Droplet Interactions and Spray Processes

Description

This book provides a selection of contributions to the DIPSI workshop 2019 (Droplet Impact Phenomena & Spray Investigations) as well as recent progress of the Int. Research Training Group “DROPIT”.The DIPSI workshop, which is now at its thirteenth edition, represents an important opportunity to share recent knowledge on droplets and sprays in a variety of research fields and industrial applications. The research training group “DROPIT” is focused on droplet interaction technologies where microscopic effects influence strongly macroscopic behavior. This requires the inclusion of interface kinetics and/or a detailed analysis of surface microstructures. Normally, complicated technical processes cover the underlying basic mechanisms, and therefore, progress in the overall process modelling can hardly be gained. Therefore, DROPIT focuses on the underlying basic processes. This is done by investigating different spatial and/or temporal scales of the problems and by linking them through a multi-scale approach. In addition, multi-physics are required to understand e.g. problems for droplet-wall interactions, where porous structures are involved. 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