PARTICLE DISPERSION BY COHERENT STRUCTURES IN FREE SHEAR FLOWS

ABSTRACT

The dispersion of particles in turbulent flows is poorly understood. Previous approaches to this problem have been found to be inadequate for nonisotropic turbulent flows. An approach involving a new physical concept is presented. This approach assumes that coherent vortex structures control the particle dispersion process in free shear flows. A simple computational model employing Stuart's vortices is used to simulate particle motion in a two-dimensional free shear layer. The results of this simulation are in reasonable agreement with previous experiments. For the first time, experimental observations indicating particle dispersion rates greater than fluid dispersion rates in free shear flows can be plausibly explained.     

A particle–particle Reynolds stress transportation model of swirling particle-laden-mixtures turbulent flows

On the basis of the gas–particle Euler–Euler two-fluid approach, a new particle–particle Reynolds stress transportation model is proposed for closing the constitution equations of particle-laden-mixtures turbulent flows. In this model, binary particle-particle interaction originating from large-scale particle turbulent diffusions are fully considered in view of an extension closure idea of second-order-moment disperse gas–particle turbulent flows. The binary-particles turbulent flows with different density and same diameter are numerically simulated. The number density, the time-averaged velocity, the fluctuation velocity, the multiphase fluctuation velocity correlations, the normal and the shear Reynolds stress are obtained. Simulated results are in good agreement with experimental data. Binary mixture system has a unique transportation behavior with a stronger anisotropy due to particle inertia and multiphase turbulence diffusions. Fluctuation velocity correlation of axial–axial gas–particle is about twice larger than those of axial–axial particle–particle interaction. Moreover, both normal and shear Reynolds stress are redistributed.     

Role of coherent structures in turbulent shear flows

A definition for the large-scale coherent structure is presented, and the nature and role of coherent structures in turbulent shear flows are examined. The equations governing the coherent motions and the experimental considerations as well as constraints in the investigations of coherent structures in wall-bounded and free turbulent shear flows are discussed. Results from a few of our recent and ongoing studies of coherent structures in excited and unexcited free turbulent shear flows are reviewed. These results show that coherent structures are dominant in transport in the early stages of their formation, but not in the self-preserving regions of turbulent shear flows.     

PARTICLE DISPERSION IN ANISOTROPIC HOMOGENEOUS TURBULENCE

A numerical study of particle dispersion in anisotropic homogeneous turbulent flows is reported. The stochastic turbulent field is represented by a set of random numbers with a pre-set covariance simulating the Reynolds stress in a turbulent flow. The effects of turbulence intensity, aerodynamic response time and Reynolds stress on the particle dispersion are presented.     

PARTICLE DISPERSION IN ANISOTROPIC HOMOGENEOUS TURBULENCE

ABSTRACT

A numerical study of particle dispersion in anisotropic homogeneous turbulent flows is reported. The stochastic turbulent field is represented by a set of random numbers with a pre-set covariance simulating the Reynolds stress in a turbulent flow. The effects of turbulence intensity, aerodynamic response time and Reynolds stress on the particle dispersion are presented.     

Analysis and optimisation of particle mixing performance in fluid phase resonance mixers based on Euler/Lagrange calculations

A novel mixing principle utilising oscillating liquid columns was analysed numerically with regard to particle dispersion characteristics. For producing fluid oscillations a pipe (diameter 100 mm) was immersed centrally into a vessel (diameter 450 mm) filled with liquid (filling height 700 mm) and periodically pressurised (frequency 1.2 Hz). The outlet geometry of the central pipe, just ending near the vessel bottom, has a strong effect on mixing and was optimised in this study. The principle of a FPR-mixer does not require rotating stirrers and in the turbulent regime it has power numbers comparable to propellers. The numerical calculations were conducted by a Euler/Lagrange approach neglecting two-way coupling as well as inter-particle collisions for clarity in order to only focus on the effect of interfacial forces on particle dispersion. The continuous phase was calculated in an unsteady way based on the Reynolds-averaged equations combined with the k-ω-SST (shear stress transport) turbulence model. Lagrangian tracking was conducted considering all relevant forces; drag, gravity/buoyancy, fluid inertia, added mass, Basset force and transverse lift forces due to shear and particle rotation. The importance of these forces was analysed with respect to the turbulent particle Stokes number (considered range 0.004 < St < 10.0) and particle/liquid density ratio (i.e. 1.05, 1.5 and 2.5). Finally, the significance of Basset force and shear-rotation lift force (i.e. Magnus effect) on the dispersion process was quantified by mixing parameters.     

