CFD modeling of liquid–solid fluidization: Effect of drag correlation and added mass force

Computational fluid dynamics (CFD) has been widely used to study the hydrodynamics of gas–solid fluidization; however, its applications in liquid–solid fluidization are relatively rare. In this study, CFD simulations of a liquid–solid fluidized bed are carried out, focusing on the effect of drag correlation and added mass force on the hydrodynamics of liquid–solid fluidization. It is shown that drag correlation has a significant effect on the simulation results and the correlation proposed by Beetstra et al. (2007) gives the best agreement with experimental data. We further show that the added mass force does play an important role in CFD simulation of liquid–solid fluidization, and therefore should not be ignored in CFD simulations.     

Drag law for monodisperse gas–solid systems using particle-resolved direct numerical simulation of flow past fixed assemblies of spheres

Gas–solid momentum transfer is a fundamental problem that is characterized by the dependence of normalized average fluid–particle force F on solid volume fraction ? and the Reynolds number based on the mean slip velocity Re_m. In this work we report particle-resolved direct numerical simulation (DNS) results of interphase momentum transfer in flow past fixed random assemblies of monodisperse spheres with finite fluid inertia using a continuum Navier–Stokes solver. This solver is based on a new formulation we refer to as the Particle-resolved Uncontaminated-fluid Reconcilable Immersed Boundary Method (PUReIBM). The principal advantage of this formulation is that the fluid stress at the particle surface is calculated directly from the flow solution (velocity and pressure fields), which when integrated over the surfaces of all particles yields the average fluid–particle force. We demonstrate that PUReIBM is a consistent numerical method to study gas–solid flow because it results in a force density on particle surfaces that is reconcilable with the averaged two-fluid theory. The numerical convergence and accuracy of PUReIBM are established through a comprehensive suite of validation tests. The normalized average fluid–particle force F is obtained as a function of solid volume fraction ? (0.1 ? ? ? 0.5) and mean flow Reynolds number Re_m (0.01 ? Re_m ? 300) for random assemblies of monodisperse spheres. These results extend previously reported results of  and  to a wider range of ?, Re_m, and are more accurate than those reported by Beetstra et al. (2007). Differences between the drag values obtained from PUReIBM and the drag correlation of Beetstra et al. (2007) are as high as 30% for Re_m in the range 100–300. We take advantage of PUReIBM’s ability to directly calculate the relative contributions of pressure and viscous stress to the total fluid–particle force, which is useful in developing drag correlations. Using a scaling argument, Hill et al. (2001b) proposed that the viscous contribution is independent of Re_m but the pressure contribution is linear in Re_m (for Re_m > 50). However, from PUReIBM simulations we find that the viscous contribution is not independent of the mean flow Reynolds number, although the pressure contribution does indeed vary linearly with Re_m in accord with the analysis of Hill et al. (2001b). An improved correlation for F in terms of ? and Re_m is proposed that corrects the existing correlations in Re_m range 100–300. Since this drag correlation has been inferred from simulations of fixed particle assemblies, it does not include the effect of mobility of the particles. However, the fixed-bed simulation approach is a good approximation for high Stokes number particles, which are encountered in most gas–solid flows. This improved drag correlation can be used in CFD simulations of fluidized beds that solve the average two-fluid equations where the accuracy of the drag law affects the prediction of overall flow behavior.     

Drag models for simulating gas–solid flow in the turbulent fluidization of FCC particles

This paper examines the suitability of various drag models for predicting the hydrodynamics of the turbulent fluidization of FCC particles on the Fluent V6.2 platform. The drag models included those of Syamlal–O’Brien, Gidaspow, modified Syamlal–O’Brien, and McKeen. Comparison between experimental data and simulated results showed that the Syamlal–O’Brien, Gidaspow, and modified Syamlal–O’Brien drag models highly overestimated gas–solid momentum exchange and could not predict the formation of dense phase in the fluidized bed, while the McKeen drag model could not capture the dilute characteristics due to underestimation of drag force. The standard Gidaspow drag model was then modified by adopting the effective particle cluster diameter to account for particle clusters, which was, however, proved inapplicable for FCC particle turbulent fluidization. A four-zone drag model (dense phase, sub-dense phase, sub-dilute phase and dilute phase) was finally proposed to calculate the gas–solid exchange coefficient in the turbulent fluidization of FCC particles, and was validated by satisfactory agreement between prediction and experiment.     

