A two-scale second-order moment two-phase turbulence model for simulating dense gas-particle flows

A two-scale second-order moment two-phase turbulence model accounting for inter-particle collision is developed, based on the concepts of particle large-scale fluctuation due to turbulence and particle small-scale fluctuation due to collision and through a unified treatment of these two kinds of fluctuations. The proposed model is used to simulate gas-particle flows in a channel and in a downer. Simulation results are in agreement with the experimental results reported in references and are near the results obtained using the sin- gle-scale second-order moment two-phase turbulence model superposed with a particle collision model （USM-θ model） in most regions.

Two-phase turbulence models for simulating dense gas-particle flows

The two-fluid model is widely adopted in simulations of dense gas-particle flows in engineering facili- ties. Present two-phase turbulence models for two-fluid modeling are isotropic. However, turbulence in actual gas-particle flows is not isotropic. Moreover, in these models the two-phase velocity correlation is closed using dimensional analysis, leading to discrepancies between the numerical results, theoretical analysis and experiments. To rectify this problem, some two-phase turbulence models were proposed by the authors and are applied to simulate dense gas-particle flows in downers, risers, and horizontal channels; Experimental results validate the simulation results. Among these models the USM-O and the two-scale USM models are shown to give a better account of both anisotropic particle turbulence and particle-particle collision using the transport equation model for the two-phase velocity correlation.

From micro-scale to technical dimension—Challenges in the simulation ofdense gas-particle flows

Supported by the Sino-German Center for Research Promotion, an organization jointly founded by the National Natural Science Foundation of China （NSFC） and the German Research Foundation （DFG）, a joint Sino-German workshop on particle fluid systems was held for the fourth time on May 19-20, 2008 in Hamburg. Previous workshops were held on August 30-31, 1999 in Ham- burg,

Large Eddy Simulation of Particle Wake Effect and RANS Simulation of Turbulence Modulation in Gas-Particle Flows

The turbulence enhancement by particle wake effect is studied by large eddy simulation （LES） of turbulent gas flows passing a single particle. The predicted time-averaged and root-mean-square fluctuation velocities behind the particle are in agreement with the Reynolds-averaged Navier-Stokes modeling results and experimental results. A semi-empirical turbulence enhancement model is proposed by the present-authors based on the LES resuits. This model is incorporated into the second-order moment two-phase turbulence model for simulating vertical gas-particle pipe flows and horizontal gas-particle channel flows. The simulation results show that compared with the model not accounting for the particle wake effect, the present model gives simulation results for the gas turbulence modulation in much better agreement with the experimental results.

SIMULATION OF SUDDEN-EXPANSION AND SWIRLING GAS-PARTICLE FLOWS USING A TWO-FLUID PARTICLE-WALL COLLISION MODEL WITH CONSIDERATION OF THE WALL ROUGHNESS

A two-fluid particle-wall collision model with consideration of wall roughness is pro- posed.It takes into account the effects of the friction,restitution and in particular the wall roughness, and hence the redistribution of Reynolds stress in different directions,the absorption of turbulent en- ergy from the mean motion and the attenuation of particle motion by the wall.The proposed model is used to simulate sudden-expansion and swirling gas-particle flows and is validated by comparing with experimental results.The results show that the proposed model gives better results than those obtained by the presently used zero-gradient condition.Hence,it is suggested that the proposed model should be used as the wall boundary condition for the particle phase in place of the presently used boundary condition.

Advances in LES of Two-phase Combustion(Ⅱ) LES of Complex Gas-Particle Flows and Coal Combustion

Large-eddy simulation(LES) is under its rapid development and is recognized as a possible second generation of CFD methods used in engineering.Large-eddy simulation of two-phase flows and combustion is particularly important for engineering applications.Some investigators,including the present authors,give their review on LES of spray combustion in gas-turbine combustors and internal combustion engines.However,up to now only a few papers are related to the state-of-the-art on LES of gas-particle flows and combustion.In this paper a review of the advances in LES of complex gas-particle flows and coal combustion is presented.Different sub-grid scale(SGS) stress models and combustion models are described,some of the main results are summarized,and some research needs are discussed.