Effects of momentum transfer on particle dispersions of dense gas–particle two-phase turbulent flows

A modified momentum transfer coefficient of dense gas–particle two-phase turbulent flows is developed and its effect on particle dispersion characteristics in high particle concentration turbulent downer flows has been numerically simulated incorporating into a second-order moment (USM) two-phase turbulent model and the kinetic theory of granular flow (KTGF) to consider particle–particle collisions. The particle fractions, the time-averaged axial particle velocity, the particle velocities fluctuation, and their correlations between gas and particle phases based on the anisotropic behaviors and the particle collision frequency are obtained and compared using traditional momentum transfer coefficients proposed by Wen (1966), Difelice (1985), Lu (2003) and Beetstra (2007). Predicted results of presented model are in good agreement with experimental measurement by Wang et al. (1992). The particle fluctuation velocity and its fluctuation velocity correlations along axial–axial and radial–radial directions have stronger anisotropic behaviors. Furthermore, the presented model is in a better accordance with Lu’s model in light of particle axial velocity fluctuation, particle temperature, particle kinetic energy and correlations of particle–gas axial–axial velocity fluctuation. Also, they are larger than those of other models. Beetstra’s model is not suitable for this downer simulation due to the relative lower particle volume fraction, particle collision and particle kinetic energy.     

Effects of higher wall roughness on dense particle–laden dispersion behaviors

To analyze the effects of higher wall roughness on dense particle–laden dispersion behaviors under reduced gravity environments, a dense gas–particle two-phase second-order-moment turbulent model are developed. In this model, the wall roughness function and the kinetic theory of granular flows are coupled and closed. Anisotropy of gas–solid two-phase stresses and the interaction between gas–particle are fully considered using two-phase Reynolds stress model and the two-phase correlation transport equation. Numerical simulation test is validated by Sommerfeld and Kussin (2003) experiments data with higher wall roughness 8.32 μm. Predicted results showed that the particle concentration distribution, particle fluctuation velocity, particle temperature and particle collision frequency are greatly affected by higher wall roughness, as well as particle Reynolds stress and interactions between gas and particle turbulent flows are redistributed. Under microgravity conditions, particle temperature and collision frequency are greatly less than those of earth and lunar gravity.     

A NUMERICAL MODEL FOR THE TURBULENT FLUCTUATION AND DIFFUSION OF GAS-PARTICLE FLOWS AND ITS APPLICATION IN THE FREEBOARD OF A FLUIDIZED BED

A numerical model for the turbulent fluctuation and diffusion of gas-particle flows is presented. This model is based on the idea of treating a turbulent gas flow field as a set of k-ε equations, and of modeling the turbulent fluctuation velocity of gas flow as a random Fourier series based on the fluctuation frequency and spectrum. The particle properties (trajectory and velocity) are described by a Lagrangian approach. Hence this model is known as the fluctuation-spectrum-random-trajectory () model. Finally, particle movements in the freeboard of a fluidized bed and in a turbulent gas-particle-laden jet are analyzed to illustrate the applicability of the model.     

On a local predictor of shear instability and the initiation of local turbulence

The stability of a local laminar shear flow and its transition into turbulent flow is considered as a local phenomenon. This transition may remain local, in which case the flow field is partially laminar and partially turbulent, or it may spread and make the whole field turbulent. One of the applications of this analysis is the prediction of local heat-convection rates, which are enhanced by local turbulence. Another application is in heart-lung blood pumps, where excessive shear rates are detrimental to red blood cells.The analysis is Lagrangian, which concentrates on the stability of a fluid particle in maintaining its position in a laminar shear flow. This stability is shown to depend on the magnitude of a non-dimensional parameter, namely the local Reynolds numberRe _L =ha ²/v whereh is the local shear rate,a is the particle radius andv is the fluid's kinematic viscosity. It is shown that when, locally,Re _L > 530, the flow is, locally, unstable. The application of this criterion is simple and direct, and in certain cases it can be shown that the resulting unstable flow is indeed turbulent.Because the analysis relies on an experimental coefficient which has been obtained for a rigid sphere, rather than for a fluid particle, the criterion is introduced at this stage as a conjecture. Several examples are presented which demonstrate the criterion's ability to yield correct predictions for instability.     

