Discrete particle modeling of granular temperature distribution in a bubbling fluidized bed

The discrete hard sphere particle model (DPM) is applied in this work to study numerically the distributions of particle and bubble granular temperatures in a bubbling fluidized bed. The dimensions of the bed and other parameters are set to correspond to those of Müller et al. (2008). Various drag models and operational parameters are investigated to find their influence on particle and bubble granular temperatures. Various inlet superficial gas velocities are used in this work to obtain their effect on flow characteristics. It is found that the superficial gas velocity has the most important effect on granular temperatures including bubble granular temperature, particle translational granular temperature and particle rotational granular temperature. The drag force model affects more seriously the large scale variables such as the bubble granular temperature. Restitution coefficient influences all granular temperatures to some degree. Simulation results are compared with experimental results by Müller et al. (2008) showing reasonable agreement.     

Rotation characteristic and granular temperature analysis in a bubbling fluidized bed of binary particles

In this work, a discrete particle model (DPM) was applied to investigate the dynamic characteristics in a gas–solid bubbling fluidized bed of binary solid particles. The solid phase was simulated by the hard-sphere discrete particle model. The large eddy simulation (LES) method was used to simulate the gas phase. To improve the accuracy of the simulation, an improved sub-grid scale (SGS) model in the LES method was also applied. The mutative Smagorinsky constant case was compared with the previously published experimental data. The simulation by the mutative Smagorinsky constant model exhibited better agreement with the experimental data than that by the common invariant Smagorinsky constant model. Various restitution coefficients and different compositions of binary solids were investigated to determine their influences on the rotation characteristics and granular temperatures of the particles. The particle translational and rotational characteristic distributions were related to certain simulation parameters.     

Rotation characteristic and granular temperature analysis in a bubbling fluidized bed of binary particles

In this work,a discrete particle model(DPM) was applied to investigate the dynamic characteristics in a gas-solid bubbling fluidized bed of binary solid particles.The solid phase was simulated by the hardsphere discrete particle model.The large eddy simulation(LES) method was used to simulate the gas phase.To improve the accuracy of the simulation,an improved sub-grid scale(SGS) model in the LES method was also applied.The mutative Smagorinsky constant case was compared with the previously published experimental data.The simulation by the mutative Smagorinsky constant model exhibited better agreement with the experimental data than that by the common invariant Smagorinsky constant model.Various restitution coefficients and different compositions of binary solids were investigated to determine their influences on the rotation characteristics and granular temperatures of the particles.The particle translational and rotational characteristic distributions were related to certain simulation parameters.     

Analytical solutions for a single blade in vertical axis turbine motion in two-dimensions

An analytical model for a time dependent two dimensional flow around a moving profile is developed. The model is suitable for fast aerodynamic and aeroelastic coupling calculations. It determines the inviscid pressure distribution in the vicinity of one blade and the force on the blade in arbitrary two dimensional motion. The method is more flexible than previous analysis: it can represent any profile, pitching motion and blade attachment position. The method is based on conformal mapping techniques and Laurent's series decomposition and is faster and more accurate than standard panel methods. A main idea is to directly treat the singularities of the flow in a mapped plane where any geometrical plane is simplified to a circle. The vorticity is assumed to be shed in the form of a continuous vortex sheet near the trailing edge.     

Analytical solutions for tapering quadratic and cubic rat-holes in highly frictional granular solids

New exact analytical solutions are presented for both stress and velocity fields for a Coulomb–Mohr granular solid assuming non-dilatant double-shearing theory. The solutions determined apply to highly frictional materials for which the angle of internal friction φ is assumed equal to 90°. This major assumption is made primarily to facilitate exact analytical solutions, and it is discussed at length in the Introduction, both in the context of real materials which exhibit large angles of internal friction, and in the context of using the solutions derived here as the leading term in a regular perturbation solution involving powers of 1−sinφ. The analytical velocity fields so obtained are illustrated graphically by showing the direction of the principal stress as compared to the streamlines. The stress solutions are also exploited to determine the static stress distribution for a granular material contained within vertical boundaries and a horizontal base, which is assumed to have an infinitesimal central outlet through which material flows until a rat-hole of parabolic or cubic profile is obtained, and no further flow takes place. A rat-hole is a stable structure that may form in storage hoppers and stock-piles, preventing any further flow of material. Here we consider the important problems of two-dimensional parabolic rat-holes of profile y=ax², and three-dimensional cubic rat-holes of profile z=ar³, which are both physically realistic in practice. Analytical solutions are presented for both two and three-dimensional rat-holes for the case of a highly frictional granular solid, which is stored at rest between vertical walls and a horizontal rigid plane, and which has an infinitesimal central outlet. These solutions are bona fide exact solutions of the governing equations for a Coulomb–Mohr granular solid, and satisfy exactly the free surface condition along the rat-hole surface, but approximate frictional conditions along the containing boundaries. The analytical solutions presented here constitute the only known solutions for any realistic rat-hole geometry, other than the classical solution which applies to a perfectly vertical cylindrical cavity.     

