Particles In Turbulent Flow Research Articles

Clustering instability of the spatial distribution of inertial particles in turbulent flows.

A theory of clustering of inertial particles advected by a turbulent velocity field caused by an instability of their spatial distribution is suggested. The reason for the clustering instability is a combined effect of the particles inertia and a finite correlation time of the velocity field. The crucial parameter for the clustering instability is the size of the particles. The critical size is estimated for a strong clustering (with a finite fraction of particles in clusters) associated with the growth of the mean absolute value of the particles number density and for a weak clustering associated with the growth of the second and higher moments. A new concept of compressibility of the turbulent diffusion tensor caused by a finite correlation time of an incompressible velocity field is introduced. In this model of the velocity field, the field of Lagrangian trajectories is not divergence free. A mechanism of saturation of the clustering instability associated with the particles collisions in the clusters is suggested. Applications of the analyzed effects to the dynamics of droplets in the turbulent atmosphere are discussed. An estimated nonlinear level of the saturation of the droplets number density in clouds exceeds by the orders of magnitude their mean number density. The critical size of cloud droplets required for cluster formation is more than 20 microm.

Nonequilibrium Reynolds stress for the dispersed phase of solid particles in turbulent flows

The nonequilibrium turbulent transport of dispersed-solid phase is investigated theoretically, and confirmed with simple numerical experiments. The nonequilibrium form of the particle Reynolds stress was obtained as a function of Stokes number, Stτ (=τp/τ), where τp is the particle relaxation time and τ the characteristic time scale of particle–turbulence interaction. The nonequilibrium memory effect could be explicitly expressed as a damped residual contribution of initial particle Reynolds stress. Major interest is given to the region of τ∼O(τL), where τL is the integral time scale associated with the Lagrangian autocorrelation of fluctuating velocities of carrier turbulence. In two-dimensional (2D) simple shear flows with stationary homogeneous turbulence, explicit expressions for the equilibrium and nonequilibrium particle Reynolds stress were obtained, and their characteristics were analyzed extensively for a wide range of particle relaxation time and various conditions of mean shearing of the carrier phase. The reliability of theoretical predictions was tested through a comparison with results of stochastic simulation of particle motion. It was shown that the particle inertia and the mean shearing of the carrier phase seriously affect the relaxation time of particle Reynolds stress required to reach its equilibrium state in such a way that the relaxation time to equilibrium increases in proportional to the increase of τp and this trend is augmented by increasing the mean shearing of the carrier phase. Finally, a nonequilibrium constitutive equation for the dispersed phase Reynolds stress was obtained in a form usable in the two-fluid Eulerian approach for two-phase turbulent flows.

On the collision rate of particles in turbulent flow with gravity

Formula for the collision rate of inertial particles in a homogeneous isotropic stationary turbulent flow with gravity is derived. The obtained formula yields correct results for two special cases, where the formula by Saffman and Turner [J. Fluid Mech. 1, 16 (1956)] fails. In the case of the particles with the same size, the collision rate predicted by Saffman and Turner is 29% higher than that predicted by the obtained formula. Turbulence effects on the collision rate are estimated for the conditions pertinent to droplets in atmospheric clouds.

Dynamics of soot formation by turbulent combustion and thermal decomposition of natural gas

This study investigates the formation process of soot particles in turbulent flows within fuel-rich natural gas flames. Research on carbon formation from relatively simple hydrocarbons under real process conditions and harsh environments allows new insights into the general understanding of soot formation. Experimental work was undertaken on a small-scale gas furnace based on the design of a modern oil-fired carbon black furnace. The combustion system investigated is fired by a nonpremixed, swirl stabilized, confined methane-air flame. The study comprises establishing conditions under which the production of soot particles takes place, progressing toward quantified analysis. A large number of process parameters have been investigated, and the relative role of incomplete combustion and thermal decomposition in the process of carbon particulate formation has been illustrated. Maximum solid carbon formation was realized at maximum air temperature and maximum furnace temperature. Experimental investigations, using carbon particle concentration measurements coupled with on-line gas analysis showed that slightly fuel rich conditions are governed by incomplete combustion only, whereas richer combustion systems are governed by thermal decomposition processes. Both processes are found to be strongly temperature dependent, whereby an increase in temperature reduces particle production in the former process, but enhances it in the latter. A 3-D simulation of the simultaneous processes of incomplete fuel combustion and fuel decomposition in turbulent combustion systems, using a novel integration of fluid mechanics, chemical kinetics, and a standard soot model, facilitates discrimination between the two main sources of carbonaceous particulate matter, and indicates reasonable agreement with experimental trends.

