Particle Reynolds Stress Research Articles

Turbulent channel flow of a binary mixture of neutrally buoyant ellipsoidal particles

A turbulent channel flow of a binary mixture of finite-size neutrally buoyant ellipsoidal particles is studied by using a parallel direct-forcing fictitious domain method at a friction Reynolds number of 180 and the particle aspect ratios of 1/3 (oblate particle) and 4 (prolate particle), respectively. The total particle volume fraction is fixed at 14.16% and 21.24% and the relative fraction of prolate and oblate particles are varied. The mean velocity profile normalized by the bulk velocity shows a strong difference between the single phase flow and particulate flow, while showing a small difference between mono-disperse and bi-disperse particulate flow cases. The lower fluid and particle Reynolds stress contributions in a high oblate particle volume fraction ratio cases lead to the drag reduction. Under moderate particle volume concentration, the oblate and prolate particle results show self-similarity of velocity profiles of solid phase, including particle velocity, concentration, orientation, and rotation. Both kinds of ellipsoidal particles tend to align their long axes with the streamwise direction in the whole channel.

A novel particle subgrid scale modeling of large eddy simulation for swirling particle-laden turbulent flow

How to describe the effects of subgrid scale (SGS) gas flow on particle dynamics in large eddy simulation (LES) is a challenge for modeling and simulation of particle-laden swirling turbulent flow. SGS four-way coupling interaction mechanisms of gas-to-particle, particle-to-gas, and particle-particle collision have not been considered fully. A novel particle SGS kinetic turbulent energy-granular temperature (SGS-kp-θp) model is proposed firstly to model this effect on particle motions and dispersions. Second-order moment algorithm to establish the anisotropic two-phase Reynolds stress equations and their closure correlations is utilized. Validations by experiment results and Moissette (MOB) particle dispersion model built-in OpenFoam software are performed with better agreements for mean and fluctuation velocities. Anisotropic behaviors of Reynolds stresses and particle collisions are distinctively, smaller-scale particle fluctuations originating from particle collisions lead to the redistribution and dissipation of Reynolds stresses. Power spectrum density is utilized to analyze statistically the particle number density fluctuations and Reynolds stresses, dominant frequencies are roughly 2.5 Hz and 1.0 Hz marking the internal and the corner recirculation regions. Compared to those of inlet flow regions, normal and tangential Reynolds stresses at development flow regions approximately increased by twice and decreased by 3.0 times. Modeling strategy for multiphase interactions are of great importance for capturing particle dynamics in accurate.

Particle–fluid–wall interaction of inertial spherical particles in a turbulent boundary layer

Abstract

Hydrodynamic Modeling of Swirling Binary Mixture Gas-Particle Flows Using a Second-Order-Moment Turbulence Model.

The polydisperse behaviors of a binary ultralight–heavy mixture particle flow in a swirling axisymmetric chamber were investigated based on a developed second-order-moment gas–particle turbulent model. A binary particle Reynolds stress transport equation to depict the anisotropic interactions between gas-mixture particles and binary ultralight–heavy particles was established to close the governing equations. Hydrodynamic parameters, including particle number density, particle and gas velocities, and fluctuation velocities, Reynolds stress tensors, and their invariants, turbulent kinetic energy, and vortex structure, are numerically simulated. The detailed effects of the density, the diameter of the particle, the Stokes number, and the ultralight particle mass loading ratios on the flow status were studied. It is shown that normal and shear Reynolds stresses and kinetic turbulent energies of mixture particles have been redistributed, particularly, they are very sensitive to the mass loading ratios. Higher particle mass loading ratios enhanced the anisotropic characteristics. The particle number density at central regions of the farthest downstream is approximately three times larger than those of smaller mass loading ratios. Larger Stokes number particles reinforced the axial fluctuations up to 1.2 times that of the light particles, whereas ultralight particles increased tangential fluctuation to 2.5 times for axial ones.

Development of a Momentum Transfer Coefficient in Particle Horizontal Channel Flow

Abstract A developed momentum transfer coefficient based on Wen’s 1966 model was proposed, in which the two threshold values were used to keep the continuous particle porosity function. A second-order moment gas–particle two-fluid turbulent model that coupled this coefficient, was established to model and simulate the particle horizontal channel flows. An improved Reynolds stresses transport to close fluctuation velocities correlation between gas and particle phases was set to reveal the fully anisotropic characteristics of particle dispersions. The hydrodynamics of horizontal gas–particle turbulent flow was numerically simulated and validated by experimental measurement with satisfied agreements. Distributions of particle Reynolds stresses are significantly affected by two-phase interactions, turbulent diffusions and particle collisions. Much wider size and flatter profiles distributions were obtained in terms of the horizontal and vertical root-means-square of particle velocities in comparison with Wen’s 1966 model.

