Development of a filtered interphase heat transfer model based on fine-grid simulations of gas–solid flows

The filtered interphase heat-transfer coefficient for coarse-grid simulations of gas–solid flows can be obtained via a correction (Q) to its microscopic counterpart. The numerical results show that a good linear correlation between Q and the subgrid drift temperature exists at various filtered solid volume fractions, filter sizes and Reynolds numbers, where the subgrid drift temperature is the correlation between the fluctuating temperature of the gas phase and the fluctuation of the gas volume fraction. Since Q can be determined solely by one subgrid quantity, closure for Q is directly pursued. It is found that Q correlates surprisingly well with the product of the filtered solid volume fraction and the filtered temperature difference between the two phases normalized by the filtered heat transfer at a larger scale than the considered coarse grid. A fitting correlation is formulated based on this observation, and its predictability is evaluated in an a priori test.     

Development of a filtered reaction rate model for reactive gas–solid flows based on fine-grid simulations

The filtered reaction rate for the coarse-grid simulations of reactive gas–solid flows can be obtained via a correction to its microscopic reaction rate. The correction term is defined as the mesoscale effectiveness factor η_Δ , which is the ratio of the reaction rate obtained from the fine-grid simulations to that obtained from the coarse-grid simulations. The considered reaction is an isothermal, solid-catalyzed surface reaction with a power law reaction rate model. The simulation results show that the mean η_Δ is almost invariant with the reaction orders at the same Damköhler number. A closure correlation for the mean η_Δ is formulated. However, the standard deviation of η_Δ is found to be quite large. A presumed probability density function model is proposed to capture the fluctuating properties of η_Δ . The predictability of the closure correlations are evaluated via performing the filtered two fluid model simulations in circulating fluidized beds of ozone decomposition.     

Scale and structure dependent drag in gas–solid flows

Drag plays a crucial role in hydrodynamic modeling and simulations of gas–solid flows, which is significantly affected by particle Reynolds number, solid volume fraction, heterogeneity, granular temperature, particle-fluid density ratio, and so on. To clarify and quantify the multiscale effects of these factors, large-scale particle-resolved direct numerical simulations of gas–solid flows with up to 115,200 freely moving particles are conducted. Both domain-averaged kinetic properties and local averaged dimensionless drag are sampled and analyzed. It is revealed that the complex scale-dependence of drag is attributed to the multiscale effects of heterogeneous structures and particle fluctuating velocity. The granular temperature and the scalar variance of solid volume fraction are also found to be scale-dependent. On account of these, a new drag correlation as the function of Froude number is proposed with consideration of scale-dependence.     

Effect of the injection-nozzle geometry on the interaction between a gas–liquid jet and a gas–solid fluidized bed

In industrial fluid cokers, bitumen is first mixed with steam in a premixer, and then fed to the atomization nozzle. The objective of this work was to evaluate the impact of both the premixer and the nozzle geometrical configuration on the quality of the liquid–solid contact resulting from injections of liquid into a gas–solid fluidized bed. To assess the quality of the liquid–solid contact a method based on electric conductance measurements of the bed material previously developed by the authors [9] was used. Liquid atomization efficiency in open air, spray geometry, and spray stability were also characterized to evaluate their effects on the nozzle spraying performance within the fluidized bed. This study indicated that spray stability is highly beneficial to the liquid–solid contact efficiency. In particular, fluid constrictions such as the series of converging and diverging sections within the nozzle have a stabilizing effect on the spray. Future optimization of the existing liquid-injection systems should consider alternative gas–liquid premixers and nozzle geometries to enhance the jet stability.     

Numerical simulations of gas–liquid flow in thermal sorption processes

Thermal storage systems, used, e.g., for domestic heating, must be able to compensate the mismatch between supply and demand. The most efficient techniques for thermal storage are based on sorption storage processes. Usually in sorption, the adsorption process occurs in combination with a solid state adsorbent, whereas absorption takes place in a liquid/gas system. During such sorption processes the flow behavior of the carrier medium is crucial for the efficiency of a falling film absorber. In this work the hydrodynamics of the falling liquid film in two geometrical setups, namely on an inclined plane and over two horizontal parallel tubes, is studied. For the simulation the Eulerian–Eulerian model of the software ANSYS CFX and the interFoam application of the open source software OpenFOAM were used. The numerical results of the two geometries were compared with each other and also with existing data from literature to predict the performance of a sorption storage regarding the specific wetted area and the needed height for gravity driven film absorption.     