Experimental study and numerical simulation of gas-particle flows with radial bias combustion and centrally fuel rich swirl burners

Numerical simulation is applied to gas-particle flows of the primary and the secondary air ducts and burner region, and of two kinds of swirl burners. The modeling results of Radial Bias Combustion (RBC) burner well agreed with the data from the three-dimensional Phase-Doppler anemometry (PDA) experiment by Li, et al. The modeling test conducted in a 1025 t/h boiler was to study the quality of aerodynamics for a Central Fuel Rich (CFR) burner, and the Internal Recirculation Zone (IRZ) was measured. In addition, gas-particle flows with a CFR burner were investigated by numerical simulation, whose results accorded with the test data fundamentally. By analyzing the distribution of gas velocity and trajectories of particles respectively, it is found that the primary air’s rigidity of CFR burner is stronger than that of RBC burner, and the primary air mixes with the secondary air later. Furthermore, high concentration region of pulverized coal exists in the burner’s central zone whose atmosphere is reduced, and trajectories of particles in IRZ of CFR burner are longer than that of RBC burner. They are favorable to coal’s ignition and the reduction of NOx emission.

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 （30μm, 50μm, and 95μm） and the gasparticle velocity correlation for 30μm and 50μm 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.

Research on numerical simulation of flow field in shallow-bath dense-medium separator

介绍了浅槽重介分选机的结构、工作原理和技术特点，并采用Fluent软件，对浅槽重介分选机内部的流场进行了分析和研究，得出了各主要位置的速度和速度变化规律。揭示了浅槽重介分选机在分选过程中的悬浮液体流场形态及运动规律，以为其结构设计和改进提供理论依据。

Numerical simulations of dense granular flow in a two-dimensional channel:The role of exit position

Molecular dynamics simulations have been performed to elucidate the influence of exit position on a dense granular flow in a two-dimensional channel. The results show that the dense flow rate remains constant when the exit is far from the channel wall and increases exponentially when the exit moves close to the lateral position. Beverloo’s law proves to be successful in describing the relation between the dense flow rate and the exit size for both the center and the lateral exits.Further simulated results confirm the existence of arch-like structure of contact force above the exit. The effective exit size is enlarged when the exit moves from the center to the lateral position. As compared with the granular flow of the center exit, both the vertical velocities of the grains and the flow rate increase for the lateral exit.

STUDY ON RESISTANCE CHARACTERISTICOF GAS-SOLID DENSE EXTRUSION FLOW

An experimental study is made on the resistance characteristic ofthe dense extrusion flow with pulverized coal and nitrogen as medium in thispaper. Through the analysis of gas compressibility , solids continuity and lam-mar flow of both gas and solids, a

AN ANALYTIC SOLUTION OF DENSE TWO-PHASE FLOW IN A VERTICAL PIPELINE

According to a mathematical model for dense two-phase flows presented in the previous pape[1],a dense two-phase flow in a vertical pipeline is analytically solved, and the analytic expressions of velocity of each continuous phase and dispersed phase are respectively derived. The results show that when the drag force between twophasesdepends linearly on their relative velocity, the relative velocity profile in the pipeline coincides with Darcy's law except for the thin layer region near the pipeline wall, and that the theoretical assumptions in the dense two-phase flow theory mentioned are reasonable.

THE FLOW STRUCTURE OF DILUTE GAS-PARTICLE SUSPENSIONS BEHIND A SHOCK WAVE MOVING ALONG A FLAT SURFACE

The asymptotic and numerical investigations of shock-induced boundary layers in gas-particle mixtures are presented. The Saffman lift force acting on a particle in a shear flow is taken into account. It is shown that particle migration across the boundary layer leads to intersections of particle trajectories. The corresponding modification of dusty gas model is proposed in this paper.The equations of two-phase sidewall boundary layer behind a shock wave moving at a constant speed are obtained by using the method of matched asymptotic expansions. The method of the calculation of particle phase parameters in Lagrangian coordinates is described in detail. Some numerical results for the case of small particle concentration are given.

Numerical simulation of dense particle-gas two-phase flow using the minimal potential energy principle

A simulation method of dense particle-gas two-phase flow has been developed. The binding force is introduced to present the impact of particle clustering and its expression is deduced according to the principle of minimal potential energy. The cluster collision, break-up and coalescence models are proposed based on the assumption that the particle cluster are treated as one discrete phase. These models are used to numerically study the two-phase flow field in a circulating fluidized bed （CFB）. Detailed results of the cluster structure, cluster size, particle volume fraction, gas velocity, and particle velocity are obtained. The correlation between the simulation results and experimental data justifies that these models and algorithm are reasonable, and can be used to efficiently study the dense particle-gas two-phase flow.

