Multiphase Flow Dynamics 4

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Multiphase Flow Dynamics 5

Author : Nikolay Ivanov Kolev
Publisher : Springer Science & Business Media
ISBN 13 : 3642206018
Total Pages : 839 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Multiphase Flow Dynamics 5 by : Nikolay Ivanov Kolev

Download or read book Multiphase Flow Dynamics 5 written by Nikolay Ivanov Kolev and published by Springer Science & Business Media. This book was released on 2011-10-18 with total page 839 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present Volume 5 of the successful book package "Multiphase Flow Dynamics" is devoted to nuclear thermal hydraulics which is a substantial part of nuclear reactor safety. It provides knowledge and mathematical tools for adequate description of the process of transferring the fission heat released in materials due to nuclear reactions into its environment. It step by step introduces into the heat release inside the fuel, temperature fields in the fuels, the "simple" boiling flow in a pipe described using ideas of different complexity like equilibrium, non equilibrium, homogeneity, non homogeneity. Then the "simple" three-fluid boiling flow in a pipe is described by gradually involving the mechanisms like entrainment and deposition, dynamic fragmentation, collisions, coalescence, turbulence. All heat transfer mechanisms are introduced gradually discussing their uncertainty. Different techniques are introduced like boundary layer treatments or integral methods. Comparisons with experimental data at each step demonstrate the success of the different ideas and models. After an introduction of the design of the reactor pressure vessels for pressurized and boiling water reactors the accuracy of the modern methods is demonstrated using large number of experimental data sets for steady and transient flows in heated bundles. Starting with single pipe boiling going through boiling in the rod bundles the analysis of complete vessel including the reactor is finally demonstrated. Then a powerful method for nonlinear stability analysis of flow boiling and condensation is introduced. Models are presented and their accuracies are investigated for describing critical multiphase flow at different level of complexity. Basics of designing of steam generators, moisture separators and emergency condensers are presented. Methods for analyzing a complex pipe network flows with components like pumps, valves etc. are also presented. Methods for analysis of important aspects of the severe accidents like melt-water interactions, external cooling and cooling of layers of molten nuclear reactor material are presented. Valuable sets of thermo-physical and transport properties for severe accident analysis are presented for the following materials: uranium dioxide, zirconium dioxide, stainless steel, zirconium, aluminum, aluminum oxide, silicon dioxide, iron oxide, molybdenum, boron oxide, reactor corium, sodium, lead, bismuth, and lead-bismuth eutectic alloy. The emphasis is on the complete and consistent thermo dynamical sets of analytical approximations appropriate for computational analysis. Therefore the book presents a complete coverage of the modern Nuclear Thermal Hydrodynamics. This present second edition includes various updates, extensions, improvements and corrections. This present second edition includes various updates, extensions, improvements and corrections.

Fundamentals of Multiphase Flow

Author : Christopher E. Brennen
Publisher : Cambridge University Press
ISBN 13 : 9780521848046
Total Pages : 376 pages
Book Rating : 4.8/5 (48 download)

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Book Synopsis Fundamentals of Multiphase Flow by : Christopher E. Brennen

Download or read book Fundamentals of Multiphase Flow written by Christopher E. Brennen and published by Cambridge University Press. This book was released on 2005-04-18 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: Publisher Description

Computational Techniques for Multiphase Flows

Author : Guan Heng Yeoh
Publisher : Elsevier
ISBN 13 : 0080914896
Total Pages : 658 pages
Book Rating : 4.0/5 (89 download)

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Book Synopsis Computational Techniques for Multiphase Flows by : Guan Heng Yeoh

Download or read book Computational Techniques for Multiphase Flows written by Guan Heng Yeoh and published by Elsevier. This book was released on 2009-10-07 with total page 658 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mixed or multiphase flows of solid/liquid or solid/gas are commonly found in many industrial fields, and their behavior is complex and difficult to predict in many cases. The use of computational fluid dynamics (CFD) has emerged as a powerful tool for the understanding of fluid mechanics in multiphase reactors, which are widely used in the chemical, petroleum, mining, food, beverage and pharmaceutical industries. Computational Techniques for Multiphase Flows enables scientists and engineers to the undertand the basis and application of CFD in muliphase flow, explains how to use the technique, when to use it and how to interpret the results and apply them to improving aplications in process enginering and other multiphase application areas including the pumping, automotive and energy sectors. - Understandable guide to a complex subject - Important in many industries - Ideal for potential users of CFD

