Download or read book Small Scale Modeling and Simulation of Incompressible Turbulent Multi Phase Flow written by Stéphane Vincent and published by Springer Nature. This book was released on 2022-10-06 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Modeling and Simulation of Turbulent Multiphase Flows written by Zhaorui Li and published by . This book was released on 2008 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Multiphase Flow Analysis Using Population Balance Modeling written by Guan Heng Yeoh and published by Butterworth-Heinemann. This book was released on 2013-08-19 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by leading multiphase flow and CFD experts, this book enables engineers and researchers to understand the use of PBM and CFD frameworks. Population balance approaches can now be used in conjunction with CFD, effectively driving more efficient and effective multiphase flow processes. Engineers familiar with standard CFD software, including ANSYS-CFX and ANSYS–Fluent, will be able to use the tools and approaches presented in this book in the effective research, modeling and control of multiphase flow problems. Builds a complete understanding of the theory behind the application of population balance models and an appreciation of the scale-up of computational fluid dynamics (CFD) and population balance modeling (PBM) to a variety of engineering and industry applications in chemical, pharmaceutical, energy and petrochemical sectors The tools in this book provide the opportunity to incorporate more accurate models in the design of chemical and particulate based multiphase processes Enables readers to translate theory to practical use with CFD software

Download or read book New Approaches in Modeling Multiphase Flows and Dispersion in Turbulence Fractal Methods and Synthetic Turbulence written by F.C.G.A. Nicolleau and published by Springer Science & Business Media. This book was released on 2011-10-29 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a collection of the main contributions from the first five workshops held by Ercoftac Special Interest Group on Synthetic Turbulence Models (SIG42. It is intended as an illustration of the sig’s activities and of the latest developments in the field. This volume investigates the use of Kinematic Simulation (KS) and other synthetic turbulence models for the particular application to environmental flows. This volume offers the best syntheses on the research status in KS, which is widely used in various domains, including Lagrangian aspects in turbulence mixing/stirring, particle dispersion/clustering, and last but not least, aeroacoustics. Flow realizations with complete spatial, and sometime spatio-temporal, dependency, are generated via superposition of random modes (mostly spatial, and sometime spatial and temporal, Fourier modes), with prescribed constraints such as: strict incompressibility (divergence-free velocity field at each point), high Reynolds energy spectrum. Recent improvements consisted in incorporating linear dynamics, for instance in rotating and/or stably-stratified flows, with possible easy generalization to MHD flows, and perhaps to plasmas. KS for channel flows have also been validated. However, the absence of "sweeping effects" in present conventional KS versions is identified as a major drawback in very different applications: inertial particle clustering as well as in aeroacoustics. Nevertheless, this issue was addressed in some reference papers, and merits to be revisited in the light of new studies in progress.

Download or read book Introduction to Multiphase Flow written by George Yadigaroglu and published by Springer. This book was released on 2017-08-19 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the maiden volume in a new series devoted to lectures delivered through the annual seminars “Short Courses on Multiphase Flow,” held primarily at ETH Zurich continuously since 1984. The Zurich short courses, presented by prominent specialists in the various topics covered, have attracted a very large number of participants. This series presents fully updated and when necessary re-grouped lectures in a number of topical volumes. The collection aims at giving a condensed, critical and up-to-date view of basic knowledge on multiphase flows in relation to systems and phenomena encountered in industrial applications. The present volume covers the background of Multiphase Flows (MPF) that introduces the reader to the particular nature and complexity of multiphase flows and to basic but critical aspects of MPFs including concepts and the definition of the quantities of interest, an introduction to modelling strategies for MPFs, flow regimes, flow regime maps and tr ansition criteria. It also deals with the ubiquitous needs of the multiphase-flow modeller, namely pressure drop and phase distribution, i.e., the void fraction and the topology of the phases that determines the flow regimes.

