Convective instability of a homogeneous fluidized bed

Convective motions of the phases in a homogeneous fluidized bed are considered. The motions of the phases are described by a simple model of two ideal interpenetrating interacting fluids. The model admits an increasing concentration of the solid particles with the height, which leads to circulatory flows. Approximate equations of motion of the liquid and the solid particles are obtained, and these are analogous to the Boussinesq approximation in the case of natural convection in a pure liquid. The equations contain a parameter which is analogous to the Rayleigh number and characterizes the stability of the layer. An approximate analytic solution to the corresponding eigenvalue problem is found. The spectrum of Rayleigh numbers and the sizes of the convective cells are determined. The obtained results provide an explanation for the existence of the multicenter circulatory motions of the phases frequently observed in a fluidized beds and make it possible to determine the sizes of the circulatory regions. Information about the Rayleigh number spectrum and the sizes of the regions is needed to solve the problem of the scale transition and also to enable the choice of measures to suppress or intensify the displacement processes.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 39–46, July–August, 1982.     

Separation of screw-sensed particles in a homogeneous shear field

The Stokes motions of three-dimensional screw-sensed slender particles in a homogeneous shear field are investigated, including the effects of buoyancy. Conclusions are drawn about the possibility of achieving a separation of mixtures of right- and left-handed particles. The linearity of the Stokes equations allows complex flows to be solved by adding the effects of the several terms which describe the flow in which the particle is immersed. The homogeneous shear flow considered here consists of three such terms; solutions for a series of 12 unit motions are sufficient to determine the hydrodynamic resistance tensors. The forces and torques experienced by screw-sensed particles are calculated from these 51 resistance tensors, using slender-filament theory. The results allow an estimate of the range of buoyancy parameters for which gravitational sedimentation can be neglected. The fundamental component of the particle motion is a rotation, at approximately the same angular velocity as that of the fluid. Superimposed on this are variations, of large period, in the particle orientation. A phase plane analysis is used to find the terminal orientations. Very long calculation times are required for the phase portrait. An approximate method based on azimuthally-averaged equations is developed to avoid the requirements for long time integration.     

Fluidization of a bed of solid particles

As is known, fluidization of a bed of solid particles by liquid or gas filtration takes place for certain critical values of the parameters of the filtration regime. The determination of these critical values and the nature of the transition is of interest in connection with the development of fluidization technology in many branches of industry, and also in connection with certain other questions, among which we note the problem of the suspension of a sand plug in an oil well.The two-dimensional fluidization problem has been examined previously [1] as the problem of the limiting equilibrium of a medium which cannot withstand arbitrarily small tensile stresses. This model describes well the behavior of many types of bulk media encountered in practice. However, many cases lie beyond the limits of this model because of the presence of bonding forces between the particles. Bonding may be due to the adhesive forces which arise during the fluidization of fine powders [2, 3], and/or to magnetic and electrostatic forces [3, 4]. Another example is the agglomeration of particles during gas fluidization when small amounts of liquid are injected [5]; still another is the case in which sand particles are surrounded by thin films of oil when a sand plug is suspended in an oil well.In the present paper an extension of the results obtained in [1] is used to examine fluidization of a bed with account taken of the bonding forces between the particles. The two- and three-dimensional problems are studied.     

Diffusion of heavy spherical particles in a turbulent flow

A connection is established between the statistical characteristics of a turbulent flow and the coefficient of diffusion of spherical particles suspended in the flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 142–144, November–December, 1979.     

Micro/meso simulation of a fluidized bed in a homogeneous bubbling regime

Due to the wide range of spatial scales and the complex features associated to fluid/solid and solid/solid interactions in a dense fluidized bed, the system can be studied at different length scales, namely micro, meso and macro. In this work, we select a flow configuration relevant of a homogeneous liquid/solid fluidization and compare computed results from Particle Resolved Simulation (PRS) with those from locally averaged Euler/Lagrange simulation. PRS at the micro-scale is carried out by a parallel Distributed Lagrange Multiplier (DLM) solver in the framework of fictitious domain methods (Wachs, 2011a, 2015). For meso-scale simulations, the set of mass and momentum conservation equations is averaged in control volumes encompassing few particles and momentum transfer between the two phases is modeled using appropriate drag laws. Both methods are coupled to a Discrete Element Method (DEM) combined with a soft-sphere contact model to solve the Newton–Euler equations with collisions for the particles in a Lagrangian framework (Wachs et al., 2012). A test case of intermediate size with 2000 spheres is chosen as a sensible compromise between size limitations of the meso-scale model for an appropriate averaging process and computational resources required to run micro-scale simulations. These two datasets yield new insight on momentum transfer at different spatial scales in the flow, and question the validity of certain approximations adopted in the meso-scale model. Results demonstrate an acceptable agreement between the micro- and meso-scale predictions on integral measures as pressure drop and bed height. Investigating more detailed features of the flow, it has been shown that particles fluctuations are considerably suppressed in meso-scale simulations and in particular the particles transverse motion is underestimated, regardless of the selected drag law. The origin of these dependencies is carefully investigated by reconstructing the closure laws based on PRS results and comparing them to the closure laws proposed in the literature.     

