Instabilities in self-fluidized beds—II experiments

Experimental studies of the behavior of self-fluidized beds in both 2-D and 3-D are reported. The experimental system used was the drying of silica gel under vacuum, and wide ranges of particle sizes and drying rates were covered. Both flow visualization and dynamical measurements of flow rates were utilized in the study. The observations indicate that self-fluidization is always unstable above the source strength required for minimum fluidization. The instability takes one of two forms, depending upon the degree of supercriticality. The primary instability consists of a quasi-steady array of spatially periodic spouts. A secondary instability leads to the emergence and dominance of larger spouts, which are observed to appear and disappear in a cyclic fashion. Measurements are made of wavelengths of the primary instability and the frequency of the secondary instability as functions of the operating variables, and the secondary instability is seen to occur at the same normalized flow rate for all the particles studied. Plausible mechanisms for these instabilities are proposed and discussed.     

Prediction of coating uniformity in batch fluidized-bed coating process

Coating of particulate materials in fluidized beds is a widely used technique to eliminate particle agglom-eration,provide slow release of an active substance,o...     

Prediction of coating uniformity in batch fluidized-bed coating process

Coating of particulate materials in fluidized beds is a widely used technique to eliminate particle agglomeration, provide slow release of an active substance, or protect active ingredients. When thin polymer shells are applied on a particle surface, it is important to determine the process parameters that provide coating uniformity. In this study, the degree of coverage, defined as the fraction of the coated surface of the particles, is proposed as a quantitative criterion of coating uniformity. A new model for the batch fluidized-bed coating process is presented. The model allows prediction of the function of particle distribution according to the degree of coverage at a given process time and thereby enables assessment of coating uniformity. An algorithm for the numerical solution of model equations for a batch fluidized-bed coater is described. The influences of the main process parameters on the coating uniformity were shown.     

Suppression of oscillatory congestion via trunk link bandwidth and control gain in star network

The time delay-induced instability in an Internet congestion control model is investigated. The star topology is considered, and the link bandwidth ratio and the control gain are selected as the tunable parameters for congestion suppression. The stability switch boundary is obtained by the eigenvalue analysis for the linearized system around the equilibrium. To investigate the oscillatory congestion when the equilibrium becomes unstable, the center manifold reduction and the normal form theory are used to study the periodic oscillation induced by the delay. The theoretical analysis and numerical simulation show that the ratio between bandwidths of the trunk link and the regular link,rather than these bandwidths themselves, is crucial for the stability of the congestion control system. The present results demonstrate that it is not always effective to increase the link bandwidth ratio for stabilizing the system, and for some certain delays, adjusting the control gain is more efficient.     

Fluid Permeability in Stratified Unconsolidated Particulate Bed

Fluid permeability of polydisperse particulate bed with finite thickness has been examined. On the assumption of creeping flow, the permeability of monodisperse particles with arbitrary arrangement is calculated by means of Stokesian dynamics approach in which the interaction between individual particles and interstitial fluid is described by multipole expansion of the Oseen tensor. We have extended such calculation method to polydisperse particulate systems which have not so dense structures (up to particle volume fraction ${\phi \sim}$ 0.2). The particles are located infinitely in space and their interaction has been taken into account by Ewald summation technique. For the spatial distribution of polydisperse particles, we consider locally stratified particulate beds and define stratification degree as a parameter which apparently and mathematically represents the thickness of the mixing region of different-sized particles. The permeability profiles in the particulate beds with different stratification degree show the dependence of local permeability on the spatial and size distribution of particles. Consequently, the calculation results indicate that the permeability of non-uniform polydisperse particulate bed can be predicted by integrating the local permeation resistance which is determined by the local specific surface area.     