Modeling of three-phase heavy oil–water–gas bubbly flow in upward vertical pipes

A bubbly gas–bubbly oil flow pattern may occur when water, heavy oil and gas flow simultaneously in vertical pipes in such a way that water is the continuous phase. In this work, a one-dimensional, thermal, transient two-fluid mathematical model, for such flow, is presented. The model consists of mass, momentum and energy conservation equations for every phase whose numerical solution is based on the finite difference technique in the implicit scheme. The model is able to predict pressure, temperature, volumetric fraction and velocity profiles. For accurate modeling of multiphase flows, the key issue is to specify the adequate closure relationships, thus drag and virtual mass forces for the gas and oil phases were taken into account and special attention was paid on the gas–oil drag force. When this force was included into the model it was found that: (1) such force had the same order of magnitude than the oil drag force and both forces were smaller than the gas drag force, (2) the pressure, gas and oil velocities and gas and oil volume fraction profiles were affected, (3) the numerical stability was increased. The model predictions are in agreement with experimental data reported in literature.     

Extending EMMS-based models to CFB boiler applications

Recently, EMMS-based models are being widely applied in simulations of high-throughput circulating fluidized beds (CFBs) with fine particles. Its use for low flux systems, such as CFB boiler (CFBB), still remains unexplored. In this work, it has been found that the original definition of cluster diameter in EMMS model is unsuitable for simulations of the CFB boiler with low solids flux. To remedy this, we propose a new model of cluster diameter. The EMMS-based drag model (EMMS/matrix model) with this revised cluster definition is validated through the computational fluid dynamics (CFD) simulation of a CFB boiler.     

A stability condition for turbulence model: From EMMS model to EMMS-based turbulence model

The closure problem of turbulence is still a challenging issue in turbulence modeling. In this work, a stability condition is used to close turbulence. Specifically, we regard single-phase flow as a mixture of turbulent and non-turbulent fluids, separating the structure of turbulence. Subsequently, according to the picture of the turbulent eddy cascade, the energy contained in turbulent flow is decomposed into different parts and then quantified. A turbulence stability condition, similar to the principle of the energy-minimization multi-scale (EMMS) model for gas–solid systems, is formulated to close the dynamic constraint equations of turbulence, allowing the inhomogeneous structural parameters of turbulence to be optimized. We name this model as the “EMMS-based turbulence model”, and use it to construct the corresponding turbulent viscosity coefficient. To validate the EMMS-based turbulence model, it is used to simulate two classical benchmark problems, lid-driven cavity flow and turbulent flow with forced convection in an empty room. The numerical results show that the EMMS-based turbulence model improves the accuracy of turbulence modeling due to it considers the principle of compromise in competition between viscosity and inertia.     

Modeling the hydrodynamics of cocurrent gas–solid downers according to energy-minimization multi-scale theory

Cocurrent gas–solid downer reactors have many applications in industry because they possess the technological advantages of a lower pressure drop, shorter residence time, and less solid backmixing when compared with traditional circulating fluidized bed risers. By introducing the concept of particle clusters explicitly, a one-dimensional model with consideration of the interphase interactions between the fluid and particles at both microscale and mesoscale is formulated for concurrent downward gas–solid flow according to energy-minimization multi-scale (EMMS) theory. A unified stability condition is proposed for the differently developed sections of gas–solid flow according to the principle of the compromise in competition between dominant mechanisms. By optimizing the number density of particle clusters with respect to the stability condition, the formulated model can be numerically solved without introducing cluster-specific empirical correlations. The EMMS-based model predicts well the axial hydrodynamics of cocurrent gas–solid downers and is expected to have a wider range of applications than the existing cluster-based models.     

