Calculation of Drag Force on an Object Settling in Gas-Solid Fluidized Beds

Gas-solid fluidized beds can be used for dry beneficiation of minerals. Estimation of the drag force on separated materials is important for the design and operation of separators. Previous research was based on the empirical correlation or on the hypothesis that fluidized beds behave as a Newtonian fluid. However, much experimental evidence showed that the hypothesis of Newtonian fluid was suspect. The drag forces on spheres passing through fluidized beds were calculated using the Bingham fluid model. The plastic viscosity and yield stress of a fluidized bed can be obtained by measurement of the terminal settling velocity of spheres. The relationship between drag coefficient (C D ), sphere size (d o ), settling velocity (u t ), bed bulk density ( 𝜌 b ), plastic viscosity (), and yield stress ( 0 ) is expressed as C D = 24/ Re m (1 + 0.15 Re 0.687 m ), Re m = d o u t 𝜌 b /( + 0 d o /3 u t The calculated results agree well with the experimental data.     

Artificial Neural Network Approach to Segregation Characteristic of Binary Heterogeneous Mixtures in Promoted Gas-Solid Fluidized Beds

Binary mixtures of particles of the same size but of different densities are fluidized in a 15 cm diameter column with a perforated plate distributor and two coaxial promoters. In the present work an attempt has been made to study the fluidization and the segregation characteristic of density-variant solids of the same size in terms of segregation distance. The dimensionless segregation distance has been correlated with other dimensionless groups relating to various system parameters: ratio of the density of jetsam particles to that of flotsam, initial static bed height, height of layer of particles above the bottom grid, superficial gas velocity, and average density of the mixture on the basis of the dimensional analysis approach for both un-promoted and promoted beds. Correlations have also been developed with the above system parameters by using an artificial neural network approach for different types of fluidized beds, and the findings with respect to both approaches have been compared with each other. The values of segregation distance for promoted beds have also been compared with those for the un-promoted bed in this work.     

Solid Flow Transition in Liquid and Three-Phase Fluidized Beds

Flow transition of solids in liquid and three phase fluidized beds of Newtonian and non-Newtonian fluids have been studied in a 15.2 cm-ID pyrex glass column. The relation between the fluid flow rate and the bed porosity in three phase fluidized beds have been determined in terms of effective volumetric flux of fluid phases from the modification of the Richardson and Zaki's equation. The modified particle Reynolds Number exhibited its maximum value with the variation of bed porosity in liquid and three phase fluidized beds. The drag coefficient changed its slope apparently at the bed porosity where the maximum value of the modified particle Reynolds number could be attained. At the flow transition condition, the continuity wave velocity, energy dissipation rate, and the continuity shock wave velocity found to have their maximum values. Also, the immersed heater-to-bed and wall-to-bed heat transfer coefficients, wall-to-bed mass transfer coefficient, liquid radial mixing coefficient and solid particle diffusivity in the literature data were found to have maximum values at the transition condition of liquid and three phase fluidized beds.     

Solid Flow Transition in Liquid and Three-Phase Fluidized Beds

ABSTRACT

Flow transition of solids in liquid and three phase fluidized beds of Newtonian and non-Newtonian fluids have been studied in a 15.2 cm-ID pyrex glass column. The relation between the fluid flow rate and the bed porosity in three phase fluidized beds have been determined in terms of effective volumetric flux of fluid phases from the modification of the Richardson and Zaki's equation. The modified particle Reynolds Number exhibited its maximum value with the variation of bed porosity in liquid and three phase fluidized beds. The drag coefficient changed its slope apparently at the bed porosity where the maximum value of the modified particle Reynolds number could be attained. At the flow transition condition, the continuity wave velocity, energy dissipation rate, and the continuity shock wave velocity found to have their maximum values. Also, the immersed heater-to-bed and wall-to-bed heat transfer coefficients, wall-to-bed mass transfer coefficient, liquid radial mixing coefficient and solid particle diffusivity in the literature data were found to have maximum values at the transition condition of liquid and three phase fluidized beds.     