Eddy diffusivity of particles in turbulent flow in rough channels

The eddy diffusivity coefficient of particles depends on the flow characteristics and on the physical properties of the particles. Experimental data and theoretical considerations suggest that the ratio of the eddy diffusion coefficient of particles ( D TP) to the eddy diffusion coefficient of fluid ( D T) is dependent mainly on the friction velocity of fluid (U ∗) , the sedimentation velocity of the particles ( V s), the Reynolds number ( Re) of the flow and also the relative roughness of channel ( ε/ D). It is shown here that this relation among these parameters may be represented as D TP /D T = μ R ∝(U ∗ m /V S ) n , where m and n are empirical constants. Some new empirical relationships are proposed for the eddy diffusion coefficient of particles in the turbulent flow in vertical or horizontal channels. The results compare favorably with experimental data from the literature.

Turbulent thermal diffusion and barodiffusion of passive scalar and dispersed phase of particles in turbulent flows.

It is shown that direct interaction approximation closure solutions for passive scalar and dispersed inertial particles in compressible turbulent flows result in the phenomena, proposed by Elperin et al. [Phys. Rev. E 58, 3113 (1998)], of turbulent thermal diffusion and turbulent barodiffusion. A more rigorous analysis of Lagrangian history direct interaction approximation for the dispersed phase in the kinetic approach framework is used to accurately quantify the phenomena.

Agent for treating raw coal

Modeling particle dispersion in turbulent flows is very complex. Several publications in this field have dealt with both the experimental and modeling aspects of turbulent particle dispersion. This paper gives a broad overview of different modeling techniques discussed in the literature in order to describe the problem of particle dispersion in dilute flows. Unlike other reviews of this subject, this paper maintains a simple approach in explaining mathematically and conceptually the complex issues involved in modeling. Some fundamental concepts, such as key characteristics of turbulent flow and the nature of interaction between turbulence and an individual particle under simplified conditions, are discussed. The authors have attempted to present several definitions (such as homogeneous flow, stationary condition, and integral time scale) that are commonly used to imply certain assumptions or as conceptual tools to derive a model. As indicated, a review of models that are capable of predicting the dispersion of dilute concentration of particles in turbulent flows is presented. The models are described in a simplistic way through use of previously explained ideas and concepts. One of the important practical applications of such dilute two-phase flow models deals with the problem of pulverized-coal combustion. The final part of the paper discusses some of the key issues involved in comprehensive pulverized-coal combustion models. The primary objective of this work is to provide a basic understanding of the subject and hence to serve as an introduction to the theoretical world of turbulent particle dispersion.

Numerical simulation of the gas–particle turbulent flow in riser reactor based on k– ε– kp– εp– Θ two-fluid model

A k– ε– k p – ε p – Θ two-fluid model is established to simulate the gas–article turbulent flow in the riser section of a circulating fluidized bed (CFB) reactor. The model, based on the kinetic theory of granular flow simulates both the gas phase and particle phase by low Reynolds number turbulent model, taking into account the turbulent interaction between gas and particles. The model is coded and solved using a computational fluid dynamic software package CFX4 by AEAT to simulate the two-dimensional, isothermal flow in a riser reactor. The predicted results show satisfactory agreements with experimental data. Moreover, the detailed analysis indicates that the interaction between the turbulence of gas and that of particles is a crucial factor that influences the predicted results.

