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1.
Sun Dan Lu Huilin Shen Zhiheng Wang Shuai Wei Lixin 《Chemical engineering science》2009,64(23):5013-225
A gas-solid two-fluid model with the second-order moment method is presented to close the set of equations applied to fluidization. With the kinetic theory of granular flow, transport equations for the velocity moments are derived for the particle phase. Closure equations for the third-order moments of velocity and for the fluid-particle velocity correlation are presented. The former is based on a modified model with the contribution of the increase of the binary collision probability, and the latter uses an algebraic model proposed by Koch and Sangani [1999. Particle pressure and marginal stability limits for a homogeneous monodisperse gas-fluidized bed: kinetic theory and numerical simulations. Journal of Fluid Mechanics 400, 229-263]. Boundary conditions for the set of equations describing flow of particles proposed by Strumendo and Canu [2002. Method of moments for the dilute granular flow of inelastic spheres. Physical Review E 66, 041304/1-041304/20] are modified with the consideration of the momentum exchange by collisions between the wall and particles. Flow behavior of gas and particles is performed by means of gas-solid two-fluid model with the second-order moment model of particles in the bubbling fluidized bed. The distributions of velocity and moments of particles are predicted in the bubbling fluidized bed. Predictions are compared with experimental data measured by Muller et al. [2008. Granular temperature: comparison of magnetic resonance measurements with discrete element model simulations. Powder Technology 184, 241-253] and Yuu et al. [2000. Numerical simulation of air and particle motions in bubbling fluidized bed of small particles. Powder Technology 110, 158-168]. in the bubbling fluidized beds. The simulated second-order moment in the vertical direction is 1.1-2.5 [Muller, C.R., Holland, D.J., Sedeman, A.J., Scott, S.A., Dennis, J.S., Gladden, L.F., 2008. Granular temperature: comparison of magnetic resonance measurements with discrete element model simulations. Powder Technology 184, 241-253] and 1.1-4.0 [Yuu, S., Umekage, T., Johno, Y., 2000. Numerical simulation of air and particle motions in bubbling fluidized bed of small particles. Powder Technology 110, 158-168] times larger than that in the lateral direction because of higher velocity fluctuations for particles in the bubble fluidized bed. The bubblelike Reynolds normal stresses per unit bulk density used by Gidaspow et al. [2004. Hydrodynamics of fluidization using kinetic theory: an emerging paradigm 2002 Flour-Daniel lecture. Powder Technology 148, 123-141.] are computed from the simulated hydrodynamic velocities. The predictions are in agreement with experimental second-order moments measured by Muller et al. [2008. Granular temperature: comparison of magnetic resonance measurements with discrete element model simulations. Powder Technology 184, 241-253] and fluctuating velocity of particles measured by Yuu et al. [2000. Numerical simulation of air and particle motions in bubbling fluidized bed of small particles. Powder Technology 110, 158-168]. 相似文献
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The behaviour of a gas-solid flow in a bubbling fluidized bed operated near the minimum fluidization condition is strongly influenced by the frictional stresses between the particles, these being highly concentrated and their motion dominated by enduring contact among them and with the walls.The effect of the introduction of frictional stresses in a Eulerian-Eulerian two fluid model based on the kinetic theory of the granular flow is evaluated. The models of Johnson and Jackson [1987. Frictional-collisional constitutive relations for granular materials, with application to plane shearing. Journal of Fluid Mechanics 176, 67-93], Syamlal et al. [1993. Mfix documentation: volume I, theory guide. Technical Report DOE/METC-9411004, NTIS/DE9400087, National Technical Information Service, Springfield, VA], and Srivastava and Sundaresan [2003. Analysis of a frictional-kinetic model for gas-particle flow. Powder Technology 129, 72-85] are compared with the kinetic theory of the granular flow and with experimental data both in a bubbling fluidized bed with a central jet and in a bubbling fluidized bed with a porous distributor. The predicted evolution of the bubble diameter along the height of the fluidized beds is examined, the shapes of the bubbles predicted by the models are compared and the