Barsky Critical Regimes of Two-Phase Flows with a Polydisperse Solid Phase

1. Auflage 2010
ISBN: 978-90-481-8838-3
Verlag: Springer Netherlands
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 93, 348 Seiten

Reihe: Fluid Mechanics and Its Applications

Critical regimes of two-phase flows with a polydisperse solid phase form the basis of such widespread industrial processes as separation of various powdery materials and minerals dressing. It is impossible to describe such complicated flows analytically. Therefore, this study concentrates on invariants experimentally revealed and theoretically grounded for such flows. This approach can be compared with the situation in gases, where in order to determine principal parameters of their state, one does not need to measure the kinetic energy and velocity of each molecule and find its contribution to the temperature and pressure. These parameters are determined in a simple way for the system on the whole. A novel conception of two-phase flows allowing the formulation of their statistical parameters is physically substantiated. On the basis of the invariants and these parameters, a comprehensive method of estimating and predicting mass transfer in such flows is developed. It is noteworthy that the presented results are mostly phenomenological. Such an approach can be successfully extended to the separation of liquids, gases and isotopes. The book is intended for students and specialists engaged in chemical technology, mineral dressing, ceramics, microelectronics, pharmacology, power generation, thermal engineering and other fields in which flows carrying solid particles are used in the technological process.

Autoren/Hrsg.

Barsky, Eugene

Inhaltsverzeichnis

1;FM;2
1.1;Critical Regimes of Two-Phase Flowswith a Polydisperse Solid Phase;2
1.2;Critical Regimes ofTwo-Phase Flows with aPolydisperse Solid Phase;4
1.3;Annotation;6
1.4;Introduction;8
1.5;Contents;14
2;Chapter 1: General Ideas of Mass Transfer Processes in Critical Regimes;18
2.1;Granulometric Characteristics of Bulk Material;18
2.2;Distribution of Different Fractions in the Process of Separation;22
2.3;Fractional Separation Curves and Their Properties;24
2.3.1;Initial Composition;27
2.3.2;Solid Phase Concentration in the Flow;28
2.3.3;Process Stability;30
2.3.4;Flow Velocity and Particle Size;30
3;Chapter 2: Principles of Modeling Processes in Moving Media;35
3.1;Correlation Between a Full-Scale Process and Its Model;35
3.2;Mathematical Models Construction;37
3.3;Similarity Criteria Determination;42
4;Chapter 3: System of Particles of the Same Size Class in a Critical Flow;48
4.1;Dynamics of Mass Motion of Particles in a Flow;48
4.2;Definition of a Statistical System;53
4.3;Estimation of the State of a Statistical System;59
4.4;Principal Statistical Characteristics of the Separation Factor;68
5;Chapter 4: System of Particles of Several Size Classes;73
5.1;Interaction of Particles in a Flow;73
5.2;Forces Caused by Interactions of Particles of Various Classes;78
5.3;Two-Phase Flow Entropy in Critical Flow Regimes;81
5.4;Main Features of Entropy in Critical Regimes;87
5.5;Mobility Factor;95
5.6;Statistical Identities;100
6;Chapter 5: Principal Statistical Relations of Mass Transfer in Critical Flow;106
6.1;Mass Exchange Between the Zone and the Apparatus;106
6.2;Determination of Average Values;109
6.3;Cell and Apparatus, Entropy;111
6.4;Separation at Low Concentrations;113
6.5;General Regularities for the Zone;117
7;Chapter 6: Correlation Between the Apparatus and the Cell;119
7.1;Coarse Particles Separation;119
7.2;Fine Particles Separation;120
7.3;Definition of Mass Transfer Parameters;121
7.4;Cellular Model of Separation;126
7.5;Physical Meaning of Separation Factors;130
7.5.1;Chaotizing Factor;130
7.5.2;Flow Mobility;130
7.5.3;Separation Factor;130
7.5.4;Concentration Effect;131
7.5.5;Potential Extraction;133
7.6;Extraction from a Cell Located in the Zone;134
8;Chapter 7: Structural Model of Mass Transfer in Critical Regimes of Two-Phase Flows;137
8.1;Validation of the Distribution Coefficient;137
8.2;Physical Meaning of the Distribution Coefficient;139
8.2.1;Turbulent Overflow of Particles and Turbulent Regime of the Medium Motion in the Apparatus;144
8.2.2;Laminar Overflow Regime;146
8.2.3;Intermediate Regime of Overflow;147
8.3;Analysis of Distribution Coefficient;148
8.4;Analysis of Experimental Dependencies from the Standpoint of Structural Models;153
8.5;Check of the Structural Model Adequacy;159
8.6;Correlation Between the Structural and Cellular Models of the Process;163
9;Chapter 8: Correlation Between Statistical and Empirical Results;165
9.1;Approximation of Universal Separation Curve;165
9.2;Principal Separation Parameters Depending on the Apparatus Height;168
9.3;Equal Extractability of Various Size Classes;172
10;Chapter 9: Entropy of Composition: Optimization Criterion;181
10.1;Entropy and Particles Stratification;181
10.2;Evaluation of Heterogeneity of Powder Composition;185
10.3;Binary Separation;187
10.4;Multi-product Separation;188
10.5;Algorithms of Optimization of Separation into n Components;189
10.5.1;Algorithm 1: Complete Sorting-Out;190
10.5.2;Algorithm 2: Greedy Algorithm;190
10.5.3;Optimization of Separation into Four Components;192
10.6;Mathematical Model of Separation into n Components;198
10.7;Optimum Conditions for Binary Separation;199
10.8;Optimum Conditions for Multi-Product Separation;201
11;Chapter 10: Stability and Kinetic Aspects of Mass Distribution in Critical Regimes;208
11.1;Entropy Stability;208
11.2;Particles Distribution over the Channel Height;215
11.3;Velocity Distribution of Particles of a Narrow Size Class;218
11.4;Kinetic Aspect of the Material Distribution;221
12;Chapter 11: Critical Regimes of Two-Phase Flows in Complicated Systems;226
12.1;Problem Setting;226
12.2;Mathematical Model of a Duplex Cascade;227
12.3;Mathematical Model of a Cascade Process Allowing Control of the Effect of the Material Feed Site on Separation Results;231
12.4;Cascade Model with Two or More Material Inputs into the Apparatus;234
12.5;Combined Cascade Classifiers;236
12.5.1;Combined Cascades of n(z)Type;236
12.5.2;Working Schemes for Combined Cascades of n(z) Type;238
12.5.3;Connection Functions for Combined Cascades;240
12.5.4;Experimental Verification of the Adequacy of Mathematical Models of Combined Cascades;245
12.6;Quality Criterion for Combined Cascades;248
12.7;Fractal Principle of the Construction of Schemes of Combined Classifiers;252
12.7.1;Fractal Principle of Combination;252
12.7.2;Progressive Nature of Multi-element Apparatuses;255
12.7.3;Combined Scheme with Successive Recirculation of Both Products;257
12.7.4;Combined Cascade with an Alternating Bypass of Both Products;258
12.7.5;On the Potential of Fractal Combined Schemes;263
12.8;Some Methods of Combined Schemes Optimization;266
12.8.1;Multi-row Classifier;266
12.8.2;Method of Estimating a Multi-row Classifier;269
12.8.3;Optimal Scheme of a Multi-row Industrial Classifier;271
13;Chapter 12: Stochastic Model of Critical Regimes of Two-Phase Flows;276
13.1;Principal Definitions;276
13.2;Statistical Description of Gravitational Separation in Turbulent Flows;278
13.3;Equations of Particles Motion Taking into Account Their Rotation Around the Center of Mass in a Turbulent Flow;282
13.4;Description of One-Dimensional Stationary Process of Gravitation Separation in a Turbulent Flow;285
13.5;One-Dimensional Model of a Non-stationary Process;289
13.6;Statistical Equations of a Random Process of Gravitational Separation;289
13.7;Computation of Fractional Separation of a Narrow Class;292
13.8;Approximate Computation Method;294
14;Chapter 13: Mass Transfer in Critical Regimes of Two-Phase Flows;298
14.1;Mathematical Model of a Separating Cascade;298
14.2;Discrete Stationary Model of Critical Regimes of Vertical Two-Phase Flows;316
14.3;Optimization of Principal Parameters of Multi-stage Separation;330
15;Chapter 14: Universal Curves Criteria;343
15.1;Substantiation of the Curves Universality;343
15.2;Generalizing Criteria;347
15.2.1;Turbulent Regimes of Particles Overflow;350
15.2.2;Laminar Regimes of Particles Overflow;352
15.3;Universal Curves;354
16;Bibliography;355

