Preface	6
	Contents	9
	Editors and Contributors	11
	Multiphase Flow Fundamentals	15
	1 Introduction to Droplets and Sprays: Applications for Combustion and Propulsion	16
	Abstract	16
	2 Towards Combined Deterministic and Statistical Approaches to Modeling Dispersed Multiphase Flows	20
	2.1 Introduction	21
	2.1.1 Fully Resolved (FR) Approach	22
	2.1.2 Point-Particle (PP) Approach	23
	2.1.3 Euler--Lagrange Interphase Coupling Models	25
	2.2 Single-Particle Drag	28
	2.2.1 Reynolds Number Effects	30
	2.2.2 Turbulence Effects	32
	2.3 Beyond Single-Particle DNS	35
	2.3.1 FR-DNS of Random Arrays	36
	2.3.2 Computational Drag Laws	36
	2.3.3 Developing LE Particle Force Models from FR-DNS	38
	2.4 Deterministic Coupling Models	40
	2.4.1 Neighbors Matter	41
	2.4.2 PIEP Model	43
	2.4.3 PIEP Results	44
	2.5 Stochastic Models	45
	2.5.1 Particle Dispersion and Turbulence Modulation in Dilute Turbulent Flow	45
	2.5.2 Neighbor Effects in Non-dilute Gas--Solid Flow with Mean Slip	48
	2.6 Outlook and Challenges	49
	References	51
	Droplet Evaporation and Combustion	56
	3 Modelling of Droplet Heating and Evaporation	57
	3.1 Introduction	57
	3.2 Heating of Non-evaporating Droplets	58
	3.3 Hydrodynamic Models (Mono-component Droplet Heating and Evaporation)	62
	3.4 Hydrodynamic Models (Multi-component Droplet Heating and Evaporation)	68
	3.5 Kinetic and Molecular Dynamics Models	78
	References	81
	4 Combustion of Multi-component Fuel Droplets	88
	4.1 Introduction and Background	88
	4.2 Numerical Studies on Droplet Evaporation and Combustion	90
	4.3 Experimental Studies on Multi-component Droplet Combustion	102
	4.3.1 Review of Experimental Approaches in Droplet Combustion	103
	4.3.2 Disruptive Phenomena in Multi-component Miscible Droplets	105
	4.3.3 Disruptive Phenomena in Emulsion Droplets	111
	4.4 Introduction to Combustion of Nanofuel Droplet	115
	4.5 Conclusion	121
	References	121
	Atomization Principles and Injection Strategies	126
	5 On Primary Atomization in Propulsive Device Fuel Injectors—A Short Review	127
	Abstract	127
	5.1 Introduction	127
	5.2 Primary Atomization	128
	5.3 Primary Atomization in Pressure-Atomizing Nozzles	131
	5.3.1 Pressure Jet Atomizer	131
	5.3.2 Experimental Approaches in Primary Atomization	132
	5.3.3 Pressure Swirl Atomizer	138
	5.4 Primary Atomization in Twin-Fluid Atomizer	140
	5.4.1 Plain Coaxial Air-Assisted Atomizer	141
	5.4.2 Swirl Coaxial Air-Assist Atomization	144
	5.5 Summary and Conclusions	148
	Acknowledgements	148
	References	148
	6 A Comprehensive Model for Estimation of Spray Characteristics	151
	Abstract	151
	6.1 Introduction	152
	6.2 Design of Atomizer	154
	6.3 Model Description	156
	6.3.1 Internal Hydrodynamics: Computational Fluid Dynamics	156
	6.3.2 Linear Stability Analysis	161
	6.3.3 Comparison with In-house Experiments	164
	6.3.4 Maximum Entropy Formulation	168
	6.4 Constraint Conditions	169
	6.5 Conclusions	173
	References	173
	7 Modeling of Flash Boiling Phenomenon in Internal and Near-Nozzle Flow of Fuel Injectors	176
	7.1 Introduction	177
	7.2 Model Formulation	179
	7.2.1 Nozzle Geometry and Computational Domain	180
	7.2.2 Governing Equations	182
	7.3 Results and Discussions	184
	7.3.1 Boundary and Operating Conditions	184
	7.3.2 Turbulence Models	184
	7.3.3 Blended Fuels	186
	7.4 Summary and Concluding Remarks	189
	References	189