Dynamics of Multiphase Flows

Author : Chao Zhu
Publisher : Cambridge University Press
ISBN 13 : 1108473741
Total Pages : 621 pages
Book Rating : 4.1/5 (84 download)

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Book Synopsis Dynamics of Multiphase Flows by : Chao Zhu

Download or read book Dynamics of Multiphase Flows written by Chao Zhu and published by Cambridge University Press. This book was released on 2021-06-17 with total page 621 pages. Available in PDF, EPUB and Kindle. Book excerpt: Address physical principles and unified theories governing multiphase flows, with methods, applications, and problems.

Multiphase Flow Dynamics 4

Author : Nikolay Ivanov Kolev
Publisher : Springer Science & Business Media
ISBN 13 : 3540929185
Total Pages : 761 pages
Book Rating : 4.5/5 (49 download)

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Book Synopsis Multiphase Flow Dynamics 4 by : Nikolay Ivanov Kolev

Download or read book Multiphase Flow Dynamics 4 written by Nikolay Ivanov Kolev and published by Springer Science & Business Media. This book was released on 2009-06-12 with total page 761 pages. Available in PDF, EPUB and Kindle. Book excerpt: The nuclear thermal hydraulic is the science providing knowledge about the physical processes occurring during the transferring the fission heat released in structural materials due to nuclear reactions into its environment. Along its way to the environment the thermal energy is organized to provide useful mechanical work or useful heat or both. Chapter 1 contains introductory information about the heat release in the re- tor core, the thermal power and thermal power density in the fuel, structures and moderator, the influence of the thermal power density on the coolant temperature, the spatial distribution of the thermal power density. Finally some measures are introduced for equalizing of the spatial distribution of the thermal power density. Chapter 2 gives the methods for describing of the steady and of the transient temperature fields in the fuel elements. Some information is provided regarding influence of the cladding oxidation, hydrogen diffusion and of the corrosion pr- uct deposition on the temperature fields. Didactically the nuclear thermal hydraulic needs introductions at different level of complexity by introducing step by step the new features after the previous are clearly presented. The followed two Chapters serve this purpose. Chapter 3 describes mathematically the “simple” steady boiling flow in a pipe. The steady mass-, momentum- and energy conservation equations are solved at different level of complexity by removing one after the other simplifying assu- tions. First the idea of mechanical and thermodynamic equilibrium is introduced.

Multiphase Flow Dynamics 4

Author : Nikolay Ivanov Kolev
Publisher : Springer Science & Business Media
ISBN 13 : 3642207499
Total Pages : 337 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Multiphase Flow Dynamics 4 by : Nikolay Ivanov Kolev