Settling of small particles near vortices and in turbulence

The trajectories of small heavy particles in a gravitational field, having fall speed in still fluid V˜T and moving with velocity V˜ near fixed line vortices with radius R˜v and circulation Γ˜, are determined by a balance between the settling process and the centrifugal effects of the particles' inertia. We show that the main characteristics are determined by two parameters: the dimensionless ratio VT = V˜TR˜v/Γ˜ and a new parameter (Fp) given by the ratio between the relaxation time of the particle (t˜p) and the time (Γ˜/V˜2T) for the particle to move around a vortex when VT is of order unity or small.The average time ΔT˜ for particles to settle between two levels a distance Y˜0 above and below the vortex (where Y˜0 [Gt ] Γ˜/VT) and the average vertical velocity of particles 〈Vy〉L along their trajectories depends on the dimensionless parameters VT and Fp. The bulk settling velocity 〈Vy〉B = 2Y˜0/〈ΔT˜〉, where the average value of 〈ΔT˜〉 is taken over all initial particle positions of the upper level, is only equal to 〈V˜y〉L for small values of the effective volume fraction within which the trajectories of the particles are distorted, α = (Γ˜/V˜T)2/ Y˜20. It is shown here how 〈Vy〉B is related to Δ&η;(X˜0), the difference between the vertical settling distances with and without the vortex for particles starting on (X˜0, Y˜0) and falling for a fixed period Δt˜T [Gt ] &Γtilde;/V˜2T; 〈V˜y〉B = V˜T[1 − αD], where D = ∫∞−∞(Δ&η;dX˜0/ (&Γtilde;/V˜T)2) is the drift integral. The maximum value of 〈V˜〉B for any constant value of VT occurs when Fp = FpM ∼ 1 and the minimum when Fp = Fpm > FpM, where typically 3 < Fpm < 5.Individual trajectories and the bulk quantities D and 〈Vy〉B have been calculated analytically in two limits, first Fp → 0, finite VT, and secondly VT [Gt ] 1. They have also been computed for the range 0 < Fp < 102, 0 < VT < 5 in the case of a Rankine vortex. The results of this study are consistent with experimental observations of the pattern of particle motion and on how the fall speed of inertial particles in turbulent flows (where the vorticity is concentrated in small regions) is typically up to 80% greater than in still fluid for inertial particles (Fp ∼ 1) whose terminal velocity is less than the root mean square of the fluid velocity, ũ′, and typically up to 20% less for particles with a terminal velocity larger than ũ′. If V˜T/ũ′ > 4 the differences are negligible.

The importance of the forces acting on particles in turbulent flows

The analysis of the importance of the forces that act over an ensemble of particles in a turbulent field has been carried out by using direct numerical simulation for a wide range of density ratios (2.65<ρ<2650). It has been observed that, compared to the Stokes drag, the added mass is always negligible, the pressure drag is relevant for density ratios O(1), and the Basset force is appreciable for the whole range investigated. However, the effect of these forces on the particle dispersion is about 1% for ρ∼1 as well as for large density ratios.

A statistical model for transport and deposition of high-inertia colliding particles in turbulent flow

The objective of the paper is to present a statistical model for predicting transport and deposition of high-inertia colliding particles in two-phase turbulent flows. This model is based on a kinetic equation for the probability density function (PDF) of the particle velocity distribution in a turbulent flow field. The model developed is applied to the simulation of fluctuating particle motion and deposition in vertical pipe flow.

Spectral characteristics of eddy interaction models

The eddy interaction model (EIM) is in common use in simulations of turbulent particulate flow. In the model, particle motions are determined by interactions with random-velocity fluid eddies. Spatial and temporal velocity autocorrelations (and therefore wave number and frequency spectra) are characterised by the probability distributions of the velocity, length and time scales of the eddies. In this paper, spectral behaviour of both standard and modified EIMs is examined. The whole range of behaviours of the EIM, characterised by polynomial velocity autocorrelation functions, is studied. It is shown that each of the resulting spectra exhibits unphysical characteristics. Consequences for modelling are discussed briefly.

Numerical Simulation of Particle Trajectory in Relation to the Formation of a Striped Pattern Deposition Layer.

Motion and trajectory of small particles in turbulent airflow are numerically studied to clarify a striped pattern deposition layer. In the simulation, the striped deposition layers are considered as obstacles on a flat wall, and the turbulent airflow fields in a rectangular channel are calculated by the k-e model. The equation of particle motion includes drag force, gravitational force, and shear-induced lift force. To simulate the random motion of particles in turbulent flow, the Monte Carlo method is also applied, and the particle trajectories are calculated with the Lagrangian method. The effects of the shape and size of the obstacle on the particle trajectory and the deposition on channel wall are analyzed, and the frequency distribution of deposited particles are discussed in detail; namely, the non-deposition section behind the obstacle is equivalent to the interval between striped deposition layers, which increases with obstacle height, air velocity, and particle diameter.

