fluidization dynamics

//SYS21///SYS21/D/B&H3B2/FLD/REVISES(31-08-01)/0750650036-CH000-PRELIMS.3D ± i ± [1±24/24] 3.9.2001 11:31am Fluidization-dynamics //SYS21///SYS21/D/B&H3B2/FLD/REVISES(31-08-01)/0750650036-CH000-PRELIMS.3D ± ii ± [1±24/24] 3.9.2001 11:31am //SYS21///SYS21/D/B&H3B2/FLD/REVISES(31-08-01)/0750650036-CH000-PR ELIM S. 3D ± iii ± [1±24/24] 11:31am 11:31am Fluidization-dynamics The formulation and applications of a predictive theory for the fluidized state L.G. Gibilaro University of L'Aquila, L'Aquila, Italy OXFORD AUCKLA ND BOST ON JOHANNESBURG MELBOURNE NEW DELHI //SYS21///SYS21/D/B&H3B2/FLD/REVISES(31-08-01)/0750650036-CH 000-P R ELI MS.3D ± iv ± [1±24/24] 11:31am 11:31am Butterworth-Heinemann Linacre House, Jordan Hill, Oxford OX2 8DP 225 Wildwood Avenue, Woburn, MA 01801-2041 A division of Reed Educational and Professional Publishing Ltd A member of the Reed Elsevier plc group First published 2001 # L.G. Gibilaro 2001 All rights reserved. No part of this publication may be reproduced in any material form (including photocopying or storing in any medium by electronic means and whether or not transiently or incidentally to some other use of this publication) without the written permission of the copyright holder except in accordance with the provisions of the Copyright, Designs and Patents Act 1988 or under the terms of a licence issued by the Copyright Licensing Agency Ltd, 90 Tottenham Court Road, London, England W1P 0LP. Applications for the copyright holder's written permission to reproduce any part of this publication should be addressed to the publishers British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloguing in Publication Data A catalogue record for this book is available from the Library of Congress ISBN 0 7506 5003 6 For information on all Butterworth-Heinemann publications visit our website at www.bh.com Typeset in India by Integra Software Services Pvt Ltd, Pondicherry, India 605005; www.integra-india.com //SYS21///SYS21/D/B&H3B2/FLD/REVISES(31-08-01)/0750650036-CH000-PRELIMS.3D ± v ± [1±24/24] 3.9.2001 11:31am Contents Preface ix Acknowledgements xi Research origins xv Notation xxi 1 Introduction: the fluidized state 1 2 Single particle suspension 8 The unhindered terminal settling velocity, particle drag in the creeping flow and inertial regimes, drag coefficient, general relations, dimensionless relations 3 Fluid flow through particle beds 14 Fluid pressure loss in packed beds: tube flow analogies for viscous and inertial regimes, the Ergun equation; Fluid pressure loss in expanded particle beds: revised tube-flow analogies, tortuosity, inertial regime friction factor; Relation of particle drag to pressure loss, the fully expanded bed limit, general relations, experiments in expanded particle beds 4 Homogeneous fluidization 31 The unrecoverable pressure loss for fluidization, steady-state expansion of homogeneous beds, derivation of the Richardson±Zaki law for the viscous and inertial regimes, general constitutive relations; Primary forces on a fluidized particle, buoyancy and drag, general relations //SYS21///SYS21/D/B&H3B2/FLD/REVISES(31-08-01)/0750650036-CH 000-P R ELI MS.3D ± vi ± [1±24/24] 11:31am 11:31am 5 A kinematic description of unsteady-state behaviour 42 Response of homogeneous beds to fluid flux changes: interface stability, bed surface response, gravitational instabilities, the kinematic-shock and kinematic-wave velocities, limitations of the kinematic model 6 A criterion for the stability of the homogeneously fluidized state 52 Compressible fluid analogy for the particle phase, the dynamic-wave velocity, an explicit form for the Wallis stability criterion 7 The first equations of change for fluidization 59 A general formulation of the equations of change, the linearized particle-phase equations, the travelling-wave solution, instability of the homogeneously fluidized state 8 The particle bed model 70 The primary interaction forces; fluid-dynamic elasticity of the particle phase, the particle bed model, the particle phase equations for gas fluidization; Stability analysis, the linearized particle phase equations, the stability criterion 9 Single-phase model predictions and experimental observations 85 Powder classification for fluidization by a specified fluid: stability map for ambient air fluidization; The minimum bubbling point, sources of error, experimental measurements and model predictions; The kinematic and dynamic wave velocities: experimental measurements and model predictions 10 Fluidization quality 106 Behaviour spectra for fluidization, perturbation propagation velocity and amplitude growth rate, fluidization quality criteria, the fluidization quality map, homogeneous fluidization 11 The two-phase particle bed model 126 The two-phase particle bed model: the combined momentum equation, the two-phase dynamic wave velocity and stability criterion Contents vi //SYS21///SYS21/D/B&H3B2/FLD/ REVISE S(31-08 -01)/075065 0036-CH000 -PRELIM S.3D ± vii ± [1±24/24] 11:31am 11:31am 12 Two-phase model predictions and experimental observations 133 Comparison of one- and two-phase models, liquid- fluidized systems, stability map for ambient water fluidization, indeterminate