Particle Reynolds stress model for wall turbulence with inertial particle clustering

The modification of Zaichik particle Reynolds stress transport model for turbulent particle-laden flows is developed taking into account the clustering phenomenon of inertial particles. The main novelty is the new boundary condition for the particle Reynolds stress, which is posed at some distance from the wall in the viscous sublayer and is consistent with the power-law singularity of particle concentration at the wall. The modified model avoids the spurious bifurcation of the solution, which observed for non-modified Zaichik model with the near-equilibrium wall boundary condition.

Developing theory of probability density function for stochastic modeling of turbulent gas-particle flows

Turbulent gas-particle flows are studied by a kinetic description using a probability density function (PDF). Unlike other investigators deriving the particle Reynolds stress equations using the PDF equations, the particle PDF transport equations are directly solved either using a finite-difference method for two-dimensional (2D) problems or using a Monte-Carlo (MC) method for three-dimensional (3D) problems. The proposed differential stress model together with the PDF (DSM-PDF) is used to simulate turbulent swirling gas-particle flows. The simulation results are compared with the experimental results and the second-order moment (SOM) two-phase modeling results. All of these simulation results are in agreement with the experimental results, implying that the PDF approach validates the SOM two-phase turbulence modeling. The PDF model with the SOM-MC method is used to simulate evaporating gas-droplet flows, and the simulation results are in good agreement with the experimental results.

Modeling and simulation of particle dispersion in dense particle‐laden flow

AbstractTraditional drag force coefficient with regard to modeling gas–particle flows is generally established on the semiempirical or full empirical measurement data with isotropic hypothesis resulting in neglection of true particle dispersions, especially for anisotropic characteristics. A developed drag force coefficient to fully consider the anisotropics was applied to model and simulate dense particle‐laden flows. Coupled with a unified second‐order moment, 2‐fluid turbulent model consisting of a set of fluctuation velocity Reynolds transport equations was employed for predicting dense particle‐laden flows in pseudo‐2D horizontal chamber. Simulated results showed that they are in good agreement with measurement data. Particle Reynolds stresses have been redistributed by the momentum transfer interaction term between gas and particle phases, the turbulent diffusion term, and the particle collision term. Compared with traditional Wen's model, horizontal and vertical root‐mean‐square of particle velocities exhibited much more flatter and wider distribution behaviors. Due to limitation of two‐dimensional model and wall conditions, errors near wall regions should be improved in future work.

Edge shear flows and particle transport near the density limit of the HL-2A tokamak

Edge shear flow and its effect on regulating turbulent transport have long been suspected to play an important role in plasmas operating near the Greenwald density limit nG. In this study, equilibrium profiles as well as the turbulent particle flux and Reynolds stress across the separatrix in the HL-2A tokamak are examined as is approached in ohmic L-mode discharges. As the normalized line-averaged density is raised, the shearing rate of the mean poloidal flow drops, and the turbulent drive for the low-frequency zonal flow (the Reynolds power ) collapses. Correspondingly, the turbulent particle transport increases drastically with increasing collision rates. The geodesic acoustic modes (GAMs) gain more energy from the ambient turbulence at higher densities, but have smaller shearing rate than low-frequency zonal flows. The increased density also introduces decreased adiabaticity which not only enhances the particle transport but is also related to reduction in the eddy-tilting and the Reynolds power. Both effects may lead to cooling of edge plasmas and therefore the onset of MHD instabilities that limit the plasma density.

Effect of particle stress tensor in simulations of dense gas–particle flows in fluidized beds

A two-fluid model based on the kinetic theory of granular flow for the rapid-flow regime and the Coulomb friction law for the quasi-static regime is applied to predict the hydrodynamics of dense gas–particle flow in a three-dimensional fluidized bed. Two different models for the particle stress tensor that use different constitutive equations in the elastic-inertial regime are examined to assess their ability to predict bed dynamics. To understand how particle stress models affect structural features of the flow, a quantitative analysis is performed on some important aspects of the mechanics of bubbling beds that have received relatively little attention in the literature. Accordingly, different flow regimes are identified in the context of fluidized beds through the dimensionless inertial number, and the main characteristics of each regime are discussed. In addition, how the particle stress tensor manifests itself in the bubble characteristics, natural frequency of the bed, and particle Reynolds stress are investigated, all of which help to better understand the complex dynamics of the fluidized bed. The numerical results are validated against published experimental data and demonstrate the significant role of the stress tensor in the elastic-inertial regime.

