Introduction to Multiphase Flow : Basic Concepts, Applications and Modelling.

Intro -- Preface -- Contents -- 1 Nature of Multiphase Flows and Basic Concepts -- 1.1 The Nature of Multiphase Flows -- 1.2 Phases, Components, Fields -- 1.3 Multiphase Flow Phenomena -- 1.3.1 Phenomena Unique to Multiphase Flows -- 1.3.2 Phenomena Complicated by the Presence of Many Phases -- 1.4 Flow Regimes -- 1.5 Some Important Multiphase Flow Systems -- 1.6 Averaging in Two-Phase Flows -- 1.6.1 Space Averaging -- 1.6.2 Time Averaging -- 1.7 Void Fractions and Their Measurement -- 1.7.1 The Local Void Fraction -- 1.7.2 The Chordal Void Fraction -- 1.7.3 The Cross-Sectional Void Fraction -- 1.7.4 The Volume-Average Void Fraction -- 1.7.5 Averages of Products -- 1.8 Phase Flow Rates and Flow Quality -- 1.8.1 Determination of the Flow Quality -- 1.9 Velocities, the Triangular Relationship and Other Useful Relations -- 1.9.1 Velocities of the Centre of Volume and Mass -- 1.9.2 Homogeneous Flow -- 1.10 A Few Useful Non-dimensional Numbers -- 1.11 System of Units -- 1.12 Sources of Information -- References -- 2 Modelling Strategies and Two-Phase Flow Models -- 2.1 Two-Phase Flows and Their Analysis -- 2.1.1 General Methods of Solution -- 2.1.2 Special Features of Two-Phase Flows -- 2.1.3 Two-Phase Flow Equipment -- 2.2 The Empirical Approach -- 2.2.1 The Empirical Approach Versus Phenomenological Modelling -- 2.3 Phenomenological Modelling -- 2.3.1 Example: Case of Annular Flow -- 2.4 Multi-fluid Models and One-Dimensional Conservation Equations -- 2.4.1 Simple Derivation of Two-Fluid Conservation Equations -- 2.4.2 Practical Set of Two-Fluid Equations -- 2.4.3 Closure Laws Required -- 2.4.4 Implementation Difficulties: Application to Horizontal Stratified Flow -- 2.4.5 The Drift Flux Model -- 2.5 Separated Flow and Mixture Models -- 2.6 The Homogeneous Model -- 2.7 Computational Multiphase Flow Dynamics.

2.7.1 Treatment of Separated Phases as Single-Phase Flow -- 2.7.2 One-Fluid Formulation with Interface Tracking Versus Two-Fluid Formulations -- 2.7.3 Multiplicity of Scales -- 2.7.4 DNS of Turbulent Multiphase Flows -- 2.8 Conclusions -- References -- 3 Interfacial Instabilities -- 3.1 Introduction: The Stability of Two Fluid Layers -- 3.2 Rayleigh-Taylor (RT) Instability -- 3.2.1 Case when σ = 0 -- 3.2.2 Generalization -- 3.3 Kelvin-Helmholtz Instability -- 3.3.1 Applications -- 3.3.2 Departure from Nucleate Boiling (DNB) in Pool Boiling -- 3.3.3 Minimum Film Boiling (MFB) Point -- 3.3.4 Weber-Number Stability Criteria for Drops, Jets, etc. -- 3.3.5 Stability and Breakup of Fluid Particles -- References -- 4 Flow Regimes -- 4.1 Introduction -- 4.1.1 Flow Regime Observations and Maps -- 4.1.2 Flow Regime Transitions -- 4.1.3 Need to Know the Flow Regime -- 4.2 Flow PatternsFlow regimes-Physical Descriptions -- 4.2.1 Flow Patterns in Vertical Co-current Flow -- 4.2.1.1 Bubble or Bubbly Flow -- 4.2.1.2 Slug Flow -- 4.2.1.3 Churn Flow -- 4.2.1.4 Annular Flow -- 4.2.1.5 Wispy Annular Flow -- 4.2.2 Flow Patterns in Horizontal Co-current Flow -- 4.2.2.1 Bubble Flow -- 4.2.2.2 Stratified Flow -- 4.2.2.3 Annular Flow -- 4.2.2.4 Plug Flow -- 4.2.2.5 Slug Flow -- 4.2.3 Flow Patterns in Other Situations -- 4.3 Empirical Flow Regime Maps -- 4.3.1 The Baker Map for Horizontal Flow -- 4.3.2 The Hewitt and Roberts Generalized Map -- 4.4 Analytical Treatment of Flow Pattern Transitions-Flow Pattern Maps -- 4.4.1 The Bubbly-to-Slug Flow Transition -- 4.4.2 The Slug-to-Churn Transition in Vertical Upwards Flow -- 4.4.3 Transitions in Horizontal Flow -- 4.4.3.1 Transition from Horizontal-Stratified to Intermittent or Annular Flow -- 4.4.3.2 Appearance of Waviness in Stratified Horizontal Flow -- 4.4.3.3 Transition from Intermittent Horizontal to Dispersed Bubbly Flow.