stability 13 The scaling relations 144 Cold-model simulations, the dimensionless equations of change, one- and three-dimensional scaling relations for fluidization, example applications, experimental verifications; Fluidization quality characterization, a generalized powder classification map, fluid pressure fluctuations 14 The jump conditions 168 Large perturbations in fluidized beds, bubbles as `shocks', derivation of the jump conditions, the shock velocity, criteria for shock stability, compatibility with linear analysis, void fraction jump magnitude, verification of the two-phase theory for gas fluidization, the metastable state, bed collapse at minimum bubbling, effect of fluid pressure, experimental verifications, effect of a fluid pressure jump 15 Slugging fluidization 188 Solid and fluid slugs, square- and round-nosed fluid slugs; Fluid-dynamic controlled behaviour: slug velocities, kinetic and potential energy requirements, fluid pressure loss; Particle±particle and particle±wall frictional effects: angle of internal friction, solid slug length, bed surface displacement and oscillation frequency; Experimental verifications 16 Two-dimensional simulation 209 The two-phase, two-dimensional particle bed model: primary force interactions, fluid-dynamic elasticity of the particle phase, the equations of change, boundary and initial conditions; Numerical simulations: expansion and contraction of liquid-fluidized beds, response to distributor-induced perturbations, fluidization quality matching Author index 230 Subject index 231 Contents vii //S YS21///SYS21/D/B&H3B2/FLD/REVISES(31-08-01)/0750650036-CH000-PRELIMS.3D ± viii ± [1±24/24] 11:31am 11:31am //SYS21///SYS21/D/B&H3B2/FLD/REVISES(31-08-01)/0750650036-CH 000-P R ELI MS.3D ± ix ± [1±24/24] 11:31am 11:31am Preface This book is intended for scientists and engineers who find themselves involved, for reasons ranging from pure academic interest to dire indus- trial necessity, in problems concerning the fluidized state. It has been written with two purposes in mind. The first is to present an analysis directed at the prediction of fluidized bed behaviour in systems for which empirical data is limited or unavailable. This represents a relevant goal; because alongside the advantages in the choice of a fluidized environment for achieving a processing objective there exist worrying uncertainties regarding the precise nature of the fluidization that will ensue; particles free of direct constraints on their positions and trajectories may well comport themselves in a manner that is highly disadvantageous to the purpose for which they are employed. Such occurrences are not unknown; disastrous mistakes have been made in the past, which inhibit the adop- tion of appropriate process solutions in the present. The second objective is to provide a treatment of fluidization-dynamics that is readily accessible to the non-specialist. A stray encounter with the fluid-dynamic literature on the subject can be a disconcerting experience for the engineers seeking to improve their effectiveness in the practical application of fluidization technology. The linear approach adopted in this book, starting with the formulation of predictive expressions for the primary forces acting on a fluidized particle, is aimed at providing a clear route into the theory, and the incorporation of the force terms in the conservation equations for mass and momentum, and subsequent appli- cations, is presented in a manner which assumes only the haziest recollec- tion of elementary fluid-dynamic principles. Although reference is made throughout to primary source material the approach in this respect, as in others, is a focused one, no attempt having //SYS21///SYS21/D/B&H3B2/FLD/REVISES(31-08-01)/0750650036-CH000-PRELIMS.3D ± x ± [1±24/24] 3.9.2001 11:31am been made to mix into the narrative a comprehensive survey of the back- ground literature; to have done so would have resulted in a very different book from the one intended. In deciding on how much detail to include I have been guided by experience in presenting much of this material in Master's level degree courses in Italy and the UK. Students on the whole have no problem with being reminded of simple standard procedures, and a number positively welcome it; I have extrapolated these responses to the anticipated read- ership. In order to avoid clutter some common manipulations are given in small-type paragraphs, which may be easily skipped over. In this way I hope to have defused objections to having, say, spelt out the steps in the formulation of a differential equation from a control volume balance, or the subsequent linearization procedure. Such criticism as may remain in that respect I feel can be lived with. What I have strenuously tried to avoid is the all too familiar cry for help from careful readers of the scientific literature: where on earth does that come from? The analyses presented in this book represent, by and large, a body of research that has appeared in numerous publications (predominantly in the chemical engineering literature) ± some quite recent, others going back over nearly 20 years. In gathering these together for the purpose of producing a coherent narrative I have taken the opportunity to re-order much of the material, to correct errors and inconsistencies, and to add the details and clarifications that space constraints prohibit in journal pub- lications. The book could form the basis for university course modules in engineering and applied science at both undergraduate and graduate level, as well as for focused post-experience courses for the process and allied industries. L.G. Gibilaro Preface x [...]