Dispersion Coefficient Of Particles Research Articles

Dispersion of initially-static and initially-excited particles in a turbulent fluid flow

The motion of a particle released into a fluid flow depends upon the velocity of the fluid in the immediate vicinity of the particle. In a turbulent flow, the fluid velocity is a random quantity, so that particle motions are also random. Knowledge of certain statistical characteristics of the fluid motion allows for determination of mean properties of the particle motions. In this paper, dispersion of particles is analysed by assuming a simple form for the auto-correlation of the fluid motions following the particle in homogeneous, isotropic and stationary turbulence. Two cases are considered, one where the particles are initially at rest, the second where the particles are initially ‘excited’. Particle velocity auto-correlations, particle dispersion coefficients and related quantities are determined as functions of time for both cases. Expressions for development times for heavy particles are derived.

On the inertia effect in eddy interaction models

It has been demonstrated experimentally and theoretically that the dispersion coefficients of non-fluid particles in isotropic turbulent flows can exceed the dispersion coefficient of fluid particles. This “inertia effect” cannot be allowed for in eddy interaction models in which it has been shown that the long-time dispersion coefficient of non-fluid particles is always less than that of fluid particles. In the limit of infinitely heavy particles, the difference between the dispersion coefficients is due to the difference between the Lagrangian and Eulerian integral time scales τ L and τ E and it can be shown that τ E< τ L in existent eddy interaction models. In this paper, the relationship between τ E and τ L is investigated for a modified eddy interaction model for which is is possible that τ E τ L, which will lead to greater long-time dispersion of heavy non-fluid particles than of fluid particles. Numerical simulations are carried out to quantify the effect of the modifications on the dispersion of finite size particles.

Numerical Simulation of Heavy Particle Dispersion—Scale Ratio and Flow Decay Considerations

Lagrangian statistical quantities related to the dispersion of heavy particles were studied numerically by following particle trajectories in a random flow generated by Fourier modes. An experimental fluid velocity correlation was incorporated into the flow. Numerical simulation was performed with the use of nonlinear drag. The simulation results for glass beads in a nondecaying turbulent air showed a difference between the horizontal dispersion coefficient and vertical dispersion coefficient. This difference was related to the differences of both the velocity scale and the time scale between the two direction. It was shown that for relatively small particle sizes the particle time scale ratio dominates the value of the diffusivity ratio. For large particles, the velocity scale ratio reaches a value of 1/2 and thus fully determines the diffusivity ratio. Qualitative explanation was provided to support the numerical findings. The dispersion data for heavy particles in grid-generated turbulences were successfully predicted by the simulation when flow decay was considered. As a result of the reduction in effective inertia and the increase in effective drift caused by the flow decay, the particle dispersion coefficient in decaying flow decreases with downstream location. The particle rms fluctuation velocity has a slower decay rate than the fluid rms velocity if the drift parameter is large. It was also found that the drift may substantially reduce the particle rms velocity.

Effect of Particle Residence Time on Particle Dispersion in a Plane Mixing Layer

A particle dispersion has been experimentally investigated in a two-dimensional mixing layer with a large relative velocity between particle and gas-phase in order to clarify the effect of particle residence time on particle dispersion. Spherical glass particles 42, 72, and 135 μm in diameter were loaded directly into the origin of the shear layer. Particle number density and the velocities of both particle and gas phase were measured by a laser Doppler velocimeter with modified signal processing for two-phase flow. The results confirmed that the characteristic time scale of the coherent eddy apparently became equivalent to a shorter characteristic time scale due to a less residence time. The particle dispersion coefficients were well correlated to the extended Stokes number defined as the ratio of the particle relaxation time to the substantial eddy characteristic time scale which was evaluated by taking account of the particle residence time.

Particle dispersion in a binary solid‐liquid fluidized bed

AbstractThe mixing and segregation behavior of liquid fluidized beds containing two different‐sized particle species are described mathematically. This model is based on a mass balance, rather than a volume balance, which has been used by most previous researchers. The model also includes the effects of density gradients that are present in the bed. Particle dispersion coefficients in a binary‐solid fluidized bed are evaluated using this model. Further, a correlation that allows the calculation of these particle dispersion coefficients is presented, which describes not only dispersion coefficients calculated using the above model, but also those presented by other researchers. It is applicable over a broad range of variables of practical interest and is based on relevant dimensionless parameters to account for the influence of important particle and fluid properties on the particle dispersion characteristics.