Fundamental studies on the hydrodynamics and mixing of gas and solid in a downer reactor

The effect of flow direction on hydrodynamics and mixing in the upflow and downflowcirculating fluidized beds is discussed in details.Similar profiles of gas and solids velocities andsolids concentration are found in both risers and downers.When the flow is in the direction ofgravity(downer),the radial profiles of gas and particle velocity are more uniform than that inthe riser,the solids mixing is very small and the flow pattern approaches plug flow,while theflow is against gravity(riser),the solids backmixing significantly increase and the flow pattern isfar from plug flow.Among many of factors the flow direction has the largest influence onhydrodynamics and axial mixing of gas and solids.     

Horizontal gas and gas/solid jet penetration in a gas–solid fluidized bed

In this paper, the real time, dynamic phenomena of the three-dimensional horizontal gas and gas/solid mixture jetting in a 0.3 m (12 in) bubbling gas–solid fluidized bed are reported. The instantaneous properties of the shape of the jets and volumetric solids holdup are qualified and quantified using the three-dimensional electrical capacitance volume tomography (ECVT) recently developed in the authors’ group. It is found that the horizontal gas jet is almost symmetric along the horizontal axis during its penetration. As the jet width expands, the total volume of the gas jet increases. A mechanistic model is also developed to account for the experimental results obtained in this study. Comparison of jet penetration length and width between the model prediction and ECVT experiment shows that both the maximum penetration length and the maximum width of the horizontal gas jet increase with the superficial gas velocity. When the horizontal gas jet coalesces with a bubble rising from the bottom distributor, it loses its symmetric shape and can easily penetrate into the bed. For the horizontal gas/solid mixture jet penetration in the bed, the tail of the jet at the nozzle shrinks and the jet loses its jet shape immediately when the jet reaches its maximum penetration length, which are different from the characteristics exhibited by the gas jet. The solids holdup in the core region of the gas/solid mixture jet is higher than that in the gas jet. The penetration length of the horizontal gas/solid mixture jet is also larger than that of the gas jet.     

Hydrodynamic simulations of gas–solid spouted bed with a draft tube

Flow behavior of particles in a two-dimensional spouted bed with a draft tube is studied using a continuous kinetic-friction stresses model. The kinetic stress of particles is predicted from kinetic theory of granular flow, while the friction stress is computed from a model proposed by Johnson et al. (1990). A stitching function is used to smooth from the rapid shearing viscous regime to the slow shearing plastic regime. The distributions of concentration and velocities of particles are predicted in the spouted bed with a draft tube. Simulated results compare with the vertical velocity of particles (Zhao et al., 2008) measured and in the spout bed with draft plates and solid circulation rate (Ishikura et al., 2003) measured in the spouted bed with a draft tube. The impact of the friction stress of particles on the spout, annulus, fountain and entrancement regions is analyzed in gas–solid spouted bed with a draft tube. Numerical results show that the gas flow rate through the annulus increases with the increase of the entrainment zone. The solids circulation rate decreases with the decrease of inlet gas velocity and the height of the entrainment zone. The effect of spouting gas velocity on distributions of concentration, velocity and particle circulation is discussed.     

Numerical simulation of micro-mixing in gas–liquid and solid–liquid stirred tanks with the coupled CFD-E-model

The coupled CFD-E-model for multiphase micro-mixing was developed, and used to predict the micro-mixing effects on the parallel competing chemical reactions in semi-batch gas–liquid and solid–liquid stirred tanks. Based on the multiphase macro-flow field, the key parameters of the micro-mixing E-model were obtained with solving the Reynolds-averaged transport equations of mixture fraction and its variance at low computational costs. Compared with experimental data, the multiphase numerical method shows the satisfactory predicting ability. For the gas–liquid system, the segregated reaction zone is mainly near the feed point, and shrinks to the exit of feed-pipe when the feed position is closer to the impeller. Besides, surface feed requires more time to completely exhaust the added H⁺ solution than that of impeller region feed at the same operating condition. For the solid–liquid system, when the solid suspension cloud is formed at high solid holdups, the flow velocity in the clear liquid layer above the cloud is notably reduced and the reactions proceed slowly in this almost stagnant zone. Therefore, the segregation index in this case is larger than that in the dilute solid–liquid system.     

Numerical simulation of local and global mixing/segregation characteristics in a gas–solid fluidized bed

Researches on solids mixing and segregation are of great significance for the operation and design of fluidized bed reactors. In this paper, the local and global mixing and segregation characteristics of binary mixtures were investigated in a gas–solid fluidized bed by computational fluid dynamics-discrete element method (CFD-DEM) coupled approach. A methodology based on solids mixing entropy was developed to quantitatively calculate the mixing degree and time of the bed. The mixing curves of global mixing entropy were acquired, and the distribution maps of local mixing entropy and mixing time were also obtained. By comparing different operating conditions, the effects of superficial gas velocity, particle density ratio and size ratio on mixing/segregation behavior were discussed. Results showed that for the partial mixing state, the fluidized bed can be divided into three parts along the bed height: complete segregation area, transition area and stable mixing area. These areas showed different mixing/segregation processes. Increasing gas velocity promoted the local and global mixing of binary mixtures. The increase in particle density ratio and size ratio enlarged the complete segregation area, reduced the mixing degree and increased the mixing time in the stable mixing area.     

