Effect of Particle Size Distribution on Radiative Heat Transfer in High-Temperature Homogeneous Gas-Particle Mixtures

The weighted-sum-of-gray-gas(WSGG)model and Mie theory are applied to study the influents of particle size on the radiative transfer in high temperature homogeneous gas-particle mixtures,such as the flame in aero-engine combustor.The radiative transfer equation is solved by the finite volume method.The particle size is assumed to obey uniform distribution and logarithmic normal(L-N)distribution,respectively.Results reveal that when particle size obeys uniform distribution,increasing particle size with total particle volume fraction fvunchanged will result in the decreasing of the absolute value of radiative heat transfer properties,and the effect of ignoring particle scattering will also be weakened.Opposite conclusions can be obtained when total particle number concentration N0 is unchanged.Moreover,if particle size obeys L-N distribution,increasing the narrowness indexσor decreasing the characteristic diameter Dˉwith the total particle volume fraction fvunchanged will increase the absolute value of radiative heat transfer properties.With total particle number concentration N0 unchanged,opposite conclusions for radiative heat source and incident radiation terms can be obtained except for radiative heat flux term.As a whole,the effects of particle size on the radiative heat transfer in the high-temperature homogeneous gas-particle mixtures are complicated,and the particle scattering cannot be ignoring just according to the particle size.

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.

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.

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.

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.

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.

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.

Effects of the nozzle structure and fluidized gas composition on the gas-particle two-phase jet characteristic in a powder fuel scramjet

The interaction between nozzle design and fluidization gas composition significantly influences the dynamics within a powder fuel scramjet's combustion chamber.To investigate this relationship,an experimental study utilized high-speed shadow imaging technology to explore the macroscopic aspects of powder fuel injection.The investigation examined various convergence angles,nozzle throat lengths,and fluidized gas compositions.Key findings include:During jet development,powder fuel initially concentrates near the axis,with non-convergence angle nozzles exhibiting longer concentrated distribution periods than convergence angle conditions.Decreasing nozzle convergence angles lead to increased penetration distance,frontal velocity,and radial diffusion distance during the initial stages of jet development.Additionally,stable jet shapes show larger divergence angles as nozzle convergence angle decreases,with the largest divergence angle observed atα=60°.In the initial 0-7 ms of jet development,the powder fuel jet demonstrates greater penetration distance and frontal velocity under certain conditions.Moreover,penetration distance and frontal velocity increase with throat length from 7 to 20 ms,accompanied by changes in divergence angles.Specifically,at a throat length(l)of 2 mm,the near-field divergence angle measures 46.50°,and the far-field divergence angle is 22.25°.Conversely,at l=8mm,the near-field divergence angle is 33.49°,and the far-field divergence angle is 23.21°.The fluidization gas composition minimally affects jet penetration distance and frontal velocity during the initial 0-3 ms.However,due to hydrogen's low density,hydrogen/powder fuel jets exhibit shorter distances and velocities compared to nitrogen/powder fuel jets.Hydrogen fluidization also results in larger divergence angles,particularly in the near field.These findings underscore the importance of nozzle design and fluidization gas composition in optimizing scramjet performance and efficiency.

Gas-Particle Flow and Combustion Characteristics of Pulverized Coal Injection in Blast Furnace Raceway

The two-dimensional steady-state discrete phase mathematical model is developed to analyze gas-particle flow and combustion characteristics of coal particles, as well as components concentration and temperature distribu- tion of coal gas in the process of pulverized coal injection of blast furnace raceway. The results show that a great deal of coal gas discharges on the top of raceway away from the tuyere, and the residence time of coal particles in the re- gion of blowpipe and tuyere is 20 ms or so and 50 ms when it reaches raceway boundary. The pressure is the highest at the bottom of raceway and the maximal temperature is about 2 423 K. The char combustion is mainly carried out in the raceway and the maximum of char burn-out rate attains 3× 10-4 kg/s.