Boiling model for a fluidized bed of particles

A mechanism for boiling of a fluidized bed was examined in [1]. Due to hydrodynamic instability the solid particles acquire random motion, and as a result of collisions between particles part of the energy of random motion is converted to rotation of the particles. A rotating particle experiences a Magnus force which considerably increases the random motion and leads to spontaneous boiling of the layer. For this mechanism there is typically a minimum boiling time , defined basically as the time to develop a hydrodynamic instability. It is shown in this study that besides the spontaneous mechanism there is an induced mechanism for boiling of the bed arising from the generation of random motion in one particle layer. Particles in that layer boil, transmitting a perturbation to the energy of the next layer, and leading to layer boiling in a manner analogous to the propagation of a detonation wave in solids.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 89–94, May–June, 1984.     

The pseudoturbulent diffusion of particles in homogeneous suspensions

The effective diffusion coefficients for suspended particles caused by their pseudoturbulent pulsations, are treated. Derivatives of the dynamic variables which determine the average motion of the locally homogeneous suspension are neglected.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol. 11, No. 1, January–February, pp 67–72, 1970.     

DEM simulation of polydisperse systems of particles in a fluidized bed

Numerical simulations based on three-dimensional discrete element model (DEM) are conducted for mono-disperse, binary and ternary systems of particles in a fluidized bed. Fluid drag force acting on each particle depending on its size and relative velocity is assigned. The drag coefficient corresponding to Ergun’s correlation is applied to the system of fluidized bed with particle size ratios of 1:1 for the mono-disperse system, 1:1.2, 1:1.4 and 1:2 for the binary system and 1:1.33:2 for the ternary system b...     

Mass transfer between bubbles and the continuous phase in a pseudofluidized layer

The problem of mass transfer between an isolated bubble and the continuous phase in a pseudofluidized layer is considered, when the rising velocity of the bubble exceeds the pseudofluidization rate. In this case the bubble with the surrounding region, a so-called two-phase system, is surrounded by a surface current impermeable to the liquid [1–3], and the problem reduces to determining the concentration field and the total flow on the material surface. The problem is solved for large and small Peclet numbers by a boundary layer diffusion method and by asymptotic expansion matching.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 42–49, July–August, 1973.     

Formation of waves on a horizontal erodible bed of particles

The mechanisms responsible for the initial growth of sand waves on the surface of a settled layer of particles are studied experimentally and theoretically. Experiments employ water-glycerin solutions of 1–14 cP and glass spheres (_s = 2.4 g/cm³) that are either 100 or 300 μm in diameter. The particle Reynolds number and Shields parameter are of order one and the flow Reynolds number is of order 1000 to 10,000. Experimentally obtained regime maps of sand wave behavior and data on the wavelengths of the sand waves that first appear on the surface of the settled bed are presented. Turbulence in the clear liquid is not necessary for formation of waves and there is no dramatic change in behavior as the flowrate is increased across the turbulent transition. The initial wavelength varies as the Fronde number to the first power. Because a flowing suspension phase is observed before waves form, linear stability analysis of the clear-layer—suspension-layer cocurrent two-phase flow is presented. The suspension phase is modeled as a continuum that has an either constant or exponentially increasing viscosity. Neither of the models correctly predicts the wavelength for the first observed waves, their growth rate or their speed. However, the initial wavelength is found to agree well with the trajectory length for a saltating particle obtained from a model for forces on individual particles.     