Download or read book Multiphase Flow Dynamics 4 written by Nikolay Ivanov Kolev and published by Springer Science & Business Media. This book was released on 2011-09-24 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present Volume 4 of the successful monograh package “Multiphase Flow Dynamics”is devoted to selected Chapters of the multiphase fluid dynamics that are important for practical applications but did not find place in the previous volumes. The state of the art of the turbulence modeling in multiphase flows is presented. As introduction, some basics of the single phase boundary layer theory including some important scales and flow oscillation characteristics in pipes and rod bundles are presented. Then the scales characterizing the dispersed flow systems are presented. The description of the turbulence is provided at different level of complexity: simple algebraic models for eddy viscosity, simple algebraic models based on the Boussinesq hypothesis, modification of the boundary layer share due to modification of the bulk turbulence, modification of the boundary layer share due to nucleate boiling. The role of the following forces on the mathematical description of turbulent flows is discussed: the lift force, the lubrication force in the wall boundary layer, and the dispersion force. A pragmatic generalization of the k-eps models for continuous velocity field is proposed containing flows in large volumes and flows in porous structures. A Methods of how to derive source and sinks terms for multiphase k-eps models is presented. A set of 13 single- and two phase benchmarks for verification of k-eps models in system computer codes are provided and reproduced with the IVA computer code as an example of the application of the theory. This methodology is intended to help other engineers and scientists to introduce this technology step-by-step in their own engineering practice. In many practical application gases are solved in liquids under given conditions, released under other conditions and therefore affecting technical processes for good of for bad. Useful information on the solubility of oxygen, nitrogen, hydrogen and carbon dioxide in water under large interval of pressures and temperatures is collected, and appropriate mathematical approximation functions are provided. In addition methods for the computation of the diffusion coefficients are described. With this information solution and dissolution dynamics in multiphase fluid flows can be analyzed. For this purpose the non-equilibrium absorption and release on bubble, droplet and film surfaces under different conditions is mathematically described. A systematic set of internally consistent state equations for diesel fuel gas and liquid valid in broad range of changing pressure and temperature is provided. This new second edition includes various updates, extensions, improvements and corrections. In many practical application gases are solved in liquids under given conditions, released under other conditions and therefore affecting technical processes for good of for bad. Useful information on the solubility of oxygen, nitrogen, hydrogen and carbon dioxide in water under large interval of pressures and temperatures is collected, and appropriate mathematical approximation functions are provided. In addition methods for the computation of the diffusion coefficients are described. With this information solution and dissolution dynamics in multiphase fluid flows can be analyzed. For this purpose the non-equilibrium absorption and release on bubble, droplet and film surfaces under different conditions is mathematically described. A systematic set of internally consistent state equations for diesel fuel gas and liquid valid in broad range of changing pressure and temperature is provided. This new second edition includes various updates, extensions, improvements and corrections.

Computational Methods for Multiphase Flow

Author : Andrea Prosperetti
Publisher : Cambridge University Press
ISBN 13 : 1139459902
Total Pages : 392 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Computational Methods for Multiphase Flow by : Andrea Prosperetti

Download or read book Computational Methods for Multiphase Flow written by Andrea Prosperetti and published by Cambridge University Press. This book was released on 2009-06-25 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: Thanks to high-speed computers and advanced algorithms, the important field of modelling multiphase flows is an area of rapid growth. This one-stop account – now in paperback, with corrections from the first printing – is the ideal way to get to grips with this topic, which has significant applications in industry and nature. Each chapter is written by an acknowledged expert and includes extensive references to current research. All of the chapters are essentially independent and so the book can be used for a range of advanced courses and the self-study of specific topics. No other book covers so many topics related to multiphase flow, and it will therefore be warmly welcomed by researchers and graduate students of the subject across engineering, physics, and applied mathematics.

Multiphase Flow Analysis Using Population Balance Modeling

Author : Guan Heng Yeoh
Publisher : Butterworth-Heinemann
ISBN 13 : 0080982336
Total Pages : 385 pages
Book Rating : 4.0/5 (89 download)

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Book Synopsis Multiphase Flow Analysis Using Population Balance Modeling by : Guan Heng Yeoh

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

Direct Numerical Simulations of Gas–Liquid Multiphase Flows

Author : Grétar Tryggvason
Publisher : Cambridge University Press
ISBN 13 : 1139496700
Total Pages : 337 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Direct Numerical Simulations of Gas–Liquid Multiphase Flows by : Grétar Tryggvason

Download or read book Direct Numerical Simulations of Gas–Liquid Multiphase Flows written by Grétar Tryggvason and published by Cambridge University Press. This book was released on 2011-03-10 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: Accurately predicting the behaviour of multiphase flows is a problem of immense industrial and scientific interest. Modern computers can now study the dynamics in great detail and these simulations yield unprecedented insight. This book provides a comprehensive introduction to direct numerical simulations of multiphase flows for researchers and graduate students. After a brief overview of the context and history the authors review the governing equations. A particular emphasis is placed on the 'one-fluid' formulation where a single set of equations is used to describe the entire flow field and interface terms are included as singularity distributions. Several applications are discussed, showing how direct numerical simulations have helped researchers advance both our understanding and our ability to make predictions. The final chapter gives an overview of recent studies of flows with relatively complex physics, such as mass transfer and chemical reactions, solidification and boiling, and includes extensive references to current work.

