Turbulent Particle Motion Research Articles

Identification of a particle collision as a finite-time blowup in turbulence

We propose an Eulerian approach to investigate the motion of particles in turbulence under the assumption that the motion of particles remains smooth in space and time until a collision between particles occurs. When the first collision happens, particle velocity loses C^1 continuity, resulting in a finite-time blowup. The corresponding singularities in particle velocity gradient, particle number density, and particle vorticity for various Stokes numbers and gravity factors are numerically investigated for the first time in a simple two-dimensional Taylor-Green vortex flow, two-dimensional decaying turbulence, and three-dimensional isotropic turbulence. In addition to the critical Stokes number above which a collision begins to occur, the flow condition leading to collision is revealed; particles tend to collide in very thin shear layer constructed by two parallel same-signed vortical structures when Stokes number is above the critical one.

Effect of current density, MoS2 content and bath agitation on tribological properties of electrodeposited nanostructured Ni-MoS2 composite coatings

ABSTRACTNanostructured nickel coatings with molybdenum disulphide particles were electrodeposited to form composite coatings. Three different current densities, i.e. 3, 5 and 7 A/dm2 were investigated initially. The best results were obtained with 5 A/dm2 for codeposition of nanostructured Ni-MoS2 composite coatings. With the addition of 1–4 g/L molybdenum disulphide to the bath, the weight percentages of MoS2 particles in the coatings were 23–38%. This increase of MoS2 content was accompanied with decrease in friction coefficient of the coatings from 0.35 to 0.08. Wear resistance of the coatings was increased with increasing MoS2 content and the weight loss was decreased from 1.4 to 0.7 mg. Hardness was decreased from 585 to 400 VHN with increasing the MoS2 content. By increasing bath agitation speed up to 150 rpm, more MoS2 particles were embedded in the matrix and the coatings showed better wear resistance. However, increase of agitation speed from 150 to 200 rpm caused a decrease of MoS2 particles in the nickel matrix due to the turbulent motion of particles in the bath. Overall, it was shown that the lubricating effect of MoS2 in the coating was more influential than the nanocrystallinity of the nickel matrix in improving tribological properties of these composite coatings.

Effects of rotation speed and rice sieve geometry on turbulent motion of particles in a vertical rice mill

Performance optimization of a rice mill is an issue of great significance in the rice milling industry. By means of Discrete Element Method (DEM), this work examines how the turbulent motion of particles in the vertical rice mill is affected by the cross-section shape of rice sieve and the rotation speed of roller shaft. The random motion of particles is analyzed in terms of velocity field and velocity distribution in different directions. In addition, a kinetic analytic method for evaluating the intensity of turbulent motion of particles via average turbulent kinetic energy during a grinding process was investigated. The results showed that the collision rate and average collision energy in a milling chamber increase linearly with the average turbulent kinetic energy for the same type of rice sieve, which confirm the validity and practicability of the average turbulent kinetic energy. Furthermore, an average rate of clearance change is proposed to characterize the cavity shape variation in the milling chamber. It was found that there exists a strong correlation between the average turbulent kinetic energy and the average rate of clearance change, irrespective of the cross-section shape of regular polygon sieve. This revealed that the cavity shape variation, which is determined by the geometric parameters of rice sieve and rotation speed, has a great influence on the turbulent motions of particles in the milling chamber. Overall, the results are useful for developing a fundamental understanding of the kinematic and dynamic characteristics of particle behavior, which will help design and control practical processes.

A general mixture model for sediment laden flows

A mixture model for general description of sediment-laden flows is developed based on an Eulerian-Eulerian two-phase flow theory, with the aim at gaining computational speed in the prediction, but preserving the accuracy of the complete two-fluid model. The basic equations of the model include the mass and momentum conservation equations for the sediment-water mixture, and the mass conservation equation for sediment. However, a newly-obtained expression for the slip velocity between phases allows for the computation of the sediment motion, without the need of solving the momentum equation for sediment. The turbulent motion is represented for both the fluid and the particulate phases. A modified k-ε model is used to describe the fluid turbulence while an algebraic model is adopted for turbulent motion of particles. A two-dimensional finite difference method based on the SMAC scheme was used to numerically solve the mathematical model. The model is validated through simulations of fluid and suspended sediment motion in steady open-channel flows, both in equilibrium and non-equilibrium states, as well as in oscillatory flows. The computed sediment concentrations, horizontal velocity and turbulent kinetic energy of the mixture are all shown to be in good agreement with available experimental data, and importantly, this is done at a fraction of the computational efforts required by the complete two-fluid model.

A simple dynamic subgrid-scale model for LES of particle-laden turbulence

A dynamic model for LES is proposed to describe the motion of small inertial particles in turbulence. The model is simple, has low computational overhead, contains no adjustable parameters, and can be deployed in any type of flow solver and grid, including unstructured setups.