Instability waves and the origin of bubbles in fluidized beds: Part 1: Experiments

Statistically significant measurements of the propagation properties of instability waves in a two-dimensional liquid fluidized bed are reported. Visual and quantitave measurements show that although the waves experience an initially exponential growth in amplitude, the ultimate state of motion exhibited is that of the complicated formation and destruction of cylindrical bubble-like structures. Expected values of their amplitude, frequency, and velocity are measured, and preliminary scaling laws are proposed. The implication is that bubbles in gas-fluidized beds are a result of the same instability of the state of uniform fluidization.     

THE SERIAL MODEL IN LIQUID FLUIDIZATION AND ITS LIMITATIONS

The serial model of Epstein et al. (1981) is demonstrated to predict successfully the overall voidage of the mixed layer of incompletely segregated binary and ternary mixtures of liquid-fluidized solids that differ only in shape. Some speculations are then offered on the conditions for the success and failure of this model. Finally, methods proposed in the literature for estimating the deviations from the serial model for a binary-solids bed, which manifest themselves as a bed contraction, are discussed, with emphasis on packing models.     

Rayleigh-Marangoni-Benard instability in two-layer fluid system

Rayleigh-Marangoni-Bénard instability in a system of two-layer fluids is studied numerically. The convective instabilities in the system of Silicon Oil (10cSt) and Fluorinert (FC70) liquids have been analyzed. The critical parameters at onset of convection are presented in a large range of two-layer depth ratios from 0.2 to 5.0. Numerical results show that the instability of the two-layer system depends strongly on its depth ratio. When the depth ratio increases, the instability mode changes from mechanical coupling to thermal coupling. Between these two typical coupling modes, a time-dependent oscillation is detected. Nevertheless, traveling wave states are found in the case of oscillatory instability. The oscillation mode results from the competition between Rayleigh instability and Marangoni effect. The project supported by the National Natural Science Foundation of China (10372105) and the Knowledge Innovation Program of Chinese Academy of Sciences (KJCX2-SW-L05)     

Modelling of massive particulates for breakwater engineering using coupled FEMDEM and CFD

The seaward slope of many breakwaters consists of thousands of interlocking units of rock or concrete comprising a massive granular system of large elements each weighing tens of tonnes. The dumped quarry materials in the core are protected by progressively coarser particulates. The outer armour layer of freely placed units is intended to both dissipate wave energy and remain structurally stable as strong flows are drawn in and out of the particulate core. Design guidance on the mass and shape of these units is based on empirical equations derived from scaled physical model tests. The main failure mode for armour layers exposed to severe storms is hydraulic instability where the armour units of concrete or rock are subjected to uplift and drag forces which can in turn lead to rocking, displacement and collisions sufficient to cause breakage of units. Recently invented armour unit designs making up such granular layered system owe much of their success to the desirable emergent properties of interlock and porosity and how these combine with individual unit structural strength and inertial mass. Fundamental understanding of the forces governing such wave-structure interaction remains poor. We use discrete element and combined finite-discrete element methods to model the granular solid skeleton of randomly packed units coupled to a CFD code which resolves the wave dynamics through an interface tracking technique. The CFD code exploits several methods including a compressive advection scheme, node movement, and general mesh optimization. We provide the engineering context and report progress towards the numerical modelling of instability in these massive granular systems.     

Modelling of massive particulates for breakwater engineering using coupled FEMDEM and CFD

The seaward slope of many breakwaters consists of thousands of interlocking units of rock or concrete comprising a massive granular system of large elements each weighing tens of tonnes.The dumped quarry materials in the core are protected by progressively coarser particulates.The outer armour layer of freely placed units is intended to both dissipate wave energy and remain structurally stable as strong flows are drawn in and out of the particulate core.Design guidance on the mass and shape of these units is based on empirical equations derived from sealed physical model tests.The main failure mode for armour layers exposed to severe storms is hydraulic instability where the armour units of concrete or rock are subjected to uplift and drag forces which can in turn lead to rocking,displacement and collisions sufficient to cause breakage of units.Recently invented armour unit designs making up such granular layered system owe much of their success to the desirable emergent properties of interlock and porosity and how these combine with individual unit structural strength and inertial mass. Fundamental understanding of the forces governing such wave-structure interaction remains poor.We use discrete element and combined finite-discrete element methods to model the granular solid skeleton of randomly packed units coupled to a CFD code which resolves the wave dynamics through an interface tracking technique.The CFD code exploits several methods including a compressive advection scheme, node movement, and general mesh optimization.We provide the engineering context and report progress towards the numerical modelling of instability in these massive granular systems.     

