Difference In Terminal Velocity Research Articles

Effect of terminal velocities on macroscopic and microscopic hydrodynamic mixing of stratified suspensions.

We performed numerical experiments to investigate the mixing of stratified suspensions composed of different particle types by gravitational sedimentation. The mixing process is controlled by a dimensionless group Y_{m}∼U_{f}/U_{St1}, where U_{f} is a typical velocity of a macroscopic sedimenting finger and U_{St1} is the Stokes settling velocity of a single spherical particle in the upper suspension. The effects of components of Y_{m}, in particular, terminal velocities of particles, were investigated. For Y_{m}=100, no large difference was observed for the difference of components of Y_{m}, and it was confirmed that the mixing rate is determined by Y_{m}, because macroscopic (vessel-scale) mixing is dominant for large Y_{m}. For Y_{m}=5, macroscopic mixing and microscopic (individual particle-level) mixing due to the particle terminal velocity difference are of the same order, while completely different mixing patterns were observed for positive, zero, and negative terminal velocity differences: macroscopic mixing is promoted by the increase in apparent density due to microscopic mixing, small macroscopic mixing is suppressed by the individual particle settling, and jetting mixing occurs owing to pure liquid layer formation.

Terminal Velocity Determinations for Switchgrass Nodes and Internodes

HighlightsA vertical wind tunnel was fabricated to aerodynamically suspend switchgrass particles to measure terminal velocity.Overall terminal velocity estimates for node and internode were 8.04 and 5.68 m s-1, respectively.Terminal velocity prediction equation for spherical particles (Mohsenin, 1970) produced values almost identical to experimental values unlike an equation for infinite-length cylindrical particles.Hollow switchgrass particle behavior was complex with particle bouncing, rolling, tumbling, and other dynamic behaviors during aerodynamic equilibrium. Abstract. Terminal velocity is a fundamental aerodynamic property often used to separate plant anatomical components. A vertical wind tunnel was fabricated to investigate whether terminal velocities of switchgrass stem internodes and nodes were distinctly different. Wind tunnel features included a clear observation section for suspended particles and fine adjustment of airflow. Each sample terminal velocity was measured with 45 anemometer readings from nine locations and five repeated measures. The experiment evaluated two sample moisture contents (52% and 15% wet basis, hereafter referred to as w.b.), three particle lengths (0.64, 1.27, and 2.54 cm), node versus internode, and 12 replications. The 6,480 anemometer readings provided significant differences between factors and interactions. The greatest magnitude in mean terminal velocity difference was 4.55 m s-1 (i.e. 9.62 to 5.07) that resulted in a velocity ratio of 190% [(9.62/5.07) x 100]. The least magnitude of mean terminal velocity difference, while significant, was 0.36 m s-1 (i.e. 6.59 to 6.23). This offered a limited difference and may indicate that separations may need to be confined within groups of moisture category and/or particle length. Terminal velocity measurements were most similar to those calculated using the Mohsenin (1970) spherical particle equation yielding a mean (6.86 vs. 6.91 m s-1), standard deviation (1.41 vs. 1.42 m s-1), minimum (4.65 vs. 4.69 m s-1), and maximum (9.95 vs. 10.03 m s-1) for measurement and spherical particle equation, respectively. Keywords: Anatomical component, Biomass property, Physical experiment, Separation, Sorting, Switchgrass, Vertical wind tunnel.

Nonlinear Distributed Model Predictive Control for Multiple Missiles Against Maneuvering Target with a Trajectory Predictor

This study aims to solve the problem of multi-missile simultaneous attacks on maneuvering target. The challenges include multi-missile cooperative control and target’s trajectory prediction. A controller based on nonlinear distributed model predictive control (NDMPC) is designed for multiple missiles against a maneuvering target, and a trajectory prediction method based on particle swarm optimization (PSO) algorithm is proposed. This study has mainly completed the following three aspects of work. Firstly, the cost function of the controller is constructed to optimize the accuracy and synchronization of the multi-missile system with consideration of collision avoidance. Secondly, the velocity control of the leading missile is designed by using the range-to-go information in real time to ensure the attack efficiency and the control of the terminal velocity difference. Finally, a kinematic model of the target is estimated by using short-term real-time data with the PSO algorithm. The established model is employed to predict the target trajectory in the interval between radar scans. Numerical simulation results of two different scenarios demonstrate the effectiveness of the proposed cooperative guidance approach.

