不同圆球复合无序堆积床内流动传热数值分析

圆球堆积床内孔隙分布影响其内部流场及温度场分布, 且小管径-球径比堆积床由于壁面限制, 内部孔隙率变化剧烈, 其内部流动和传热不均匀现象明显。针对D/d_p为3的圆球无序堆积床构建了3种非等直径圆球复合堆积结构:径向分层复合堆积、轴向分层复合堆积以及随机复合堆积结构, 并采用DEM-CFD方法建模计算, 从径向及整体角度分析比较不同复合堆积床内流动换热特性及其流场和温度场分布的均匀性。结果表明:孔隙率及孔隙大小分布共同影响堆积床内流场和温度场分布;相对于单一等直径圆球堆积, 采用复合堆积结构能使堆积床内部孔隙率分布更均匀, 其内部流场和温度场分布也更为均匀;对于D/d_p为3的堆积通道, 径向分层堆积结构对于提高整体流动换热性能及改善内部流动换热均匀性都有显著效果。     

Co-ordination number distribution of spherical particles in a packed cylindrical bed

In modeling transport phenomena of packed particles, it is useful to make an assumption regarding the arrangement of particles and the number of contact points with neighboring particles. In this paper the distribution of co-ordination number (contact points) has been determined for a cylindrical bed packed with uniform-sized spheres. For a randomly poured bed with a porosity of 0.39, the average number of contact points was found to be approximately 8. Except for a sharp reduction in value at the wall, the co-ordination number was found to be nearly constant over the interior of the bed. Since an array of particles configured as body-centered orthorhombic has the same number of contact points and porosity, the study suggests that this regular configuration could be used in modeling effective transport properties of random packed beds, except near a container wall.     

Random stacking template of polymer spheres and water soluble particles to fabricate porous hydroxyapatite with interconnected pores

Particle stacking simulation is applied in the fabrication of porous hydroxyapatite (HA) ceramics to predict the relationship between the template preparation process and the porosity of porous ceramics. The stacking of multi-diameter spherical particles, such as polymer spheres and NaCl particles, in three-dimensional space is simulated by using continuous generation method. The porosity of porous HA is predicted by calculating the stacking density of large spheres (the ratio of large sphere volume and container volume). The model of three-dimensional random stacking spheres is implemented by using the C++ program. Porous HA ceramics with interconnected spherical pores were fabricated by slipcasting which the use of a polymer template. Templates were produced by randomly stacking polymer spheres and NaCl particles. The arithmetic average error between the porosity of porous HA ceramics and the stacking density of polymer spheres (large spheres) is 3.52%. Simulation results obtained by using the proposed method are consistent with the experimental results.     

Near-wall porosity characteristics of fixed beds packed with wood chips

Packed beds of fuel wood chips are commonly found in thermal conversion processes such as combustion or gasification. Wood chips in particular are mostly used as fuel for small-scale domestic heating boilers but also for commercial-scale combustion units. The characterization of spatial voidage distribution inside the wood chip beds is of great importance for flow and reactor modelling. This study focuses on the radial porosity variations of cylindrical beds of three different types of commercially available wood chips including chips classified as G30 size class. The conventional technique of consolidating packed beds with a resin was chosen as the experimental procedure. The radial voidage distribution in different cylindrical beds is determined by image analysis of sections of the solidified packings. Additionally, a packing of monosized spheres was investigated in order to assess the selected procedure in comparison with widely available literature data for spheres. The results are discussed and summarized in a mathematical expression correlating the radial voidage distribution depending on average wood chip size, packing core porosity and dimensionless distance from the tube wall.     

Derivation of pacticle size distributions from measurements on plane sections through particle beds. Effect of regularity of particle packing

When the size distribution of particles embedded in an opaque, continuous solid phase is required, the general approach is to deduce the distribution from the size distribution of particle cross-sections in a plane cut through the particle bed. When the particles are approximately spherical, this deduction can be performed by making the assumption that the distances from the plane of cut to the particle centers are rectangularly distributed. The validity of this assumption does not, however, appear to have been investigated in previously published work, and in the present contribution the assumption has been considered more closely.The distribution of the distances between the sphere centers and a random plane has been investigated both theoretically and experimentally, starting with regular packings of monosized spheres, and extending the treatment to monosized spheres packed at random and finally to packings of polysized spheres.The distribution of particle center to cutting plane distances will approach a rectangular distribution with increasing sample size even for strictly regular packings. However, for finite samples, the packing regularity may significantly affect the extent to which such a distribution is realized.     