THEORY OF NONFLUIDIZED GAS SOLIDS FLOW AND ITS APPLICATION

A theory of nonfluidized gas-solids flow, which combines the theory of multiphase flow with the mechanics of particulate media, was proposed on the basis of understanding that the particles contact each other, solids and gas are in movement, and the drag force on the particles caused by interstitial gas flow is similar to gravity force having the property of mass force. Then this theory was verified by experiments on vertical and inclined moving beds, and was applied to calculation and design of equipment and devices with moving beds, such as pneumatic moving bed transport,dipleg, V-value, L-valve, orifice flow, and arching prevention. It can be used to guide the design and operation of moving beds and fixed beds.     

Transient natural convection flow of a particulate suspension through a vertical channel

Continuum equations governing transient, laminar, fully-developed natural convection flow of a particulate suspension through an infinitely long vertical channel are developed. The equations account for particulate viscous effects which are absent from the original dusty-gas model. The walls of the channel are maintained at constant but different temperatures. No-slip boundary conditions are employed for the particle phase at the channel walls. The general transient problem is solved analytically using trigonometric Fourier series and the Laplace transform method. A parametric study of some physical parameters involved in the problem is performed to illustrate the influence of these parameters on the flow and thermal aspects of the problem.     

Vibration and stability of an axially moving beam immersed in fluid

Vibration and stability are investigated for an axially moving beam in fluid and constrained by simple supports with torsion springs. The equations of motion of the beam with uniform circular cross-section, moving axially in a horizontal plane at a known rate while immersed in an incompressible fluid are derived first. An “axial added mass coefficient” and an initial tension are implemented in these equations. Based on the Differential Quadrature Method (DQM), a solution for natural frequency is obtained and numerical results are presented. The effects of axially moving speed, axial added mass coefficient, and several other system parameters on the dynamics and instability of the beam are discussed. Particularly, natural frequency in terms of the moving speed is presented for fixed–fixed, hinged–hinged and hybrid supports with torsion spring. It is shown that when the moving speed exceeds a certain value, the beam becomes subject to buckling-type instability. The variations of the lowest critical moving speed with several key parameters are also investigated.     

Mathematical simulation of radial heat transfer in packed beds by pseudohomogeneous modeling

Uniform flow regime and constant effective thermal conductivity inside packed beds are commonly accepted in the evaluation of the fluid dynamics and heat transfer in such systems.However,several authors have confirmed the presence of an oscillatory velocity profile caused by the effective contribution of porosity profile in the fluid dynamic behavior of packed beds,which directly influences the heat transfer inside the beds.This paper describes the application of a pseudo-homogeneous mathematical ...     

Magnetohydrodynamics instability of interfacial waves between two immiscible incompressible cylindrical fluids

The problem of nonlinear instability of interfacial waves between two immiscible conducting cylindrical fluids of a weak Oldroyd 3-constant kind is studied. The system is assumed to be influenced by an axial magnetic field, where the effect of surface tension is taken into account. The analysis, based on the method of multiple scale in both space and time, includes the linear as well as the nonlinear effects. This scheme leads to imposing of two levels of the solvability conditions, which are used to construct like-nonlinear Schr6dinger equations （1-NLS） with complex coefficients. These equations generally describe the competition between nonlinearity and dispersion. The stability criteria are theoret- ically discussed and thereby stability diagrams are obtained for different sets of physical parameters. Proceeding to the nonlinear step of the problem, the results show the appearance of dual role of some physical parameters. Moreover, these effects depend on the wave kind, short or long, except for the ordinary viscosity parameter. The effect of the field on the system stability depends on the existence of viscosity and differs in the linear case of the problem from the nonlinear one. There is an obvious difference between the effect of the three Oldroyd constants on the system stability. New instability regions in the parameter space, which appear due to nonlinear effects, are shown.     

