthetic ash particles. The ash chemistry and furnace temperature dictate the wetting potential of the ash particles and the melting ability of the deposit surface; particle size and density not only control the particle kinetic energy, but also affect the particle temperature. The furnace velocity condition has been identified as being able to influence the selective deposition behaviour, where the maximum deposition efficiency moves to smaller particles when increasing the gas velocity. In addition, the thermophoresis effect on the arrival rate of the particles reduces with increasing the gas velocity. Further, increasing the melting degree of the deposit layer could greatly enhance the predicted deposition formation, in particular for the high furnace velocity condition.     

激光熔覆中金属粉末粒子与激光相互作用模型

为了对同轴激光熔覆过程中运动的金属粉末粒子的速度和温度进行理论分析,并研究各工艺参量的影响,建立了运动中金属粉末粒子的运动模型和热模型.模拟结果表明,粉嘴几何尺寸、粒子直径以及气/粉两相流初始速度是影响粒子运动行为的重要因素;粉嘴几何尺寸、激光焦点位置、激光发散角、激光功率、粒子直径以及气/粉两相流初始速度是影响粒子热行为的重要因素.在相同的工艺参量下(粉嘴出口内径r=2 mm,粉嘴倾角α=60°,初始气流速度v0=0.8 m/s),基于数字粒子图像测速(DPIV)技术,对316L不锈钢粉末粒子运动模型进行了实验验证.结果表明,运动理论模型是可靠的.该模型是掌握同轴激光熔覆过程中金属粉末粒子运动行为的有效工具;同时,热模型也是分析粉末粒子温度随不同参量变化的重要工具.     

Electrostatic charging behaviour of dielectric particles in a pressurized gas–solid fluidized bed

The charging behaviour of insulating particles in pressurized fluidized beds was investigated by fluidizing five polyethylene resins in a column of 150 mm inner diameter and 2.0 m height. Seven collision ball probes at different levels and radial positions monitored the electrostatic charge generation in the bed. The influences of operating pressure and superficial gas velocity on the degree of electrification were studied. For each polyethylene resin, the electrostatic charges of the particles in the upper part of the bed gained a polarity which differed from the particles in the lower part of the bed due to bipolar charging and particle segregation. The hydrodynamics in the fluidized bed significantly influenced the particle electrification. Due to increased bubble size and rise velocity, electrostatic charge generation was enhanced as the superficial gas velocity increased. However, it was difficult to predict the influence of elevated pressure on the charging behaviour of each resin as a result of the complex impacts of pressurization on the hydrodynamics and electrification.     

Design and Performance Evaluation of Low‐Volume PM2.5 Inlet for Analyzing Chemical Composition

A new PM_2.5 inlet, based on the particle cup impactor configuration, was designed for sampling fine particles smaller than 2.5 μm in aerodynamic diameter and for operating at a flow rate of 5 l/min, as the devices, which are used to analyze the chemical composition of the particles, have good efficiency only at low‐volume flow rates. The performance of the inlet was evaluated in a test chamber, and the optimum dimensions of the particle cup impactor were determined by varying the nozzle‐to‐cup distance. Additional experiments covering flow rates between 3 and 10 l/min with particle sizes between 0.8 and 5.0 μm were carried out in the test chamber. The performance indicated that a nozzle‐to‐cup distance of 1.1 mm would yield a sharp size cutoff. The results from the tests showed that the inlet had a cutoff size of 2.55 μm in aerodynamic diameter at a flow rate of 5 l/min.     

Sizing Polydisperse Dispersions by Focused Beam Reflectance and Small Angle Static Light Scattering

In this work, two different methods for particle characterization, namely focused beam reflectance and small angle static light scattering, are quantitatively compared. The results are presented in the form of moment ratios of the particle size distribution, i.e., the number weighted diameter, D_1/0, and the volume weighted diameter, D_4/3, for a broad range of particle size distributions ranging from 20 to 400 μm. Various aqueous dispersions including narrow, broad, and bimodal particle size distributions of spherical shaped ceramic beads were used in the comparison. It was found that the moment ratios obtained by focused beam reflectance measurements and small angle static light scattering correlate well, in the case of spherical particles. Furthermore, it was found that the D_1/0 values obtained by focused beam reflectance measurements are more sensitive to the presence of a small fraction of fine particles in a bimodal distribution than those obtained by small angle static light scattering.     

Copper and Copper Oxide Nanoparticle Formation by Chemical Vapor Nucleation From Copper (II) Acetylacetonate

Crystalline nanometer-size copper and copper (I) oxide particle formation was studied by thermal decomposition of copper acetylacetonate Cu(acac)₂ vapor using a vertical flow reactor at ambient nitrogen pressure. The experiments were performed in the precursor vapor pressure range of P _prec = 0.06 to 44 Pa at furnace temperatures of 431.5°C, 596.0°C, and 705.0°C. Agglomerates of primary particles were formed at P _prec0.1 Pa at all temperatures. At 431.5°C the number mean size of the primary particles increased from D _p = 3.7 nm (with geometric standard deviation _g = 1.42) to D _p = 7.2 nm (_g = 1.33) with the increasing precursor vapor particle pressure from 1.8 to 16 Pa. At 705.0°C the primary particle size decreased from D _p = 24.0 nm (_g=1.57) to D _p = 7.6 nm (_g = 1.54), respectively.At furnace temperatures of 431.5°C and 596.0°C only crystalline copper particles were produced. At 705.0°C the crystalline product of the decomposition depended on the precursor vapor pressure: copper particles were formed at P _prec>10 Pa, copper (I) oxide at P _precleq 1 Pa, and a mixture of the metal and its oxide at intermediate vapor pressures. A kinetic restriction on copper particle growth was shown, which leads to the main role of Cu₂ molecule participation in the particle formation. The formation of copper (I) oxide particles occurs due to the surface reaction of the decomposition products (mainly carbon dioxide). For the explanation of the experimental results, a model is proposed to build a semiempirical phase diagram of the precursor decomposition products.     