PREDICTION OF MINIMUM SPOUTING VELOCITY IN TWO-DIMENSIONAL FLAT BOTTOM SPOUTED BEDS

Spouted beds have been used in industry for operations such as drying, catalytic reactions, and granulation. Conventional cylindrical spouted beds suffer from the disadvantage of scaleup. Two-dimensional beds have been proposed by other authors as a solution for this problem. Minimum spouting velocity has been studied for such two-dimensional beds. A force balance model has been developed to predict the minimum spouting velocity and the maximum pressure drop. Effect of porosity on minimum spouting velocity and maximum pressure drop has been studied using the model. The predictions are in good agreement with the experiments as well as with the experimental results of other investigators.     

Creeping flow mass transfer to a single active sphere in a random spherical inactive particle cloud at high schmidt numbers

Using the solution by Tam of Navier-Stokes equations for creeping flow around an active sphere surrounded by a random cloud of inactive spheres, an asymptotic solution of the convective diffusion equation is obtained for high Schmidt numbers. The Sherwood number for the overall mass transfer coefficient to the active sphere has been analytically related to the Peclet number as

It agrees very well with the experimental mass transfer data on single active spheres for σ = 0476, Re < 10 and large Sc. This analytical result becomes invalid as σ decreases to 0.33. Pfeffer's model for the same problem has excellent agreement with the mass transfer data on single active spheres for σ = 026, Re < 10 and Sc = 1600. Pfeffer's model seems to be quite satisfactory for the usual range of void volume fractions in packed beds. The present model seems to be more accurate at higher values of void volume fractions in packed and distended beds.     

Radial porosity distribution in cylindrical beds packed with spheres

Experimental determinations of radial porosity for cylindrical beds packed with spheres are reported. The data indicate that, for a wide range of bed and sphere sizes, porosity varies significantly and regularly near the container wall. For uniformly sized spheres, the oscillations in porosity can be detected up to a distance of about 5 particle diameters from the wall. For mixtures of spheres of two sizes, regular oscillations are detected only up to 2 or 3 diameters from the wall and for three sizes the effect of the wall is observed only within a distance of 1 particle diameter.     

Radial porosity in packed beds of spheres

A functional approach has been developed to investigate the radial porosity of mono-sized spheres in cylinders. Analytical and semi-analytical equations have been developed to calculate the local radial porosity and the radial porosity distribution, respectively, within a cylindrical packing structure. The analytical equations are based upon fundamental principles and are simple, straightforward and provide highly accurate results for the radial porosity with minimal computational prerequisites. The analytical equations have been developed for the fixed packing of identical spheres in cylindrical containers with D/d ≥ 2.0. The predicted results for the local radial porosity and the radial porosity distributions are benchmarked with an existing analytical equation and available experimental data, respectively, for mono-sized spheres in cylindrical containers.     

Wall to fluid heat transfer in liquid fluidised beds: Part 2

Wall to fluid heat transfer coefficients and radial temperature profiles have been obtained for beds of hydrodynamically similar spheres fluidized with water in a 2.058 inch pipe at a constant heat flux. From packed bed to open pipe conditions, heat transport occurs mainly by turbulent mixing, although conduction through the particles and possibly particle convection have some effect at low porosities. This result contradicts a previously published prediction based on model calculations using erroneous temperature profiles⁽²⁴⁾. The model predicts a minor role for particle convection when appropriate temperature profiles are used. A series model based on the observed shift of thermal resistance from the wall region to the bulk of the bed with decreasing porosity is used to correlate heat transfer coefficients. The shift in resistance largely accounts for the maximum in heat transfer coefficient plots.     

An analysis of transport phenomena for multi-solid particle systems at higher reynolds numbers by a standard Karman—Pohlhausen method—I Mass transfer

Using the velocity profiles, based on the concentric spheres free surface model and a standard 4th polynomial Karman—Pohlhausen method in Part 1, the diffusion equation was solved numerically at higher Reynolds numbers. The mass transfer rate for multi-solid particle systems so computed agreed with the exprerimental data of single solid spheres, and packed and fluidized beds at higher Reynolds numbers.     

SLOW NON-NEWTONIAN FLOW PAST AN ASSEMBLAGE OF RIGID SPHERES

Previous work on slow flow of non-Newtonian fluids past particles assemblages has been reviewed. Using a combination of Happel's free surface model and variational principles, bounds on the drag have been obtained for the creeping flow of a Carreau Model fluid past an assemblage of rigid spheres. The bounds are related to friction factor for flow through fixed beds of spherical particles. Numerical results covering a wide range of model parameters and bed voidages are presented.

Theoretical predictions are validated by comparing with experimental results reported in the literature that involve viscoelastic fluids. Arithmetic averages of the two bounds compare well for 182 data points with an average error of 12%. It is demonstrated that the present analysis, though based on a purely viscous model, can predict creeping flow behaviour in rigid particles assemblage for both inelastic and viscoelastic fluids.     