Study of Dry Mineral Separation Behavior in Dry Density Separators

Mineral dry density separation behavior (mineral beneficiation) involves segregation of high density particles and low density particles in the feed, i.e., in nutshell, mineral dry density beneficiation is density segregation in physics terms. In dry beneficiation, this density segregation is achieved using air as fluidized medium. Density segregation on dry separators can be achieved in two ways: (1) using minimum fluidization velocity differences and (2) using terminal velocity difference between different density particles. Dry separators based on minimum fluidization velocities follow two steps for dry beneficiation: (1) vertical density stratification and (2) horizontal segregation. Particles due to buoyancy, drag and gravitational forces get vertically density stratified and later frictional, gravity and external (vibrational, etc.) forces horizontally segregate different density particles. Dry separators based on terminal velocities follow single step for dry beneficiation of mineral, and air velocity in this type of dry density separators is maintained between terminal velocity of high density and low density particles. Velocity of air is higher for low density particles, which leads to higher drag and buoyancy forces to get pushed out of system with air and get collected at further distance than high density particles leading to density segregation. Mathematical models have been developed using force balance on particles and simulated in MATLAB for both type of separators to explain the physics of separation. Solutions to the simulated mathematical model equations are the particle trajectories of different density particles in the two dry separators. Iron ore is used as feed for studying separation futures in mathematical modeling on dry separators.

Effect of inlet speed on gravitational air separator for cenospheres accumulation from fly ash: modeling using computational fluid dynamics (CFD)

Dry gravity separation is widely used in industries due to its low operational cost. Furthermore, it does not require water to perform its separation process. Commonly used gravity separator is cyclone separator. Unfortunately, this type of separator is unable to yield various purities for its products. A modified gravity separator as an alternative relies on terminal velocity difference for different diameter and density is evaluated in this paper. The separated particles are coal fly ash and cenosphere which are the results of coal combustion where the content of cenosphere is generally 0.1% of total mass. Separated cenospehere can be used for various applications in the field of materials. In this simulation we use a particle model with a ratio of fly-ash to cenosphere mass of 1:1. Particles behavior in this gravity separator is affected by terminal velocity, linear speed, as well as rheology. Modeling with CFD (Computational Fluid Dynamics) using the Discrete Phase Model can take into account the behavior of particles that are affected by these factors. This model assumes that the simulated particles are perfectly round in shape. It uses the Euler-Lagrange framework in which the perfectly rounded particles (discrete phases, Lagrange frames) interact with air (continuous phase, Euler framework) and performed with ANSYS Fluent software. This study evaluates the effect of speed variation on Newton efficiency (NE) on a given geometry. Simulations were performed with variations of inlet velocity: 0.1 m/s; 0.25 m/s; 0.5 m/s; 1 m/s; 2 m/s; and 3 m/s. It was found that the lower the speed, the higher the NE and the optimum NE of 0.41 is obtained with 0.25 m/s inlet velocity.