Validation of an anisotropic model of turbulent flows containing dispersed solid particles applied to gas–solid jets

A mathematical model of turbulent flows containing dispersed solid particles is described together with its application to gas–solid jets. Flow fields are predicted by solution of the density-weighted transport equations expressing conservation of mass and momentum, with closure achieved through the k–? turbulence model and a second-moment closure. The particle phase is calculated using a Lagrangian particle tracking technique which involves solving the particle momentum equation in a form that accounts for the spatial, temporal and directional correlations of the Reynolds stresses experienced by a particle. The two phases are coupled via modification of the fluid-phase momentum equations. Predictions of the complete model are validated against available experimental data on a number of single-phase and two-phase, gas–solid jet flows with various particle loadings, and both mono- and poly-dispersed particle size distributions. Overall, predictions of the models compare favourably with the data examined, with results obtained from the anisotropic second-moment turbulence closure being superior to eddy viscosity-based predictions.     

On the effects of the flow macro-scale over sub-grid modelling in dense gas–solid fluidized flows

Multiscale modelling of gas–particle fluidized flows is frequently approached by means of sub-grid modelling, which provides constitutive closures for filtered formulations applied to large scale simulations. A widely practiced procedure for the derivation of sub-grid models consists of filtering over predictions from highly resolved simulations under two-fluid modelling. The present work is intended as a contribution in this field by providing new supporting evidence for the enhancement of sub-grid closure models. Most of the efforts in the area have been directed to providing sub-grid models dependent on meso-scale filtered effects alone, and under low gas Reynolds number suspension conditions. In this work, macro-scale conditions are added to the analysis thereby accounting for flow topology, particularly for dense gas–solid fluidized flows. Two macro-scale variables are considered in the simulations, namely the domain average solid volume fraction and the domain average gas Reynolds number. So, in addition to the usual meso-scale filtered markers, relevant filtered parameters are also related to those macro-scale conditions. The filtered parameters of interest here are the effective interphase drag coefficient and filtered and residual stresses in both of the phases. Various domain average solid volume fractions and domain average gas Reynolds numbers were enforced, thereby providing for a variety of macro-scale dense conditions. It was found that both these macro-scale parameters considerably affect the meso-scale and the resulting filtered parameters of dense gas–solid flows, even though this occurs in a milder way when compared to results for dilute flow conditions available in the literature.     

Numerical simulation of fine particle liquid–solid flow in porous media based on LBM-IBM-DEM

Fine particle liquid–solid flow in porous media is involved in many industrial processes such as oil exploitation, geothermal reinjection, and filtration systems. It is of great significance to master the behaviours of the fine particle liquid–solid flow in porous media. At present, there are few studies on the influences of the migration of fine particles on the flow field in porous media, and the effects of the porosity of porous media and inlet fluid velocity on the migration behaviours of fine particles in porous media. In this paper, a liquid–solid flow model was established based on the lattice Boltzmann method (LBM)-immersed boundary method (IBM)-distinct element method (DEM) and verified by the classical Drag Kiss Tumble (DKT) phenomena and flow around a cylinder successfully. In this model, the interaction between solid particles is analyzed using the distinct element method, and the interaction between fine particles and flow field is handled by IBM. Then, the migration and blockage of fine particles in porous media was studied using this model. It is found that, in addition to the blockage, a large amount of blocked-surface sliding-separation occur in fine particles. At the same time, the decrease in porosity increases the damage degree of fine particles on the permeability. The porosity exerts great influence on the penetration rate and dispersion behaviour of fine particles. The inlet fluid velocity mainly affects the residence time of fine particles and the average velocity of motion in the direction perpendicular to the main flow direction.     

