Marchisio / Fox Multiphase reacting flows: modelling and simulation

1. Auflage 2007
ISBN: 978-3-211-72464-4
Verlag: Springer Vienna
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 492, 269 Seiten

Reihe: CISM International Centre for Mechanical Sciences

This book describes the most widely applicable modeling approaches. Chapters are organized in six groups covering from fundamentals to relevant applications. The book covers particle-based methods and also discusses Eulerian-Eulerian and Eulerian-Lagrangian techniques based on finite-volume schemes. Moreover, the possibility of modeling the poly-dispersity of the secondary phases in Eulerian-Eulerian schemes by solving the population balance equation is discussed.

Autoren/Hrsg.

Marchisio, Daniele L.

Fox, Rodney O.

Inhaltsverzeichnis

1;PREFACE;5
2;CONTENTS;7
3;Introduction and Fundamentals of Modeling Approaches for Poly disperse Multiphase Flows;9
3.1;1 Introduction;9
3.1.1;1.1 Number density functions;9
3.1.2;1.2 Transport in phase space;13
3.1.3;1.3 Moment equations;15
3.1.4;1.4 Physical-space transport;17
3.2;2 Generalized Population Balance Equation;20
3.2.1;2.1 Granular systems;20
3.2.2;2.2 Fluid-particle systems;23
3.2.3;2.3 Derivation of the GPBE;25
3.2.4;2.4 Moment transport equations;28
3.3;3 An Example Application: The Spray Equation;34
3.3.1;3.1 Williams spray equation;34
3.3.2;3.2 Moment transport equation;35
3.3.3;3.3 Moment closures for the spray equation;38
3.4;4 Summary and Conclusions;46
3.5;Bibliography;47
4;Quadrature Method of Moments for Poly-Disperse Flows;49
4.1;1 Generalized Population Balance Equation;49
4.2;2 The Quadrature Method of Moments (QMOM);52
4.2.1;2.1 QMOM for mono-variate spatially homogeneous and single-phase problems;53
4.2.2;2.2 Extension to spatiaUy heterogeneous problems;59
4.2.3;2.3 Extension to multi-phase problems;62
4.3;3 The Direct Quadrature Method of Moments (DQMOM);64
4.3.1;3.1 DQMOM for mono-variate spatially homogeneous and single-phase problems;65
4.3.2;3.2 Extension to spatially heterogeneous problems;67
4.3.3;3.3 DQMOM for bi-variate homogeneous problems;68
4.3.4;3.4 Extension to spatially heterogeneous problems;72
4.3.5;3.5 Extension to multi-phase problems;73
4.4;4 Application to Solid-Liquid Turbulent Systems;75
5;Eulerian Multi-Fluid Models for Polydisperse Evaporating Sprays;86
5.1;1 Introduction;86
5.2;2 The Starting Point: A semi-kinetic model conditioned by size;90
5.2.1;2.1 Modeling fundamentals in a simplified framework;90
5.2.2;2.2 Extension to turbulent flows;95
5.3;3 Mathematical Issues - Singularities;98
5.3.1;3.1 Laminar case - pressure-less gas dynamics;98
5.3.2;3.2 Turbulent case - shock wave formation;102
5.3.3;3.3 Conclusion;103
5.4;4 Multi- Fluid Model and Related Numerical Methods;105
5.4.1;4.1 Discretization in the size phase space;105
5.4.2;4.2 Treatment of transport in physical space;107
5.4.3;4.3 Evaporation and drag;108
5.4.4;4.4 Time integration using splitting methods;109
5.5;5 Numerical Validation;109
5.5.1;5.1 Counterflow spray diffusion flames;109
5.5.2;5.2 Coalescence for dense sprays in a conical nozzle;110
5.5.3;5.3 Taylor-Green configuration;115
5.5.4;5.4 Spatially decaying turbulence;120