PARTICLE DISPERSION BY LARGE SCALE VORTEX STRUCTURES

This paper demonstrates the effect of large scale structures found in free shear layers on the dispersion of solid particles. Numerical simulation of a free shear layer using a psuedo-spectral code were carried out with the addition of discrete particles. It was shown that the dispersion of particles is strongly dependent on the Stokes number with the possibility of particle dispersions being greater than the fluid dispersion at certain values of the Stokes number. These trends compare qualitatively with flow visualization of a free shear flow with solid particles.     

Cross-sectional and axial flow characteristics of dry granular material in rotating drums

Cross-sectional and axial flow behaviors of dry granular material in rotating drums are closely related to the dynamic characteristics and velocity distributions between the surface layer and bed material. In this study, both 2D and 3D dry granular flow patterns in horizontal rotating drums are experimentally investigated with flow imaging analysis. A dimensionless flow parameter combining the effects of Froude number, relative particle size and volume filling is proposed in this study, which controls the flow characteristics in a rational drum such as dynamic angle of repose, thickness of the flowing layer, relative free surface velocity, and the shear rates in the flowing layer. The dimensionless granular temperature exhibits linear distribution in the flowing layer, being maximum at the free surface and being negligible at the interface in the rolling regime. The measured shear rate of the plug flow departs from drum angular velocity under the wall slip conditions when the drum surface is smooth. Due to the existence of axial convection and lateral surface profile, the mass flux in the flowing layer is always less than that of the plug flow in the 3D granular flows based on sidewall particle images. One the other hand, the mass flux in the flowing layer is always equal or greater than that of the plug flow in the 2D granular flows. 2D granular flows exhibit higher angles of repose and surface velocities than those of the 3D granular flows at the same volume fillings.     

Primary cementing of oil and gas wells in turbulent and mixed regimes

We present a detailed derivation of a practical two-dimensional model for turbulent and mixed regimes in narrow annular displacement flows, such as are found during the primary cementing of oil and gas wells. Such mixed cross regimes, including those in which different regimes exist in the same annular cross section, are relatively common in primary cementing. The modelling approach considers scaling based on the disparity of length-scales, which allows a narrow-gap averaging approach to be effective. With respect to the momentum equations, the leading-order equations correspond to a turbulent shear flow in the direction of the modified pressure gradient. This leads to a nonlinear elliptic problem that is the natural extension of the laminar displacement model in Bittleston et al. (J Eng Math 43:229–253, 2002). The mass transport equations that model the miscible displacement are however quite different. To leading-order turbulence effectively mixes the fluids. Changes in concentrations within the annular gap arise due to the combined effects of advection with the mean flow, anisotropic Taylor dispersion (along the streamlines) and turbulent diffusivity. The diffusive and dispersive effects are modelled for fully turbulent and transitional flows following Maleki and Frigaard (J Non-Newt Fluid Mech 235:1–19, 2016). The model derived allows the investigation of different well geometries and inclinations, pumping sequences and fluid rheologies, all of which can have importance. A number of computed examples are presented with the aim of demonstrating the complexity of turbulent displacements.     

Appraisal of energy recovering sub-grid scale models for large-eddy simulation of turbulent dispersed flows

Current capabilities of Large-Eddy Simulation (LES) in Eulerian–Lagrangian studies of dispersed flows are limited by the modeling of the Sub-Grid Scale (SGS) turbulence effects on particle dynamics. These effects should be taken into account in order to reproduce accurately the physics of particle dispersion since the LES cut-off filter removes both energy and flow structures from the turbulent flow field. In this paper, we examine the possibility of including explicitly SGS effects by incorporating ad hoc closure models in the Lagrangian equations of particle motion. Specifically, we consider candidate models based on fractal interpolation and approximate deconvolution techniques. Results show that, even when closure models are able to recover the fraction of SGS turbulent kinetic energy for the fluid velocity field (not resolved in LES), prediction of local segregation and, in turn, of near-wall accumulation may still be inaccurate. This failure indicates that reconstructing the correct amount of fluid and particle velocity fluctuations is not enough to reproduce the effect of SGS turbulence on particle near-wall accumulation.     

