Local porosity in conical spouted beds consisting of solids of varying density

Local bed voidage has been measured in conical spouted beds by means of an optical fibre, for different geometric factors of the contactor (angle and inlet diameter) and under different experimental conditions (height of the stagnant bed, particle diameter and air velocity). The study has been carried out with glass beads and materials of lower density (high- and low-density polyethylene, polypropylene and extruded and expanded polystyrene). From the results, a correlation has been proposed for calculation of the local bed voidage in the spout and annular zones. The effect of the experimental conditions on the bed voidage in the solid ascent (core) and descent (periphery) regions of the fountain has been studied and the fountain has been proven to be of greater importance in the design of conical spouted beds, as solid density and shape factor are lower.     

Minimum spouting velocity for the pyrolysis of scrap tyres with sand in conical spouted beds

The effect of temperature (in the 298-973 K range) on minimum spouting velocity has been studied in conical spouted beds made up of mixtures of tyre and sand particles, for different sizes of tyre particles and for different tyre/sand ratios. The good fit to the experimental results confirms the validity of the correlations already proposed by Olazar et al. [M. Olazar, M.J. San José, A.T. Aguayo, J.M. Arandes, J. Bilbao, Stable operation conditions for gas-solid contact regimes in conical spouted beds, Ind. Eng. Chem. Res. 31 (1992) 1784-1791] for room temperature, which is due to the fact that they take into account the density and viscosity of the gas. For fine particles, the effect of density prevails on the effect of viscosity and the equations proposed by Bai et al. [D. Bai, Y. Masuda, N. Nakagawa, K. Kato, Hydrodynamic behavior of a binary solids fluidized bed, J. Chem. Eng. Jpn. 29 (1996) 211-216] are suitable for the calculation of the average particle size and density, in order for them to be used in the calculation of minimum spouting velocity. For coarse particles, the effect of gas viscosity is insignificant compared to the effect of density and the equation of Goossens et al. [W.R.A. Goossens, G.L. Dumont, G.L. Spaepen, Fluidization of binary mixtures in the laminar flow region, Chem. Eng. Prog. Symp. Ser. 67 (1971) 38-45] is suitable for the calculation of the average particle size required for ascertaining minimum spouting velocity.     

Simulation of a spouted bed reactor for solid catalyst alkylation

A process simulator was developed to afford a better understanding of the performance of a butene-isobutane alkylation plant that uses a three-phase spouted bed reactor and a super acid solid catalyst. The mass and energy balances were numerically solved using lump of reactions and kinetic expressions previously developed. The results indicate the strong influence of the gas linear velocity and temperature in the riser and downcomer behavior that affects the activity, selectivity, and stability of the catalytic systems that cannot be predicted otherwise. The optimal operating conditions were determined for a particular catalyst and set of costs. The impacts of the recycling alkylate and isobutane to the reactor as well as the presence of hydrogen to control the coke formation are analyzed.     

Numerical simulations of flow behavior of gas and particles in spouted beds using frictional-kinetic stresses model

Flow behavior of gas and particles is simulated in the spouted beds using a Eulerian-Eulerian two-fluid model on the basis of kinetic theory of granular flow. The kinetic-frictional constitutive model for dense assemblies of solids is incorporated. 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 and Jackson (1987) and the frictional shear viscosity model proposed by Schaeffer (1987) to account for strain rate fluctuations and slow relaxation of the assembly to the yield surface. An inverse tangent function is used to provide a smooth transitioning from the plastic and viscous regimes. The distributions of concentration, velocity and granular temperature of particles are obtained in the spouted bed. Calculated particle velocities and concentrations in spouted beds are in agreement with the experimental data obtained by He et al. (1994a, b). Simulated results indicate that flow behavior of particles is affected by the concentration of the transition point in spouted beds.     