... two quite different fluid-dynamic environments brought about by the fluidization process itself They may be regarded as somewhat extreme examples of fluidization 5 //SYS21///SYS21/D/B&H3B2/FLD/REVISES(31-08-01)/0750650036-CH001.3D ± 6 ± [1±7/7] 3.9.2001 11:32AM Fluidization- dynamics Increasing fluid flow rate Figure 1.3 Homogeneous fluidization ± from packed bed to single particle suspension quality,... particles to the minimum fluidization point forms rising bubbles, which cause considerable particle mixing and give the bed the appearance of a boiling liquid Various terms have been adopted to describe these two quite different manifestations of the fluidized state We shall refer to them as homogeneous and bubbling fluidization respectively Fluidization quality Homogeneous and bubbling fluidization represent... sand and //SYS21///SYS21/D/B&H3B2/FLD/REVISES(31-08-01)/0750650036-CH001.3D ± 2 ± [1±7/7] 3.9.2001 11:32AM Fluidization- dynamics the high-density brass one is placed on the surface; a compressed air supply to the bottom of the bed is then turned on and the flow progressively increased When the fluidization point is reached the brass duck sinks to the bottom and the plastic one pops to the surface, where... starting point for the examination of the mechanism of the fluidization process, which involves the suspension of a very large number of solid particles in an upwardly flowing fluid, is the much simpler case of the single particle 3 //SYS21///SYS21/D/B&H3B2/FLD/REVISES(31-08-01)/0750650036-CH001.3D ± 4 ± [1±7/7] 3.9.2001 11:32AM Fluidization- dynamics up ut uf Increasing fluid flow rate Figure 1.1 Single... that fluidization quality is a key factor in determining the performance of a fluidized bed as a chemical reactor A major incentive for the analyses reported in the following chapters has been the urgent need for means of quantifying the essential factors that determine fluidization quality; and for predicting, on the basis of the particle and fluid properties and conditions of operation, the fluidization. .. x relative to datum value bold type x vector quantities xxiv //SYS21///SYS21/D/B&H3B2/FLD/REVISES(31-08-01)/0750650036-CH001.3D ± 1 ± [1±7/7] 3.9.2001 11:32AM 1 Introduction: the fluidized state Fluidization Fluidization is a process whereby a bed of solid particles is transformed into something closely resembling a liquid This is achieved by pumping a fluid, either a gas or a liquid, upwards through... L'Aquila worked on aspects of slugging fluidization described in Chapter 15, and who subsequently, on his own initiative, embarked on the two-dimensional numerical simulation studies reported in Chapter 16, which have now come to represent the starting point for new programmes of computational research From its inception, the work has involved close collaboration between the fluidization research teams of... publish, but only after his key conclusion had already been accorded the status of an established truth The second episode in the unfolding saga bears some similarity to the first In 1962 a paper on fluidization- dynamics, of prophetic importance as it turned out, was also submitted to the Journal of Fluid Mechanics, this time by Graham Wallis ± a name soon to become widely associated with seminal advances... such time as the relative velocity of the fluid (uf À up ) has fallen to that of the critical, minimum fluidization condition and equilibrium is re-established; from this point on the particle assembly would proceed up the tube, piston-like, at constant velocity Such behaviour, following the minimum fluidization point, does not occur in practice unless the particles are glued together What precisely... was to have a profound effect in cementing views on the nature of the fluidization process It seemed that however the interaction between fluid and particles is described, the essential conclusion remains unchanged: the uniform fluidized state remains intrinsically unstable So when irrefutable experimental evidence for stable gas fluidization became available in the mid-1970s, the initial reaction was . model predictions 10 Fluidization quality 106 Behaviour spectra for fluidization, perturbation propagation velocity and amplitude growth rate, fluidization quality criteria, the fluidization quality. 3.9.2001 11:31am //SYS21///SYS21/D/B&H3B2/FLD/REVISES(31-08-01)/0750650036-CH000-PR ELIM S. 3D ± iii ± [1±24/24] 11:31am 11:31am Fluidization- dynamics The formulation and applications of a predictive theory for the fluidized state L.G general relations, experiments in expanded particle beds 4 Homogeneous fluidization 31 The unrecoverable pressure loss for fluidization, steady-state expansion of homogeneous beds, derivation of