Computational Methods for Multiphase Flows in Porous Media

Author : Zhangxin Chen
Publisher : SIAM
ISBN 13 : 0898716063
Total Pages : 551 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Computational Methods for Multiphase Flows in Porous Media by : Zhangxin Chen

Download or read book Computational Methods for Multiphase Flows in Porous Media written by Zhangxin Chen and published by SIAM. This book was released on 2006-04-01 with total page 551 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a fundamental and practical introduction to the use of computational methods. A thorough discussion of practical aspects of the subject is presented in a consistent manner, and the level of treatment is rigorous without being unnecessarily abstract. Each chapter ends with bibliographic information and exercises.

Thermo-fluid Dynamics of Two-Phase Flow

Author : Mamoru Ishii
Publisher : Springer Science & Business Media
ISBN 13 : 0387291873
Total Pages : 462 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Thermo-fluid Dynamics of Two-Phase Flow by : Mamoru Ishii

Download or read book Thermo-fluid Dynamics of Two-Phase Flow written by Mamoru Ishii and published by Springer Science & Business Media. This book was released on 2006-09-28 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book has been written for graduate students, scientists and engineers who need in-depth theoretical foundations to solve two-phase problems in various technological systems. Based on extensive research experiences focused on the fundamental physics of two-phase flow, the authors present the detailed theoretical foundation of multi-phase flow thermo-fluid dynamics as they apply to a variety of scenarios, including nuclear reactor transient and accident analysis, energy systems, power generation systems and even space propulsion.

Multiphase Flow Dynamics 2

Author : Nikolay Ivanov Kolev
Publisher : Springer Science & Business Media
ISBN 13 : 9783540221074
Total Pages : 730 pages
Book Rating : 4.2/5 (21 download)

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Book Synopsis Multiphase Flow Dynamics 2 by : Nikolay Ivanov Kolev

Download or read book Multiphase Flow Dynamics 2 written by Nikolay Ivanov Kolev and published by Springer Science & Business Media. This book was released on 2005 with total page 730 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multi-phase flows are part of our natural environment such as tornadoes, typhoons, air and water pollution and volcanic activities as well as part of industrial technology such as power plants, combustion engines, propulsion systems, or chemical and biological industry. The industrial use of multi-phase systems requires analytical and numerical strategies for predicting their behavior. In its third extended edition this book contains theory, methods and practical experience for describing complex transient multi-phase processes in arbitrary geometrical configurations. This book provides a systematic presentation of the theory and practice of numerical multi-phase fluid dynamics. In the present second volume the mechanical and thermal interactions in multiphase dynamics are provided. This third edition includes various updates, extensions, improvements and corrections.

Multiphase Flow

Author : Peter Vorobieff
Publisher : WIT Press
ISBN 13 : 1784663115
Total Pages : 467 pages
Book Rating : 4.7/5 (846 download)

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Book Synopsis Multiphase Flow by : Peter Vorobieff

Download or read book Multiphase Flow written by Peter Vorobieff and published by WIT Press. This book was released on 2018-04-18 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: The selected papers contained in this book present the latest research in one of the most challenging, yet most universally applicable areas of technology. Multiphase flows are found in all areas of technology and the range of related problems of interest is vast, including many areas of science and engineering. Recently multiphase fluid dynamics have generated a great deal of attention, leading to many notable advances in experimental, analytical and numerical studies. It is perhaps, however, work on numerical solutions which is the most noticeable owing to the continuing improvements in computer software tools. Progress in numerical methods has permitted the solution of many practical problems, helping to improve our understanding of the physics involved. The presented papers illustrate the close interaction between numerical modellers and researchers working to gradually resolve the many outstanding issues in our understanding of multiphase flow.