Computational fluid dynamics (CFD) modeling of spouted bed: Influence of frictional stress, maximum packing limit and coefficient of restitution of particles

Following the previous article [Du, W., Bao, X., Xu, J., Wei, W., 2006. Computational fluid dynamics (CFD) modeling of spouted bed: assessment of drag coefficient correlations. Chemical Engineering Science 61 (5), 1401-1420], this contribution describes the influences of the frictional stress, maximum packing limit and coefficient of restitution of particles on CFD simulation of spouted beds. Using the two-fluid method embedded in the commercial CFD simulation package Fluent 6.1, the spouting hydrodynamics of a cylindrical-conical spouted bed was simulated and verified with the experimental data of He et al. [He, Y.L., Lim, C.J., Grace, J.R., Zhu, J.X., Qin, S.Z., 1994a. Measurements of voidage profiles in spouted beds. Canadian Journal of Chemical Engineering 72 (4), 229-234; He, Y.L., Qin, S.Z., Lim, C.J., Grace, J.R., 1994b. Particle velocity profiles and solid flow patterns in spouted beds. Canadian Journal of Chemical Engineering 72(8), 561-568]. The results showed that, for coarse particles, the frictional stress is important only for the annulus computation and has no obvious effects on the hydrodynamics of the solids flow in the spout region. The specification of the maximum packing limit could significantly affect the properties of the pseudo-fluid phase of the particles by changing the radial distribution function. The strong dependence of the pseudo-fluid properties of the particle phase, such as pressure, bulk viscosity and shear viscosity, on the granular temperature accounts for the influence of the coefficient of restitution of particles on CFD modeling. The solids volume fraction at loose packing state is suitable for spouted bed simulations, and a pretest of the coefficient of restitution of particles must be conducted when no experimental datum is available.     

摩擦-动力应力模型研究喷动床内气固两相流动过程

考虑颗粒滑动的半持续性接触应力和颗粒碰撞瞬时接触应力对颗粒相应力的贡献,建立了喷动床内气体颗粒两相流动计算模型。采用颗粒动理学和Johnson 等的摩擦应力模型,数值模拟喷动床颗粒流动过程,获得了喷动床喷射区、环隙区和喷泉区内颗粒流动特性。模拟计算与He等的实验结果进行了对比。同时分析了摩擦应力模型对颗粒相黏度变化的影响,表明中速颗粒流的颗粒相摩擦应力模型将直接影响喷动床气体颗粒两相流动的预测。     

Stability analysis and CFD validation of a new fluid-particle interaction force for mono-component gas-solid fluidized beds

A new closure relationship for the fluid-particle interaction force has been developed for the CFD modelling of gas fluidized beds. As a first step in verifying the applicability of the new closure, the mono-dimensional version of the equations of change for the fluid and solid phases has been examined analytically. Here, linear stability analysis theory has been applied to the continuity and momentum equations in the face of small fluctuations in the voidage or particle velocity. The effort leads to the development of a new stability criterion for homogenous gas fluidized beds with better predictive capability than the Foscolo and Gibilaro [P. Foscolo, L. Gibilaro, A fully predictive criterion for the transition between particulate and aggregate fluidisation, Chem. Eng. Sci. 39 (1984) 1667-1675.] criterion. This was attributed to the better predictive ability of the dynamic wave velocity developed in this work and which is expressed as a function of the local concentration of the particles. CFD validation of the drag force closure equation is also carried out. Here predictions of bed height and bed voidage obtained from the CFD simulation of a Geldart [D. Geldart, Types of gas fluidization, Powder Technol. 7 (1973) 285.] Group A material FCC catalyst (70 μm) were used to validate the model. Results from simulations showed a very good agreement with predictions from the Richardson-Zaki [J. Richardson, W. Zaki, Sedimentation and fluidization, Trans. Inst. Chem. Eng. 32 (1954) 35.] equation. In the final part of the paper, CFD simulations of three Group B industrial powders are presented comparing the model predictions obtained for the case where the solid stress tensor is at first neglected and subsequently included in the model via the standard granular kinetic theory, results revealed that the collisional stresses do not dominate the macroscopic fluid bed predictions for bubbling dense gas-solid systems.     

