Small Scale Modeling and Simulation of Incompressible Turbulent Multi-Phase Flow (CISM International Centre for Mechanical Sciences, 607)

The book provides basic and recent research insights concerning the small scale modeling and simulation of turbulent multi-phase flows. By small scale, it has to be understood that the grid size for the simulation is smaller than most of the physical time and space scales of the problem. Small scale modeling of multi-phase flows is a very popular topic since the capabilities of massively parallel computers allows to go deeper into the comprehension and characterization of realistic flow configurations and at the same time, many environmental and industrial applications are concerned such as nuclear industry, material processing, chemical reactors, engine design, ocean dynamics, pollution and erosion in rivers or on beaches. The work proposes a complete and exhaustive presentation of models and numerical methods devoted to small scale simulation of incompressible turbulent multi-phase flows from specialists of the research community. Attention has also been paid to promote illustrations and applications, multi-phase flows and collaborations with industry. The idea is also to bring together developers and users of different numerical approaches and codes to share their experience in the development and validation of the algorithms and discuss the difficulties and limitations of the different methods and their pros and cons. The focus will be mainly on fixed-grid methods, however adaptive grids will be also partly broached, with the aim to compare and validate the different approaches and models. Acknowledgements Collaborators Technical Aspects Financial Support Contents 1 Introduction and Motivations 1.1 Governing Equations for DNS of Multiphase Flows 1.1.1 Mass Conservation 1.1.2 Momentum Conservation 1.1.3 Fluid Assumptions 1.2 Interface and Jump Conditions 1.2.1 Surface Tension 1.2.2 Viscosity 1.3 The Final Model 2 DNS of Resolved Scale Interfacial and Free Surface Flows with Fictitious Domains 2.1 One-Fluid Model 2.2 General Discretization and Solvers 2.2.1 Pressure-Velocity Coupling and Solvers 2.2.2 Jump Conditions 2.2.3 Boundary Conditions 2.2.4 Poisson Pressure Solver 2.3 Methods for Handling Interfaces 2.3.1 Interface Tracking Methods 2.3.2 Front-Capturing (Implicit Interface) 2.3.3 SPH Methods 2.4 Capillary Effects and Jump Conditions at Interface 2.4.1 Ghost Fluid 2.4.2 Continuum Surface Force 2.5 Validations of Interface Tracking and Fictitious Domains 2.5.1 Comparison of Interface Tracking Methods 2.5.2 Density and Viscosity Averages 2.5.3 Capillary Forces 3 Interface Tracking 3.1 VOF 3.1.1 Introduction to VOF Methods 3.1.2 Initialization of the Color Function C 3.1.3 A Library to Initialize the Volume Fraction Field 3.1.4 Algebraic Methods for the Advection of the Color Function 3.1.5 Simple Geometric Methods for the Advection of the Color Function 3.1.6 VOF-PLIC Methods: Interface Reconstruction 3.1.7 VOF-PLIC Methods: Interface Advection 3.2 Level Set 3.2.1 Level Set Definition 3.2.2 Numerical Method 3.2.3 Coupled Level-Set Volume of Fluid 3.2.4 Advection of the Level-Set Function and the Volume Fraction 3.3 Front Tracking 4 Adaptive Mesh Refinement 4.1 Introduction 4.2 AMR 4.3 Poisson Solver 4.4 Numerical Results 5 Numerical Treatment of Constraints with Fictitious Domains 5.1 Augmented Lagrangian Methods 5.2 Penalty Methods 5.3 Remarks on Time Splitting Approaches 5.4 Validation of Penalty Techniques 6 Compressible (Low-Mach) Two-Phase Flows 6.1 Mass Conservation 6.2 Momentum Conservation 6.3 Energy Conservation 6.4 Comparison with Classical ``Low Mach Number'' Model 6.5 Synthesis of Models 6.6 Validation of Isothermal Compressible One-Fluid Model 7 Large Eddy Simulation of Resolved Scale Interfacial Flows 7.1 Filtering 1-Fluid Navier-Stokes Equations—Continuous Media Framework 7.2 Filtering Discrete Mechanics Equations 7.3 Structural LES and Approximate Deconvolution Models (ADM) 7.4 LES of Multiphase Flows 8 DNS of Particulate Flows 8.1 Fictitious Domain and Penalty Approaches 8.1.1 Physical Characteristics of the Equivalent Fluid 8.1.2 Eulerian-Lagrangian VOF Method for Particle Tracking 8.1.3 Numerical Modeling of Particle Interaction 8.1.4 Parallel Implementation 8.1.5 Sum up of the Implemented Eulerian-Lagrangian Algorithm 8.2 Validations 8.2.1 Monodispersed Arrangements of Spheres 8.2.2 Bidisperse Arrangements of Spheres 8.2.3 Fluidized Beds 8.2.4 Interaction Between Particles and Turbulence 9 Multiscale Euler–Lagrange Coupling 9.1 Introduction 9.2 Governing Equations 9.3 Resolved Liquid Structures—Eulerian Modelling 9.3.1 Interface Tracking 9.3.2 Temporal Integration 9.3.3 Adaptive Mesh Refinement 9.4 Multi-scale Approach 9.4.1 Treatment of Medium Structures 9.4.2 Small Droplets 9.5 Results and Validation 9.5.1 Drop in a Uniform Flow 9.5.2 Drop-Free Surface Collision 9.5.3 Assisted Atomization of a Liquid Sheet 10 Applications and Perspectives Appendix Bibliography