Study on mixing and segregation behaviors in particulate fluidized bed system for mineral processing

In order to identify the mixing and segregation behaviors in a mineral processing operation, present study aimed on the hydrodynamics of solid–liquid fluidization. The study was carried out in a fluidization column with tapings at different height of the bed to collect the sample. The binary particles considered in this study are hematite (4800kg/m3) and quartz (2600kg/m3) at different size fractions in the range of average size 87×10−6m to 400×10−6m. It is observed that for various binary mixtures, both quartz and hematite particles share the equal composition by mass (50%) at a particular height of fluidized bed, referred as “locus point” of mixing. Study indicates that the mixing zone volume will increase for a continuous fluidized bed plant operation. It is observed that the number of locus points varies from 1 to 3 signifying their dependency on the size ratios of binary mixture. Whenever, the difference in terminal velocity between quartz and hematite particles approaches to zero, mixing is enhanced. Further, the present study is extended to find the segregation index for the different size ratios of quartz and hematite particles. It is evident that depending on the size ratios, various regions such as complete segregation, partial mixing and complete mixing can be observed.

The Spectral Ice Habit Prediction System (SHIPS). Part IV: Box Model Simulations of the Habit-Dependent Aggregation Process

Abstract The purpose of this paper is to assess the prediction of particle properties of aggregates and particle size distributions with the Spectral Ice Habit Prediction System (SHIPS) and to investigate the effects of crystal habits on aggregation process. Aggregation processes of ice particles are critical to the understanding of precipitation and the radiative signatures of cloud systems. Conventional approaches taken in cloud-resolving models (CRMs) are not ideal to study the effects of crystal habits on aggregation processes because the properties of aggregates have to be assumed beforehand. As described in Part III, SHIPS solves the stochastic collection equation along with particle property variables that contain information about crystal habits and maximum dimensions of aggregates. This approach makes it possible to simulate properties of aggregates explicitly and continuously in CRMs according to the crystal habits. The aggregation simulations were implemented in a simple model setup, assuming seven crystal habits and several initial particle size distributions (PSDs). The predicted PSDs showed good agreement with observations after rescaling except for the large-size end. The ice particle properties predicted by the model, such as the mass–dimensional (m-D) relationship and the relationship between diameter of aggregates and number of component crystals in an aggregate, were found to be quantitatively similar to those observed. Furthermore, these predictions were dependent on the initial PSDs and habits. A simple model for the growth of a particle’s maximum dimension was able to simulate the typically observed fractal dimension of aggregates when an observed value of the separation ratio of two particles was used. A detailed analysis of the collection kernel indicates that the m-D relationship unique to each crystal habit has a large impact on the growth rate of aggregates through the cross-sectional area or terminal velocity difference, depending on the initial equivalent particle distribution. A significant decrease in terminal velocity differences was found in the inertial flow regime for all the habits but the constant-density sphere. It led to formation of a local maximum in the collection kernel and, in turn, formed an identifiable mode in the PSDs. Remaining issues that must be addressed in order to improve the aggregation simulation with the quasi-stochastic model are discussed.

A Traveling Time Model as Function of Water Density and Vegetable Size, Shape and Density

A Traveling Time Model as Function of Water Density and Vegetable Size, Shape and Density In this research, the possibility of using the rising and dropping time of vegetables through water as a means of hydro-sorting of tomato and potato was studied. The dropping time of potato and rising time of tomato were theoretically formulated and then determined experimentally using water column. The best models for dropping time of potato (cv. Analytic) and rising time of tomato (cv. Rio grand s) as a function of water and vegetable densities, shape factor and vegetable volume were modelled with determination coefficients of 0.95 and 0.91, respectively. It was found that difference between vegetables and water densities had major effect on rising and dropping time. It can be concluded that in the sorting systems, difference in terminal velocities of vegetables can be used as a suitable factor for design the sorting system devices.