Download or read book Theory and Modeling of Dispersed Multiphase Turbulent Reacting Flows written by Lixing Zhou and published by Butterworth-Heinemann. This book was released on 2018-01-25 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: Theory and Modeling of Dispersed Multiphase Turbulent Reacting Flows gives a systematic account of the fundamentals of multiphase flows, turbulent flows and combustion theory. It presents the latest advances of models and theories in the field of dispersed multiphase turbulent reacting flow, covering basic equations of multiphase turbulent reacting flows, modeling of turbulent flows, modeling of multiphase turbulent flows, modeling of turbulent combusting flows, and numerical methods for simulation of multiphase turbulent reacting flows, etc. The book is ideal for graduated students, researchers and engineers in many disciplines in power and mechanical engineering. Provides a combination of multiphase fluid dynamics, turbulence theory and combustion theory Covers physical phenomena, numerical modeling theory and methods, and their applications Presents applications in a wide range of engineering facilities, such as utility and industrial furnaces, gas-turbine and rocket engines, internal combustion engines, chemical reactors, and cyclone separators, etc.

Download or read book Subgrid scale Modeling and Wavelet Analysis for Preferential Concentration of Inertial Point Particles in Turbulent Flows written by Maxime Bassenne and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: A striking feature of particle-laden turbulent flows is the presence of particle clouds that result from the tendency of inertial particles to preferentially sample specific regions of the flow field. This phenomenon is central to a number of important physical processes. However, computational predictions of preferential concentration at high Reynolds numbers are challenging, since the numerical resolution of the participating scales is typically unaffordable. This dissertation contributes both to the analysis of the preferential concentration phenomenon and the development of subgrid-scale models for the prediction of preferential concentration in large-eddy simulations of particle-laden turbulence. First, direct numerical simulations of incompressible homogeneous-isotropic turbulence laden with a dilute suspension of inertial point particles are performed in conjunction with a wavelet multi-resolution analysis of the results. The use of spatially localized wavelet basis functions enables the simultaneous consideration of physical and scale spaces in the spectral characterization of the flow field of the carrier phase and the concentration field of the disperse phase. The multi-resolution analysis of the disperse phase provides statistical information about the spatial variability of a scale-dependent coarse-grained number density field and the local energy spectra of its fluctuations, characterizing the sensitivities of those quantities to variations in scale and Stokes number. In particular, the spatial variabilities of the wavelet energy spectrum of the particle concentration fluctuations are observed to be maximum in regimes where the particles preferentially concentrate. The results highlight the scale-dependent inhomogeneities of the structures in the concentration field generated by preferential concentration, and the existence of characteristic scales of interaction between the disperse and carrier phases. Additionally, an inter-phase multi-resolution analysis is performed that indicates the occurrence of a spatial anti-correlation between the enstrophy and kinetic-energy spectra of the carrier phase and the particle concentration at small scales in regimes where preferential concentration is important. This anti-correlation vanishes as the scale is increased, and is largely suppressed when the preferential-concentration effect is negligible. Secondly, a wavelet-based method for extraction of clusters of inertial particles in turbulent flows is presented that is based on decomposing Eulerian particle number-density fields into the sum of a coherent (organized) and an incoherent (disorganized) components. The coherent component is associated with the clusters and is extracted by filtering the wavelet-transformed particle number-density field based on an energy threshold. The analysis shows that in regimes where the preferential concentration is important, the coherent component representing the clusters can be described by just 1.6% of the total number of wavelet coefficients, thereby illustrating the sparsity of the particle number-density field. On the other hand, the incoherent portion is visually structureless and much less correlated that the coherent one. An application of the method is illustrated in the form of a grid-adaptation algorithm that results in non-uniform meshes with fine and coarse elements near and away from particle clusters, respectively. In regimes where preferential concentration in clusters is important, the grid adaptation leads to a reduction of the number of control volumes by one to two orders of magnitude. Thirdly, two dynamic models for turbulent velocity fluctuations are proposed for large-eddy simulations of dispersed multiphase flows. The first model is simple, involves no significant computational overhead, contains no adjustable parameters, and is flexible enough to be deployed in any type of flow solvers and grids, including unstructured setups. The approach is based on the use of elliptic differential filters to model the subgrid-scale velocity. The only model parameter, which is related to the nominal filter width, is determined dynamically by imposing consistency constraints on the estimated subgrid energetics. The second model constructs a velocity that contains scales smaller than the coarse-grid resolution, thereby enabling the prediction of small-scale phenomena such as the preferential concentration of particles in high-strain regions. The construction of the spectrally enriched velocity field in physical space is made dynamically, and is based on 1) modeling the smallest resolved eddies of sizes comparable to the grid size via approximate deconvolution, and 2) reconstructing the subgrid-scale fluctuations via non-linear generation of small-scale turbulence. The model does not contain tunable parameters, can be deployed in non-uniform grids, and is applicable to inhomogeneous flows subject to arbitrary boundary conditions. The performance of both models is tested in large-eddy simulations of homogeneous-isotropic turbulence laden with particles, where improved agreement with direct numerical simulation results is obtained for the statistics of preferential concentration. Lastly, application to wall-modeled large-eddy simulations of particle-laden channel flow is presented. Results of the application of existing wall models to particle-laden turbulent channel flows are described, and prospective pathways for improving their performance are suggested. The focus is on the prediction of the spatial distribution statistics of the disperse phase. It is observed that wall-modeled large-eddy simulations without particular treatment for the particles in the wall-adjacent cells overpredict the near-wall accumulation of particles. The choice of the continuous representation of the velocity field between the first grid point and the wall is shown to be of primary importance. A wall-modeling strategy is explored that performs well at large Stokes numbers. It relies on using interpolation kernels near the wall that mimic the law of the wall for the wall-parallel velocity, and direct numerical simulation profiles of the fluctuations for the wall-perpendicular velocity. Applications of the two developed subgrid-scale models are shown to improve the prediction of preferential concentration, but have no effect on the mean concentration profile.