PREDICTION OF CONFINED TURBULENT GAS-PARTICLE JETS BY AN ENERGY EQUATION MODEL OF PARTICLE TURBULENCE

Based on a kinetic energy equation of particle turbulence, a k-ε-kk model for turbulent gas-particle flows is proposed. The prediction of confined plane gas-particle jets shows a good agreement with experimental data. This model is proved to be far superior to the presently used k-ε-A.P. model based on the algebraic model of particle turbulence.

NUMERICAL STUDY OF PARTICLE DISTRIBUTION IN THE WAKE OF GAS-PARTICLE TWO-PHASE FLOWS PAST A CIRCULAR CYLINDER AT HIGH REYNOLDS NUMBER

Particle-laden gas flows past a circular cylinder at the Reynolds number of 2×10^(5) were numerically investigated. The Discrete Vortex Method (DVM) was employed to evaluate the unsteady gas flow fields and a Lagrangian approach was applied for tracking individual solid particles. The vortex patterns and the distributions of particles with different Stokes numbers were obtained. Numerical results show that: (1) at small Stokes number (St=0.01) the particles move with the fluid and could be found evenly throughout the flow, (2) the regions around the vortex cores, where few particles exist, become wider as the stokes number of particles increases from 0.01 to 1.0, (3) at middle Stokes number (St=1.0, 10) centrifugal forces throw the particles out of the wake vortices, (4) at high Stokes number (St=100, 1000) the particles are not affected by the vortices,and their motion is determined by their inertia effects.

Numerical investigation of gas-particle flow in the primary air pipe of a low NO_x swirl burner-The DEM-CFD method

The gas-particle flow in the primary air pipe （PAP） of a low NOx swirl burner was investigated using the computational fluid dynamics （CFD） coupled with the discrete element method （DEM）. The mathematical models were validated using the measured values obtained at the outlet of the primary pipe through a phase Doppler anemometer （PDA） system. Particles of different Stokes numbers in the primary air pipe （PAP） were investigated, and the effects of the structure of the primary air pipe and the particle-particle interaction on particle dispersion were analyzed. The results indicate that particles under the combined effects of the Venturi pipe and the spindle body are concentrated into a narrow band area and that the PAP structure can more efficiently concentrate particles with large Stokes numbers. The formed fuel rich/lean jet persists for a long distance out of the burner, thereby favoring of air-staged combustion and NOx reduction. The particle collision frequency and its fluctuation range increase as the particle Stokes number increases. The collisions among particles result in an increase of the spanwise dispersion of particles. Experimental results indicate that the models that take particle-particle collision into consideration are more able to predict particle concentration.

A TWO-SCALE SECOND-ORDER MOMENT PARTICLE TURBULENCE MODEL FOR GAS-PARTICLE FLOW

A two-scale second-order moment two-phase turbulence model was developed and used to simulate gas-particle flow in a sudden-expansion chamber and a channel. The simulation results were in agreement with the experimental results, and the results were compared with those of the single-scale second-order moment two-phase turbulence model. Several improved features show that the two-scale model is to a certain extent better than the single-scale model, which may be attributed to the fact that particle turbulence is well characterized by the two-scale turbulence model.

Experimental Studies on Swirling Gas-Particle Flows in a Spouting-Cyclone Combustor

The gas and particle time-averaged velocity rand RMS fluctuation velocity of swirling gas-particle flows in a spouting-cyclone combustor were measured by a hot-ball probe and a conventional LDV system. The results show large velocity slip between the two phases both in tangential and axial directions and high nonisotropic turbulence of the two phases were also observed which is favorable to coal combustion. The particle RMS fluctuation velocity is higher than the gas RMS fluctuation velocity only in some regions of the flow field.