Physical properties that govern fiber separation from distillers dried grains with solubles (DDGS) using sieving and air classification

Distillers dried grains with solubles (DDGS) is a coproduct of the dry grind corn to fuel ethanol process. Recently, we showed that Elusieve process, the combination of sieving and elutriation (air flow), was effective in separating fiber from DDGS. DDGS was sieved into different fractions and the sieved fractions were air classified to separate fiber. In this study, we determine relevant physical properties and terminal velocities of fiber and nonfiber that govern fiber separation from DDGS. Particle densities were determined using a pycnometer and equivalent spherical diameters were calculated from mean particle volume, obtained as mean particle mass divided by particle density. Sphericity of fiber was calculated as the ratio of surface area of sphere having the same volume as fiber to the actual surface area of fiber. Sphericity of nonfiber was calculated from experimentally determined terminal velocities of nonfiber and using the correlation between terminal velocity and sphericity. Terminal velocities of fiber and nonfiber are the lowest air velocities at which fiber and nonfiber, respectively, were carried by air. Particle density of fiber was higher than particle density of nonfiber. It was visually observed that fiber was flat and nonfiber was not flat. Sphericity of fiber and nonfiber ranged from 0.19 to 0.47 and 0.72 to 0.92, respectively. Within each sieved fraction, fiber particles had lower or comparable equivalent spherical diameters relative to nonfiber particles. Fiber particles experienced higher drag force and aspirated at low air velocities because: (1) they had lower or comparable mass relative to nonfiber particles and (2) their shape was flatter than nonfiber particles. The difference in shapes and equivalent spherical diameters of fiber and nonfiber within each sieved fraction resulted in difference in their terminal velocities within sieved fractions. This difference in terminal velocities allows separation of fiber from DDGS. Sieving of DDGS into fractions and then blowing air through sieved fractions was effective in separating fiber.

高性能微粒発泡ビース製造のための流動層焼成炉のスケールアップ研究および実用化技術開発

High-quality and fine-grade (150-1200μm) foamed ceramic particles were prepared using a bubbling fluidized bed furnace of a pilot plant scale at residence times ranging between 300-1200s and bed temperatures above 1363K. The particle size lies in the intermediate size range between artificial lightweight aggregates (ALAs) for civil engineering and micro fillers.Three bubbling fluidized bed furnaces (i. d.=40, 100 and 700mm) were developed for scale up research. Continuous semi-batch operation was achieved by elutriation separation of products from the fluidized bed of inert bed materials due to the difference in terminal velocities of particles. The accumulated temperature control method improved the uniformity in sintering from batch to batch operations and the error was in the order of 3 percent. At the pilot plant scale (i. d. 700mm), a production rate of over 150kg/h was achieved. The fluidized bed products showed comparable tensile strengh and Weible coefficient higher than the other products.

EFFECT OF ACCESSION AND MOISTURE CONTENT ON AERODYNAMIC PROPERTIES OF AFRICAN YAM BEAN (SPHENOSTYLIS STENOCARPA)

Theoretical and experimental terminal velocities of two African yam bean accessions (TSs 137 and TSs 138) atmoisture levels of 4, 8, 12, and 16% wet basis(w.b.), levels useful in the design of processing and handling equipment, werestudied. A Split Plot in Randomized Complete Block Design (RCBD) was used for statistical analysis of data. The theoreticalterminal velocities were determined for particles by the commonly used aerodynamic equations while the actual terminalvelocity ranges were measured with an aspirator column. The observed terminal velocity range for the two accessions forall moisture content levels and feed rates was between 9.9 and 18.7 m/s. The theoretical values, calculated using thecorrelation of Cd NRe2 versus NRe, were found to be within 13% of the measured values. For different moisture contents andfeed rates, the limits of terminal velocity varied little but the intermediate paths were distinctly different. The curves of percentmaterial carried away versus velocity followed a sigmoid path. There was no statistically significant difference in terminalvelocities between accessions. There was a highly significant effect (p < 0.05) of moisture content and the method used tocalculate terminal velocities.