5.6;6 Conclusions and Future Directions;125
6;Multi-fluid CFD Analysis of Chemical Reactors;131
6.1;1 Introduction;131
6.1.1;1.1 Basic considerations;131
6.1.2;1.2 Objective and contents of Chapter;132
6.2;2 Basics of the Multi- fluid Approach;133
6.2.1;2.1 Introduction;133
6.2.2;2.2 Local instantaneous formulation;133
6.2.3;2.3 Averaging techniques;137
6.2.4;2.4 Averaged balance equations;139
6.3;3 Closure Framework;144
6.3.1;3.1 General;144
6.3.2;3.2 Bubble liquid;145
6.4;4 Closure Framework for Particle (Solids) Gas Flows;153
6.4.1;4.1 Kinetic theory of granular flow (KTGF) for mono-sized particles;153
6.4.2;4.2 Summary of Governing Equations for Fluid/Multi-sized particle flows;160
6.5;5 Additional Sub Models;165
6.5.1;5.1 Bubble size models;165
6.5.2;5.2 Interfacial heat transfer;166
6.5.3;5.3 Mass transfer in bubble liquid flows;167
6.5.4;5.4 Chemical reaction;168
6.6;6 Numerical Solution Procedure;171
6.6.1;6.1 General;171
6.6.2;6.3 Momentum equations;173
6.6.3;6.4 Equation for the pressure;175
6.7;7 Applications;177
6.7.1;7.1 Bubble columns;177
6.7.2;7.2 Stirred tanks;178
6.7.3;7.3 Circulating fluidized beds;179
6.8;8 Summary;181
7;The Lattice-Boltzmann Method for Multiphase Fluid Flow Simulations and Euler-Lagrange Large-Eddy Simulations;186
7.1;1 Cellular Automata;186
7.2;2 Lattice Gas Automatoil;187
7.3;3 Lattice-Boltzmann Method;188
7.4;4 From Lattice-Boltzmann to Navier-Stokes;188
7.5;5 Some Practical Aspects of the Lattice-Boltzmann Method for Single- Phase Flows;193
7.5.1;5.1 Implementation of the lattice-Boltzmann method in computer code;193
7.5.1.1;5.2 Setting boundary conditions;196
7.5.1.2;5.3 Alternative collision operators;197
7.6;6 Direct Numerical Simulations of Solid-Liquid Suspensions;198
7.6.1;6.1 Some results for solid-liquid fluidization;201
7.6.2;6.2 DNS of turbulently agitated solid-liquid suspensions;203
7.7;7 Single Phase Turbulence;205
7.8;8 Numerical Simulation of Fluid Flow;207
7.8.1;8.1 Direct numerical simulation (DNS);208
7.8.2;8.2 Large-eddy simulation (LES);209
7.8.3;8.3 Subgrid-scale modeling in LES;210
7.8.4;8.4 Examples of single-phase LES by means of the lattice-Boltzmann method;214
7.9;9 Point Particles in LES;219
7.10;10 Passive Scalar Transport;225
7.11;11 Filtered Density Functions for Reactive Flows;228
8;Direct Numerical Simulation of Sprays: Turbulent Dispersion, Evaporation and Combustion;234
8.1;1 Introduction;234
8.2;2 Direct Numerical Simulation;236
8.2.1;2.1 Compressible formulation;237
8.2.2;2.2 Low Mach number approximation;238
8.3;3 Dispersed-Phase Lagrangian Description;239
8.3.1;3.1 Position and velocity;239
8.3.2;3.2 Heating and evaporation;240
8.4;4 Eulerian/Lagrangian Coupling;241
8.5;5 Reaction Rates;243
8.5.1;5.1 Definitions;245
8.5.2;5.2 Arrheniuslaw;246
8.5.3;5.3 GKAS procedure;247
8.6;6 Dispersion and Evaporation;251
8.6.1;6.1 Configuration;251
8.6.2;6.2 Preferential segregation of non-evaporating droplets;254
8.6.3;6.3 Evaporation;257
8.7;7 Laminar Spray Combustion;258
8.7.1;7.1 Local equivalence ratio;259
8.7.2;7.2 Laminar spray combustion;261
8.8;8 Spray Combustion Diagrams;263
8.9;9 Acknowledgments;271
8.10;Bibliography;271