鼓泡床内双组分颗粒流动行为的数值模拟

为了模拟预测粒径和密度同时存在差异的双组分颗粒体系的分级混合行为,基于欧拉-欧拉方法建立多流体模型,采用颗粒动力学理论描述颗粒相性质,分别通过Gidaspow和Syamlal曳力模型描述气-固相曳力和固-固相作用力。结果表明,模拟得到的轴向和径向颗粒浓度分布与实验数据吻合较好;当在较小气流速度下出现分级行为时,床层底部富沉积组分层中沉积组分的运动十分有限,而在较大气流速度下处于完全混合状态时,床层内部颗粒运动较为剧烈。     

低雷诺数下管状非球形颗粒群的阻力系数

以红豆、黑米、铺路石、垫片、大瓷管、中瓷管作为非球形颗粒物料,以硅油作为流态化介质,通过测量液固散式流化床的流速与空隙率的关系,测量了非球形颗粒群在层流区的阻力系数。根据阻力系数和散式流态化Richarson和Zaki指数的实验结果,经研究和分析,提出了低雷诺数时非球形颗粒群阻力系数的计算公式为CD=24(εnψ0.83Re)-1。     

振动力对流化床内气泡行为影响的数值模拟

为了分析振动力对气-固流化床中气泡行为的影响,探究振动力改善流化床中颗粒流化状态的深层原因,采用计算流体力学方法,运用Fluent14.5及PBM模块模拟了振动流化床中气泡的尺寸、上升速度及床层波动等变化规律,通过物理模型构建、数学模型修正、网格划分、边界条件设定、实验验证等环节,揭示了振动力加入前、后床内气泡尺寸分布、气泡上升速率沿高度分布、床层压力的脉动信号变化的周期性等的变化特征。结果表明:未加振动时,气泡尺寸分布比较均匀,大气泡较少,气泡直径随着床层高度增加而增大;加入振动后,气泡在床内分布不均匀,大气泡较多;在气泡上升初期,气泡直径不断变大,气泡上升速度也不断增大,而后期气泡上升速度不断减小;床层压力脉动信号的周期性明显增强。     

稀相气-固流化床分选电厂磨机返料中黄铁矿的实验与模拟

为了降低燃煤电厂的磨机功耗,减少锅炉燃烧后的污染排放,通过分析磨煤机分离器返料的粒度和密度分布,对电厂采样物料进行稀相流化床分选去除黄铁矿等矿物质的实验研究,并对物料分选过程进行数值模拟。结果表明,粒径小于0.500 mm的分离器返料在流化床中具有较小的起始流化速度1.62 cm/s,流化床各层的密度和粒度具有很好的稳定性;物料中的黄铁矿等矿物质得到分离,上层和底层物料灰分质量分数分别为33.34%、73.42%,硫分质量分数分别为1.12%、8.96%,底层物中硫主要以黄铁矿的形式存在;气-固两相流稀相分选床的流场形态及颗粒运动数值模拟验证了实验结论。     

Preliminary Hydrodynamic Modeling of Fluidized Beds of Single Component and Binary Particle System in Compartmented Gasifier

In the present study, three-dimensional simulation using computational fluid dynamics (CFD, FLUENT 6.3.26) and experiments were conducted on a transparent cold-flow gas-solid bubbling compartmented fluidized bed gasifier (CFBG) model with identical diameter as the pilot-scaled CFBG. Using Eulerian-Eulerian granular model with closure laws according to the kinetic theory of granular flow that based on modified drag model simulations were conducted to model the hydrodynamics of CFBG in terms of gas-solid flow pattern, bed expansion ratio, bed pressure drop and bubble diameter. The model was resolved by semi-implicit method for pressure-linked equation (SIMPLE) algorithm in CFD. Different inerts like river sand, quartz sand, and alumina were used to examine the hydrodynamics behaviors both in single component and binary system where biomass, palm shell, was mixed with river sand. The modeling predictions compared reasonably well with experimental bed expansion ratio measurements and qualitative gas-solid flow patterns. Pressure drops predicted by the simulations were in relatively close agreement with experimental measurements. Furthermore, the simulated bubble diameters showed similarities with the Darton et al., bubble size equation.     

Investigating the Drag Force of Luffa Tendril Due to Free Coiling

Abstract: Tendrils of some species of plants freely coil between their bases and tips to drag up the shoot and ensure no waste of shoot growth. In this study, the drag force generated by tendrils of the luffa plant (Luffa cylindrica) during free coiling was evaluated using a force measurement system that consisted of cantilever wire apparatus, CCD camera and finite element analysis software. How the stiffness of an object to which is attached the tip of tendrils affects the development of drag force because of free coiling was investigated. Experimental results showed that the tendril attached to a stiffer support could take longer to develop drag force and generate stronger drag force than one attached to a less stiff support. The drag force developed by free coiling of the luffa tendril could be on the order of 0.17 N. This force is sufficient to pull up more than eight times the internodal weight of the luffa shoot without other support. The relation between the magnitude of drag force generated by free coiling and the contraction ratio of the tendril was elucidated. The drag force–time curves show that the rate of increase in drag force resulting from free coiling of luffa tendrils in the first 20 h is higher than that after 20 h.     