An analysis of the chaotic motion of particles of different sizes in a gas fluidized bed

The dynamic behavior of individual particles during the mixing/segregation process of particle mixtures in a gas fluidized bed is analyzed. The analysis is based on the results generated from discrete particle simulation, with the focus on the trajectory of and forces acting on individual particles.Typical particles are selected representing three kinds of particle motion:a flotsam particle which is initially at the bottom part of the bed and finally fluidized at the top part of the bed; a jetsam particle which is initially at the top part of the bed and finally stays in the bottom de-fluidized layer of the bed; and a jetsam particle which is intermittently joining the top fluidized and bottom de-fluidized layers. The results show that the motion of a particle is chaotic at macroscopic or global scale, but can be well explained at a microscopic scale in terms of its interaction forces and contact conditions with other particles, particle-fluid interaction force, and local flow structure. They also highlight the need for establishing a suitable method to link the information generated and modeled at different time and length scales.     

An analysis of the chaotic motion of particles of different sizes in a gas fluidized bed

The dynamic behavior of individual particles during the mixing/segregation process of particle mixtures in a gas fluidized bed is analyzed. The analysis is based on the results generated from discrete particle simulation, with the focus on the trajectory of and forces acting on individual particles. Typical particles are selected representing three kinds of particle motion： a flotsam particle which is initially at the bottom part of the bed and finally fluidized at the top part of the bed; a jetsam particle which is initially at the top part of the bed and finally stays in the bottom de-fluidized layer of the bed; and a jetsam particle which is intermittently joining the top fluidized and bottom de-fluidized layers. The results show that the motion of a particle is chaotic at macroscopic or global scale, but can be well explained at a microscopic scale in terms of its interaction forces and contact conditions with other particles, particle-fluid interaction force, and local flow structure. They also highlight the need for establishing a suitable method to link the information generated and modeled at different time and length scales.     

Relaxation of a fluidized bed to the state of a continuous medium

The kinetic equation proposed in [1,2] for describing the behavior of a system of particles in a gas flow differs from the usual Boltzmann equation with respect to the additional terms that take into account random variations of the particle velocity under the influence of the flow. As shown in [2], the collision operator and the Brownian-type operator in the starting kinetic equation describe essentially different simultaneous physical processes of change of state of the particle system: equalization of the mean kinetic energy of the particles and change of energy due to the action of the viscous forces associated with the suspending flow. Therefore the method of solving the kinetic equation used in [2], a direct generalization of the Chapman-Enskog method of solving the kinetic equation it is necessary to investigate method of solving the kinetic equation it is necessar y to investigate the relaxation processes in the system. Moreover, the relaxation of systems of the fluidized-bed type to the continuum state is also of independent interest in connection with the analysis of fast processes in the system, i.e., processes with a characteristic duration of the order of the mean free time.     

Application of CFD-DEM to the study of solid exchange in a dual-leg fluidized bed

The CFD-DEM model was developed to simulate solid exchange behavior between two half beds in a bench-scale two-dimensional dual-leg fluidized bed （DL-FB）. Power spectrum density （PSD） analysis was applied to obtain the dominant frequency （F） of the simulated differential particle number （APLR） between the two half beds. Effects of fluidization velocity （u） and bed material inventory （H） on the solid exchange behavior were studied using the CFD-DEM model. Not only snapshots of the simulated particle flow patterns using the OpenGL code but also the dominant frequency of APLR was similar to the experimental results. The simulation results show that higher fluidization velocity assists the exchange of more particles between the two half beds, but the dispersion of clusters on the bed surface into single particles decreases the cluster exchange frequency. A greater bed material inventory results in more intense cluster exchange. The cluster exchange frequency decreases with an increase of the bed material inventory.     

Experimental coating and heat transfer studies in a vibrating fluidized bed

This work presents an experimental study of the heat transfer in a vibrofluidized bed and an investigation of the vibrofluidized bed coating process of thin copper plates.At superficial velocities close to that of minimum fluidization the heat transfer coefficient increases with the air flow rate and also with the immersion depth in the bed. It is independent of the initial object temperature.For different experimental conditions the obtained vibrofluidized bed coating thicknesses increase with the initial object temperature and immersion time. When compared with the theoretical predictions calculated for a regular fluidized bed, they show a good agreement. The temperature-time histories of the coated object are also recorded and compared to theoretical results.     