4.5 Flow Regime Maps Based on Transition Criteria: The Dukler-Taitel-Barnea Work -- 4.5.1 Transitions from Horizontal or Near-Horizontal Flows-the Taitel and Dukler Map -- 4.5.1.1 The Equilibrium Liquid Height -- 4.5.2 The DTB Map and Unified Model for the Whole Range of Inclinations -- 4.5.2.1 Transitions D and G from Dispersed-Bubble (DB) Flow -- 4.5.2.2 Case of High Flow Rates (Transitions D and G) -- 4.5.2.3 Transition B to Intermittent Flow -- 4.5.2.4 Transition J from Annular to Intermittent Flow -- 4.6 Flow Regime Maps and Transition Criteria for Vertical Upwards Flow-Ishii and Co-workers -- References -- 5 Void Fraction-Empirical Methods -- 5.1 Introduction-the Empirical Methods -- 5.2 Void Fraction Measurement Techniques -- 5.2.1 Photographic Techniques -- 5.2.2 Optical or Electrical Techniques -- 5.2.3 Techniques for Cross-Sectional Averages -- 5.2.4 Volume Average Void Fraction -- 5.3 Prediction Methods -- 5.3.1 The Homogeneous Void Fraction and Density -- 5.3.2 Empirical Correlations for Separated Flows -- 5.4 The Drift-Flux Model -- 5.4.1 Basic Derivation -- 5.4.2 Physical Significance of the DF Model Parameters -- 5.4.3 Velocities in Terms of DF Parameters -- 5.4.4 Use of Experimental Data -- 5.5 Determination of the Parameters of the DF Model -- 5.5.1 The EPRI (1996) Chexal-Lellouche Correlation -- 5.6 Comparisons of Various Correlations -- 5.7 Correlations for Horizontal or Inclined Pipes -- 5.7.1 Void Fraction Correlations for Inclined Pipes -- 5.7.2 Mechanistic Models Based on Two-Fluid Formulation -- References -- 6 Pressure Drop-Empirical Methods -- 6.1 Introduction -- 6.2 The Pressure Gradient in Two-Phase Flow -- 6.3 Gravitational Pressure Gradient -- 6.4 Accelerational Pressure Gradient -- 6.5 Frictional Pressure Gradient -- 6.5.1 Parallel with Single-Phase Flow Situation -- 6.5.2 Two-Phase Flow Situation.

6.5.3 The Homogeneous-Flow Model -- 6.5.4 Two-Phase-Multiplier Methods for the Frictional Pressure Gradient -- 6.5.5 The Martinelli et al. Method -- 6.5.6 The Friedel Correlation -- 6.5.7 The EPRI Chexal-Harrison Approach -- 6.6 Comparisons of Available Correlations -- 6.7 Pressure Drop Work for Large and Inclined Pipes Used in the Oil-and-Gas Industry -- 6.7.1 Experimental Data -- 6.7.2 Pipeline Design -- 6.7.3 Mechanistic Models Based on Two-Fluid Formulation -- 6.8 Two-Phase Pressure Drop in Singularities -- Appendix -- References -- Appendix A: Tutorial -- A.1 Recall of the Single-Phase Flow Conservations Equations -- Outline placeholder -- A.1.1 The Conservation Equations for "Closed Systems" -- A.1.2 Conservation Equations for a Control Volume -- A.1.3 One-Dimensional, Differential form of the Equations -- A.1.4 Thermodynamic Variables -- A.2 On the Two Most Important Closure Relationships -- Outline placeholder -- A.2.1 An Important Remark Regarding the Heat Transfer Coefficient -- Appendix B: Common Nomenclature -- Appendix C: Most Useful Conversion Factors Between British and Si Units -- Index.

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