Combined three‐dimensional lattice Boltzmann method and discrete element method for modelling fluid–particle interactions with experimental assessment

A general algorithmic framework is established in this paper for numerical simulations of three‐dimensional fluid–particle interaction problems with a large number of moving particles in turbulent flows using a combined lattice Boltzmann method (LBM) and discrete element method (DEM). In this approach, the fluid field is solved by the extended three‐dimensional LBM with the incorporation of the Smagorinsky turbulence model, while particle interactions are modelled by the DEM. The hydrodynamic interactions between fluid and particles are realized through the extension of an existing two‐dimensional fluid–particle hydrodynamic interaction scheme. The main computational aspects comprise the lattice Boltzmann formulation for the solution of fluid flows, the incorporation of a large eddy simulation‐based turbulence model within the framework of the three‐dimensional LBM for turbulent flows, the moving boundary condition for hydrodynamic interactions between fluid and moving particles, and the discrete element modelling of particle‐particle interactions. To assess the solution accuracy of the proposed approach, a much simplified laboratory model of vacuum dredging systems for mineral recovery is employed. The numerical results are compared with the experimental data available. It shows that the overall correspondence between numerical results and experimental measurements is good and thus indicates, to a certain extent, the solution accuracy of the proposed methodology. Copyright © 2009 John Wiley & Sons, Ltd.     

A STUDY OF PARTICLE MOTION IN TURBULENT SHEAR FLOW OF A SUSPENSION

A report is made on the measurement of turbulent shear flows of a two-phase suspension of particles in a carrier fluid by the recently developed laser-Doppler anemometry particle sizing techniques, one for small particles (smaller than 240 μm) and one for large particles (larger than 240 μm). A good deal of insights of the dynamics at the individual particle level has thus been gained which defy the explanations offered by the conventional macroscopic theories.

These new experimental findings have stimulated the development of a series of new theoretical approaches which are based on the individual particle's dynamical frequency response characteristics in a turbulent flow. These new theories provide explanations to the measured peculiar features of flow behavior as well as a better understanding of the physics of such flows.     

PARTICLE DISPERSION BY LARGE SCALE VORTEX STRUCTURES

ABSTRACT

This paper demonstrates the effect of large scale structures found in free shear layers on the dispersion of solid particles. Numerical simulation of a free shear layer using a psuedo-spectral code were carried out with the addition of discrete particles. It was shown that the dispersion of particles is strongly dependent on the Stokes number with the possibility of particle dispersions being greater than the fluid dispersion at certain values of the Stokes number. These trends compare qualitatively with flow visualization of a free shear flow with solid particles.     

Particle Adhesion and Detachment in Turbulent Flows Including Capillary Forces

The effect of capillary forces on particle adhesion and removal mechanism in turbulent flows is studied. Different detachment theories are used and the increase of adhesion force by the capillary effect is included in the analysis. The criteria for incipient rolling and sliding detachments are evaluated. The sublayer and burst models, which account for the structure of turbulent near-wall flows, are used for evaluating the air velocity condition near the substrate. The critical shear velocities for removing particles of different sizes under different conditions are evaluated, and the results are compared with those obtained in the absence of the capillary force. Comparisons of the model predictions with the available experimental data are also presented.     

A STUDY OF PARTICLE MOTION IN TURBULENT SHEAR FLOW OF A SUSPENSION

ABSTRACT

A report is made on the measurement of turbulent shear flows of a two-phase suspension of particles in a carrier fluid by the recently developed laser-Doppler anemometry particle sizing techniques, one for small particles (smaller than 240 μm) and one for large particles (larger than 240 μm). A good deal of insights of the dynamics at the individual particle level has thus been gained which defy the explanations offered by the conventional macroscopic theories.

These new experimental findings have stimulated the development of a series of new theoretical approaches which are based on the individual particle's dynamical frequency response characteristics in a turbulent flow. These new theories provide explanations to the measured peculiar features of flow behavior as well as a better understanding of the physics of such flows.