Turbulence effects on the collision kernel. II: Increase of the swept volume of colliding drops

An equation is deduced which gives the relative velocity between drops falling in three-dimensional turbulent flow. The turbulence is assumed to be homogeneous and isotropic. In describing the flow, both the inertial and viscous turbulent ranges are taken into account. It is demonstrated that the inertia of drops leads to the formation of a significant relative velocity between them, which for small droplets can be greater than the gravity-driven velocity difference. For a turbulence dissipation rate of ϵ = 100 cm2s−3, typical of small early cumulus clouds, the turbulence-induced relative velocity of drops with radii up to 30 μm is nearly twice the difference in their terminal velocities induced by gravity. At ϵ = 400 cm2s−3 turbulence driven relative drop velocity for drop radii up to 50 μm can be five times as great as their terminal-velocity difference. Factors giving rise to the relative drop velocity are discussed. It is indicated that, for small drops, the inertial acceleration term dominates the terms for the vertical shear and the vertical shear of the inertial acceleration. Calculations of the evolution of the drop spectrum using the stochastic coalescence equation were carried out. In the expression widely used for collision kernels, the difference in terminal velocities was replaced by the root-mean-square difference in drop velocities. The results indicate that cloud turbulence influences the rate of generation of large drops significantly. For example, the formation of rain drops with radii of 100 μm starting from an initial narrow droplet-spectrum centred at about 10 μm takes 12 minutes for ϵ = 200 cm2s−3 and about 24 minutes for ϵ = 50 cm2s−3. When, during this period, turbulence is put to zero, no rain drops form.

Turbulence effects on the collision kernel. II: Increase of the swept volume of colliding drops

AbstractAn equation is deduced which gives the relative velocity between drops falling in three‐dimensional turbulent flow. The turbulence is assumed to be homogeneous and isotropic. In describing the flow, both the inertial and viscous turbulent ranges are taken into account. It is demonstrated that the inertia of drops leads to the formation of a significant relative velocity between them, which for small droplets can be greater than the gravity‐driven velocity difference. For a turbulence dissipation rate of ϵ = 100 cm2s−3, typical of small early cumulus clouds, the turbulence‐induced relative velocity of drops with radii up to 30 μm is nearly twice the difference in their terminal velocities induced by gravity. At ϵ = 400 cm2s−3 turbulence driven relative drop velocity for drop radii up to 50 μm can be five times as great as their terminal‐velocity difference. Factors giving rise to the relative drop velocity are discussed. It is indicated that, for small drops, the inertial acceleration term dominates the terms for the vertical shear and the vertical shear of the inertial acceleration. Calculations of the evolution of the drop spectrum using the stochastic coalescence equation were carried out. In the expression widely used for collision kernels, the difference in terminal velocities was replaced by the root‐mean‐square difference in drop velocities. The results indicate that cloud turbulence influences the rate of generation of large drops significantly. For example, the formation of rain drops with radii of 100 μm starting from an initial narrow droplet‐spectrum centred at about 10 μm takes 12 minutes for ϵ = 200 cm2s−3 and about 24 minutes for ϵ = 50 cm2s−3. When, during this period, turbulence is put to zero, no rain drops form.

銅製錬自溶炉のシャフト内の反応解析 （第２報） 反応シャフトにおける銅精鉱粒子の酸化および衝突挙動

Water-quenched samples were collected from the reaction shaft of a pilot scale flash furnace, in which copper concentrate was processed together with silicious sand. The samples were subjected to size distribution measurements and chemical analyses. Based on the results, the following conclusions have been obtained:(1) The sampling method used in this study can collect not only coarse particles but fine ones equally.(2) The desulfurization reaction of copper concentrate is not completed in the reaction shaft, but proceeds even in the settler to some extent.(3) A copper concentrate particle impinges on other particles about 40 times while falling down 4m from the shaft roof to the bath, and its final diameter becomes more than 250μm or 5 times as large as the original diameter.(4) Such increase in particle diameter is not brought about by the agglomeration of the particles during feeding nor difference in terminal velocity of the particles, but by turbulence in the reaction shaft.