L’analyse isotopique du plomb : un outil utile en santé au travail en cas de multi-expositions

A mixture model for general description of sediment-laden flows is developed based on an Eulerian-Eulerian two-phase flow theory, with the aim at gaining computational speed in the prediction, but preserving the accuracy of the complete two-fluid model. The basic equations of the model include the mass and momentum conservation equations for the sediment-water mixture, and the mass conservation equation for sediment. However, a newly-obtained expression for the slip velocity between phases allows for the computation of the sediment motion, without the need of solving the momentum equation for sediment. The turbulent motion is represented for both the fluid and the particulate phases. A modified k-ε model is used to describe the fluid turbulence while an algebraic model is adopted for turbulent motion of particles. A two-dimensional finite difference method based on the SMAC scheme was used to numerically solve the mathematical model. The model is validated through simulations of fluid and suspended sediment motion in steady open-channel flows, both in equilibrium and non-equilibrium states, as well as in oscillatory flows. The computed sediment concentrations, horizontal velocity and turbulent kinetic energy of the mixture are all shown to be in good agreement with available experimental data, and importantly, this is done at a fraction of the computational efforts required by the complete two-fluid model.

METHODOLOGY OF CALCULATION THE TERMINAL SETTLING VELOCITY DISTRIBUTION OF SPHERICAL PARTICLES FOR HIGH VALUES OF THE REYNOLD’S NUMBER

Abstract The particle settling velocity is the feature of separation in such processes as flowing classification and jigging. It characterizes material forwarded to the separation process and belongs to the so-called complex features because it is the function of particle density and size. i.e. the function of two simple features. The affiliation to a given subset is determined by the values of two properties and the distribution of such feature in a sample is the function of distributions of particle density and size. The knowledge about distribution of particle settling velocity in jigging process is as much important factor as knowledge about particle size distribution in screening or particle density distribution in dense media beneficiation. The paper will present a method of determining the distribution of settling velocity in the sample of spherical particles for the turbulent particle motion in which the settling velocity is expressed by the Newton formula. Because it depends on density and size of particle which are random variable of certain distributions, the settling velocity is a random variable. Applying theorems of probability, concerning distributions function of random variables, the authors present general formula of probability density function of settling velocity for the turbulent motion and particularly calculate probability density function for Weibull’s forms of frequency functions of particle size and density. Distribution of settling velocity will calculate numerically and perform in graphical form. The paper presents the simulation of calculation of settling velocity distribution on the basis of real distributions of density and projective diameter of particles assuming that particles are spherical.

Numerical Investigation of Phase Distribution and Liquid Turbulence Modulation in Dilute Particle-Laden Flow

Studies on the motion of particles in turbulence and interactions between particles and turbulence are extremely significant, which can help us to improve the efficiency of industrial processes. In this article, we investigated the particle distribution and particle-turbulence interaction in a solid-liquid channel flow with the Euler-Lagrange two-way model. The liquid phase was solved using direct numerical simulation (DNS), and the particle motion was tracked by Newtonian equations of motion considering effects of drag force, pressure gradient force, and gravity. Two-way coupling was used to explain the effect of particles on the turbulence structure. The results show that the local void fraction of particles indicates the wall-peaked profile, particles scatter uniformly in the spanwise direction, and the injection of particles suppresses the turbulence activities in the near wall region. Suppression of the liquid turbulence is mainly caused by vortexes decay of different sizes.

Lagrangian Formulation of Turbulent Premixed Combustion

The lagrangian point of view is adopted to study turbulent premixed combustion. The evolution of the volume fraction of combustion products is established by the Reynolds transport theorem. It emerges that the burned-mass fraction is led by the turbulent particle motion, by the flame front velocity, and by the mean curvature of the flame front. A physical requirement connecting particle turbulent dispersion and flame front velocity is obtained from equating the expansion rates of the flame front progression and of the unburned particles spread. The resulting description compares favorably with experimental data. In the case of a zero-curvature flame, with a non-markovian parabolic model for turbulent dispersion, the formulation yields the Zimont equation extended to all elapsed times and fully determined by turbulence characteristics. The exact solution of the extended Zimont equation is calculated and analyzed to bring out different regimes.

Separation of Heavy Particles in Turbulence

We study motion of small particles in turbulence when the particle relaxation time falls in the range of inertial time scales of the flow. Because of inertia, particles drift relative to the fluid. We demonstrate that the collective drift of two close particles makes them see local velocity increments fluctuate fast. This allows us to introduce Langevin description for separation dynamics. We describe the behavior of the Lyapunov exponent and give the analogue of Richardson's law for separation above viscous scale.