evolution in time of the bubbles is shown. In the case of the bed with a central jet, the bubble detachment time is also calculated. The results show that the introduction of a frictional stress model improves the prediction of the bubbles diameter in a bubbling fluidized bed with a central jet and positively affects the bubbles diameter distribution in a uniformly fed bubbling fluidized bed. The high sensitivity of the model to the value of the particulate phase fraction at which frictional stresses start to be accounted for is pointed out through a sensitivity analysis performed on the Srivastava and Sundaresan [2003. Analysis of a frictional-kinetic model for gas-particle flow. Powder Technology 129, 72-85] model. 相似文献
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Flow behavior of particles in a circulating fluidized bed (CFB) riser is numerically simulated using a two-fluid model incorporating with the kinetic theory for particle rotation and friction stress models. The particle rotations resulting from slightly friction particle-particle collisions was considered by introducing an effective coefficient of restitution based on the kinetic theory for granular flow derived by Jenkins and Zhang [2002. Kinetic theory for identical, frictional, nearly elastic spheres. Physics of Fluids 14, 1228-1235]. The normal friction stress model proposed by Johnson et al. [1990. Frictional-collisional equations of motion for particles flows and their application to chutes. Journal of Fluid Mechanics 210, 501-535] and a modified frictional shear viscosity model proposed by Syamlal et al. [1993. MFIX Documentation and Theory Guide, DOE/METC94/1004, NTIS/DE94000087] were used as the particle frictional stress model. The drag force between gas and particle phases was modified with cluster-based approach (CBA). The flow behavior of particles and the cluster size in a riser of Wei et al. [1998. Profiles of particle velocity and solids fraction in a high-density riser. Powder Technology 100, 183-189] and Issangya et al. [2000. Further measurements of flow dynamics in a high-density circulating fluidized bed riser. Powder Technology 111, 104-113] experiments are predicted. Effects of the rotation and friction stress models on the computed results are analyzed. It is concluded that particle rotations reduce the cluster size and alter the particle flows and distributions through more particle fluctuation energy dissipations. Effects of frictional stress on flow behavior and cluster size are not significant because the particle phase in the CFB riser is not dense enough to take into account for the particle-particle contact interactions. 相似文献
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运用考虑颗粒自旋转流动对颗粒碰撞能量交换和耗散影响的颗粒动理学方法,建立鼓泡流化床气固两相Euler-Euler双流体模型,数值模拟流化床内气体颗粒两相流动特性。分析表明,颗粒平动温度与旋转温度之比是法向和切向颗粒弹性恢复系数和摩擦系数的函数。与不考虑颗粒旋转效应计算结果相比,考虑颗粒旋转效应后床内较容易形成气泡,颗粒自旋转运动将导致床内非均匀结构更明显。并且床层平均空隙率和床层膨胀高度增加,床中心区域颗粒轴向速度提高,床内颗粒平动温度下降。考虑颗粒旋转效应后预测的颗粒轴向速度和颗粒脉动速度与文献实验结果基本吻合。考虑颗粒旋转效应后获得的气泡直径更接近于前人经验关联式。 相似文献
5.
Fluidized bed technology has diverse industrial applications ranging from the gasification of coal in the power industry to chemical reactions for the plastic industry. Due to their complex chaotic non-linear behaviour understanding the hydrodynamic behaviour in fluidized beds is often limited to pressure drop measurements and a mass balance of the system. Computational fluid dynamics has the capability to model multiphase flows and can assist in understanding gas-solid fluidized beds by modeling their hydrodynamics. The multiphase Eulerian-Eulerian gas-solid model, extended and validated here improves on the kinetic theory of granular flow by including a closure term for the quasi-static stress associated with the long term particle contact at high solid concentrations. Similar quasi-static models have been widely applied to slow granular flow such as chute flow, flow down an incline plane and geophysical flow. However combining the kinetic theory of granular flow and the quasi-static stress model for the application of fluidized beds is limited. The objective of the present paper is to compare two quasi-static stress models to the experimental fluidized bed data of Bouillard et al. [4]. A quasi-static granular flow model (QSGF) initially developed by Gray and Stiles [18] is compared to the commonly used Srivastava and Sundaresan [37]. Both models show good agreement with the experimental bubble diameter and averaged porosity profiles. However only the QSGF model shows a distinct asymmetry in the bubble shape which was documented by Bouillard et al. [4]. 相似文献
6.