Download or read book Simulation and Modeling of Turbulent Flows written by Thomas B. Gatski and published by Oxford University Press. This book was released on 1996-07-11 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides students and researchers in fluid engineering with an up-to-date overview of turbulent flow research in the areas of simulation and modeling. A key element of the book is the systematic, rational development of turbulence closure models and related aspects of modern turbulent flow theory and prediction. Starting with a review of the spectral dynamics of homogenous and inhomogeneous turbulent flows, succeeding chapters deal with numerical simulation techniques, renormalization group methods and turbulent closure modeling. Each chapter is authored by recognized leaders in their respective fields, and each provides a thorough and cohesive treatment of the subject.

Download or read book Modeling Approaches and Computational Methods for Particle laden Turbulent Flows written by Shankar Subramaniam and published by Academic Press. This book was released on 2022-10-20 with total page 588 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modelling Approaches and Computational Methods for Particle-laden Turbulent Flows introduces the principal phenomena observed in applications where turbulence in particle-laden flow is encountered while also analyzing the main methods for analyzing numerically. The book takes a practical approach, providing advice on how to select and apply the correct model or tool by drawing on the latest research. Sections provide scales of particle-laden turbulence and the principal analytical frameworks and computational approaches used to simulate particles in turbulent flow. Each chapter opens with a section on fundamental concepts and theory before describing the applications of the modelling approach or numerical method. Featuring explanations of key concepts, definitions, and fundamental physics and equations, as well as recent research advances and detailed simulation methods, this book is the ideal starting point for students new to this subject, as well as an essential reference for experienced researchers. Provides a comprehensive introduction to the phenomena of particle laden turbulent flow Explains a wide range of numerical methods, including Eulerian-Eulerian, Eulerian-Lagrange, and volume-filtered computation Describes a wide range of innovative applications of these models