Leseproben

Eulerian Multi-Fluid Models for Polydisperse Evaporating Sprays (p. 78-79)

Marc Massot

Laboratoire EM2C - CNRS UPR 288, Ecole Centrale Paris, France

Abstract In this contribution we propose a presentation of Eulerian multi-fluid models for polydisperse evaporating sprays. The purpose of such a model is to obtain a Eulerian-type description with three main criteria: to take into account accurately the polydispersity of the spray as well as size-conditioned dynamics and evaporation, to keep a rigorous link with the Williams spray equation at the kinetic, also called mesoscopic, level of description, where elementary phenomena such as coalescence can be described properly, to have an extension to take into account non-resolved but modeled fluctuating quantities in turbulent flows. We aim at presenting the fundamentals of the model, the associated precise set of related assumptions as well as its implication on the mathematical structure of solutions, robust numerical methods able to cope with the potential presence of singularities and finally a set of validations showing the efficiency and the limits of the model.

1 Introduction

In many industrial combustion applications such as Diesel engines, fuel is stocked in condensed form and burned as a disperse liquid phase carried by a gaseous flow. Tw^o-phase effects as well as the polydisperse character of the droplet size distribution (since the droplet dynamics depend on their inertia and are conditioned by size) can significantly influence flame structure. Size distribution effects are also encountered in a crucial way in solid propellant rocket boosters, where the cloud of alumina particles experiences coalescence and become polydisperse in size, thus determining their global dynamical behavior (Hylkema, 1999, Hylkema and Villedieu, 1998). The coupling of dynamics, conditioned on particle size, with coalescence or aggregation as well as with evaporation can also be found in the study of fluidized beds (Tsuji et al., 1998) and planet formation in solar nebulae (Bracco et al., 1999, Chavanis, 2000). Consequently, it is important to have reliable models and numerical methods in order to be able to describe precisely the physics of two-phase flows where the disperse phase is constituted of a cloud of particles of various sizes that can evaporate, coalesce or aggregate, break-up and also have their own inertia and size-conditioned dynamics. Since our main area of interest is combustion, we will work with sprays throughout this paper, keeping in mind the broad application fields related to this study.

By spray, we denote a disperse liquid phase constituted of droplets carried by a gaseous phase. Even with this seemingly precise definition, two approaches corresponding to two levels of description can be distinguished. The first, associated with a full direct numerical simulation (DNS) of the process, provides a model for the dynamics of the interface between the gas and liquid, as well as the exchanges of heat and mass between the two phases using various techniques such as the Volume of Fluids (VOF) or Level Set methods (see, for example, Aulisa et al, 2003, Herrmann, 2005, Josserand et al., 2005, Tanguy and Berlemont, 2005). This "microscopic" point of view is very rich in information on the detailed properties at the single-droplet level concerning, for example, the resulting drag exerted on a droplet depending on its surroundings flow or the details of one event of droplet break-up following the geometry of the interface between the phases. The second approach, based on a more global point of view (thus called "mesoscopic") describes the droplets as a cloud of point particles for which the exchanges of mass, momentum and heat are described using a statistical point of view, with eventual correlations, and the details of the interface behavior, angular momentum of droplets, detailed internal temperature distribution inside the droplet, etc., are not predicted. Instead, a finite set of global properties such as size of spherical droplets, velocity of the center of mass, and temperature are modeled. Because it is the only one for which numerical simulations at the scale of a combustion chamber or in a free jet can be conducted, this "mesoscopic" point of view will be adopted in the present work.