A model of bubbles rising in a fluidized bed

A model for a single fully developed bubble moving in an unbounded fluidized bed is presented. The model allows bubble growth or shrinkage during the rise inside the bed, as well as dependence of the rise velocity upon specified bed parameters. Limiting cases of nearly spherical bubbles and of sufficiently large bubbles whose form resembles that of a spherical segment are considered in more detail. The form of bubbles rising in either fluidized beds or one-phase liquids, and its dependence on the effective “surface tension” acting on the bubble boundary are discussed.     

Magnetic filtration with magnetized granular beds： Basic principles and filter performance

This study is devoted to the explanation of different characteristics of magnetic filtration and the way these characteristics affect the important filtration parameters. Magnetic fields in pores and the force effect of these fields on magnetic particles and the magnetization properties of packed beds composed of ferromagnetic spheres and metal chips are evaluated. The profile of accumulation and capture regions of the particles, the variation of the fluid velocity in these regions and analytic expressions of particle capture radius are presented. The effects of filtration regime parameters on magnetic filter performance were investigated. An analytical expression has been obtained for the dependence of the logarithmic efficiency coefficient on filtration velocity, the geometry of filter elements, the particle size and other parameters of filtration. The stationary and non-stationary equations of the magnetic filtration processes are given. An expression of magnetic filter performance is shown with dimensionless parameters obtained from the filtration system. These relations are useful for calculations in engineering practice, including the design of magnetic filters, provision of suggestions on construction, and optimization and control of filter operation.     

Mode coupling instability in friction-induced vibrations and its dependency on system parameters including damping

Friction-induced vibrations due to coupling modes can cause severe damage and are recognized as one of the most serious problems in industry. In order to avoid these problems, engineers must find a design to reduce or to eliminate mode coupling instabilities in braking systems. Though many researchers have studied the problem of friction-induced vibrations with experimental, analytical and numerical approaches, the effects of system parameters, and more particularly damping, on changes in stable-unstable regions and limit cycle amplitudes are not yet fully understood.The goal of this study is to propose a simple non-linear two-degree-of-freedom system with friction in order to examine the effects of damping on mode coupling instability. By determining eigenvalues of the linearized system and by obtaining the analytical expressions of the Routh–Hurwitz criterion, we will study the stability of the mechanical system's static solution and the evolution of the Hopf bifurcation point as functions of the structural damping and system parameters. It will be demonstrated that the effects of damping on mode coupling instability must be taken into account to avoid design errors. The results indicate that there exists, in some cases, an optimal structural damping ratio between the stable and unstable modes which decreases the unstable region. We also compare the evolution of the limit cycle amplitudes with structural damping and demonstrate that the stable or unstable dynamic behaviour of the coupled modes are completely dependent on structural damping.     

Numerical simulations of high pressure carbon dioxide fluid fluidized beds

Hydrodynamics of carbon dioxide fluid-particle mixtures are predicted using a low density ratio-based kinetic theory of granular flow in high pressure carbon dioxide fluid fluidized beds. A coexistence of particle waves and particle aggregates exists along bed height. The threshold to identify the occurrence of particle aggregates is suggested based on standard deviation of solid volume fractions in aggregative fluidization. The existence time fractions and frequencies of particle aggregates are predicted along axial direction. The effect of carbon dioxide fluid temperature and pressure on volume fraction and velocity distributions are analyzed at different inlet carbon dioxide velocities and particle densities in high pressure carbon dioxide fluidized beds. Simulated results indicate that the carbon dioxide-particles fluidization transits from particulate to aggregative states with the increase of inlet carbon dioxide velocities. The computed fluid volume fractions and heterogeneity indexes are close to the measurements in a high pressure carbon dioxide fluidized bed.