Download or read book Turbulent Multiphase Flows with Heat and Mass Transfer written by Roland Borghi and published by John Wiley & Sons. This book was released on 2013-12-11 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerous industrial systems or natural environments involve multiphase flows with heat and mass transfer. The authors of this book present the physical modeling of these flows, in a unified way, which can include various physical aspects and several levels of complexity. Thermal engineering and nuclear reactors; the extraction and transport of petroleum products; diesel and rocket engines; chemical engineering reactors and fluidized beds; smoke or aerosol dispersion; landslides and avalanches − the modeling of multiphase flows with heat and mass transfer for all these situations can be developed following a common methodology. This book is devoted to the description of the mathematical bases of how to incorporate adequate physical ingredients in agreement with known experimental facts and how to make the model evolve according to the required complexity. Contents Part 1. Approach and General Equations 1. Towards a Unified Description of Multiphase Flows. 2. Instant Equations for a Piecewise Continuous Medium. 3. Description of a “Mean Multiphase Medium”. 4. Equations for the Mean Continuous Medium. Part 2. Modeling: A Single Approach Adaptable to Multiple Applications 5. The Modeling of Interphase Exchanges. 6. Modeling Turbulent Dispersion Fluxes. 7. Modeling the Mean Gas–Liquid Interface Area per Unit Volume. 8. “Large Eddy Simulation” Style Models. 9. Contribution of Thermodynamics of Irreversible Processes. 10. Experimental Methods. 11. Some Experimental Results Pertaining to Multiphase Flow Properties that Are Still Little Understood. Part 3. From Fluidized Beds to Granular Media 12. Fluidized Beds. 13. Generalizations for Granular Media. 14. Modeling of Cauchy Tensor of Sliding Contacts. 15. Modeling the Kinetic Cauchy Stress Tensor. Part 4. Studying Fluctuations and Probability Densities 16. Fluctuations of the Gas Phase in Reactive Two-Phase Media. 17. Temperature Fluctuations in Condensed Phases. 18. Study of the PDF for Velocity Fluctuations and Sizes of Parcels. About the Authors Roland Borghi is Professor Emeritus at Ecole Centrale Marseille in France and works as a consultant in the space, petrol and automobile sectors. His research activities cover fluid mechanics, combustion and flames, and multi-phase and granular flows. He was a member of the CNRS scientific committee and a laureate of the French Academy of Science. Fabien Anselmet is Professor at Ecole Centrale Marseille in France. His research activities focus on the turbulence of fluids and its varied applications in industry and in fields linked to the environment. With a unified, didactic style, this text presents tangible models of multiphase flows with heat and mass transfer with attention to various levels of complexities. It addresses thermal engineering and nuclear reactors, extraction and transport of petroleum products, diesel engines and rocket engines, chemical engineering reactors and fluidized beds, smoke or aerosol dispersion, and landslides and avalanches. Engineers, researchers, and scientists will appreciate the discussions of modeling principles, flows and granular media, and fluctuations around averages.

Download or read book Modeling and Simulation of Turbulent Flows written by Roland Schiestel and published by John Wiley & Sons. This book was released on 2010-01-05 with total page 751 pages. Available in PDF, EPUB and Kindle. Book excerpt: This title provides the fundamental bases for developing turbulence models on rational grounds. The main different methods of approach are considered, ranging from statistical modelling at various degrees of complexity to numerical simulations of turbulence. Each of these various methods has its own specific performances and limitations, which appear to be complementary rather than competitive. After a discussion of the basic concepts, mathematical tools and methods for closure, the book considers second order closure models. Emphasis is placed upon this approach because it embodies potentials for clarifying numerous problems in turbulent shear flows. Simpler, generally older models are then presented as simplified versions of the more general second order models. The influence of extra physical parameters is also considered. Finally, the book concludes by examining large Eddy numerical simulations methods. Given the book’s comprehensive coverage, those involved in the theoretical or practical study of turbulence problems in fluids will find this a useful and informative read.

Download or read book Turbulent Flows written by G. Biswas and published by CRC Press. This book was released on 2002 with total page 478 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book allows readers to tackle the challenges of turbulent flow problems with confidence. It covers the fundamentals of turbulence, various modeling approaches, and experimental studies. The fundamentals section includes isotropic turbulence and anistropic turbulence, turbulent flow dynamics, free shear layers, turbulent boundary layers and plumes. The modeling section focuses on topics such as eddy viscosity models, standard K-E Models, Direct Numerical Stimulation, Large Eddy Simulation, and their applications. The measurement of turbulent fluctuations experiments in isothermal and stratified turbulent flows are explored in the experimental methods section. Special topics include modeling of near wall turbulent flows, compressible turbulent flows, and more.

Download or read book Multiphase reacting flows modelling and simulation written by Daniele L. Marchisio and published by Springer Science & Business Media. This book was released on 2007-10-16 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Multiscale and Multiresolution Approaches in Turbulence written by Pierre Sagaut and published by Imperial College Press. This book was released on 2006 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique book gives a general unified presentation of the use of the multiscale/multiresolution approaches in the field of turbulence. The coverage ranges from statistical models developed for engineering purposes to multiresolution algorithms for the direct computation of turbulence. It provides the only available up-to-date reviews dealing with the latest and most advanced turbulence models (including LES, VLES, hybrid RANS/LES, DES) and numerical strategies. The book aims at providing the reader with a comprehensive description of modern strategies for turbulent flow simulation, ranging from turbulence modeling to the most advanced multilevel numerical methods. Sample Chapter(s). Chapter 1: A Brief Introduction to Turbulence (4,125 KB). Contents: A Brief Introduction to Turbulence; Turbulence Simulation and Scale Separation; Statistical Multiscale Modeling; Multiscale Subgrid Models: Self-Adaptivity; Structural Multiscale Subgrid Models: Small Scale Estimations; Unsteady Turbulence Simulation on Self-Adaptive Grids; Global Hybrid RANS/LES Methods; Zonal RANS/LES Methods. Readership: Researchers and engineers in academia and industry in aerospace, automotive and other aerodynamics-oriented fields; masters-level students in fluid mechanics, computational fluid dynamics and applied mathematics.