	8 Novel Fuel Injection Systems for High-Speed Combustors	191
	Abstract	191
	8.1 Introduction	191
	8.2 Fuel Injector Needs and Challenges in High-Speed Combustors	192
	8.3 Fuel Injection System in High-Speed Combustors	194
	8.3.1 Transverse Fuel Injection System	194
	8.3.2 Parallel Injection Systems	195
	8.4 Conventional Standalone Atomizers	198
	8.4.1 Coaxial Atomizers	198
	8.4.2 Flash-Boiling Atomizer	200
	8.4.3 Effervescent Atomizer	203
	8.4.4 Working Principle	204
	8.4.5 Electrospray	206
	8.4.6 Ultrasonic Atomizer	208
	8.5 Hybrid Atomizers	209
	8.5.1 Why Hybrid Atomizer?	209
	8.5.2 Effervescent Cum Air-Assist Atomizer	210
	8.5.2.1 Design	211
	8.5.2.2 Experimental Conditions and Procedure	211
	8.5.2.3 Working Principle	213
	8.5.3 Size Distribution	215
	8.5.4 Influence of Design and Operational Parameters	216
	8.5.5 Combined Electrostatic and Pressure Jet Atomizer	216
	8.5.6 Flash-Boiling Cum Pressure Jet Atomizer	218
	8.5.7 Externally Forced Sprays	220
	8.6 Summary and Conclusions	221
	Acknowledgements	221
	References	221
	9 Experimental Investigation of Spray Characteristics of Kerosene, Ethanol, and Ethanol-Blended Kerosene Using a Gas Turbine Hybrid Atomizer	225
	Abstract	225
	9.1 Introduction	226
	9.2 Equipment and Method	231
	9.2.1 Atomizer	231
	9.2.2 Blend	234
	9.2.3 Experimental Setup and Image Capturing Technique	236
	9.3 Results and Discussion	237
	9.3.1 Breakup Phases	240
	9.3.2 Macroscopic Spray Characteristics	248
	9.4 Conclusions	251
	References	252
	10 Two-Phase Characterization for Turbulent Dispersion of Sprays: A Review of Optical Techniques	254
	10.1 Introduction	255
	10.2 Challenges for Two-Phase Measurements in Sprays	259
	10.2.1 Droplet Measurement Techniques	259
	10.2.2 Two-Phase Measurement Techniques	259
	10.3 Planar Techniques for Two-Phase Measurements in Sprays	261
	10.3.1 Dense Spray Measurements	263
	10.3.2 Dilute Spray Measurements	268
	10.4 Summary and Outlook	275
	References	276
	Turbulent Spray Combustion	281
	11 Turbulent Spray Combustion	282
	Abstract	282
	11.1 Introduction	283
	11.2 Turbulent Combustion Characteristics	287
	11.2.1 Optical Diagnostics and Analysis	287
	11.2.2 Reacting Spray: Fundamental and Characteristics	293
	11.2.3 Partially Premixed Combustion	302
	11.3 Numerical Approaches	305
	11.3.1 RANS and LES Modeling	307
	11.3.2 Direct Numerical Simulation (DNS)	310
	11.4 Further Discussion	311
	11.5 Summary	312
	11.6 Disclaimer and Funding Acknowledgement	312
	References	312
	12 Modelling of Variance and Co-variance in Turbulent Flame–Droplet Interaction: A Direct Numerical Simulation Analysis	318
	Abstract	318
	12.1 Introduction	323
	12.2 Mathematical Formulation of Flame–Droplet Interaction	325
	12.2.1 Fuel Mass Fraction Variance \widetilde{{{{\bf Y}}_{{{\bf F}}}^{{{\prime \prime }\thinspace 2}} }} Transport Equation	330
	12.2.2 Mixture Fraction Variance \widetilde{{{\varvec \xi}^{{{\prime \prime }\thinspace 2}} }} Transport Equation	330
	12.2.3 Co-variance \widetilde{{{\varvec Y}_{{\varvec F}}^{{{\varvec ''}}}{\varvec \xi}^{{\prime \prime }} }} Transport Equation	331
	12.3 Attributes of DNS Data and Numerical Implementation	332
	12.4 Result and Discussion	334
	12.4.1 Flame Behaviour	334
	12.4.2 Modelling of Fuel Mass Fraction Variance \widetilde{{{{\bf Y}}_{{{\bf F}}}^{{{\prime \prime }\thinspace 2}} }}	336