A STUDY OF SPINLINE DYNAMICS USING ORTHOGONAL COLLOCATION

Previous work on slow flow of non-Newtonian fluids past particles assemblages has been reviewed. Using a combination of Happel's free surface model and variational principles, bounds on the drag have been obtained for the creeping flow of a Carreau Model fluid past an assemblage of rigid spheres. The bounds are related to friction factor for flow through fixed beds of spherical particles. Numerical results covering a wide range of model parameters and bed voidages are presented.

Theoretical predictions are validated by comparing with experimental results reported in the literature that involve viscoelastic fluids. Arithmetic averages of the two bounds compare well for 182 data points with an average error of 12%. It is demonstrated that the present analysis, though based on a purely viscous model, can predict creeping flow behaviour in rigid particles assemblage for both inelastic and viscoelastic fluids.     

Pressure drop across packed beds in the low Knudsen number regime

The solutions of Happel and Kuwabara describing flow through systems of multiple spheres have been compared with available pressure drop data to determine the applicability of cell models for analyzing flow in packed beds. The comparisons indicate that these solutions describe the flow with reasonable accuracy. Of the two solutions, the Kuwabara flow field has been found to give better agreement between predictions and experimental results. In order to describe flow in beds operating at low Knudsen numbers the Kuwabara solution has been extended by allowing for gas slippage at the collecting surfaces. The resulting solution is presented as a correction to the Basset-Millikan expression and accounts for the presence of neighboring spheres in low Knudsen number flows. Using this extended solution, the pressure drop across packed beds is predicted as a function of Knudsen number and packing density.     

Packing of multi-sized mixtures of wet coarse spheres

The effect of water addition on the packing of multi-sized coarse spheres has been experimentally investigated under standard poured packing conditions. The results indicate that porosity is strongly affected by particle characteristics such as particle sizes and their distribution, in addition to water content. The packing features in the relationship between porosity and moisture content for wet multi-sized spheres are found to be similar to those for wet mono-sized spheres, implying that the same governing mechanisms apply. The comparison between the dry and wet packing systems confirms that there is a similarity between them, suggesting that the packing of wet particles can be predicted within the framework of a packing model developed for dry coarse particles. Future work in this direction is also discussed.     

Extension of the kinetic theory of granular flow to include dense quasi-static stresses

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].     

Predicting the effective thermal conductivity of polydispersed beds of softwood bark and softwood char

In this paper, the effective thermal conductivity (ETC) of softwood bark and softwood char particle beds which are highly polydispersed has been studied theoretically and experimentally. Use of the linear packing theory and unit cell model of heat conduction enabled to express ETC of polydisperded beds as a function of particle size distribution. Each of the softwood bark and softwood char samples were sieved into seven fractions. The initial porosity and binary packing size ratio of the particles have been characterized as a function of mean sieve size. ETC of polydispersed beds of bark and char has been predicted as a function of particle size distribution. Model predictions were in good agreement with the experimental measurements. The proposed approach can be used to predict the ETC of any size distribution of softwood bark and softwood char beds without measuring the in situ bed porosity.     

Simulation of Turbulent Flow in a Packed Bed

Numerous models for simulating the flow and transport in packed beds have been proposed in the literature with few reported applications. In this paper, several turbulence models for porous media are applied to the gas flow through a randomly packed bed and are examined by means of a parametric study against some published experimental data. These models predict widely different turbulent eddy viscosity. The analysis also indicates that deficiencies exist in the formulation of some model equations and selection of a suitable turbulence model is important. With this realization, residence time distribution and velocity distribution are then simulated by considering a radial profile of porosity and turbulence induced dispersion, and the results are in good agreement with the available experimental data.     

Variation in the local packing density near the wall of a randomly packed bed of equal spheres

In randomly packed beds of spherical particles, a damped oscillatory variation in the local packing density appears near the containing walls and dies away in the interior. This paper presents detailed data obtained from a computer-simulated random loose packing. The molecular pair-correlation function from statistical mechanics yields a theoretical variation in local packing density which agrees with values from the simulation. The variation is similar to the short-range order of the arrangement of spheres in the interior of the random assemblage.     

Angular porosity distributions in fixed packed beds of low diameter aspect ratio

The angular porosity distribution for fixed packed beds of monosized spheres in cylindrical containers with low diameter aspect ratios (1 ≤ D/d ≤ 2) is determined from the spheres' center coordinates. By dividing the packed bed into a large number of identical wedge-shaped segments, the angular porosity distribution is established from the local angular porosity and the angular positions within the cylindrical container. A correlation which accurately predicts the local angular porosity is determined from the angular porosity distributions. The correlation is a function of D/d and the angular position in the cylindrical container.