Wang Shuai Hao Zhenhua Lu Huilin Liu Goudong Wang Jiaxing Xu Pengfei 《American Institute of Chemical Engineers》2012,58(2):440-455
Collisional motion of inelastic rough spheres is analyzed on the basis of the kinetic theory for flow of dense, slightly inelastic, slightly rough sphere with the consideration of gas–solid interactions. The fluctuation kinetic energy of particles is introduced to characterize the random motion of particles as a measure of the translational and rotational velocities fluctuations. The kinetic energy transport equation is proposed with the consideration of the redistribution of particle kinetic energy between the rotational and translational modes and kinetic energy dissipation by collisions. The solid pressure and viscosity are obtained in terms of the particle roughness and restitution coefficient. The partition of the random‐motion kinetic energy of inelastic rough particles between rotational and translational modes is shown to be strongly affected by the particle restitution coefficient and roughness. Hydrodynamics of gas–solid bubbling fluidized beds are numerically simulated on the basis of the kinetic theory for flow of rough spheres. Computed profiles of particles are in agreement with the experimental measurements in a bubbling fluidized bed. The effect of roughness on the distribution of energy dissipation, kinetic energy, and viscosity of particles is analyzed. © 2011 American Institute of Chemical Engineers AIChE J, 2012 相似文献
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A numerical modelling approach for the dynamic simulation of solid-liquid fluidized beds is evaluated. This approach is based on an Eulerian two-fluid formulation of the transport equations for mass, momentum and fluctuating kinetic energy. The solid-phase fluctuating motion model is derived in the frame of granular medium kinetic theory accounting for the viscous drag influence of the interstitial liquid phase. Solid-liquid fluidized bed two-dimensional simulations were performed for flow configurations taken from the experimental work of Zenit et al. [1997. Collisional particle pressure measurements in solid-liquid flows. Journal of Fluid Mechanics 353, 261-283], for three types of solid particles of contrasted inertia in water at high particle Reynolds number (nylon, glass and steel beads). Experimental and numerical granular pressures exhibit a satisfactory agreement with both low and high inertia particles, the best level of prediction being observed with the most inertial particles. Sensitivity of the predictions to the phenomenological laws used in the model is also presented and it appears that, due to non-linear correlations, the average granular pressure in the bed is a less sensitive variable than the fluctuating kinetic energy (or granular temperature). The transport mechanisms of the mean granular temperature in the bed are therefore analyzed as a function of the solid fraction and the particle inertia. At low and moderate Stokes number (nylon and glass beads) and in all range of solid-phase fraction, the dominant production mechanism of fluctuating kinetic energy is due to the mean velocity gradient, whereas the main dissipation term is that induced by the viscous drag. At higher Stokes number (steel beads) and concentration, the production of the granular temperature is controlled by the compressibility effects via the granular pressure. In this case, the dissipation is mainly provided by inter-particle collisions. 相似文献
10.
Flow behavior of gas and particles is performed by means of gas-solid two-fluid model with the second-order moment model of particles in the bubbling fluidized bed. The distributions of velocity and moments of particles are predicted in the bubbling fluidized beds. Predictions are compared with experimental data measured by Jung et al. (2005) in a bubbling fluidized bed and Patil et al. (2005) experiments in a bubbling fluidized bed with a jet. The simulated second-order moment in the vertical direction is on average 1.5-2.3 times larger than that in the lateral direction in the bubbling fluidized bed (Jung et al., 2005). For a bubbling fluidized bed with a jet, the ratio of normal second-order moment in the vertical direction to in the lateral direction is in the range of 0.5-2.5 (Patil et al., 2005). The bubblelike Reynolds normal stresses per unit bulk density used by Gidaspow et al. (2002) are computed from the simulated hydrodynamic velocities. The simulated bubblelike Reynolds normal stresses in the vertical direction is on average 4.5-6.0 times larger than that in the lateral direction in the bubbling fluidized bed (Jung et al., 2005). The predictions are in agreement with experimental second-order moments measured by Jung et al. (2005) and porosity measured by Patil et al. (2005). 相似文献
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M. van Sint Annaland G.A. Bokkers M.J.V. Goldschmidt O.O. Olaofe M.A. van der Hoef J.A.M. Kuipers 《Chemical engineering science》2009,64(20):4237-4604
Particle mixing and segregation rates in a bi-disperse freely bubbling fluidised bed have been studied with a new multi-fluid model (MFM) based on the kinetic theory of granular flow for multi-component systems (see Part I). The MFM simulation results have been compared with digital image analysis experiments obtained by Goldschmidt et al. [2003. Digital image analysis of bed expansion in dense gas-fluidised beds. Powder Technology 138, 135-159] for bi-disperse mixtures of glass beads. In strong contrast to MFMs previously described in the literature, that strongly overestimate the segregation rates, the new MFM seems to underestimate the segregation rates at longer times. This underprediction of the segregation rate is probably related to the neglect of frictional stresses associated with long-term multiple-particle contacts resulting in an overestimation of the mobility of the emulsion phase, which is corroborated by discrete particle simulations without friction between the particles and the particles and the wall. The level of the granular temperature of the segregating system, as computed with the new MFM, compares reasonably well with the granular temperatures found in the DPM simulation. 相似文献
13.
