Preface
Mathematical and Engineering Modelling
Scope of the Book
Topics and Assumptions
References
Contents
1 Spray Formation and Penetration
1.1 Spray Formation
1.1.1 Classical WAVE Model
1.1.2 TAB and Stochastic Models
1.1.3 Modified WAVE Models
1.2 Spray Penetration
1.2.1 The Initial Stage
1.2.2 Two-Phase Flow
1.2.3 Effects of Turbulence
1.3 Vortex Ring-Like Structures in Sprays
1.3.1 Conventional Vortex Rings
1.3.2 Turbulent Vortex Rings
1.3.3 Translational Velocities of Vortex Rings-Like Structures
1.3.4 Confined Vortex Rings
1.3.5 Two-Phase Vortex Ring Flows
References
2 Heating of Non-evaporating Droplets
2.1 Convective Heating
2.1.1 Stagnant Droplets
2.1.2 Moving Droplets
2.2 Radiative Heating
2.2.1 Basic Equations and Approximations
2.2.2 Mie Theory
2.2.3 Integral Absorption of Radiation in Droplets
2.2.4 Geometric Optics Analysis
References
3 Heating and Evaporation of Mono-component Droplets
3.1 Empirical Correlations
3.2 Classical Models
3.2.1 Maxwell and Stefan–Fuchs Models
3.2.2 Abramzon and Sirignano Model
3.2.3 Yao, Abdel-Khalik and Ghiaasiaan Model
3.2.4 Tonini and Cossali Model
3.2.5 Fully Transient Models
3.2.6 d2 and d1.5 Laws
3.3 Effects of Real Gases
3.4 Effects of the Moving Interface
3.4.1 Basic Equations and Approximations
3.4.2 Solution for the Case when Rd(t) is a Linear Function
3.4.3 Solution for the Case of Arbitrary Rd(t) but Td0(R)=const
3.4.4 Solution for Arbitrary Rd(t) and Td0(R)
3.4.5 A Comparison between Model Predictions
3.5 Conventional and Alternative Approaches to Modelling
3.6 Heating and Evaporation of Spheroidal Droplets
3.6.1 Background Research: Non-spherical Droplets
3.6.2 The Tonini and Cossali Model (Spheroidal Droplets)
3.6.3 The Coupled Liquid/Gas Model (Spheroidal Droplets)
3.6.4 Miscellaneous Models
3.7 Effect of Droplet Support
3.8 Modelling Versus Experimental Data
3.8.1 Monodisperse Droplet Stream
3.8.2 Suspended Droplets
References
4 Heating and Evaporation of Multi-component Droplets
4.1 Background
4.2 Discrete Component Model
4.2.1 An Analytical Solution for Rd = const
4.2.2 An Analytical Solution for Rd neq const
4.2.3 Bi-component Droplets
4.2.4 Biodiesel Droplets
4.2.5 Kerosene Droplets
4.2.6 Drying Droplets
4.3 Quasi-discrete Model
4.3.1 Description of the Quasi-discrete Model
4.3.2 Application to Diesel and Petrol Fuel Droplets
4.4 Multi-dimensional Quasi-discrete Model
4.4.1 Description of the Model
4.4.2 Application to Diesel Fuel Droplets
4.4.3 Application to Petrol Fuel Droplets
4.4.4 Heating, Evaporation and Ignition of Fuel Droplets
4.4.5 Biodiesel/Diesel/Ethanol/Petrol Droplets
4.4.6 Auto-selection of Quasi-components/Components
4.5 Gas Phase Models for Multi-component Droplets
4.6 Other Approaches to Modelling Multi-component Droplets
4.7 Heating and Evaporation of Multi-component Liquid Films
4.7.1 Mono-component Liquid Film
4.7.2 Multi-component Liquid Film
4.7.3 Solution Algorithm
4.7.4 Validation of the Model
4.7.5 Verification of the Model
References
5 Processes in Composite Droplets
5.1 Background
5.2 A Simple Analytical Model
5.2.1 Basic Equations and Approximations
5.2.2 Analysis
5.3 A Simple Numerical Model
5.3.1 Key Equations and Approximations
5.3.2 Preliminary Analysis
5.3.3 Boiling Versus Nucleation Temperature
5.3.4 Times to Puffing/Micro-Explosion
5.4 Puffing/Micro-Explosion in the Presence of Coal Particles
5.4.1 Rapeseed Oil/Water Droplets with Coal Micro-Particles
5.4.2 Modelling Versus Experimental Results
5.5 Puffing/Micro-Explosion in Closely Spaced Droplets
5.5.1 Puffing/Micro-Explosion in Two Droplets in Tandem
5.5.2 Puffing/Micro-Explosion in a String of Three Droplets
5.6 Effects of Thermal Radiation and Support
5.7 Composite Multi-component Droplets
5.7.1 Diffusion of Components
5.7.2 Modelling and Experimental Results
5.8 The Shift Model
References