Modeling of the turbulent motion of particles in a vertical channel

The results of modeling of the statistical parameters of a turbulent particle motion in a vertical plane channel are presented. The model is based on a kinetic equation for the particle velocity probability density function. The results are compared with direct numerical simulation.

Using a random displacement model to simulate turbulent particle motion in a baroclinic frontal zone: A new implementation scheme and model performance tests

Numerical artifacts can limit accurate simulation of turbulent particle motion when Lagrangian particle-tracking models are implemented in hydrodynamic models with stratified conditions like fronts. Yet, modeling of individual particle motion in frontal regions is critical for understanding sediment dynamics as well as the transport and retention of planktonic organisms. The objective of this research was to develop a numerical technique to accurately simulate turbulent particle motions in a particle-tracking model embedded within a hydrodynamic model of a frontal zone. A new interpolation scheme, the ‘water column profile’ scheme, was developed and used to implement a random displacement model for turbulent particle motions. A new interpolation scheme was necessary because linear interpolation schemes caused artificial aggregation of particles where abrupt changes in vertical diffusivity occurred. The new ‘water column profile’ scheme was used to fit a continuous function (a tension spline) to a smoothed profile of vertical diffusivities at the x– y particle location. The new implementation scheme was checked for artifacts and compared with a standard random walk model using (1) Well Mixed Condition tests, and (2) dye-release experiments. The Well Mixed Condition tests confirmed that the use of the ‘water column profile’ interpolation scheme for implementing the random displacement model significantly reduced numerical artifacts. In dye-release experiments, high concentrations of Eulerian tracer and Lagrangian particles were released at the same location up-estuary of the salt front and tracked for 4 days. After small differences in initial dispersal rates, tracer and particle distributions remained highly correlated ( r = 0.84 to 0.99) when a random displacement model was implemented in the particle-tracking model. In contrast, correlation coefficients were substantially lower ( r = 0.07 to 0.58) when a random walk model was implemented. In general, model performance tests indicated that the ‘water column interpolation’ scheme was an effective technique for implementing a random displacement model within a hydrodynamic model, and both could be used to accurately simulate diffusion in a highly baroclinic frontal region. The new implementation scheme has the potential to be a useful tool for investigating the influence of hydrodynamic variability on the transport of sediment particles and planktonic organisms in frontal zones.

Stochastic simulation of particle charging and collection characteristics for a wire-plate electrostatic precipitator of short length

In order to estimate more exactly the performance of wire-plate electrostatic precipitators (ESP), a new computational scheme has been developed, where the involved physical phenomena such as corona-field, turbulent electrohydrodynamic (EHD) flow field, in situ particle charging and turbulent motion of particles are treated simultaneously. To overcome the deficiencies of the Eulerian method used up to now, a Lagrangian particle-tracking method coupled with the Monte-Carlo method for simulating the stochastic nature of turbulence is used. The scheme is applied to the analysis of an experimental wire-plate ESP of short length (Kihm, Ph.D. thesis, Stanford University, Stanford, 1987), where the effect of developing flow in the entrance region is substantial. The simulation results for two different flow conditions of high and low turbulent intensity at the inlet clearly reproduced the steeper increase of efficiency with voltage for low turbulence case observed in the experiment, and also the efficiency values agree very well with the experimental data for one particle size of 4 μm.

On the influence of non-Gaussianity on turbulent transport

Non-Gaussianity effects, first of all the influence of the third and fourth moments of the velocity probability density function, have to be assessed for higher-order closure models of turbulence and Lagrangian modelling of turbulent dispersion in complex flows. Whereas the role and the effects of the third moments are relatively well understood as essential for the explanation of specific observed features of the fully developed convective boundary layer, there are indications that the fourth moments may also be important, but little is known about these moments. Therefore, the effects of non-Gaussianity are considered for the turbulent motion of particles in non-neutral flows without fully developed convection, where the influence of the fourth moments may be expected to be particularly essential. The transport properties of these flows can be characterized by a diffusion coefficient which reflects these effects. It is shown, for different vertical velocity distributions, that the intensity of turbulent transport may be enhanced remarkably by non-Gaussianity. The diffusion coefficient is given as a modification of the Gaussian diffusivity, and this modifying factor is found to be determined to a very good approximation by the normalized fourth moment of the vertical velocity distribution function. This provides better insight into the effect of fourth moments and explains the varying importance of third and fourth moments in different flows.