Couette grain flow experiments: The effects of the coefficient of restitution, global solid fraction, and materials

Granular flows are complex flows of solid granular material which are being studied in several industries. However, it has been a challenge to understand them because of their non-linear and multiphase behavior. The present experimental work investigates granular flows undergoing shear, by specifically studying the interaction between rough surfaces and granular flows when the global solid fraction and the material comprising the rough shearing surface are varied. A two-dimensional annular shear cell, with a stationary outer ring and inner driving wheel, and digital particle tracking velocimetry (DPTV) technique were used to obtain local granular flow properties such as velocity, local solid fraction, granular temperature, and slip. A customized particle drop test apparatus was built to experimentally determine the coefficient of restitution (COR) between the granular and surface materials using high-speed photography. Results showed that wheel surface materials that produce higher COR values exhibit higher velocity and granular temperature values near the wheel, and lower slip velocities. The local solid fraction appears inversely related to the COR values. The global solid fraction seemed to correspond with velocity and granular temperature, while displaying an inverse relationship to slip. Results also showed an initial decrease in the kinetic energy of the flow as the global solid fraction increased, due to the formation of a distinct contact region. This was followed by a rise in kinetic energy as the global solid fraction continued to increase, based on the increase of particles present in the kinetic region of the flow.     

Investigation of the solid flow between two fluidized beds connected by an orifice

Two adjacent fluidized beds separated by a wall can exchange solids through an orifice due to the local pressure oscillations on both sides of the orifice produced by passing bubbles. This flow of solids between the two fluidized bed reactors is sufficient for some practical applications where a highly integrated, simple and cost-effective arrangement might be required. Solid transfer rates through orifices of different geometries and dimensions have been measured in this work using a novel image analysis technique. The measured solid fluxes can reach up to in some experimental conditions. An empirical correlation has been proposed to fit the available experimental data as a function of key operating conditions.     

颗粒旋转对鼓泡流化床内气固两相流动特性影响的数值模拟

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。     

Filtered and heterogeneity‐based subgrid modifications for gas–solid drag and solid stresses in bubbling fluidized beds

Two different approaches to constitutive relations for filtered two‐fluid models (TFM) of gas–solid flows are deduced. The first model (Model A) is derived using systematically filtered results obtained from a highly resolved simulation of a bubbling fluidized bed. The second model (Model B) stems from the assumption of the formation of subgrid heterogeneities inside the suspension phase of fluidized beds. These approaches for the unresolved terms appearing in the filtered TFM are, then, substantiated by the corresponding filtered data. Furthermore, the presented models are verified in the case of the bubbling fluidized bed used to generate the fine grid data. The numerical results obtained on coarse grids demonstrate that the computed bed hydrodynamics is in fairly good agreement with the highly resolved simulation. The results further show that the contribution from the unresolved frictional stresses is required to correctly predict the bubble rise velocity using coarse grids. © 2013 American Institute of Chemical Engineers AIChE J, 60: 839–854, 2014     

CFD simulations of bubbling beds of rough spheres

Hydrodynamics of three-dimensional gas-solid bubbling fluidized beds are numerically analyzed. The particle-particle interactions are simulated from the kinetic theory for flow of dense, slightly inelastic, slightly rough sphere proposed by Lun [1991. Kinetic theory for granular flow of dense, slightly inelastic, slightly rough sphere. Journal of Fluid Mechanics 233, 539-559] to account for rough sphere binary collisions and the frictional stress model proposed by Johnson et al. [1990. Frictional-collisional equations of motion for particulate flows and their application to chutes. Journal of Fluid Mechanics 210, 501-535] to consider the frictional contact forces between particles. The present model is evaluated by measured particle distributions and velocities of Yuu et al. [2001. Numerical simulation of air and particle motions in group-B particle turbulent fluidized bed. Powder Technology 118, 32-44] and experimental bed expansion of Taghipour et al. [2005. Experimental and computational study of gas-solid fluidized bed hydrodynamics. Chemical Engineering Science 60, 6857-6867]. Our computed results indicated that the present model gives better agreement with experimental data than the results from original kinetic theory for frictionless slightly inelastic sphere of Ding and Gidaspow [1990. A bubbling fluidization model using kinetic theory of granular flow. A.I.Ch.E. Journal 36, 523-538] with and without solid friction stress model.     