Numerical simulation and experimental validation of gas–solid flow in the riser of a dense fluidized bed reactor

Gas–solid flow in the riser of a dense fluidized bed using Geldart B particles (sand), at high gas velocity (7.6–15.5 m/s) and with comparatively high solid flux (140–333.8 kg/m² s), was investigated experimentally and simulated by computational fluid dynamics (CFD), both two- and three-dimensional and using the Gidaspow, O’Brien-Syamlal, Koch-Hill-Ladd and EMMS drag models. The results predicted by EMMS drag model showed the best agreement with experimental results. Calculated axial solids hold-up profiles, in particular, are well consistent with experimental data. The flow structure in the riser was well represented by the CFD results, which also indicated the cause of cluster formation. Complex hydrodynamical behaviors of particle cluster were observed. The relative motion between gas and solid phases and axial heterogeneity in the three subzones of the riser were also investigated, and were found to be consistent with predicted flow structure. The model could well depict the difference between the two exit configurations used, viz., semi-bend smooth exit and T-shaped abrupt exit. The numerical results indicate that the proposed EMMS method gives better agreement with the experimental results as compared with the Gidaspow, O’Brien-Syamlal, Koch-Hill-Ladd models. As a result, the proposed drag force model can be used as an efficient approach for the dense gas–solid two-phase flow.     

A novel multiphase DNS approach for handling solid particles in a rarefied gas

A comprehensive model is proposed for multiphase DNS simulations of gas–solid systems involving particles of size comparable to the mean free path of the gas and to that of the bounding geometry. The model can be implemented into any multiphase Direct Numerical Simulation (DNS) method. In the current work, the Volume of Fluid (VOF) method is used, and it is extended to allow for the incorporation of rarefaction effects. For unbounded flow, the model is in excellent agreement with experimental data from the literature. For flows in closed conduits, the model outperforms the alternate approach of using a slip boundary condition at the particle surface for the most relevant degrees of rarefaction and confinement. The proposed model is also able to correctly handle particle–particle interception. The model is intended for low particle Reynolds number flows, and can be applied to resolve in great detail phenomena in a large number of industrial applications (such as filtration of fine particles in porous media).     

Assessment of filtered gas–solid momentum transfer models via a linear wave propagation speed test

The propagation speeds of linear waves in gas–solid suspensions depend strongly on the solids volume fraction and the wave frequency. The latter is due to gas–solid momentum transfer and allows a simple test on filtered gas–solid momentum transfer models. Such models may predict linear wave propagation speeds different from those obtained with the non-filtered model at wave frequencies higher than the filter frequency, but not at wave frequencies lower than the filter frequency.     

气固两相流介尺度LBM-DEM模型

LBM-DEM耦合方法通常是指一种颗粒流体系统直接数值模拟算法,即是一种不引入经验曳力模型的计算方法,颗粒尺寸通常比计算网格的长度大一个量级,颗粒的受力通过表面的粘性力与压力积分获得,其优点是能描述每个颗粒周围的详细流场,产生详细的颗粒-流体相互作用的动力学信息,可以探索颗粒流体界面的流动、传递和反应的详细信息及两相相互作用的本构关系,但其缺点是计算量巨大,无法应用于真实流化床过程模拟。本文针对气固流化床中的流体以及固体颗粒间的多相流体力学行为,建立了一种稠密气固两相流的介尺度LBMDEM模型,即LBM-DEM耦合的离散颗粒模型,实现在颗粒尺度上流化床的快速离散模拟。该耦合模型采用格子玻尔兹曼方法(LBM)描述气相的流动和传递行为,离散单元法(DEM)用于描述颗粒相的运动,并利用能量最小多尺度(EMMS)曳力解决气固耦合不成熟问题,以提高其模拟精度。通过经典快速流态化的模拟,验证了介尺度LBM-DEM耦合模型的有效性。模拟结果表明介尺度LBM-DEM模型是一种探索实验室规模气固系统的有力手段。     

Development of a filtered drag model considering effect of the solid shear rate

This study investigates a 2D gas–solid fast fluidized bed of typical Geldart A particles using highly resolved simulations with two-fluid model. The results show that the solid shear rate has a considerable impact on the orientation of the meso-scale structures and hence on the filtered drag force. On the basis of the correlation for the filtered drag force established in the literature using the traditional markers (such as filtered solid volume fraction, filtered slip velocity and filter scale), a correction correlated with the solid shear rate in the direction of gravity is proposed for better prediction of the filtered drag force. The corrected model is shown to produce improved results in posterior tests of flows in different fluidization regimes including bubbling, turbulent and fast fluidization.     