Unsteady drag on a sphere at finite Reynolds number with small fluctuations in the free-stream velocity

Unsteady flow over a stationary sphere with small fluctuations in the free-stream velocity is considered at finite Reynolds number using a finite-difference method. The dependence of the unsteady drag on the frequency of the fluctuations is examined at various Reynolds numbers. It is found that the classical Stokes solution of the unsteady Stokes equation does not correctly describe the behaviour of the unsteady drag at low frequency. Numerical results indicate that the force increases linearly with frequency when the frequency is very small instead of increasing linearly with the square root of the frequency as the classical Stokes solution predicts. This implies that the force has a much shorter memory in the time domain. The incorrect behaviour of the Basset force at large times may explain the unphysical results found by Reeks & Mckee (1984) wherein for a particle introduced to a turbulent flow the initial velocity difference between the particle and fluid has a finite contribution to the long-time particle diffusivity. The added mass component of the force at finite Reynolds number is found to be the same as predicted by creeping flow and potential theories. Effects of Reynolds number on the unsteady drag due to the fluctuating free-stream velocity are presented. The implications for particle motion in turbulence are discussed.

Lagrangian Stochastic‐Deterministic (LSD) Predictions of Particle Dispersion in Turbulence

AbstractA Lagrangian model of particle motion in turbulence has been developed. The model is stochastic in the sense that the "instantaneous" fluid velocity field is generated from known turbulence energy and time scales of large eddies by using a random sampling. The particle motion during the interaction with the eddies is deterministic as being predicted from solutions of Lagrangian momentum equations. On the basis of a large number of calculated trajectories, the distributions of local particle mean and fluctuation velocity components and of the mean square particle displacement are evaluated in a flow domain. The results of the predictions for the case of particle dispersion in nearly homogeneous and isotropic turbulence behind a grid are compared with existing experimental data and satisfactory agreement is achieved. The model is also applied to the case of the particle dispersion from a point source in a nonhomogeneous turbulence of fully developed pipe flow. The agreement with experiments is satisfactory for both heavy and tracer particles. An explanation is given for the experimentally observed phenomenon that in some cases heavy particles disperse faster than fluid points.

Statistical modelling of turbulent motion of particles in random velocity fields

Article Statistical modelling of turbulent motion of particles in random velocity fields was published on January 1, 1989 in the journal Russian Journal of Numerical Analysis and Mathematical Modelling (volume 4, issue 1).

選鉱過程におけるマイクロプロセスについて (2)

The turbulent characteristics in flotation machines were recently measured and the turbulent fields were confirmed to be isotropic except the impeller zone. Thus the isotropic turbulent theory was applied to determine the local distribution of the turbulent time and space scales and to analyze the energy propagation. It was also confirmed that mineral particles damped and air bubbles enhanced the turbulent motion in flotation machines.The turbulent motion of particles must be one of the most important factors that decide the micro-processes of the flotation proce SS. Hitherto the equation of the tumbulent motion of pamticles has been analytically or numemically solved only for a mono-dispersed system. The results revealed that particles in flotation machines were able to be considered to move approximately with the fluid surrounding them under conventional flotation conditions.The collision process between mineral particles and air bubbles must be elucidated in order to build a micro-process model for a flotation process. This problem has been tried to solve using similar methods as for coagulation problems and a few studies were reviewed.The micro-processes in classification and thickening processes have been studied with equations of diffusion and the diffusion coefficients have been given by spatially average values. However a study that the turbulent characteristics were measured in a hydrocyclone showed that the turbulent diffusion coefficient was spatially distributed.The study of the micro-processes in mineral processing is now progressing and there are many problems to be solved.

The dispersion of discrete particles in a turbulent fluid field

AbstractThe degree of radial dispersion of medium size particles (ηK < dp < lf) emanating from a point source, is measured photographically in the turbulent core of a fully developed vertical pipe flow of water. From the classical theoretical results of G. Taylor, it was then possible to calculate statistical parameters which characterize the turbulent particle motion. A comparison is made between a tracer and neutrally dense, buoyant and heavy particles. Results indicate that the effect of particle intertia is negligible, and that the crossing trajectories effect dominates the dispersion process. A “wake effect” causes a buoyant particle to disperse to a greater degree than an equivalent heavy particle. An exponential‐cosine form of the Lagrangian autocorrelation coefficient provides a best fit for the dispersion data, although a purely exponential form is equally adequate for practical calculations.

BEHAVIOR OF DISPERSED PARTICLES IN TURBULENT LIQUID FLOW

Turbulent motion of particles suspended in water in a stirred tank and that of drops supplied to turbulent pipe flow of water are studied with emphasis on their scales. The scales considered are 1) sampling time scale : the very small time interval in which the displacement of a particle is measured, 2) measuring time scale : the time-duration during which a continuous measurement is run, and 3) sampling spatial scale : the width of a location in which the displacement of a particle is followed. The effects of these scales on the magnitude of turbulence velocity components are examined, and the magnitudes are evaluated with a set of values of scales which seem most appropriate to each particle motion. The magnitudes are correlated uniformly in both dispersions with particle diameters and energy dissipation rates of surrounding liquid.