Yin Lijie Wang Shuyan Lu Huilin Wang Shuai Xu Pengfei Wei Lixing He Yurong 《Chemical engineering science》2010,65(9):2664-2679
Numerical simulations of gas-particles flow in a bubble fluidized bed with two large eddy simulations of gas and solid phases are presented. For gas phase and solid phase, the sub-grid scale model for the viscosity is based on the Smagorinsky form. The sub-grid model for the particle pressure proposed by Igci et al. (2008) is modified by replacing the minimum fluidization velocity. The collisional interaction of particles is considered by the kinetic theory of granular flow. Flow behavior of gas and particles is performed by means of these two sub-grid scale models. The subgrid closure for the particle phase viscosity and pressure led to a qualitative change in the simulation results. Predictions are compared with experimental data measured by Yuu et al. (2000) and Taghipour et al. (2005) in the bubbling fluidized beds. The distributions of concentration and velocity of particles are predicted in the bubbling fluidized bed. The predicted filtered particle phase pressure increases and the filtered particle phase viscosity decreases with the increase of particle concentration. The qualitative importance of the model constant cs of particles is demonstrated. 相似文献
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A gas-solid two-fluid flow model is presented. The kinetic-frictional constitutive model for dense assemblies of solids is incorporated in the simulations of spouted beds. This model treats the kinetic and frictional stresses of particles additively. The kinetic stress is modeled using the kinetic theory of granular flow, while the friction stress is from the combination of the normal frictional stress model proposed by Johnson et al. (J. Fluid Mech. 210 (1990) 501) and the modified frictional shear viscosity model proposed by Syamlal et al. (MFIX documentation. US Department of Energy, Federal Energy Technology Center, Morgantown, 1993). The body-fitted coordination is used to make the computational grids best fit the shape of conical contour of the base in the spouted beds. The effects of inclined angle of conical base on the distributions of particle velocities and concentrations in the spout, annulus and fountain zones were numerical studied. Calculated particle velocities and concentrations in spouted beds were in agreement with experimental data obtained by He et al. (Can. J. Chem. Eng. 72 (1994a) 229; (1994b) 561) and San Jose et al. (Chem. Eng. Sci. 53 (1998) 3561). 相似文献
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Numerical simulation of flow behavior of particles and clusters in riser using two granular temperatures 总被引:1,自引:0,他引:1
Cluster in CFB riser significantly affects performance of circulating fluidized beds. To model hydrodynamic behavior in CFB risers, three phase flows were assumed in the riser, the gas phase, the dispersed particle phase, and the clusters phase. The gas-solid multi-fluid model is extended to give the macroscopic averaged equations with constitutive equations for both particle phases from kinetic theory of granular flow. The clusters and the dispersed particles have their own fluctuating energy or two individual granular temperatures. Interactions between the cluster and its surrounding dispersed particles were obtained from kinetic theory of granular flow. Drag force for gas to dispersed particles and the clusters are empirically determined. The momentum exchange between dispersed particles and clusters is modeled using the concept of molecular dynamics. Cluster properties are predicted with the cluster-based approach. The distributions of volume fractions and velocities of gas, dispersed particles and clusters are predicted. Computed solid mass fluxes and volume fractions agree with Manyele et al. [S.V. Manyele, J.H. Parssinen, J.X. Zhu, Characterizing particle aggregates in a high-density and high-flux CFB riser, Chemical Engineering Journal, 88 (2002) 151-161.] and Knowlton [T.M. Knowlton, Modelling benchmark exercise. Workshop at the Eighth Engineering Foundation Conference on Fluidization, Tours, France, 1995.] experimental data. 相似文献
17.