The Measurement of Particles Suspended in a stirred vessel using microphotography and digital image analysis

A novel technique to determine the size of particles suspended in a stirred vessel is investigated. The method uses microphotography to obtain a still image of the particles in situ. The equivalent circular diameter of the particles is obtained from the photographs using digital image analysis. The particles used for the test were certified particle size standards of a very small tolerance in diameter deviation. The size comparison was determined as a percent error between the measured particle diameter (equivalent circular diameter) and the diameter established by the particle manufacturer. To determine the limiting ranges of particle size and concentrations, spherical particles in a size range of approximately 1 to 10.0 μm (microns) in diameter were employed in the test. Concentrations varied from 0.00005% to 0.1% (mass basis). For each particle size, an aqueous solution of the particles was prepared at the desired concentration and placed in a stirred vessel. Photographs of the solutions were made at 25.5x, 40x, 60x and 80x magnification. For all sizes of particles, the entire range of concentration was examined. The results indicate a minimum size resolution of approximately 3μm, in a corresponding concentration range of 0.0001% to 0.05%. Similar limits on concentration were found for the larger diameter particles, although a true upper limit for the largest particle sizes was not established. The functional concentration range appears to shift towards higher mass concentrations with increasing particle size. For 2.92 μm diameter particles, the error in size measurement was found to be below 10% for a concentration range of 0.0005% to 0.05%. Additionally, a relationship between turbidity and the error was seen at low particle concentration levels where decreasing levels of turbidity generated increasing levels of error.     

Investigation of the performance of bipolar transverse plate ESP in the sintering flue control

In order to improve the particle collection efficiency of the electrostatic precipitator (ESP), a transverse plate ESP with bipolar discharge electrodes is proposed. The simulations of the velocity distribution have shown that when the inlet velocity is 1 m/s, within the range of 40 mm from electrode plate, the average velocities of windward side and leeward side are less than 0.7 m/s and 0.3 m/s respectively. It is clear that the velocity near the collection electrode plate of this bipolar ESP is much lower than that of the ordinary ESP at the same inlet velocity. This low velocity can lead to higher efficiency for fine dust collection due to the less dust re-entrainment in ESP. It is also found that the average velocities are getting lower when the distance between plates electrodes are greater than 150 mm in accordance with the simulations. The voltage current characteristics of the bipolar ESP are superior to the ordinary ESP. The pressure drop of the bipolar ESP is about 30% higher than that of the ordinary one. The dust penetration of the bipolar ESP is about 54% less than that of the ordinary ESP when the sintering dust with 25.405 μm mass median diameter is used as the test particulate under the condition of the electric field from 2.1 kV/cm to 3.2 kV/cm and the velocity from 1.0 m/s to 1.5 m/s.     

An Experimental Investigation of Forced Convection Heat Transfer from a Coiled Heat Exchanger Embedded in a Packed Bed

Forced convection heat transfer from a helically coiled heat exchanger embedded in a packed bed of spherical glass particles was investigated experimentally. With dry air at ambient pressure and temperature as a flowing fluid, the effect of particle size, helically coiled heat exchanger diameter, and position was studied for a wide range of Reynolds numbers. It was found that the particle diameter, the helically coiled heat exchanger diameter and position, and the air velocity are of great influence on the convective heat transfer between the helically coiled heat exchanger and air. Results indicated that the heat transfer coefficient increased with increasing the air velocity, increasing helically coiled heat exchanger diameter, and decreasing the particle size. The highest heat transfer coefficients were obtained with the packed-bed particle size of 16 mm and heat exchanger coil diameter of 9.525 mm (1/4 inch) at a Reynolds number range of 1,536 to 4,134 for all used coil positions in the conducted tests. A dimensionless correlation was proposed for Nusselt number as a function of Reynolds number, particle size, coil size, and coil position.     

Particle Mass Loading Effect on a Two-Phase Turbulent Downward Jet Flow

The particle mass loading effect on the flow structure of a two-phase turbulent jet flow was studied. A particle mass loading ratio ranging from 0 to 3.6 was used as the control parameter. The polystyrene solid particles used had nominal diameters of 210 and 780 μm. The flow Reynolds number, which was based on the pipe nozzle diameter and the fluid-phase centerline mean velocity, was 2 × 10⁴ in the current test. A two-color laser Doppler anemometer (LDA), combined with the amplitude discrimination method and the velocity filter method, was employed to measure the mean velocity distributions for the particle and fluid phases, and the turbulent intensities and Reynolds stresses of the flow. The two-phase jet flow field was measured from the initial pipe exit to 90 D downstream. Another one-component He? Ne laser LDA system was also applied to obtain the energy spectra and temporal correlations of the two-phase jet flow.