Mass transfer to particle clusters and bubbles in a fluidized bed at low Reynolds numbers

The process of mass transfer to a particle cluster or bubble rising in a developed fluidized bed rapidly enough for a region of closed circulation of the fluidizing agent (cloud) to be formed is investigated in the Stokes approximation on the basis of a model of the steady-state motion of the fluid and solid phases near the cluster or bubble [1]. Within the cloud surroundinga local inhomogeneity of the fluidized bed intense mixing of the fluid phase takes place and the mass transfer between the cloud and the surrounding medium is determined by diffusion. The method of matched asymptotic expansions is used to obtain an analytic solution of the problem of the concentration field and the diffusion mass flux to the surface of the cloud at small and large values of the Péclet number. The latter is determined from the relative velocity of the cluster, the radius of the cloud, and the effective diffusion coefficient. In the limiting case of zero concentration of the solid phase within the cluster the solution obtained describes the mass transfer to a bubble in the fluidized bed. A comparison is made with the corresponding results previously obtained within the framework of a model of the solid phase as an inviscid fluid [2]. It is shown that the effect of viscosity on the mass transfer to the bubble is most important at large Péclet numbers, and that the correction to the total diffusion flux to the surface of the closed circulation zone due to viscosity effects may reach 40%.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 60–67, July–August, 1986.     

The response of the level of a liquid fluidized bed to a sudden change in the fluidizing velocity

Summary When the fluidizing velocity in a liquid fluidized bed of solid particles is suddenly changed, a discontinuity in the porosity is introduced at the bottom of the bed. This discontinuity is propagated upwards through the bed. The boundary between the old and the new porosity broadens or remains sharp depending on whether the porosity is increased or decreased. This behaviour is reflected in the way in which the bed level changes as a function of time. For a few different systems such response curves have been measured by means of a specially designed follow-up system. On the basis of the above mechanism a quantitative theory was developed for the response of the bed level to a step-wise change in the fluidizing velocity. This theory proved to give a satisfactory agreement with the observed facts.List of symbols m.k.s. units have been used for the purpose of calculation - d _p diameter of particle - h instantaneous height of the fluidized bed - n constant in eq. (2) - t time - u average velocity of the fluidized particles with respect to the wall, positive in the direction of the liquid flow - U _s settling velocity of single particle in tube; constant in eq. (2) - v average liquid velocity with respect to the wall - w() velocity of propagation of a disturbance d at a porosity - x coordinate in the direction of flow - porosity, void fraction - _p particle density - liquid velocity in region above particles, volumetric flow per unit area of empty tube - index 0 refers to the steady situation for t 0 - index 1 refers to the steady state situation state reached after t = t ₁     

ANN modeling for diffusivity of mushroom and vegetables using a fluidized bed dryer

Drying characteristics in terms of diffusivity were studied for mushrooms and different vegetables in a fluidized bed dryer.Drying characteristics with falling rate regime were computed for all the samples.Effective diffusivity of each sample was calculated.Mass transfer coefficients were determined.Mass transfer kinetics for drying of different samples was also found out.Correlations for the diffusivity of samples were developed by relating the experimentally observed data with the different system parameters on the basis of regression analysis.The developed correlations for effective moisture diffusivity of the samples are validated by artificial neural network(ANN) modeling.Finally calculated values of diffusivity obtained through both the methods are compared with the experimentally measured values which show a very good approximation thereby indicating the wide applicability of the developed correlations for industrial uses.     

Analytical solutions for asymmetric periodic motions to chaos in a hardening Duffing oscillator

In this paper, the analytical dynamics of asymmetric periodic motions in the periodically forced, hardening Duffing oscillator is investigated via the generalized harmonic balance method. For the hardening Duffing oscillator, the symmetric periodic motions were extensively investigated with the aim of a good understanding of solutions with jumping phenomena. However, the asymmetric periodic motions for the hardening Duffing oscillators have not been obtained yet, and such asymmetric periodic motions are very important to find routes of periodic motions to chaos in the hardening Duffing oscillator analytically. Thus, the bifurcation trees from asymmetric period-1 motions to chaos are presented. The corresponding unstable periodic motions in the hardening Duffing oscillator are presented, and numerical illustrations of stable and unstable periodic motions are carried out as well. This investigation provides a comprehensive understanding of chaos mechanism in the hardening Duffing oscillator.     

Heat and mass transfer through a horizontal grid grating in a fluidized bed

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 81–88, September–October, 1990.