	12.4.2.1 Algebraic Modelling of Fuel Mass Fraction Variance \widetilde{{{{\bf Y}}_{{{\bf F}}}^{{{\prime \prime }\thinspace 2}} }}	336
	12.4.2.2 Modelled Transport Equation for \widetilde{{{{\bf Y}}_{{{\bf F}}}^{{{\prime \prime }\thinspace 2}} }}	340
	Statistical Behaviour of the Terms of \widetilde{{{\hbox{Y}}_{{\rm F}}^{{{\prime \prime }\thinspace 2}} }} Transport Equation	341
	Modelling of {\hbox{T}}_{{{{\rm Y}}1}}	342
	Modelling of {\hbox{T}}_{{{{\bf Y}}3}}	344
	Modelling of {\hbox{T}}_{{{{\bf Y}}4}}	346
	Modelling of {{D}}_{{{{\bf Y}}2}}	346
	12.4.3 Modelling of Mixture Fraction Variance \widetilde{{{{\varvec \upxi}}^{{{\prime \prime }\thinspace 2}} }}	349
	12.4.3.1 Modelled Transport Equation for \widetilde{{{{\varvec \upxi}}^{{{\prime \prime }\thinspace 2}} }}	349
	Statistical Behaviour of the Terms \widetilde{{{{\upxi}}^{{{\prime \prime }\thinspace 2}} }} Transport Equation	349
	Modelling of {\hbox{T}}_{{{{\varvec \upxi}}1}}	351
	Modelling of {\hbox{T}}_{{{{\varvec \upxi}}3}}	354
	Modelling of {\hbox{T}}_{{{{\varvec \upxi}}4}}	354
	Modelling of {\hbox{D}}_{{{{\varvec \upxi}}2}}	357
	12.4.4 Modelling of Co-variance of Fuel Mass Fraction and Mixture Fraction \widetilde{{{{\bf Y}}_{{{\bf F}}}^{{\prime \prime }} {{\varvec \upxi}}^{{\prime \prime }} }}	357
	12.4.4.1 Algebraic Modelling of Co-variance \widetilde{{{{\bf Y}}_{{{\bf F}}}^{{\prime \prime }} {{\varvec \upxi}}^{{\prime \prime }} }}	357
	12.4.4.2 Modelled Transport Equation for \widetilde{{{{\bf Y}}_{{{\bf F}}}^{{\prime \prime }} {{\varvec \upxi}}^{{\prime \prime }} }}	360
	Statistical Behaviour of the Terms of the \widetilde{{{\hbox{Y}}_{{{\rm F}}}^{{\prime \prime }} {{\varvec \upxi}}^{{\prime \prime }} }} Transport Equation	360
	Modelling of {\hbox{T}}_{{{{\bf Y\xi }}1}}	361
	Modelling of {\hbox{T}}_{{{{\rm Y}\xi }4}}	363
	Modelling of {\hbox{T}}_{{{{\rm Y}\xi }5}}	364
	Modelling of {\hbox{D}}_{{{{\rm Y}\xi }2}}	364
	12.5 Concluding Remarks	368
	Acknowledgements	369
	References	369
	Droplet and Spray Dynamics	372
	13 Dynamics of Droplet Break-Up	373
	13.1 Introduction and Background	373
	13.2 Different Aspects of Droplet Break-Up	375
	13.2.1 Free-Falling Droplets	375
	13.2.1.1 Different Break-Up Mechanisms	375
	13.2.1.2 Influence of External Flow Field	377
	13.2.2 Sessile Droplets	379
	13.2.2.1 Influence of Vibrating Surface	379
	13.2.2.2 Scaling Analysis	382
	13.2.3 Acoustically Levitated Droplets	387
	13.2.3.1 Influence of Acoustic Pressure	387
	13.2.3.2 Combined Effect of Acoustic Pressure and External Heating	389
	Pure Fluid Droplets	389
	Bicomponent Fuel Droplets	391
	Droplets with Lower Concentration of the Highly Volatile Component	392
	Droplets with Higher Concentration of the Highly Volatile Component	394
	Functionalized Droplets	396
	13.2.4 Droplet Impact on Liquid Pools	398
	13.3 Conclusions	402
	References	403
	14 Intermittency: A State that Precedes Thermoacoustic Instability	406
	14.1 Introduction	407
	14.2 Tools from Nonlinear Dynamics	412
	14.2.1 Phase Space Reconstruction	412
	14.2.2 Recurrence Plots and Quantification Analysis	414
	14.3 Experimental Set-up	416
	14.4 Results and Discussion	418
	14.4.1 Intermittency Route to Thermoacoustic Instability	418
	14.4.2 Qualitative and Quantitative Analysis of Intermittency Route	421
	14.4.3 Detection of Type of Intermittency	426
	14.5 Conclusion	430
	References	431