Gas–particle two-phase turbulent flow in horizontal and inclined ducts

Gas–particle two-phase turbulent flows at various loadings in horizontal and inclined ducts are studied. The upgraded thermodynamically consistent two-phase flow model which includes a low Reynolds number fluid-phase turbulence closure is used in the analysis. The governing equations are discretized with the aid of a semi-implicit numerical algorithm. The case of low-concentration gas–particle turbulent flow in a horizontal channel is first analyzed, and the predicted mean velocity and solid volume fraction profiles are favorably compared with the available experimental data. Additional flow properties such as the phasic fluctuation energy and fluctuation energy production and dissipation, as well as the phasic and total normal and shear stress profiles are also presented and discussed. The case of gas–particle flow in a duct with an inclination is then analyzed. Sample model predictions for both dilute and nondilute two-phase turbulent flows under various conditions are presented. The effect of particle diameter on variation of flow properties is also studied.

Zum Verständnis der hydrodynamischen Beanspruchung von Partikeln in turbulenten Rührerströmungen

de

On a eulerian and lagrangian combined model in dense particle‐laden riser flow

AbstractA new numerical model using both Eulerian and Lagrangian coordinates, and taking account of interparticle interactions, has been developed for the study of hydrodynamic aspects of dense particle‐laden rise flows. A stochastic particle dispersion model has been incorporated in the original model to describe the gas particle turbulent flows. In addition, the collisional interaction between the particles has been modeled using the kinetic theory of granular flows based on the Chapman‐Enskog theory of dense gases. A comparison with the experimental results of Miller and Gidspow (1992) shows reasonably good agreement. The present model may provide a useful approach for predicting the complex hydrodynamic behaviour of fluidized bed systems.

Derivation of a pdf kinetic equation for the transport of particles in turbulent flows

A transport equation for the particle phase space density (probability density function (pdf) kinetic equation) is derived for the motion of a dilute suspension of particles in a turbulent flow. The underlying particle equation of motion is based upon a Langevin equation but with a non-white noise driving force derived from an Eulerian aerodynamic force field whose statistics are assumed known. Specifically both the particle position and velocity are considered to be functionals of the driving force and an application of a more general form of the Furutsu-Novikov theorem leads to closed expressions for the phase space diffusion current (i.e. the net force due to the turbulence acting on the particles per unit volume of phase space). In the case of a Gaussian random driving force the closed expressions reduce to a simple Boussinesq form in gradients of the pdf with respect to particle velocity and position. As a practical application solutions of the equation are compared with results obtained from particle tracking in a developing simple shear generated by large eddy simulation.

On the collision rate of small particles in turbulent flows

A theoretical framework is developed to predict the rate of geometric collision and the collision velocity of small size inertialess particles in general turbulent flows. The present approach evaluates the collision rate for small size, inertialess particles in a given instantaneous flow field based on the local eigenvalues of the rate-of-strain tensor. An ensemble average is then applied to the instantaneous collision rate to obtain the average collision rate. The collision rates predicted by Smoluchowski (1917) for laminar shear flow and by Saffman & Turner (1956) for isotropic turbulence are recovered. The collision velocities presently predicted in both laminar shear flow and isotropic turbulence agree well with the results from numerical simulations for particle collision in both flows. The present theory for evaluating the collision rate and the collision velocity is also applied to a rapidly sheared homogeneous turbulence to assess the effect of strong anisotropy on the collision rate. Using (ε/v)1/2, in which ε is the average turbulence energy dissipation rate and v is the fluid kinematic viscosity, as the characteristic turbulence shear rate to normalize the collision rate, the effect of the turbulence structure on the collision rate and collision velocity can be reliably described. The combined effects of the mean flow shear and the turbulence shear on the collision rate and collision velocity are elucidated.

Exact analytic solutions to turbulent particle flow equations

A technique for solving a certain class of partial differential equations is used to obtain exact solutions for particle dispersion in an unbounded Gaussian random flow field in which the mean flow is a simple shear and the turbulence is homogeneous and stationary. Results are compared with those of a simple random walk simulation and those obtained from tracking particles in a simple developing shear generated by LES.

Force balance in a turbulent particulate channel flow

Turbulent flows of 70 μm copper particles and 50 μm glass particles in a channel are considered and investigated by large eddy simulations. Only the influence of the background turbulence on the motion of particles is considered and possible modifications of the structure of turbulence due to motion of particles are not accounted for. Mean velocity profiles and RMS levels are presented and are found to be in good agreement with earlier simulation data in literature. Differences between the statistical behavior of the two particle types are presented and discussed. The statistical correlations are used for a detail study of the interphase forces. The dominant contributions in the streamwise and in the wall-normal directions are pointed out.