Wenhao Pu Changsui Zhao Yuanquan Xiong Cai Liang Xiaoping Chen Peng Lu Chunlei Fan 《Chemical engineering science》2010,65(8):2500-2512
A kinetic–frictional model, which treats the kinetic and frictional stresses in an additive manner, was incorporated into the two fluid model based on the kinetic theory of granular flow to simulate three dimensional flow behaviors of dense phase pneumatic conveying of pulverized coal in horizontal pipe. The kinetic stress was modeled by the kinetic theory of granular flow, while the friction stress is from the combination of the normal frictional stress model proposed by Johnson and Jackson [1987. Frictional–collisional constitutive relations for granular materials, with application to plane shearing. Journal of Fluid Mechanics 176, 67–93] and the modeled frictional shear viscosity model proposed by Syamlal et al. [1993. MFIX documentation and theory guide, DOE/METC94/1004, NTIS/DE94000087. Electronically available from http://www.mfix.org], which was modified to fit experimental data. For the solid concentration and gas phase Reynolds number was high, the gas phase and particle phase were all treated as turbulent flow. The experiment was carried out to validate the prediction results by three kinds of measurement methods. The predicted pressure gradients were in good agreement with experimental data. The predicted solid concentration distribution at cross section agreed well with electrical capacitance tomography (ECT) image, and the effects of superficial velocity on solid concentration distribution were discussed. The formation and motion process of slug flow was demonstrated, which is similar to the visualization photographs by high speed video camera. 相似文献
18.
A multi-fluid Eularian CFD model with closure relationships according to the kinetic theory of granular flow has been applied to study the motions of particles in the gas bubbling fluidized bed with the binary mixtures. The mutual interactions between the gas and particles and the collisions among particles were taken into account. Simulated results shown that the hydrodynamics of gas bubbling fluidized bed related with the distribution of particle sizes and the amount of energy dissipated in particle-particle interaction. In order to obtain realistic bed dynamics from fundamental hydrodynamic models, it is important to correctly take the effect of particle size distribution and energy dissipation due to non-ideal particle-particle interactions into account. 相似文献
19.
Numerical simulation of bubble and particles motions in a bubbling fluidized bed using direct simulation Monte-Carlo method 总被引:1,自引:0,他引:1
Flow behavior of bubbles and particles in a bubbling fluidized bed were numerically computed using Euler-Lagrange approach. Particle collision was simulated by means of the direct simulation Monte-Carlo (DSMC) method and hard-sphere model. The computed velocities and fluctuations of particles were in agreement with experimental data of Yuu et al. [S. Yuu, H. Nishikawa, T. Umekage, Numerical simulation of air and particle motions in group-B particle turbulent fluidized bed, Powder Technol. 118 (2001) 32-44]. The distributions of velocity, concentration, granular temperature and collision frequency of particles in a bubbling fluidized bed were analyzed. The wavelet multi-resolution analysis was used to investigate flow behavior of bubbles and particles. The bubble frequency of random-like bubble fluctuation was determined from the wavelet multi-resolution analysis over a time-frequency plane. 相似文献
20.
Anders Darelius Berend van Wachem Staffan Folestad 《Chemical engineering science》2008,63(8):2188-2197
In order to enhance process understanding and to develop predictive process models in high shear granulation, there is an ongoing search for simulation tools and experimental methods to model and measure the velocity and shear fields in the mixer. In this study, the Eulerian-Eulerian approach to model multiphase flows has been used to simulate the mixer flow. Experimental velocity profiles for the solid phase at the wall in the mixer have been obtained using a high speed camera following the experimental procedure as described by Darelius et al. [2007a. Measurement of the velocity field and frictional properties of wet masses in a high shear mixer. Chemical Engineering Science, 62, 2366-2374]. The governing equations for modelling the dense mixer flow have been closed by using closure relations from the kinetic theory of granular flow (KTGF) combined with frictional stress models. The free slip and partial slip boundary conditions for the solid phase velocity at the vessel wall have been utilized. The partial slip model originally developed for dilute flows by Tu and Fletcher [1995. Numerical computation of turbulent gas-solid particle flow in a 90° bend. A.I.Ch.E. Journal, 41, 2187-2197] has been employed. It was found that the bed height could be well predicted by implementing the partial slip model, whereas the free slip model could not capture the experimentally found bed height satisfactorily. In the simulation, the swirling motion of the rotating torus formed was over-predicted and the tangential wall velocity was under-predicted, probably due to the fact that the frictional stress model needs to be further developed, e.g. to tackle cohesive particles in dense flow. The advantage of using the Eulerian-Eulerian approach compared to discrete element methods is that there is no computational limitation on the number of particles being modelled, and thus manufacturing scale granulators can be modelled as well. 相似文献