Mouvement des particules solides en fluidisation liquide solide

Solid motion in liquid fluidized beds has been analysed using a radioactive particle and two detection devices partly superimposed, dividing the be Particle velocity was determined by two different estimations, using the net flux across a zone frontier and the residence time between two successive Particle dispersion coefficients, determined from residence time distribution, were also strongly increasing with increasing liquid velocity. It was co

Experiments on particle dispersion in a turbulent mixing layer

The dispersion of solid particles in a turbulent shear layer has been investigated experimentally to clarify the dominant factors which govern the particle motion in turbulent gas flow. Spherical glass particles were loaded at the origin of a two-dimensional mixing layer. Flow measurements were carried out by a modified laser Doppler anemometer which enabled the measurement of both particle and gas phase velocities and particle number density. The particle dispersion strongly depended on the ability of the particles to follow the motion of large-scale eddies and was well-classified by the Stokes number (St). The range of St values covered in the present study turned out to involve three different stages of particle dispersion. It was confirmed from the experiments (with 0.5 < St < 2.5) that the particle dispersion coefficients became larger than the eddy diffusivity of the gas phase, i.e. the particles in the developing shear layer dispersed more than the fluid phase.

Immersed heater‐to‐bed heat transfer in liquid‐solid fluidized beds

Heat transfer characteristics of a liquid-solid fluidized bed with an immersion heater were experimentally investigated. Specifically, the axial dispersion coefficients of fluidized particles were measured by means of a relaxation method to examine the effects of particle motion on the rate of heat transfer. Furthermore, the effects of the liquid flow rate or bed porosity and of the particle size on the heat transfer resistance in the region adjacent to the heater surface and that in the bed proper were examined. The resultant data have been analyzed in terms of the two resistance-in-series model

Chaotic dynamics of heavy particle dispersion: Fractal dimension versus dispersion coefficients

The chaotic dynamics of Lagrangian motion of particles in a steady Arnold–Beltrami–Childress (ABC) flow and a pseudoturbulence are investigated and the Lyapunov exponents and fractal dimensions of particle trajectories for different particle inertia and particle drift velocity are computed. The dispersion process of particles could be characterized by the fractal dimension and dispersion coefficients. The interesting behavior of fractal dimension of particle motion in ABC flow suggested the similarity of particle motion in ABC flow and in a mixing layer. The relationship between particle dispersion coefficient and fractal dimension was nearly linear for the pseudoturbulence.

Mixing and segregation in a liquid fluidized bed of particles with different size and density

AbstractExperimental studies have been carried out on fluidization of irregular particle mixtures of different size and density. The mixing and segregation phenomena could be interpreted on the basis of the diffusion model of Kennedy and Bretton. The dependence of computed particle dispersion coefficient on liquid velocity, particle density and size has been discussed.

Experimental studies of plume dispersion in convective conditions—II. Horizontal plume dispersion

Field measurements have been made of the horizontal dispersion of four different plumes from four different sites during convective conditions. The plumes were emitted from tall stacks and values of the dispersion coefficients were obtained from overhead photography and by traversing plume-sensitive instruments through the plume at right angles to the plume direction. Values of the single particle dispersion coefficients were obtained from a mosaic of photographs. These values for a low-buoyancy plume are shown to be consistent with the calculations of Lamb (1979, In Fourth Symposium on Turbulence, Diffusion and Air Pollution, pp. 27–33) and Weil (1979, Martin Marietta Corp., Baltimore, MD) and confirm the validity of Lamb's predictions. Values of the relative dispersion coefficients were also obtained from photographs and airborne traverses. These data were scaled by the buoyancy length scale, l B = F u 3 , and the resulting values of σ y l B are shown to be a function of the non-dimensional down-wind distance, x l B , for values of ( x l B) 2 3 < ∼100 . At ( x l B) > ∼100 the buoyancy scaling ceases to provide an adequate description of the diffusion process, indicating the growing effects of ambient atmospheric turbulence on the plume. The relative diffusion data non-dimensionalized by division by z i are shown to be a function of Deardorffs' (1974, Boundary-Layer Met. 7,81–106) dimensionless time X = xw ∗ uz i . This indicates that the turbulence present in the convective boundary layer is effective at scales small enough to be responsible for relative diffusion.

Mixing Characteristics of industrial flotation columns

Flotation columsn are counter-current bubble columns that have recently been applied to froth flotation separation of minerals. A unique feature of a flotation column is the water stream applied at the top of the column for the purpose of washing entrained nonfloatable particles from the floatable bubble-particle aggregate, consequently permitting high upgrading in a single separation stage. The objective of our work is the development of a scale-up methodology for flotation columns, and as a first step toward this objective we have measured the dispersion parameters of large industrial columns. Pulsed tracer tests were performed with both liquid and solid tracers on 0.46 and 0.91 m square columns, each 13 m high. The liquid axial dispersion coefficient appears to be linearly dependent upon column radial dimension. As well, it is confirmed that the axial dispersion coefficient of mineral particles is the same as that of the liquid, and that the residence time of solid particles is unaffected by a bubble swarm.