Two-phase Turbulence Models in Eulerian-Eulerian Simulation of Gas-particle Flows and Coal Combustion

Eulerian-Eulerian (two-fluid) simulation of gas-particle flows and coal combustion are widely used because of its convenience in simulating large-size facilities. The key point is that it needs more complex closure models, compared to those in Eulerian gas-Lagrangian DEM modeling of particles. This keynote lecture will give a brief review on our many-year studies to solve these problems. The first one is the particle turbulence model. To overcome the shortcomings of the Hinze-Tchen's “particle-tracking-fluid” model, about 20 years ago, a transport equation of particle turbulent kinetic energy and transport equations of both gas and particle Reynolds stresses were proposed by us and subsequently constitute the so-called “k-ɛ-kp”, “unified second-order moment (USM)” and “non-linear k-ɛ-kp” two-phase turbulence models. Furthermore, for simulating reacting gas-particle flows and coal combustion, a full two-fluid model and a combined two-fluid-trajectory model, accounting for both particle turbulent diffusion and particle history effect due to moisture evaporation, devolatilization and char oxidation were proposed. The next is the particle-rough wall interaction. A particle-wall collision model accounting for wall roughness was proposed. Then, to overcome the limitation of the well-known kinetic theory of dense gas-particle flows, an anisotropic two-phase turbulence model, called “USM-Θ” model, accounting for both particle turbulence (large-scale fluctuation) and inter-particle collision (small-scale fluctuation) was proposed. Next, the particle-wake effect on gas turbulence modulation was studied to construct a sub-model and was added to the two-fluid modeling. At last, in recently developed two-fluid large-eddy simulation of gas-particle flows and combustion the particle sub-grid-scale (SGS) stress model is insufficiently studied. Some of them are based on a simple extension of the gas Smagorinsky SGS model without theoretical justification. Therefore, a USM-SGS two-phase stress model was proposed by us, properly accounting for the anisotropy of two-phase SGS stresses and the interaction between them.

Inter-particle collision effects on the entrained particle distribution in aeolian sand transport

Based on the Boltzmann transport equation, a theoretical model for the particle concentration distribution was developed in the aeolian sand transport to account for the inter-particle collision effects near the sand bed surface. In order to assess the inter-particle collision effects on sand transport characteristics near the sand bed surface, a set of experiments were performed in a large-scale wind tunnel with a dimension of 12,000mm×400mm×600mm (L×W×H). Two types of sand samples were prepared by screening. The free-stream wind velocity in the wind tunnel was measured by HWA (Hot Wire Anemometer). The particle velocity, concentration, and Reynolds stress were obtained by PDPA (Phase Doppler Particle Analyzer). Experimental results showed that particle concentration emerged a turning point at about 2cm from the sand-bed surface. They agreed with the numerical simulation results very well. The collision rate of particles also emerged a turning point, and the location of the turning point was approximately consistent with that of the measured concentration and the Reynolds stress. Consequently, the inter-particle collision close to the sand-bed surface, which was the main factor that altered the characteristics of particle transport, could not be neglected.

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 8.32μm. 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.

Measurement and simulation of the two-phase velocity correlation in sudden-expansion gas-particle flows

In this paper the present authors measured the gas-particle two-phase velocity correlation in sudden expansion gas-particle flows with a phase Doppler particle anemometer (PDPA) and simulated the system behavior by using both a Reynolds-averaged Navier-Stokes (RANS) model and a large-eddy simulation (LES). The results of the measurements yield the axial and radial time-averaged velocities as well as the fluctuation velocities of gas and three particle-size groups (30 µm, 50 µm, and 95 µm) and the gas-particle velocity correlation for 30 µm and 50 µm particles. From the measurements, theoretical analysis, and simulation, it is found that the two-phase velocity correlation of sudden-expansion flows, like that of jet flows, is less than the gas and particle Reynolds stresses. What distinguishes the two-phase velocity correlations of sudden-expansion flow from those of jet and channel flows is the absence of a clear relationship between the two-phase velocity correlation and particle size in sudden-expansion flows. The measurements, theoretical analysis, and numerical simulation all lead to the above-stated conclusions. Quantitatively, the results of the LES are better than those of the RANS model.