Solid Boundary as Energy Source and Sink in a Dry Granular Dense Flow: A Comparison between Two Turbulent Closure Models

Solid boundary as energy source and sink of the turbulent kinetic energy of the grains, and its influence on the mean and turbulent features of a dry granular dense flow, are investigated by using the proposed zero- and first-order turbulent closure models. The first and second laws of thermodynamics are used to derive the equilibrium closure relations, with the dynamic responses postulated by a quasi-static theory for weak turbulent intensity. Two closure models are applied to analyses of a gravity-driven flow down an inclined moving plane. While the calculated mean porosity and velocity correspond to the experimental outcomes, the influence of the turbulent eddy evolution can be taken into account in the first-order model. Increasing velocity slip on the inclined plane tends to enhance the turbulent dissipation nearby, and the turbulent kinetic energy near the free surface. The turbulent dissipation demonstrates a similarity with that of Newtonian fluids in turbulent boundary layer flows. While two-fold roles of the solid boundary are apparent in the first-order model, its role as an energy sink is more obvious in the zero-order model.

A CLOSED SYSTEM OF EQUATIONS FOR DENSE TWO-PHASE FLOW AND EXPRESSIONS OF SHEARING STRESS OF DISPERSED PHA’E AT A WALL

Inthis paper, each of the two phases in dense two-phase flow is considered as continuous medium and the fundamental equations for two-phase flow arc described in Eulerian form. The generalized constitutive relation of the Bingham fluid is applied to the dispersed phase with the analysis oj physical mechanism of dense two-phase flow. The shearing stress of dispersed phase at a wall is used to give a boundary condition. Then a mathematical model for dense two-phase flow is obtained. In addition, the expressions of shearing stress of dispersed phase at a wall is derived according to the fundamental model of the friclional collision between dispersed-plutse particles and the wall.

ON BASIC EQUATIONS OF TURBULENT SWIRLING GAS-SOLID FLOWS AND THEIR APPLICATION IN CYCLONES

The basic equations of turbulent gas-solid flows are derived by using the pseudo-fluid model of particle phase with a refined two-phase turbulence model.These equations are then applied to swirling gas-particle flows for analyzing the collection efficiency in cyclone separators.

Human Action Recognition Based on Dense Trajectories Analysis and Random Forest

This paper presents a human action recognition method. It analyzes the spatio-temporal grids along the dense trajectories and generates the histogram of oriented gradients （HOG） and histogram of optical flow （HOF） to describe the appearance and motion of the human object. Then, HOG combined with HOF is converted to bag-of-words （BoWs） by the vocabulary tree. Finally, it applies random forest to recognize the type of human action. In the experiments, KTH database and URADL database are tested for the performance evaluation. Comparing with the other approaches, we show that our approach has a better performance for the action videos with high inter-class and low inter-class variabilities.

Turbulence modulation model for gas–particle flow based on probability density function approach

he paper focuses on the turbulence modulation problem in gas–particle flow with the use of probability density function（PDF） approach. By means of the PDF method, a general statistical moment turbulence modulation model without considering the trajectory difference between two phases is derived from the Navier–Stokes equations. A new turbulence production term induced by the dispersed-phase is analyzed and considered. Furthermore, the trajectory difference between two media is taken into account. Subsequently, a new k–ε turbulence modulation model in dilute particle-laden flow is successfully set up. Then, the changes to several terms, including the turbulence production, dissipation, and diffusion terms, are well described consequently. The promoted model provides a more probable explanation for the modification of particles on the turbulence. Finally, we applied the model to simulate a gas–particle turbulence flow case in a wall jet, and found that the simulation results agree well with the experimental data.

Effect of particle Froude number on sub-grid effective drag,filtered and residual stresses in fluidized gas-particle flows

Sub-grid effective drag,filtered and residual stresses in the meso-scale of gas-particle fluidized flows are intrinsically affected by underlying micro-scale conditions as well as non-local effects related to macro-scale conditions.In this work we applied microscopic two-fluid modeling to experiment with particle Froude number in order to evaluate the impact of this micro-scale condition over the concerning meso-scale derived sub-grid parameters.We performed highly resolved simulations in periodic domains for particle Froude numbers from 12.21 to 799.22,for a wide range of macro-scale conditions.Results were filtered and classified by ranges of meso-scale markers for the various particle Froude numbers.The particle Froude number was found to considerably affect the structural refinement of the heterogeneous flow fields thereby directly impacting effective drag,filtered and residual stresses.All of those parameters showed systematic behaviors in relation to particle Froude number,thereby providing sound data for new sub-grid modeling propositions.