Measurement of the axial dispersion of particles in a liquid fluidized bed applying a random walk method

Axial dispersion coefficients of large spheres in a liquid fluidized bed have been measured. The inlet to outlet sojourn type of residence time distribution method in a system governed by the dispersion equation is applied. From the average passage time of a paramagnetic tracer particle through two detection planes, created by mutual inductors, the axial dispersion coefficient is obtained. The results are compared with those obtained by a visual technique based on the Einstein-Smoluchowski equation. The axial particle dispersion data obtained are an extension of the available literature data to higher liquid velocities; they are well in line with these data. The axial particle dispersion coefficient in liquid fluidized beds is roughly given by: ▪

Mixing of solid particles in vertical pneumatic transport

A method of mixing particulate materials during their pneumatic transport is proposed. The calculation of this operation is based on the effective particle dispersion coefficient determined in experiments. This new method of particle mixing has been used to neutralize the electric charge on the particles generated during their pneumatic transport.

A new method to measure particle turbulent dispersion using laser doppler anemometer

A laser doppler anemometer (LDA) was used to measure local dispersion coefficients of particles in turbulent flow. The experimental set-up is described along with the data acquisition equipment and processing procedures. Results for 5 μ particles dispersing from a point source in pipe flow are shown. A second estimate for the diffusivity was obtained from mean square dispersion measurements.

Lateral mixing of solids in batch gas-solids fluidized beds

The lateral dispersion coefficients of particles, D /SUB sr/, were measured in a rectangular gas-solids fluidized bed and the effects of various factors on D /SUB sr/ were studied. Based on the results, an expression has been derived to correlate D /SUB sr/ as a function of the particle characteristics, properties of the fluidizing medium, and operating conditions.

管内気流中の粒子の散乱

To study the phenomenon of particle dispersion in the air flow in a pipe, the particle flux distribution using variously shaped particles were measured. The following results are obtained: 1) The dispersion coefficient of the particles in the first turbulent diffusion zone, is 0.5-1.3 times of that of the air flow. 2) The disperion coefficient of the particles in the second turbulent diffusion zone, is (1.9-8.6)×10-4m2/s when the mean air velocity is 4-18m/s. 3) As the particle size becomes larger the dispersion coefficient of the spherical particles decreases. But if irregularly shaped particles are used, the dispersion coefficient of the particles. does not always decrease. 4) The delay time of dispersion is known in the empirical formula of the function of dk/U

Mean velocity and longitudinal dispersion of heavy particles in turbulent open-channel flow

This paper deals with the motion of a heavy particle in a turbulent flow in an open channel with a smooth bottom. For the case when the particle stays in suspension in the main body of the flow almost all the time, (a) the probability density function of the projection on a cross-sectional plane of the particle position at any instant, and (b) the mean velocity and longitudinal dispersion coefficient of particles are determined analytically by employing the Eulerian formulation and applying the Aris moment transformations. It is found that the mean particle velocity decreases and the longitudinal dispersion coefficient of particles increases with the fall velocity.

THE BEHAVIOR OF SUSPENDED SOLID PARTICLES AND LIQUID IN BUBBLE COLUMNS

The longitudinal concentration distribution of solid particles and liquid mixing in 6.6, 12.2 and 21.4 cm i. d. bubble columns were measured and were analyzed by using diffusion model. The longitudinal dispersion coefficient of solid particles and liquid based on actual mean slurry velocity, the mean settling velocity of solid particles, and the concentration of solid particles at the top of the column, respectively, were correlated with dimensionless groups. From these correlations empirical equations were obtained. The values of concentration of solid particles calculated from the empirical equations agreed with the observed values within ±20%.

HOLDUP OF GAS BUBBLES AND LONGITUDINAL DISPERSION COEFFICIENT OF SOLID PARTICLES IN FLUID-BED CONTACTORS FOR GAS-SOLID SYSTEMS

Holdup of gas bubbles and longitudinal dispersion coefficient of solid particles were measured in 3.2, 7.9, 12.0 and 19.5cm inside-diameter fluid beds of F.C.C. particles. Holdup of gas bubbles based on the emulsion bed height (Le) was dependent on superficial gas velocity (uf) and bed diameter (DT). Le was determined as the bed height obtained by extrapolating the constant rate sedimentation curve to zero time. In the range of Uf ?? 2 cm/sec, Le did not vary with uf and DT, and it was about 9% larger than the completely settled bed height for the particles used in this experiment. The experimental and literature data of the longitudinal dispersion coefficient of F.C.C.particles based on the mean density of fluidizing bed (E*s) were correlated with Peclet number (Pe=uf DT/E*s), Froude number (Fr=uf/√gDT ) and (DT+0.23), and the following empirical equation was obtained for bed diameter ranging from 0.032 to 1.5 m. Pe=19(DT+0.23)Fr/(1+6.5Fr0.8)where the unit of DT is meters.