Download or read book Turbulence and Interactions written by Michel Deville and published by Springer Nature. This book was released on 2021-02-16 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a snapshot of the state-of-art in the field of turbulence modeling, with an emphasis on numerical methods. Topics include direct numerical simulations, large eddy simulations, compressible turbulence, coherent structures, two-phase flow simulation and many more. It includes both theoretical contributions and experimental works, as well as chapters derived from keynote lectures, presented at the fifth Turbulence and Interactions Conference (TI 2018), which was held on June 25-29 in Martinique, France. This multifaceted collection, which reflects the conference ́s emphasis on the interplay of theory, experiments and computing in the process of understanding and predicting the physics of complex flows and solving related engineering problems, offers a timely guide for students, researchers and professionals in the field of applied computational fluid dynamics, turbulence modeling and related areas.

Download or read book Engineering Turbulence Modelling and Experiments 6 written by Wolfgang Rodi and published by Elsevier. This book was released on 2005-05-05 with total page 1011 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the world renowned ERCOFTAC (International Symposium on Engineering Turbulence Modelling and Measurements). The proceedings include papers dealing with the following areas of turbulence: · Eddy-viscosity and second-order RANS models · Direct and large-eddy simulations and deductions for conventional modelling · Measurement and visualization techniques, experimental studies · Turbulence control · Transition and effects of curvature, rotation and buoyancy on turbulence · Aero-acoustics · Heat and mass transfer and chemically reacting flows · Compressible flows, shock phenomena · Two-phase flows · Applications in aerospace engineering, turbomachinery and reciprocating engines, industrial aerodynamics and wind engineering, and selected chemical engineering problems Turbulence remains one of the key issues in tackling engineering flow problems. These problems are solved more and more by CFD analysis, the reliability of which depends strongly on the performance of the turbulence models employed. Successful simulation of turbulence requires the understanding of the complex physical phenomena involved and suitable models for describing the turbulent momentum, heat and mass transfer. For the understanding of turbulence phenomena, experiments are indispensable, but they are equally important for providing data for the development and testing of turbulence models and hence for CFD software validation. As in other fields of Science, in the rapidly developing discipline of turbulence, swift progress can be achieved only by keeping up to date with recent advances all over the world and by exchanging ideas with colleagues active in related fields.

Download or read book Multiphase Flow Dynamics 3 written by Nikolay Ivanov Kolev and published by Springer Science & Business Media. This book was released on 2007-06-08 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: In order to allow the application of the theory from all the three volumes also to processes in combustion engines a systematic set of internally consistent state equations for diesel fuel gas and liquid valid in broad range of changing pressure and temperature are provided also in Volume 3. Erlangen, October 2006 Nikolay Ivanov Kolev Table of contents 1 Some basics of the single-phase boundary layer theory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1. 1 Flow over plates, velocity profiles, share forces, heat transfer. . . . . . . . . . . . . . . . . . . . 1 1. 1. 1 Laminar flow over the one site of a plane. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1. 1. 2 Turbulent flow parallel to plane. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1. 2 Steady state flow in pipes with circular cross sections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1. 2. 1 Hydraulic smooth wall surface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1. 2. 2 Transition region. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1. 2. 3 Complete rough region. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1. 2. 4 Heat transfer to fluid in a pipe. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1. 3 Transient flow in pipes with circular cross sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Nomenclature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2 Introduction to turbulence of multi-phase flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2. 1 Basic ideas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2. 2 Isotropy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 2. 3 Scales, eddy viscosity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 2. 3. 1 Small scale turbulent motion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 2. 3. 2 Large scale turbulent motion, Kolmogorov-Pandtl expression. . . . . . . . . 42 2. 4 k-eps framework. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 Nomenclature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 3 Sources for fine resolution outside the boundary layer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 3. 1 Bulk sources. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 3. 1. 1 Deformation of the velocity field. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 3. 1. 2 Blowing and suction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .