流化床浸没换热管传热研究进展

论述了前人对流化床与浸没换热管间传热规律的理解和认识,介绍了常用的传热模型及其实用条件,总结了近年来在实验研究等方面所取得的进展。     

Prediction on immersed tubes erosion using two-fluid model in a bubbling fluidized bed

A numerical study based on a gas-solid two-fluid model using body-fitted coordinates to predict the immersed tube erosion rate in a bubbling fluidized bed has been conducted. Computations have been performed at various s/D ratios (ratio of the spacing between two tube centers to the diameter of the tubes) for a bed into which one, two, three or four immersed tubes were inserted. A monolayer kinetic energy dissipation model is implemented to simulate the erosion on the surfaces of the immersed tubes at the body-fitted coordinates. The effect of the s/D ratios on the erosion rate in the bubbling fluidized bed is investigated. A granular temperature distribution provides an indication of the regions on the immersed tubes that could be susceptible to fluctuation intensity of the solid phase. Wake properties influenced the erosion rate remarkably. Calculated erosion rates on the surfaces of the immersed tubes were in good agreement with previous experimental and numerical findings.     

Investigation of bubble behavior in fluidized beds with and without immersed horizontal tubes using a digital image analysis technique

Bubble characteristics such as shape, size, number and motion control the hydrodynamics and therefore heat transfer and chemical conversion in fluidized bed reactors. Thus understanding these characteristics is very important for the design and scale-up of fluidized beds. In this work a digital image analysis technique was developed to study the bubble behavior of two-dimensional bubbling beds with and without immersed horizontal tubes. Digital image analysis is a non-intrusive measurement technique which can simultaneously provide a great quantity of information without interfering with flow dynamics. The technique developed and implemented in this study allowed for the simultaneous measurement of various bubble properties, such as bubble diameter, rise velocity, aspect ratio and shape factor. A robust in-house code was developed to fully automate the image acquisition and data processing procedure. The experimental results obtained were validated and found to be in good agreement with available literature correlations.Moreover, based on the experimental results obtained new correlations for bubble growth and rise velocity as a function of bed height above the distributor were proposed. The models were in good agreement with the experimental data for a wide range of superficial velocities and particle sizes.     

Numerical simulation and experimental validation of bubble behavior in 2D gas–solid fluidized beds with immersed horizontal tubes

The two-fluid model based on the kinetic theory of granular flow is considered to be a fundamental tool for modeling gas–solid fluidized beds and has been extensively used for the last couple of decades. However its verification and quantitative validation still remain insufficient for a wide range of reactor geometries and operating conditions. In this study simulations were performed using the two-fluid model for two-dimensional (2D) bubbling gas–solid fluidized beds with and without immersed horizontal tubes. The bubble characteristics – aspect ratio, shape factor, diameter and rise velocity – predicted by the simulation were compared and validated with experimental data obtained from pseudo-2D fluidized beds using digital image analysis technique. The predicted bubble shape and diameter were in good agreement with the experimental data for fluidized beds with and without immersed tubes. The simulation predicted higher bubble rise velocity compared to the experimental results obtained. This was due to the wall effect, which was not taken into consideration during the 2D simulation. In addition the influences of different drag laws, friction packing limits and solid-wall boundary conditions on the different bubble properties were investigated. The results showed that the choice of friction packing limits, drag laws and specularity coefficients have little influence on bubble properties.     

A fractal approach for interpretation of local instantaneous temperature signals around a horizontal heat transfer tube in a bubbling fluidized bed

Temperature signals measured around a horizontal heat transfer tube in a bubbling fluidized bed have been analyzed using Hurst's rescaled range (R/S) analysis. This analysis estimates and identifies long-term persistence or correlation in measured time series. The Hurst exponent H, which is evaluated from R/S analysis, also provides the local fractal dimension of the time series. A new approach to analyze an air fluidized particle system is proposed based on the evaluation of the Hurst exponent. Two Hurst exponents can be evaluated from a single time series, one from the discrete time fractional noise (where the linearity of the signal is subtracted and short-term fluctuations are emphasized) and the other from the signal itself (without subtracting the linearity of the signal). The authors argue that the Hurst exponent obtained from discrete time fractional noise characterizes the particle motion, whereas the Hurst exponent obtained from the signal itself characterizes the bubble motion. Moreover, a comparison between these two Hurst components identifies the zones where an alternating type of contact between the tube surface and the bubble-emulsion phase occur. The results were interpreted in conjunction with the mutual information function. The mutual information function provides the relationship between the data points separated in time and uses only the statistical relationship between the data points. The mutual information functions and the Hurst exponents exhibited similar trends around the heat transfer tube.     

DEM-LES study of 3-D bubbling fluidized bed with immersed tubes

Based on Euler-Lagrange frame, a true three-dimensional numerical simulation of bubbling fluidized bed embedded with two immersed tubes is presented. The solid phase is composed of 178,200 particles of diameter and simulated by discrete element method (DEM, a soft-sphere approach). The gas phase is computed through solving the volume-averaged four-way coupling Navier-Stokes equations in which the Smagorinsky SGS tensor model is used in large eddy simulation (LES). Particle-tube collision is particularly treated as a transformation of DEM. The volume segmentation of a particle sphere for void fraction calculation is solved via a numerical sub-division approach. The numerical results are compared with the experimental results for validation. The results obtained with and without the LES model are also compared. The numerical results show a strong correlation between gas-particle interaction, particle-particle interaction, pressure drop, particle back mixing motion and bubble motion, and all of them follow a similar pattern of synchronous periodic variation though the periodicity may vary depending on different flow conditions. The effects of SGS tensor on evolution of fluidized bed are found in various aspects. Finally, the distribution of particle-tube impact frequency is given.     

Flow characteristics in an acoustic bubbling fluidized bed at high temperature

The pressure fluctuation of the quartz sand and SiO₂ particles was investigated using pressure transducer in high temperature fluidized bed with sound assistance. The effects of bed temperature, sound wave frequency, and sound pressure level (SPL) on the pressure fluctuation were examined. It indicates that the minimum fluidization velocity decreases with an increase in sound pressure level at the same sound frequency. At the same SPL and bed temperature, there always exists an optimal frequency range achieving good fluidization quality. As the sound frequency increases, the minimum fluidization velocity decreases firstly and then increases. Based on the statistical analysis of pressure signals, the effect of sound frequency on the fluidization quality at high-temperature fluidized bed was presented. On basis of discrete wavelet transform, an original signal was resolved into five-detailed scale signal. Furthermore, the peak frequency for Scale 3 detail signal represents the bubbling frequency.     

Application of the direct quadrature method of moments to polydisperse gas-solid fluidized beds

Most of today's computational fluid dynamics (CFD) calculations for gas-solid flows are carried out assuming that the solid phase is monodispersed, whereas it is well known that in many applications, it is characterized by a particle size distribution (PSD). In order to properly model the evolution of a polydisperse solid phase, the population balance equation (PBE) must be coupled to the continuity and momentum balance equations. In this work, the recently formulated direct quadrature method of moments (DQMOM) is implemented in a multi-fluid CFD code to simulate particle aggregation and breakage in a fluidized-bed (FB) reactor. DQMOM is implemented in the code by representing each node of the quadrature approximation as a distinct solid phase. Since in the multi-fluid model, each solid phase has its own momentum balance, the nodes of the DQMOM approximation are convected with their own velocities. This represents an important improvement with respect to the quadrature method of moments (QMOM) where the moments are tracked using an average solid velocity. Two different aggregation and breakage kernels are tested and the performance of the DQMOM approximation with different numbers of nodes are compared. These results show that the approach is very effective in modeling solid segregation and elutriation and in tracking the evolution of the PSD, even though it requires only a small number of scalars.     

Parametric modelling of time series of pressure fluctuations in gas-solid fluidized beds

Applying parametric models on time series of pressure fluctuations recorded in a fluidized bed, this paper shows that the bed dynamics can be expressed in analogy with a mechanical system of a certain degree. Thus, the pressure signal is assumed to be an output of a linear time-invariant system driven by a forcing function. The forcing function represents a number of apparently random events (e.g. formation of bubbles at the air-distributor, bubble eruptions at the surface of the bed) and may thereby be approximated as white noise. Parametric models are advocated for characterization of the dynamics of fluidized beds when, for various reasons, long data records are not available or when the quality of the recorded signal is poor. An autoregressive model (AR) of the time series is proposed, and it is shown that the order of the model identifies a mechanical equivalent of certain fluidization behaviour. The model is applied to four fluidization time series, previously investigated. The result indicates that fluidized beds behave like single second-order systems or multiple higher-order mechanical systems acting in parallel. Parametric methods are also used for estimation of power spectra of pressure fluctuations. The information obtained is presented in the form of Bode plots to accentuate the behaviour of fluidized beds as linear dynamical systems. The results are compared with the corresponding information obtained by nonparametric methods, now predominantly used. Data requirements (number of samples, sampling frequency) for the use of parametric models are discussed.     

Dimension measurements of hydrodynamic attractors in circulating fluidized beds

Experimental measurements of the correlation dimension, Kolmogorov entropy, and Lyapunov exponent of circulating fluidized bed (CFB) chaotic attractors were obtained by recording differential pressure and γ-ray porosity time series along the height of a cold experimental CFB operating with 75 μm diameter fluid catalytic cracking (FCC) catalyst. The attractor dimension did not vary with respect to the type of measurement taken. Both differential pressure and localized γ-ray densitometry measurements showed the existence of a low order hydrodynamic attractor, whose dimension varied between 1.5 and 2.0 over the range of gas velocities and solids fluxes studied. Differential pressure measurements indicated that the attractor dimension decreased slightly in the lower section of the CFB and at higher solids fluxes. Localized radial γ-ray bed porosity measurements indicate that the attractor dimension did not significantly vary across the bed cross-section but did show a tendency to be slightly lower near the riser wall.     

Voidage profiles in magnetically fluidized beds

Voidage profiles in a fluidized bed of iron particles (230 μm) were investigated under the influence of an external uniform axial magnetic field. Passing a direct current through five solenoids generated uniform magnetic field. The five solenoids were arranged elaborately to get larger uniform magnetic space than that generated by Helmholtz electromagnet coils. A sensitive optical measuring system, based on detection of light reflected by particles, was used to measure local voidage in both dense and dilute phases.

Local voidage was measured as a function of superficial fluidizing air velocity, magnetic field intensity and the position in the bed. At a given magnetic field intensity and at the same position in the bed, the voidage was constant for a low air velocity range (in a fixed bed). The local voidage changed irregularly with increasing air velocity for an intermediate air velocity range (in a magnetically stabilized fluidized bed, MSFB). The local voidage changed linearly with increasing air velocity for a slightly high air velocity range (in a magnetized bubbling fluidized bed, MBFB). A general correlation was developed to predict the local solids fraction at the arbitrary position in the bed: (1−)=(1−)_c+[(1−)_w−(1−)_c](r/R)^B where (1−), (1−)_c and (1−)_w represent the local solids fraction at arbitrary position in the bed, at the bed center and on the bed wall; and B, (1−)_c and (1−)_w are the function of air velocity, distance from the distributor and magnetic field intensity.     

Comparison of heat transfer models in DEM-CFD simulations of fluidized beds with an immersed probe

The basic mechanisms governing the process of surface-to-bed heat transfer in fluidized beds and their relative importance have not been fully characterized yet, mainly owing to the lack of reliable data at the particle scale. Numerical simulations based on the discrete element method may prove successful in predicting the evolution of the fluid and particles' temperature fields. In the present work, microscopic models of the fluid-particle, particle-particle, fluid-surface and particle-surface heat transfer have been implemented in a DEM-CFD hydrodynamic code. Details are discussed on the methodology adopted to include immersed objects in the computational domain. Thus, three approaches to represent particle-particle heat transfer are analysed and compared against experimental values, taken from the literature, of the heat transfer coefficient between a hot fluidized bed and a spherical probe. Unfortunately, some parameters appearing in the formulations are difficult to determine, so reasonable estimates are calculated and used in the simulations. Under conditions similar to the experiments, simulation predictions of the heat transfer coefficient range from 43 to 340 W/(m² K) depending on the model used, while the experimental values are located around 160 W/(m² K). The variability of these numerical results confirms their sensitivity to the particle-particle mechanism considered. Finally, it is shown that using the model that produces results in agreement with experiments the heat flows due to the particle convective and the fluid convective transfer are of comparable importance.     

Cartesian grid simulations of bubbling fluidized beds with a horizontal tube bundle

In this paper, the flow hydrodynamics in a bubbling fluidized bed with submerged horizontal tube bundle was numerically investigated with an open-source code: Multiphase Flow with Interphase eXchange (MFIX). A newly implemented cut-cell technique was employed to deal with the curved surface of submerged tubes. A series of 2D simulations were conducted to study the effects of gas velocity and tube arrangement on the flow pattern. Hydrodynamic heterogeneities on voidage, particle velocity, bubble fraction, and frequency near the tube circumferential surface were successfully predicted by this numerical method, which agrees qualitatively with previous experimental findings and contributes to a sounder understanding of the non-uniform heat transfer and erosion around a horizontal tube. A 3D simulation was also conducted. Significant differences between 2D and 3D simulations were observed with respect to bed expansion, bubble distribution, voidage, and solids velocity profiles. Hence, the 3D simulation is needed for quantitative prediction of flow hydrodynamics. On the other hand, the flow characteristics and bubble behavior at the tube surface are similar under both 2D and 3D simulations as far as the bubble frequency and bubble phase fraction are concerned. Comparison with experimental data showed that qualitative agreement was obtained in both 2D and 3D simulations for the bubble characteristics at the tube surface.     