Drag and Lift Force Acting on a Rotational Spherical Particle in a Logarithmic Boundary Flow

The drag and lift forces acting on a rotational spherical particle in a logarithmic boundary flow are numerically studied. The effects of the drag velocity and rotational speed of the sphere on the drag force are examined for the particle Reynolds number from 50 to 300 and for the dimensionless rotational angular speed of 0≤Ω≤1.0. The influence of dimensionless roughness height z0of the wall is also evaluated for z0≤10. The results show that the drag forces on a sphere both in a logarithmic flow and in a uniform unsheared flow increase with the increase of the drag velocity. For 50≤Rep≤300, the drag coefficient (-C)D increases with decreased roughness height z0. The time-averaged drag coefficient is also significantly affected by rotational speed of the sphere and roughness height z0 . The lift coefficient -CL increases with increased rotational speed and decreases with increased roughness height.     

计算球形颗粒自由沉降速度的一种新方法

对球形颗粒曳力系数关联式进行了分析比较，发现国内外一些教科书和文献中常用的过渡区的两个关联式误差很大．不宜推荐继续使用，但在工程设计计算中可使用优选出的形式比较简单、计算结果比较准确的关联式本文还提出一种计算球形颗粒自由沉降速度的新方法，用Ｒｅｐ－Ａｒ表或Ｒｅｐ－Ａｒ关联式可直接计算出球形颗粒的自由沉降速度，避免了试差或迭代．     

Drag on a sphere accelerating rectilinearly in an elastico-viscous fluid

The exact solution for the drag on a sphere moving in an arbitrary manner along a rectilinear path in an otherwise-still elastico-viscous fluid of infinite extent is presented. The Fourier transform technique is used to derive the solution. This technique is based on the fact that drag on an accelerating body can be obtained by integrating the drag on an oscillating body over all possible frequencies. The solution is also expressed in terms of infinite series which is suitable for numerical evaluation of the drag. The solution for the drag on a sphere suddenly brought to uniform motion is presented as an example of this study.     

小球在两平行平壁之间的牛顿流体中下落所受的阻力

本文采用奇异摄动方法的匹配法和Ｆｏｕｒｉｅｒ变换方法，求出了小球在两平行平壁之间的牛顿流体中下落所受的阻力，并给出了在小球不同程度偏向一壁情况下的数值计算结果．     

A Method of Body Shape Optimization for Decreasing the Aerodynamic Drag Force in Gas Flow

Aerodynamic flow past bodies of various geometrical shapes was studied, and the aerodynamic drag force was reduced through optimization of the body shape using a specially proposed method. The resulting drag force was compared to that for bodies formed by revolution of the profiles of well-known standard series. The study was performed using the Ansys Fluent software for isothermal laminar steady-state flows of incompressible fluid with constant density in a velocity range of 0–10 m/s. It is shown that the aerodynamic drag force for a body with the optimized shape is lower than analogous values for the bodies of revolution with Su-26 and NASA-0006 reference profiles. In comparison to the aerodynamic-drag-force level of 100% for the body of revolution with NASA-0006 profile, the drag force for Su-26 profile at airflow velocity of 10 m/s is 89.4%, while that for the proposed optimized body shape is 89.2%.     

黑色金属挤压力的智能化计算

以MATLAB应用软件作为开发平台介绍了黑色金属挤压力智能化计算软件的开发方法,设计的界面友好,操作简单,可实现冷挤压力的智能化计算以及工艺参数优化设计.软件计算的挤压力的大小与传统方法比较相对误差小于5%.     

电阻热效应对力式微固态测风传感器测量精度的影响

本文就电阻热效应对基于风的拖动力原理的微型固态测风传感器测量精度的影响进行了研究.微型固态测风传感器通过溅射在悬梁上的铂电阻测量悬梁弯曲应变来获得风速信息和简单的风向信息.风吹过铂电阻时,除了应变引起电阻阻值变化外,由于热传导、对流、辐射等热效应,其阻值也会随着风速的变化而变化.当热效应引起的电阻的变化趋势和应变引起的电阻变化趋势相反时,传感器的输出先减小后增大,风速测量产生较大误差.文中对两种铂电阻在悬梁上的放置连接方式的传感器进行了理论分析,通过对利用MEMS工艺制作的两种传感器的测试,证实理论分析与实验结果相符.