Investigation of the particle-laden airflow generated by a pseudo-machining operation

A test rig recreating a typical machining induced gas–solid flow is used to investigate the behaviour of the emitted pollutant particles and their effect upon the airflow around the machine tool. The flow is driven by a rotating cylinder and a tangential jet of inertial solid particles. Experimental data concerning both particle flow and air flow are collected by means of phase Doppler particle analyser (PDPA) and particle image velocimetry (PIV). After describing the specific treatments used to discriminate the two phases, complete results are provided and discussed. Additionally, with the main objective being to optimize the design of pollutant capture devices for machining systems, tentative numerical simulations are carried out and compared to experimental data. For the one-phase case (air flow without particles), good agreement between simulations and experiments is found and the superiority of a wall-function based large eddy simulation (LES) over realizable k–ε$k''–''\epsilon$ modelling is highlighted. For two-phase cases, combination of LES and Lagrangian tracking with two-way coupling leads to simulation results that are reasonably accurate considering the low degree of modelling and the empiricism involved. Particle-to-particle collisions, disregarded in simulations, appear to be a predominant phenomenon in the jet source region, thus partly explaining some discrepancies observed between simulations and experiments.     

A stability condition for turbulence model： From EMMS model to EMMS-based turbulence model

The closure problem of turbulence is still a challenging issue in turbulence modeling. In this work, a stability condition is used to close turbulence. Specifically, we regard single-phase flow as a mixture of turbulent and non-turbulent fluids, separating the structure of turbulence. Subsequently, according to the picture of the turbulent eddy cascade, the energy contained in turbulent flow is decomposed into different parts and then quantified. A turbulence stability condition, similar to the principle of the energy-minimization multi-scale （EMMS） model for gas-solid systems, is formulated to close the dynamic constraint equa- tions of turbulence, allowing the inhomogeneous structural parameters of turbulence to be optimized. We name this model as the ＂EMMS-based turbulence model＂, and use it to construct the corresponding turbulent viscosity coefficient. To validate the EMMS-based turbulence model, it is used to simulate two classical benchmark problems, lid-driven cavity flow and turbulent flow with forced convection in an empty room, The numerical results show that the EMMS-hased turbulence model improves the accuracy of turbulence modeling due to it considers the principle of compromise in competition between viscosity and inertia.     

Eulerian–Lagrangian simulations of unsteady gas–liquid flows in bubble columns

We studied the dynamics of gas–liquid flows in a rectangular bubble column using Eulerian–Lagrangian simulations. Three-dimensional, unsteady simulations were performed to simulate the dynamic characteristics of the oscillating bubble plume. The effect of superficial gas velocity and aerated liquid height-to-column width (H/W) ratio on the dynamic and time-averaged flow properties was studied and the simulated results were validated using wall pressure and voidage fluctuation measurements. The effect of lift force and numerical diffusion on the dynamic and time-averaged properties is discussed in detail. Further, the results obtained using the Eulerian–Lagrangian simulations were compared with the Eulerian–Eulerian simulations. The bubble scale information, which is otherwise lost in the Eulerian–Eulerian simulations, was validated using the voidage fluctuation measurements. Such experimentally validated Eulerian–Lagrangian models will be useful for the simulation of mass transfer and reactions in bubble columns.     

Quantitative measurement of solids distribution in gas–solid riser flows using electrical impedance tomography and gamma densitometry tomography

An electrical impedance tomography (EIT) system has been developed to non-invasively measure particle distributions in the riser of a pilot-scale circulating fluidized bed (CFB). Although EIT systems have often been applied to yield qualitative information about gas–solid flows, the present EIT system yields quantitative information that is validated by comparison to a gamma densitometry tomography (GDT) system. EIT and GDT were applied to the CFB riser (14-cm inner diameter, 5.77-m height) containing fluid catalytic cracking particles in air. The flows examined were annular with a dilute core and had average and near-wall solids volume fractions up to 0.25 and 0.66, respectively. For all cases, the average and near-wall solids volume fractions from EIT and GDT agreed to within 0.03 and 0.07, respectively. This good agreement suggests that, where feasible, EIT can be used in place of GDT, which is advantageous since EIT systems are often safer, less expensive, and faster than GDT systems.     