Characterization of solids mixing patterns in bubbling fluidized beds

Behavior of the solid phase in fluidized beds was studied by a 2D CFD-DEM approach to obtain more information on the solid mixing and circulation. Hydrodynamic parameters, including solid diffusivity, and internal and gross circulations were considered in this study. To validate the simulation, time-position data obtained by the Radioactive Particle Tracking (RPT) technique were used. It was shown that the 2D model can satisfactorily predict the axial diffusivity, while the radial diffusivity calculated based on the model is an order of magnitude smaller than the experimental one in 3D. The influence of aspect ratio of the bed, type of distributor, and inlet gas velocity on solids mixing pattern were also studied. The solids flow pattern in the bed changed considerably by increasing the aspect ratio. Different solid circulations were captured by numerical model for the two types of distributors, namely porous and injection types. The results suggested that increasing the superficial gas velocity caused rigorous internal and gross circulations, which in return, improved solids mixing and decreased deviations from well mixed state.     

Hydrodynamics of Geldart group A particles in gas-solid fluidized beds

Geldart group A particles were fluidized in a 10 cm i.d.×1.8 m high Plexiglas-made bed with ambient air to determine the hydrodynamic properties in a gas-solid fluidized bed. The effects of static bed heights, position of pressure measuring points, differential and absolute pressure fluctuations on the hydrodynamic behavior of a Geldart group A particles in a gas-solid fluidized bed were investigated. The particles used in this study were 80 micrometer FCC powders and 60 micrometer glass beads. The variance of pressure fluctuations was used to find the minimum bubbling velocity. The obtained minimum bubbling velocity was compared with the other methods available in the literature. This method was found to be much easier and had better data reproducibility than the classical visual method or sedimentation method. The variance of pressure fluctuations increased due to the increase of superficial gas velocity and static bed height. The obtained minimum bubbling velocity and pressure fluctuations were found to depend on the measuring position along the axial direction. The effect of measuring position was discussed. Cross-correlation of two pressure signals was used to find the delay time, then the bubble rising velocity.     

Computer simulations of gas-solid flow in spouted beds using kinetic-frictional stress model of granular flow

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).     

Multi-scale analysis on particle-phase stresses of coarse particles in bubbling fluidized beds

Despite the restless efforts devoted to the hydrodynamics of bubbling fluidized beds, the particle-phase stress, which is one of the critical issues in modeling bubbling fluidized beds by the Eulerian approach, is not well understood. To address this problem, a mathematical model is developed to describe the kinetic properties of coarse particles, such as granular temperature and granular pressure, based on a multi-scale analysis of particle velocity fluctuation. Contributions from both high-frequency particle-scale fluctuations and low-frequency bubble-induced fluctuations are considered. It is proven to agree well with experimental data available up to date from bubbling fluidized beds for Geldart B and D particles.     

Particle injection and mixing experiments in a one-quarter scale model bubbling fluidized bed

One significant factor in the operation of a fluidized bed combustor is the manner in which coal particles disperse and mix with the bed material upon entering the bed. A thermal tracing technique was used to study the mixing characteristics in a 1/4 scale model of a pressurized bubbling fluidized bed combustor. Particles cooled by liquid nitrogen are injected into the bed in the same way that pulverized coal will be injected. An array of thermistors is mounted inside the bed. They are used to trace the path of the cooled particles as they enter the bed and mix with the other bed material. The approximate concentrations can also be determined since heat transfer from the cooled particles to the fluidizing gas is negligible during the course of the experiment. Time-resolved images of the particle concentration show that the lateral motion of the injected particles is much greater than the lateral motion of an injected gas jet. The extended lateral motion is due to the substantial momentum of the injected particles.     

鼓泡流化床离散模拟中的一个局部空隙率模型

气固流化床离散颗粒模拟中通常采用面积加权平均法计算局部空隙率,不能较好地反映流化床中显著的非均匀结构特性.为了考虑非均匀结构对局部空隙率的影响,文中提出一个适用鼓泡流化床的局部空隙率模型.将流场划分为稀区(气泡区)和密区(乳相区);非均匀结构对密区局部空隙率的影响通过引入局部空隙率下限和非均匀影响系数描述;将提升管流动...