Leseproben

"Chapter 1 General Ideas of Mass Transfer Processes in Critical Regimes (p. 1-2)

Abstract Experimental studies have shown that despite a visual chaos in critical regimes of two-phase flows, there is a definite, almost deterministic order in the polyfractional solid phase distribution along the flow and counter the flow. The affinity of separation curves as a function of principal parameters of the flow in a turbulent regime is substantiated. Criteria of the affinization of separation curves are empirically established and experimentally substantiated.

Keywords Regularity - Granulometric composition - Size - Density - Concentration - Velocity - Process stability - Fractional extraction -Affinity -Separation curve -Productivity -Separation

1.1 Granulometric Characteristics of Bulk Material

First of all, we examine characteristics of a solid phase constituting a two-phase flow, because in critical regimes the process of particles separation according to their size grade or density can be organized most easily. Processing of ground materials is among the most widespread processes in today’s industry.

Many millions of tons of various materials are ground daily in mining, in various branches of chemical industry, in metallurgy, at the production of cement, ceramics, glass and other building materials, as well as in most novel branches of industry. Various natural and artificial materials become pourable when ground, and in this state they pass all the stages of technological processes, namely, extraction of useful components, production of powders with a specified particle size, compounding of necessary mixtures and compositions, treatment of particle surface and addition of various elements, drying, baking, etc. In this state it is convenient to granulate materials from particles of any composition or press products of any shape. As a rule, a solid phase is introduced into moving flows in this state only. At present, more and more low-quality raw materials are being processed because of growing production volumes.At the same time, the requirements for the quality of the final products constantly grow.

To meet these requirements, separation processes are becoming more and more important. Most often, the separation is performed by particle size or density, and more rarely – by shape, color or other parameters. While formerly, with a rather rough technology, it was sufficient to use various sieves for the separation by size, presentday operations with fine powders require separation carried out using moving media – air or water. As for separation by other parameters (density, particle shape), it can be realized only in moving media.

Before determining separation parameters, we examine principal characteristics of a bulk material. Such a material can be characterized by its specific density of particles, bulk density, humidity, porosity, etc. Usually a ground material contains, depending on its size grade, many millions of particles. These particles can differ in size, shape, surface state, etc. However, the material’s principal characteristic is connected with dispersity."