Analysis of unsteady gas–liquid flows in a rectangular tank: Comparison of Euler–Eulerian and Euler–Lagrangian simulations

We study the dynamics of gas–liquid flows experimentally and computationally in a rectangular bubble column where the gas source is introduced at the corner. The flow in this reactor is complex and inherently unsteady in nature. The two-dimensional liquid phase velocity field is calculated by an Eulerian approach solving the unsteady Reynolds Averaged Navier Stokes equations. The conservation equations are closed using a two parameter turbulence model. The two-way coupling was accounted for by adding source terms in the conservation equations of the continuous phase to take into account the interaction with the dispersed phase. Bubble tracking is achieved through a Lagrangian approach. Here the equations of motion are solved taking into account the drag, pressure, buoyancy and gravity forces. The time-averaged flows along with the variables which characterize turbulence are analyzed for a wide range of gas flow-rates using Euler–Lagrangian simulations. These simulation predictions are validated with Euler–Eulerian simulations where the gas-phase distribution is captured as a void fraction and PIV experiments. The motion of bubbles induces turbulence in the flow. The applicability of two parameter models for turbulence like the standard k–ε model on time-averaged flow properties is addressed. From the results of the time averaged velocity field, turbulence intensity, turbulent viscosity and gas hold-up profiles, it is concluded that the Euler–Lagrangian model is applicable at lower gas flow-rates. The Euler–Eulerian approach was found to be valid at lower as well as higher gas flow-rates.     

Study of fluid cell coarsening for CFD-DEM simulations of polydisperse gas–solid flows

Particle polydispersity is ubiquitous in industrial fluidized beds, which possesses a significant impact on hydrodynamics of gas–solid flow. Computational fluid dynamics-discrete element method (CFD-DEM) is promising to adequately simulate gas–solid flows with continuous particle size distribution (PSD) while it still suffers from high computational cost. Corresponding coarsening models are thereby desired. This work extends the coarse-grid model to polydisperse systems. Well-resolved simulations with different PSDs are processed through a filtering procedure to modify the gas–particle drag force in coarse-grid simulations. We reveal that the drag correction of individual particle exhibits a dependence on filtered solid volume fraction and filtered slip velocity for both monodisperse and polydisperse systems. Subsequently, the effect of particle size and surrounding PSD is quantified by the ratio of particle size to Sauter mean diameter. Drag correction models for systems with monodisperse and continuous PSD are developed. A priori analysis demonstrates that the developed models exhibit reliable prediction accuracy.     

双柱状颗粒在线性剪切流场中的动力学分析

为研究柱状颗粒在线性剪切流场中的运动状态和受力情况,本文以颗粒长径比为2,颗粒之间的初始距离ΔS_Py=4D为例,基于直接力浸入边界法数值模拟了双柱状颗粒在三维线性剪切流场中的运动过程。根据模拟结果分析了柱状颗粒周围流场参数分布,在考虑壁面对颗粒的影响和颗粒之间相互影响的条件下,研究了颗粒的受力和运动的变化,探索了流体曳力导致柱状颗粒迁移和转动的规律。研究结果表明,双柱状颗粒在线性剪切流场中易向速度大的流体区域运动;前后两颗粒运动状态和轨迹不同,颗粒之间距离较近时,曳力会产生较大的波动;只有当颗粒在壁面附近时,滞后颗粒才能追上领先颗粒,两颗粒发生牵引、翻滚和分离过程。     

双振子同异步振动主动控制湍流边界层减阻实验研究

本文以镶嵌在平板上沿展向对放的两个压电陶瓷振子为主动控制激励器,自主设计了零质量射流主动控制湍流边界层减阻实验方案.在风洞中开展了双压电振子同步和异步振动主动控制湍流边界层减阻的实验研究,实现了压电振子的周期扰动对湍流边界层多尺度相干结构的干扰和调制,施加控制后减小了壁面摩擦阻力,获得减阻效果.当异步控制100 V, 160 Hz工况时得到最大减阻率为18.54%.小波多尺度分析结果表明,施加控制工况中PZT振子的周期性扰动使得小尺度结构的湍流脉动强度增强,改变了近壁区大尺度和小尺度结构的含能分布,且异步控制工况比同步控制工况的减阻效果好.当双振子振动频率为160 Hz时,流向脉动速度的小波系数PDF曲线呈现出波动特征,尾部变宽显著,近壁湍流脉动更加有序和规则,湍流间歇性减弱.对小尺度脉动进行条件相位平均的结果表明,施加PZT周期扰动后使得大尺度结构破碎成为小尺度结构,小尺度脉动强度增强,实现减阻.随着流向位置离PZT振子越来越远,周期性扰动对相干结构的调制作用逐渐减弱.