Modified Diffusion Flux Model for Analysis of Turbulent Gas-Particle Two-Phase Flows

A modified diffusion flux model (DFM) was developed to analyze turbulent multi-dimensional gas-particle two-phase flows. In the model, the solid particles move in a modified acceleration field, g′′ , which includes the effects of various forces on the particles as if all the forces have the same effect on the particles as the gravity. The accelerations due to various forces are then taken into account in the calcula- tion of the diffusion velocities of the solid particles in the gas-particle two-phase flow. The DFM was used to numerically simulate the gas-solid two-phase flow behind a vertical backward-facing step. The numerical simulation compared well with experimental data and numerical results using both the k-ε-Ap and k-ε-kp two- fluid models available in the literature. The comparison shows that the modified diffusion flux model correctly simulates the turbulent gas-particle two-phase flow.

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.

Visualization of Coherent Structures in Acoustically Forced, Gas-Particle Turbulent Round Jet

To show the effects of the particles and forced disturbances on the instantaneous large-scale vortex structures in a gas-particle round jet, coherent structures in gas-particle turbulent round jets were investigated experimentally by flow visualization. The 45-μm and 350-μm diameter glass beads were used as the particles in the experiments. An acoustic speaker was used to introduce velocity perturbations at the jet exit. The Strouhal number based on the nozzle diameter, exit velocity, and forcing frequency was varied from 0,1 to 0.9. The Reynolds number was 9400. The coherent structures were visualized in unforced and forced single-phase jet flows and unforced and forced particle-laden jet flows with different diameter glass beads. The experimental results show that the particles have significant effects on the gas phase coherent structures. The coherent structures are controlled by the large 350-μm diameter particles, while the structures are mainly dominated by the forced disturbances in the flows w

Improved atmospheric mercury simulation using updated gas-particle partition and organic aerosol concentrations

The gaseous or particulate forms of divalent mercury(HgⅡ) significantly impact the spatial distribution of atmospheric mercury concentration and deposition flux(FLX). In the new nested-grid GEOS-Chem model, we try to modify the HgⅡ gas-particle partitioning relationship with synchronous and hourly observations at four sites in China. Observations of gaseous oxidized Hg(GOM), particulate-bound Hg(PBM), and PM 2.5 were used to derive an empirical gas-particle partitioning coefficient as a function of temperature( T) and organic aerosol(OA) concentrations under different relative humidity(RH). Results showed that with increasing RH, the dominant process of HgⅡ gas-particle partitioning changed from physical adsorption to chemical desorption. And the dominant factor of HgⅡ gas-particle partitioning changed from T to OA concentrations. We thus improved the simulated OA concentration field by introducing intermediate-volatility and semi-volatile organic compounds(I/SVOCs) emission inventory into the model framework and refining the volatile distributions of I/SVOCs according to new filed tests in the recent literatures. Finally, normalized mean biases(NMBs) of monthly gaseous element mercury(GEM), GOM, PBM, WFLX were reduced from-33%–29%, 95%–300%, 64%–261%, 117%–122% to-13%–0%,-20%–80%,-31%–50%,-17%–23%. The improved model explains 69%–98% of the observed atmospheric Hg decrease during 2013–2020 and can serve as a useful tool to evaluate the effectiveness of the Minamata Convention on Mercury.

Dense gas-particle flow in vertical channel by multi-lattice trajectory model

A multi-lattice deterministic trajectory(MLDT) model is developed to simulate dense gas-particle flow in a vertical channel.The actual inter-particle collision and particle motion are treated by a Lagrangian model with three sets of lattices to reduce computational time.Cluster formation and motion near the wall are successfully predicted with mean particle volume fraction and velocity,showing quantitatively agreement with experimental results.The mechanism of particles concentrated near the wall is investigated by considering effects of gravity,particle-wall collisions,inter-particle collisions and velocity profiles of the gas phase.It is shown that the inter-particle collision and gas-phase velocity distribution are the essential factors for cluster formation near the wall,while gravity and particle-wall collision only have minor effects on particle concentration near the wall.Particles are unable to remain in the high velocity region due to the strong inter-particle collisions,while they tend to stay in the low velocity region for weak inter-particle collisions.In addition,the effects of channel width and particle sizes on cluster formation are also investigated and it is found that particle concentration near the wall reduces with the decrease of channel width and increase of particle size.