Droplet Interactions and Spray Processes

Foreword by the University Rectors (Università degli Studi di Bergamo and Universität Stuttgart-A Strategic Partnership)
Preface
Contents
Droplet–Gas Interaction
An Analytical Approach to Model the Effect of Evaporation on Oscillation Amplitude of Liquid Drops in Gaseous Environment
	1 Introduction
	2 The Mathematical Model
		2.1 Bulk Kinetic Energy Approach
		2.2 Surface Kinetic Energy Approach
	3 Model Implementation
		3.1 The Conditions for Oscillation Damping
	4 Results and Discussion
	5 Conclusions
	Appendix
	References
Improvement of the Level-Set Ghost-Fluid Method for the Compressible Euler Equations
	1 Introduction
	2 Governing Equations
	3 Numerics
		3.1 The DGSEM Framework with Finite Volume Sub-cells
		3.2 The Solution of the Hamilton-Jacobi Equations and the Derivatives of the Level-Set Field
		3.3 The Level-Set Ghost-Fluid Method (LSGFM)
	4 Results
		4.1 Parasitic Currents Around a Stationary Droplet
		4.2 Merging Droplets Without Surface Tension
		4.3 Shock-Droplet Interaction at Ma = 2.40
	5 Conclusion and Outlook
	References
A Solver for Stiff Finite-Rate Relaxation in Baer–Nunziato Two-Phase Flow Models
	1 Introduction
	2 Model Equations
	3 Description of the Numerical Method
		3.1 Timestepping
		3.2 Iterative Computation of the Timestep Solution
		3.3 Analytical Solution of the Linearised Problem
	4 Test Problems
	5 Conclusions
	References
An Investigation of Different Splitting Techniques for the Isentropic Euler Equations
	1 Introduction
	2 A Generalized Splitting
	3 Numerical Method
		3.1 Discretization
		3.2 Calculation of the RS-IMEX Reference Solution
		3.3 Discretization of HJL and DeTa Splitting
	4 Numerical Results
		4.1 Testcase 1: HOT-Vortex
		4.2 Testcase 2: Taylor-Green-Vortex
	5 Conclusion and Outlook
	References
Enabling Simulations of Droplets  with the Direct Simulation Monte Carlo Method
	1 Introduction
	2 Liquid Surface
	3 Spheres Inside the DSMC Domain
		3.1 Extension of the Tracking Routines
		3.2 Intersection with Spheres After Boundary Interactions
		3.3 Influence of Collisions on Macroscopic Spheres
	4 Simulations
		4.1 Droplet Evaporation
		4.2 Brownian Motion
	5 Conclusion and Outlook
	References
Droplet–Wall Interaction
Fabrication and Evaluation Methods  of Micro-structured Surfaces for Droplet Impact Experiments
	1 Introduction
	2 Surface Reproduction and Experimental Methods
		2.1 Reproduction of Micro-structured Surface Samples
		2.2 Mold Insert Fabrication
		2.3 Evaluation Methods for Investigating Micro-structured Surfaces
		2.4 Experimental Test Facility for Investigating Dynamic Droplet Impacts
	3 Results and Discussion
		3.1 Surface Evaluation
		3.2 Droplet Impact on Micro-structured Surfaces
		3.3 Film Thickness Measurement of Droplet Lamella
	4 Conclusion
	References
Use of X-ray Micro Computed Tomography for the Investigation  of Drying and Salt Precipitation  in a Regular Glass Bead Structure
	1 Introduction
	2 Materials and Methods
		2.1 Tomography Equipment
		2.2 Materials
		2.3 Sample Production and Filling
		2.4 Scanning Parameters
		2.5 Reconstruction
		2.6 Segmentation
	3 Results and Discussion
		3.1 Preliminary Experiments
		3.2 Evaporation Experiments
		3.3 Pore Size Distribution
		3.4 Distribution of the Fluid Clusters
		3.5 Salt Precipitation
	4 Conclusions
	References
Image Processing of Two-Phase Data for Drop-Surface Interaction Obtained by X-Ray Microtomography
	1 Introduction
	2 Analysis and Quantification
		2.1 Segmentation
		2.2 Resolution
	3 Surface Triangulations and Curvature Estimation
	4 Conclusions
	References
A Phase Field Approach to Compressible Droplet Impingement
	1 Introduction
	2 Phase Field Models
		2.1 A Compressible Navier–Stokes–Allen–Cahn System
		2.2 Boundary Conditions
		2.3 Energy Inequality
		2.4 Surface Tension
	3 Numerical Experiments
		3.1 Choice of Parameters
		3.2 Merging Droplets
		3.3 Contact Angle
		3.4 Droplet Impingement
	4 Summary and Conclusions
	References
Numerical Simulation for Drop Impact on Textured Surfaces
	1 Introduction
	2 Numerical Methods
		2.1 FS3D\'s Advection Scheme
		2.2 Solution of the Discretized Poisson Problem
	3 Treatment of Embedded Boundaries
		3.1 The Simplified Approach
		3.2 The New Approach
	4 Results
	5 Conclusions
	References
Upscaling of Coupled Free-Flow  and Porous-Medium-Flow Processes
	1 Introduction
	2 Model and Coupling Concept