Hydrodynamic characterisation of liquid–solid two–phase fluidised beds: Vibration signature and pressure fluctuations analyses

Hydrodynamic behaviour of a two–phase liquid–solid fluidised bed was investigated over a wide range of liquid velocities by means of simultaneous vibration and pressure fluctuations analyses. The liquid velocities were set in a way that covered two most important hydrodynamic events in the bed, namely minimum fluidisation and circulating‐solid regime. To prevent solids from being carried out of the bed, the maximum liquid velocity was kept lower than the terminal velocity of solids. Statistical analysis on the vibration signatures of bed shell proved to be a strong representative for minimum fluidisation characterisation and solid regime change. The minimum fluidisation velocity can be obtained from the intersection of two linear parts in the standard deviation of vibration fluctuation signals. Moreover, the kurtosis of vibration signals could predict the minimum fluidisation and approximate solid regime transition successfully. Meanwhile, statistical parameters, such as standard deviation, skewness, and kurtosis as well as newly‐introduced parameters, namely the energy and average cycle frequency of pressure signals, determined both of minimum fluidisation condition and circulating‐solid flow regime. © 2011 Canadian Society for Chemical Engineering     

基于粗糙颗粒动理学流化床内颗粒与幂律流体两相流动特性的数值模拟研究

在颗粒动理学理论（KTGF）的基础上,通过引入表征粗糙颗粒摩擦和切向非弹性的切向弹性恢复系数β,以及综合反映颗粒平动和旋转运动脉动强度的颗粒拟总温e₀,结合输运理论建立了考虑颗粒旋转作用的颗粒相质量、动量和颗粒拟总温守恒方程。并在求解了同时具有平动和旋转运动的能量耗散和颗粒相应力等参数的前提下提出了颗粒相压力、剪切黏度和能量耗散等本构关系式以及边界条件,最终得出了粗糙颗粒动理学理论（KTRS）。通过改变液相的流变特性,分析了幂律流变模型中流动指数n和稠度系数K_l对流化床内流固两相流动特性的影响,模拟结果表明：随着流动指数和稠度系数的增大,液相湍动能耗散率逐渐增大,而颗粒相压力逐渐减小,颗粒旋转先增大后减小。     

Numerical simulation of gas-particle flow with a second-order moment method in bubbling fluidized beds

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).     

Behavior and mechanism of the stress buffer effect of the inside ceramic layer to the top ceramic layer in a double-ceramic-layer thermal barrier coating

The Double-Ceramic-Layer Thermal Barrier Coating (DCL-TBC) consists of a top ceramic layer (TC1), an inside ceramic layer (TC2), bond coat (BC) and alloy substrate. The top ceramic layer is made by new ceramic materials which has the lower thermal conductivity, such as LZ, LZ₇C₃, LMA etc. Although these materials have good high temperature performance and thermal insulation properties, their thermal expansion coefficients are very low which cause higher degree of mismatch with material properties of alloy substrate.     

A two-dimensional stress analysis of single-lap adhesive joints subjected to external bending moments

The stress distributions in single-lap adhesive joints of similar adherends subjected to external bending moments have been analyzed as a three-body contact problem using a two-dimensional theory of elasticity (plain strain state). In the analysis, both adherends and the adhesive were replaced by finite strips. In the numerical calculations, the effects of the ratio of Young's moduli of the adherends to that of the adhesive and the adhesive thickness on the stress distribution at the interfaces were examined. It was found that the stress singularity occurs at the edges of the interfaces and that the peel stress at the edges of the interfaces increases with decreasing Young's modulus of the adherends. It was noticed that the singular stress decreases at the edges of the interfaces as the adherend thickness increases. In addition, photoelastic experiments and FEM (finite element method) calculations were carried out and fairly good agreement was found between the analytical and the experimental results.     

A two-dimensional stress analysis and strength evaluation of band adhesive butt joints subjected to tensile loads

The stresses in band adhesive butt joints, in which two adherends are bonded partially at the interfaces, are analyzed, using a two-dimensional theory of elasticity, in order to demonstrate the usefulness of the joints. In the analysis, similar adherends and adhesive bonds, which are bonded at two or three regions, are, respectively, replaced by finite strips. In the numerical calculations, the effects of the ratio of Young's moduli for adherends to that for adhesives, the adhesive thickness, the bonding area and position, and the load distribution are shown on the stress distributions at interfaces. It is seen that band adhesive joints are useful when the bonding area and positions are changed with external load distributions. Photoelastic experiments and the measurement of the adherend strains were carried out. The analytical results are in a fairly good agreement with the experimental results. In addition, a method for estimating the joint strength is proposed by using the interface stress distribution obtained by the analysis. Experiments concerning joint strength were performed and fairly good agreement is found between the estimated values and the experimental results.