Induced velocities of grains embedded in a turbulent gas

A theory is presented for the dynamics of dust particles in an incompressible turbulent fluid. Grain-gas coupling occurs through friction forces that are proportional to the mean grain velocity relative to the gas. This test particle theory is applied to the case of a Kolmogoroff spectrum in a protostellar cloud. The mean turbulence induced grain velocity and the mean turbulent relative velocity of two grains are calculated. Whereas the former should determine the dust scale height, grain-grain collisions are influenced by the latter. For a resonable strength of the turbulence, the mean induced relative velocity of two particles turns out to be at least as large as the corresponding terminal velocity difference during gravitational settling.

On the Evaluation of the Collection Kernel for the Coalescence of Water Droplets

Abstract Two anomalies are described which arise in the kernel for stochastic droplet collection when it is specified by the formula of Scott and Chen for the linear collision efficiency y(R,r) and by the formula of Wobus et al. for the droplet terminal velocity V(R). It is pointed out that if accurate values for y(R,r) are to be obtained for a given droplet pair by interpolation using data for specific droplet pairs, then for large droplet radii (R<30 μm) it is desirable that these data he tabulated for 2-μm intervals of R. It is shown that if the difference in terminal velocities of two droplets is computed from a formula approximating V(R) and composed of various functions V*(R) applicable over adjoining domains of R, then it is necessary that these functions be constructed so that the formula and its derivatives, at least up to second order, are everywhere continuous. An improved formula for V(R) satisfying this criterion is described.

The Coalescence process in raindrop growth

Photographic and visual observations of a large number (> 104) of collisions between two water drops, one of cloud droplet size (70 μ diameter) and one of raindrop size (1.0–3.5 mm diameter) reveal the conditions under which a collision may result in coalescence, bouncing, or partial coalescence. Coalescence occurs for 85–95% of collisions at velocities equivalent to the difference in terminal velocities of the drop-droplet pair. Bouncing always results from collisions in which the droplet center trajectory does not intersect the collector drop surface. Partial coalescence occurs infrequently and is restricted to narrow ranges of velocities and incident angles. Barriers to coalescence are the existence of an air film between the approaching surfaces and the ability of the drop surface to deform on collision. Sufficient electrical attraction, long contact time, or high impact velocity can overcome these barriers and insure coalescence. Surface tension variations of ±15% from the value for distilled water did not affect the coalescence process at velocities equivalent to natural conditions. Electric charges of like or unlike sign on the drop pair are found to enhance coalescence once a threshold charge of 10−2 esu on the collector drop is attained (with a droplet charge of −10−5 esu); higher drop charges insure 100% coalescence. Values of coalescence efficiency E2 calculated from experiments, lead to an expression E2 = R2/(R + r)2, which is valid at least for drop radii 400 μ<R<2000 μ, and droplet radii 20 μ<r<100 μ. Sample calculations show that, because not every collision results in coalescence, previous growth rates are overestimates. In summary, it is no longer considered adequate to assume a coalescence efficiency of unity for all drop-droplet collisions.

Ultimate velocity of drops in stationary liquid media

AbstractThe effects of high field viscosity and of low inter‐facial tension on the terminal velocity of single liquid drops falling through stationary liquid fields were investigated. Drops of tetrachloroethylene, ranging from 0.08 cm. to 1.4 cm. equivalent diameter, were allowed to fall through four different types of field fluids made by the addition of carboxy methyl cellulose, Lytron 890, corn syrup, and glycerine to water. Viscosities varied from 41.3 to 514 centipoises.Low interfacial tension systems were ethylchloroacetate‐water, furfural‐water, and benzyl alcohol‐water with interfacial tensions of 16.43, 5.70, and 4.25 dynes per cm. respectively.For systems of high field viscosity, the usual drag curve appears to be more useful than the correlation proposed by Hu and Kintner. For systems of low interfacial tension (below 20 dynes/cm.) and low field viscosity (of the order of one centipoise) the latter serves to correlate accurately the data of 25 systems.A comparison of the pour technique with the usual nozzle method for the introduction of drops resulted in a terminal velocity difference of less than three percent. Wall proximity corrections were made when necessary.