Fluidization and bubbling behavior of potash particles in a deep fluidized bed

Most existing models for predicting bubble size and bubble frequency have been developed for freely bubbling fluidized beds. Accurate prediction of bubbling behavior in deep fluidized beds, however, has been a challenge due to the higher degree of bubble coalescence and break up, high probability of the slugging regime, partial fluidization, and chaotic behavior in the bubbling regime. In this work, the bubbling and fluidization behavior of potash particles was investigated in a deep fluidized bed employing a twin-plane electrical capacitance tomography (ECT) system. Solid volume fraction, average bubble velocity, average bubble diameter, and bubble frequency in both bubbling and slugging regimes were measured at two different bed height ratios (H/D = 3.5 and H/D = 3.78). This work is the first to illustrate a sequential view of bubbles at different superficial gas velocities in a fluidized bed. The results show that both the bubble diameter and rising velocity increased with increasing the superficial gas velocity for the two bed heights, with larger values observed in the deeper bed compared to the shallower one. Predicted values for bubble diameter, bubble rise velocity and bubble frequency from different models are compared with the experimental data obtained from the ECT system in this work. Good agreement has been achieved between the values predicted by the previous models and the experimental data for the bubble diameter and bubble rise velocity with an average absolute deviation of 16% and 15% for the bed height of 49 cm and 13% and 8% for the bed height of 53 cm, respectively.     

Charge transfer and bipolar charging of particles in a bubbling fluidized bed

Particle-particle and particle-wall collisions in gas-solid fluidized beds lead to charge accumulation on particles.This work evaluated the effect of fluidization time on charge transfer and bipolar charging(charge separation)and their influence on hydrodynamic structures in a fluidized bed.Experiments were performed with glass beads and polyethylene particles in a glass column.The pressure fluctuations and net electrostatic charge of particles were measured during fluidization.Wavelet and short-time Fourier transforms were used to analyze pressure fluctuations.The results revealed that bipolar charging is the dominant tribocharging mechanism in a bed of glass beads.Bipolar charging in a bed of particles with a narrow size distribution does not affect either hydrodynamic structures or the transition velocity to the turbulent regime.A large difference between the work functions of the wall and particle in the bed of polyethylene particles leads to high charge transfer.Formation of a stagnant particle layer on the wall eventually causes the energy of macro-structures to increase to its maximum.At longer fluidization times,the macro-structural energy decreases and bubbles shrink until the electrostatic charge reaches the equilibrium level.These results well describe the effect of fluidization time on hydrodynamic structures.     

Bubbling behavior of cohesive particles in a two-dimensional fluidized bed with immersed tubes

Fluidization hydrodynamics are greatly influenced by inter-particle cohesive forces. This paper studies the fluidization of large cohesive particles in a two-dimensional fluidized bed with immersed tubes using “polymer coating” to introduce cohesive force, to gain better understanding of bubbling behavior when particles become cohesive and its effect on chemical processes. The results show that the cohesive force promotes bubble splitting in the tube bank region, thereby causing an increase in the number and a decline in the aspect ratio of the bubbles. As the cohesive force increases within a low level, the bubble number increases and the bubble diameter decreases, while the aspect ratio exhibits different trends at different fluidization gas velocities. The difference in the evolution of bubble size under various cohesive forces mainly takes place in the region without tubes. When the cohesive force is large enough to generate stable agglomerates on the side walls of the bed, the bubble number and the bed expansion sharply decrease. The tubes serve as a framework that promotes the agglomeration, thus accelerating defluidization. Finally, the bubble profile around tubes was studied and found to greatly depend both on the cohesive forces and the location of tubes.     

Diffusion of suspended particles in an isotropic turbulence field

A model for turbulent motion is proposed which makes it possible to evaluate the pulsation characteristics and the diffusion coefficients of the dispersed phase and also makes it possible to describe the effect of the suspended particles on the turbulence of the dispersing medium. Specific calculations are made for the situation when the undisturbed turbulent field is isotropic.The diffusion of an admisture having inertia in a turbulent stream has been studied previously on the assumption that the three-dimensional turbulence characteristics have practically no effect on the behavior of the suspended particles, so that the random motion of the latter is described by ordinary differential equations containing the natural independent variable the motion travel time [1–4]. In many cases this assumption is incorrect and the corresponding theory is obviously deficient. For example, a fundamental result of this theory, asserting that the turbulent diffusion coefficients of the particles and of the fluid moles are equal for a long diffusion time, is obviously incorrect if the relative motion of the particles is significant [5].     

Experimental and numerical investigation of the shock-induced fluidization of a particles bed

An experimental study on unsteady two phase flow is conducted in a vertical shock tube. Shock Mach numbers range from 1.3 to 1.5 in 1 bar. The particles are initially positioned in horizontal beds of various thicknesses. Our research covers a large domain of void fraction from 1 (single particles) to 0.35 (compact beds). The experiments provide shadowgraph images for the recording of particle trajectories (effect of the gas on the particles) and side-wall pressures (action of the particles on the gas). A dense two phase flow model has been elaborated and numerically solved using a finite difference scheme with pseudoviscosity. The simulated shock-induced fluidization of a 2 cm thick bed of 1.5 mm diameter glass particles is compared to the experiment. Received 10 September 1996 / Accepted 4 January 1997