Simulation analysis of gas–solid flow characteristics and water evaporation in flue gas semi-dry desulphurization process based on CPFD method

The gas–solids flow in an industrial-scale semi-dry method desulphurization tower is simulated by the computational particle fluid dynamics (CPFD) approach. Compared with previous studies on desulphurization towers, this study focuses on analyzing particle distribution characteristics such as particle volume fraction, temperature distribution, and residence time. The simulation fully considered the particle–fluid, particle–particle, and particle–wall interactions in the desulphurization tower. Based on these considerations, the effects of flue gas inlet velocity and temperature on the gas–solid distribution characteristics of the desulphurization tower are simulated. An optimization scheme for adjusting the gas–solid flow in the desulphurization tower is proposed. The research results show that the error between the CPFD simulation data and experimental data is small and the changing trend is consistent. The particles in the bed of the desulphurization tower show a typical core–annulus flow. The distribution of gas and particles in the bed has a serious deviation with the increase of the flue gas inlet velocity and temperature. As the axial height of the desulphurization tower increases, the flue gas velocity, temperature, particle concentration, and water vapour distribution in the bed become more uniform. The relatively stable operating conditions for the gas–solid flow in the desulphurization tower is that the flue gas inlet velocity and temperature are 15 m/s and 393 K, respectively. Under these operating conditions, the pressure loss caused by the venturi accounted for 73.6% of the total pressure loss of the desulphurization tower. When the particle radius is between 0–150 μm, the particle size and the flue gas inlet velocity have the greatest influence on the particle residence time. Finally, the distribution of gas and particles before and after the adjustment of the desulphurization tower is compared, which showed that adjusting the bottom structure of the desulphurization tower could optimize the gas–solid flow.     

Profiles of solid fraction and heterogeneous phase structure in a gas–solid airlift loop reactor

The time-averaged and transient local solid fractions in a gas–solid airlift loop reactor (ALR) were investigated systematically by experiments and CFD simulations. To demonstrate the macro-flow pattern, the time-averaged local solid fractions in four regions of the ALR were measured by optical fiber probe under the conditions of different superficial gas velocities and particle circulation fluxes. The experimental results show that the lateral distribution of time-averaged local solid fraction is a core-annulus or heterogeneous structure in the three regions (draft tube, bottom region, particle diffluence region), but a uniform lateral distribution in the annulus. The operating conditions have different effects on the lateral distribution of time-averaged local solid fraction in each region. In the CFD simulation, a modified Gidaspow drag model considering the formation of particle clusters was incorporated into the Eulerian–Eulerian CFD model with particulate phase kinetic theory to simulate and analyze the transient local solid fraction and the two-phase micro-structures in the gas–solid ALR. The predicted values of solid fraction were compared with the experimental results, validating the drag model. The contours of transient flow field indicate that the flow field of the ALR should be divided into five flow regions, i.e., draft tube, annulus, bottom region, particle diffluence region and constrained back-mixing region, which further improves the understanding of the airlift reactor where only four divisions were determined from the experiments. The transient local solid fraction and its probability density function profoundly reveal the two-phase micro-structures (dilute phase and emulsion phase or cluster phase in the constrained back-mixing region) and explain the heterogeneous phenomenon of solid fraction in the ALR. The dilute phase tends to exist in the center of bed, while the emulsion phase mainly appears in the wall region. The results also indicate that the gas–solid ALR has the common characteristic of aggregative fluidization similar to that in normal fluidized beds. The simulated two-phase transient micro-structures provide the appropriate explanations for the experimental core-annulus macro-structures of time-averaged local solid fraction.     

Some accuracy related aspects in two-fluid hydrodynamic sub-grid modeling of gas–solid riser flows

Sub-grid closures for filtered two-fluid models (fTFM) useful in large scale simulations of riser flows can be derived from highly resolved simulations (HRS) with microscopic two-fluid modeling (mTFM). Accurate sub-grid closures require accurate mTFM formulations as well as accurate correlation of relevant filtered parameters to suitable independent variables. This article deals with both of those issues. The accuracy of mTFM is touched by assessing the impact of gas sub-grid turbulence over HRS filtered predictions. A gas turbulence alike effect is artificially inserted by means of a stochastic forcing procedure implemented in the physical space over the momentum conservation equation of the gas phase. The correlation issue is touched by introducing a three-filtered variable correlation analysis (three-marker analysis) performed under a variety of different macro-scale conditions typical or risers. While the more elaborated correlation procedure clearly improved accuracy, accounting for gas sub-grid turbulence had no significant impact over predictions.     

Discussion of “Numerical simulation of moisture transport in concrete based on a pore size distribution model”

This paper presents a discussion on a recent article authored by Huang et al. [Numerical simulation of moisture transport in concrete based on a pore size distribution model, Cement and Concrete Research 67 (2015) 31–43].     

Numerical simulation of gas–liquid flow in the bubble column using Wray–Agarwal turbulence model coupled with population balance model

In this paper, an improved computational fluid dynamic(CFD) model for gas–liquid flow in bubble column was developed using the one-equation Wary–Agarwal(WA) turbulence model coupled with the population balance model(PBM). Through 18 orthogonal test cases, the optimal combination of interfacial force models, including drag force, lift force, turbulent dispersion force. The modified wall lubrication force model was proposed to improve the predictive ability for hydrodynamic behavior near the wall ...