		2.1 Free Flow
		2.2 Flow in Porous Media
		2.3 Interfacial Drops
		2.4 Coupling Concept
		2.5 Numerical Model
	3 Results and Discussion
	4 Conclusions
	References
A Locally-Refined Locally-Conservative Quadtree Finite-Volume Staggered-Grid Scheme
	1 Introduction
	2 Methods
		2.1 Governing Equations
		2.2 Discretization Concept
	3 Numerical Test
	4 Conclusion
	References
Droplet–Liquid Interaction
A New Perspective for the Characterization of Crown Rim Kinematics
	1 Introduction to Rim Kinematics
		1.1 Impact Process and Morphological Features
		1.2 Experimental Set-Up and Methodology
	2 Classical Geometrical Parameters of Crown Rim and Associated Problems
		2.1 Radial and Axial Expansions of Crown Rim
		2.2 Crown Aspect Ratio Dependent on Impact Parameters
	3 Relevance of the Crown Rim Displacement from the Impact Point
		3.1 Length Scale of Crown Rim Expansion
		3.2 Quadratic Distancing from the Impact Point
	4 Conclusion
	References
Analytical Model for Crown Spreading During Drop Impact onto Wetted Walls: Effect of Liquids Viscosity on Momentum Transfer
	1 Introduction
	2 Modelling Approach
		2.1 Description of the Film Thickness Decay Rate
		2.2 Momentum Loss Estimation
		2.3 Implementation in Crown Base Evolution Model
	3 Results and Discussion
		3.1 How Momentum Transfer is Affected by Fluids Viscosity and Initial Film Thickness
		3.2 Effectiveness of SPF-Based Modelling Approach
	4 Conclusion
	References
An Implicit High-Order Discontinuous Galerkin Approach for Variable Density Incompressible Flows
	1 Introduction
	2 Variable Density Incompressible Flow Model
	3 The Discontinuous Galerkin Discretization
		3.1 Numerical Fluxes
		3.2 Working Variables
		3.3 Spurious Oscillations Control
		3.4 Time Integration
	4 Numerical Results
		4.1 Dry Bed Inviscid Dambreak Problem
		4.2 Dry Bed Inviscid Double-Dambreak Problem
	5 Conclusions
	References
Visualization Techniques for Droplet Interfaces and Multiphase Flow
	1 Introduction
	2 Interface Deformation
		2.1 Method
		2.2 Results
	3 Machine Learning for Droplet Behavior Prediction
		3.1 Method
		3.2 Results
	4 Droplet-Local Flow
		4.1 Method
		4.2 Results
	5 Conclusion
	References
On the Measurement of Velocity Field Within Wall-Film During Droplet Impact on It Using High-Speed Micro-PIV
	1 Introduction
	2 Materials and Methods
	3 Results and Discussion
	4 Conclusions
	References
Single-Camera 3D PTV Methods for Evaporation-Driven Liquid Flows in Sessile Droplets
	1 Introduction
	2 Materials and Methods
		2.1 Experimental Setup
		2.2 Single-Camera 3D PTV Methods
	3 Results and Discussion
		3.1 Ultrapure Water
		3.2 Mineral Water
		3.3 Salty Solution
		3.4 Surfactants
	4 Conclusions
	References
Towards Sprays
Drop Shape Oscillations
	1 Introduction
	2 The Physics of Drop Shape Oscillations
		2.1 Linear Oscillations
		2.2 Nonlinear Oscillations
		2.3 Shape Oscillations of Non-Newtonian Liquid Drops
	3 Measuring Techniques Building on Drop Shape Oscillations
	4 Summary and Conclusions
	References
Classical and Novel Approaches  to Modelling Droplet Heating  and Evaporation
	1 Introduction
	2 Classical Approaches
	3 The Tonini and Cossali Model
	4 Modelling of the Liquid Phase
	5 Recent Developments
	References
The Influence of Curvature  on the Modelling of Droplet Evaporation at Different Scales
	1 Introduction
	2 Drop Evaporation Models at Different Scales
		2.1 Effect of Surface Curvature at the Macroscopic Scale
		2.2 Effect of Surface Curvature at the Microscopic Scale
	3 Conclusions
	References
On the Importance of Kinetic Effects  in the Modelling of Droplet Evaporation  at High Pressure and Temperature Conditions
	1 Introduction
	2 Review of Kinetic Boundary Conditions for Engineering Applications
	3 Results
	4 Conclusion
	References
Direct Numerical Simulations  of Evaporating Droplets at Higher Temperatures: Application  of a Consistent Numerical Approach
	1 Introduction
	2 Mathematical Formulation
		2.1 Interface Capturing and Material Properties
		2.2 Conservation Equations
		2.3 Jump Conditions
	3 Numerical Approach
		3.1 Advection of Liquid and Gaseous Phase
		3.2 Phase Change Loop
	4 Results
		4.1 Single Isooctane Droplets
		4.2 Water Droplet Tandem
	5 Conclusion
	References
Effects of Very High Injection Pressures on GDI Spray Structure
	1 Introduction
	2 Materials and Methods
	3 Results and Discussion
	4 Conclusions
	References