6 Kinetic Modelling of Droplet Heating and Evaporation
6.1 Early Results
6.2 Kinetic Algorithm: Effects of the Heat and Mass Fluxes
6.2.1 Boltzmann Equations for the Kinetic Region
6.2.2 Vapour Density and Temperature at the Boundaries
6.3 Approximations of the Kinetic Results
6.3.1 Approximations for Chosen Gas Temperatures
6.3.2 Approximations for Chosen Initial Droplet Radii
6.4 Effects of Inelastic Collisions
6.4.1 Mathematical Model
6.4.2 Solution Algorithm
6.5 Kinetic Boundary Condition
6.5.1 Molecular Dynamics Simulations (Background)
6.5.2 United Atom Model
6.5.3 Evaporation Coefficient
6.6 Quantum-Chemical Models
6.6.1 Brief Overview of Quantum-Chemical Methods
6.6.2 Evaporation Rate
6.6.3 Interaction between Molecules and Clusters/Nanodroplets
6.6.4 Estimation of the Evaporation Coefficient
6.7 Results of the Kinetic Calculations
6.7.1 Results for βm=1
6.7.2 Results for βm<1
6.8 Kinetic Modelling in the Presence of Three Components
6.8.1 Preliminary Testing of the Numerical Code
6.8.2 Application to Two-Component Droplets: Solution Algorithm
6.8.3 Application to Two-Component Droplets: Results
6.9 A Self-consistent Kinetic Model
References
7 Heating, Evaporation and Autoignition of Sprays
7.1 Autoignition Modelling
7.2 Coupled Solutions: Simple Models
7.2.1 Physical Model
7.2.2 Mathematical Formulation
7.2.3 Analysis
7.2.4 Systems with Non-Lipschitzian Non-linearities
7.2.5 Spray Ignition and Combustion Model with Radiation
7.3 Coupled Solutions: Dynamic Decomposition
7.3.1 Decomposition Techniques
7.3.2 Description of the Method
7.3.3 Application of the Method
References
8 Concluding Comments
8.1 The Fully Lagrangian Approach
8.2 Non-spherical Droplets
8.3 Limitations of the ETC/ED Model
8.4 Effects of the Interaction Between Droplets
8.5 Heating and Evaporation in Near/Super-Critical Conditions
8.6 Effects of the Moving Interface due to Evaporation
8.7 Complex Multi-component Droplets
8.8 Puffing and Micro-explosion
8.9 Advanced Kinetic and Molecular Dynamics Models
8.10 Effective Approximation of the Kinetic Effects
References
Appendix A Derivation of Formula (2.86摥映數爠eflinkeq3.2.32.862)
Appendix B Derivation of Formula (2.89摥映數爠eflink3a.28aa2.892)
Appendix C Proof of Orthogonality of vn(R) with the Weight b
Appendix D Derivation of Formula (3.103摥映數爠eflink4.2.63.1033)
Appendix E The Convergence of the Series in G1 (t, τ, r)
Appendix F Numerical Solution of Equation (D.37)
Appendix G Numerical Calculation of the Improper Integrals
Appendix H Derivation of Equation (3.150摥映數爠eflinkellsps103.1503)
Appendix I Evolution of the Droplet Shape
Appendix J Derivation of Expressions (3.162摥映數爠eflinkellsps263.1623)
Appendix K Derivation of Formula (4.21摥映數爠eflink5.A2.364.214)
Appendix L Derivation of Formula (4.29摥映數爠eflink5.2.64.294)
Appendix M Derivation of Formula (L.29)
Appendix N Approximations for Alkane Fuel Properties
Appendix O Thermophysical Properties of Hydrocarbons in Diesel Fuels
Thermodynamic and Transport Properties of Alkanes
Thermodynamic and Transport Properties of Cycloalkanes
Thermodynamic and Transport Properties of Bicycloalkanes
Thermodynamic and Transport Properties of Alkylbenzenes
Thermodynamic and Transport Properties of Indanes and Tetralines
Thermodynamic and Transport Properties of Naphthalenes
Thermodynamic and Transport Properties of Tricycloalkanes, Diaromatics and Phenanthrenes
Appendix P Derivation of Expression (4.91摥映數爠eflink57.A13A14.914)
Appendix Q Derivation of Expression (5.8摥映數爠eflink6asps28aa5.85)
Appendix R Derivation of Expression (5.15摥映數爠eflink6asps15.155)
Appendix S Solution of Equation (5.40摥映數爠eflink6a2.15.405)
Appendix T Calculations of Qn based on (S.56)
Appendix U Graphical Solutions of (5.45摥映數爠eflink6aA3205.455) and (5.46摥映數爠eflink6aA4205.465)
Appendix V Verification of the Numerical Code
Appendix W Tikhonov Theorem