Evaluación de los enfoques euleriano y lagrangianopara modelar la fase dispersa en flujos turbulentosno uniformes cargados con partículas

El presente artículo considera flujos turbulentos no uniformes tipo chorro cargados con partículas. Estos flujos se encuentran frecuentemente en la industria y se caracterizan por altos valores de anisotropía de la velocidad fluctuante de las partículas, mucho mayor que la de la fase portadora. Dado que los enfoques euleriano y lagrangiano clásicos para la descripción de la fase dispersa son incapaces de estimar correctamente esa anisotropía, en este trabajo se introducen dos modelos eulerianos extendidos para la fase de las partículas; uno de ellos es algebraico (el modelo algebraico de esfuerzos, APS) y el otro es diferencial (el modelo de esfuerzos de Reynolds, PRS). El desempeño de ambos modelos y de un modelo lagrangiano clásico se evalúa con respecto a mediciones experimentales disponibles en la literatura. El modelo PRS proporciona resultados que concuerdan con los experimentos para todas las variables medidas, incluyendo la anisotropía de la velocidad fluctuante de las partículas. Las ecuaciones diferenciales que describen la fase dispersa se descomponen en sus términos básicos y se analizan separadamente. En el caso de partículas de gran inercia, se demuestra que el modelado de los términos de interacción es crucial ya que éstos gobiernan los equilibrios existentes en las ecuaciones eulerianas que describen la fase dispersa

Deposition of inertial particles from turbulent flow in channels at high Reynolds numbers

On the basis of the previously developed asymptotic theory of turbulent particle-laden flow with particle deposition in channels coupled with the transport model for the particle Reynolds stress, an asymptotic solution to the problem on the deposition of particles in the limit of high Reynolds numbers was obtained. The numerical calculations confirmed the presence, in the region of the transition from the diffusion-impaction regime of particle sedimentation to the inertia-moderated regime, bifurcation phenomenon of a solution found previously in earlier studies. Features of particle accumulation in the viscous sublayer are analyzed. On the basis of the numerical solution, correlations for particle deposition velocity were obtained. Boundary conditions of the wall-function type for particle concentration whose use allows widening the applicability limits of the equilibrium Eulerian models in terms of particle inertia are proposed.

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.

Hydrodynamic predictions of dense gas–particle flows using a second-order-moment frictional stress model

Based on the Eulerian–Eulerian two-fluid continuum approach, an improved unified second-order-moment two-phase turbulence model combining with the kinetic theory of particle collision frictional stress model is developed to simulate the dense gas–particle flows in downer, where the effective coefficient of restitution is incorporated into the particle–particle collision. The interaction term between gas and particle turbulence is fully taken into account by the transport equation of two-phase stress correlation. Hydrodynamics of high density particle flow, measured by Wang et al. [27] are predicted and the simulated results are in good agreement with experimental data. On the conditions of considering the realistic energy dissipation due to frictional stress, particle concentration and particle axial averaged velocity are closely the measured and they are better than without frictional stress model. Furthermore, the particle Reynolds stress is redistributed and the particle temperature is reduced. Effect of frictional stress leads to increase obviously the collision frequency at the outlet and inlet regions and the magnitude of frequency of particle collisions is 102.

Sand storms: CFD analysis of Reynolds stress and collision stress of particles near sand bed

Sand storm is a serious environmental threat to humans. Sand particles are transported by saltation and suspension, causing soil erosion in one place and deposition in another. In order to prevent and predict sand storms, the causes and the manners of particle motions must be studied in detail. In this paper a standard k– ɛ model is used for the gas phase simulation and the discrete element method (DEM) is used to predict the movements of particles using an in-house procedure. The data are summarized in an Eulerian–Eulerian regime after simulation to get the statistical particle Reynolds stress and particle collision stress. The results show that for the current case the Reynolds stress and the air shear stress predominate in the region 20–250 mm above the initial sand bed surface. However, in the region below 3 mm, the collision stress must be taken into account in predicting particle movement.

Particle statistics in a gas–solid coaxial strongly swirling flow: A direct numerical simulation

A direct numerical simulation of a strongly coaxial swirling particle-laden flow is conducted with reference to a previous experiment. The carrier phase is simulated as a coaxial swirling flow through a short nozzle injecting into a large container. The particle phase is carried by the primary jet, and simulated in the Lagrangian approach. The drag force, slip-shear force and slip-rotation force experienced by particles are calculated. A partial validation of the results is followed. The results are analyzed in Eulerian approach focusing on the statistical behavior of particle motion. The relative importance of the drag, slip-shear and slip-rotation forces under different Stokes numbers is indicated quantitatively. The particle velocity profiles, fluctuations, Reynolds stress, and turbulence intensity are demonstrated and analyzed respectively. An important “choke” behavior for large particles within the mainstream is found and interpreted. Additionally, the patterns of particle distribution and the helical structures of particle motion under different Stokes numbers are demonstrated qualitatively and analyzed quantitatively.