Transport Phenomena in Multiphase Flows

Author : Roberto Mauri
Publisher : Springer
ISBN 13 : 3319157930
Total Pages : 458 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Transport Phenomena in Multiphase Flows by : Roberto Mauri

Download or read book Transport Phenomena in Multiphase Flows written by Roberto Mauri and published by Springer. This book was released on 2015-04-08 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides a thorough presentation of the phenomena related to the transport of mass, momentum and energy. It lays all the basic physical principles, then for the more advanced readers, it offers an in-depth treatment with advanced mathematical derivations and ends with some useful applications of the models and equations in specific settings. The important idea behind the book is to unify all types of transport phenomena, describing them within a common framework in terms of cause and effect, respectively represented by the driving force and the flux of the transported quantity. The approach and presentation are original in that the book starts with a general description of transport processes, providing the macroscopic balance relations of fluid dynamics and heat and mass transfer, before diving into the mathematical realm of continuum mechanics to derive the microscopic governing equations at the microscopic level. The book is a modular teaching tool and can be used either for an introductory or for an advanced graduate course. The last 6 chapters will be of interest to more advanced researchers who might be interested in particular applications in physics, mechanical engineering or biomedical engineering. All chapters are complemented with exercises that are essential to complete the learning process.

Multiphase Flow Handbook, Second Edition

Author : Efstathios Michaelides
Publisher : CRC Press
ISBN 13 : 1315354624
Total Pages : 1559 pages
Book Rating : 4.3/5 (153 download)

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Book Synopsis Multiphase Flow Handbook, Second Edition by : Efstathios Michaelides

Download or read book Multiphase Flow Handbook, Second Edition written by Efstathios Michaelides and published by CRC Press. This book was released on 2016-10-26 with total page 1559 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Multiphase Flow Handbook, Second Edition is a thoroughly updated and reorganized revision of the late Clayton Crowe’s work, and provides a detailed look at the basic concepts and the wide range of applications in this important area of thermal/fluids engineering. Revised by the new editors, Efstathios E. (Stathis) Michaelides and John D. Schwarzkopf, the new Second Edition begins with two chapters covering fundamental concepts and methods that pertain to all the types and applications of multiphase flow. The remaining chapters cover the applications and engineering systems that are relevant to all the types of multiphase flow and heat transfer. The twenty-one chapters and several sections of the book include the basic science as well as the contemporary engineering and technological applications of multiphase flow in a comprehensive way that is easy to follow and be understood. The editors created a common set of nomenclature that is used throughout the book, allowing readers to easily compare fundamental theory with currently developing concepts and applications. With contributed chapters from sixty-two leading experts around the world, the Multiphase Flow Handbook, Second Edition is an essential reference for all researchers, academics and engineers working with complex thermal and fluid systems.

Multiphase Fluid Flow in Porous and Fractured Reservoirs

Author : Yu-Shu Wu
Publisher : Gulf Professional Publishing
ISBN 13 : 0128039116
Total Pages : 420 pages
Book Rating : 4.1/5 (28 download)

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Book Synopsis Multiphase Fluid Flow in Porous and Fractured Reservoirs by : Yu-Shu Wu

Download or read book Multiphase Fluid Flow in Porous and Fractured Reservoirs written by Yu-Shu Wu and published by Gulf Professional Publishing. This book was released on 2015-09-23 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multiphase Fluid Flow in Porous and Fractured Reservoirs discusses the process of modeling fluid flow in petroleum and natural gas reservoirs, a practice that has become increasingly complex thanks to multiple fractures in horizontal drilling and the discovery of more unconventional reservoirs and resources. The book updates the reservoir engineer of today with the latest developments in reservoir simulation by combining a powerhouse of theory, analytical, and numerical methods to create stronger verification and validation modeling methods, ultimately improving recovery in stagnant and complex reservoirs. Going beyond the standard topics in past literature, coverage includes well treatment, Non-Newtonian fluids and rheological models, multiphase fluid coupled with geomechanics in reservoirs, and modeling applications for unconventional petroleum resources. The book equips today's reservoir engineer and modeler with the most relevant tools and knowledge to establish and solidify stronger oil and gas recovery. - Delivers updates on recent developments in reservoir simulation such as modeling approaches for multiphase flow simulation of fractured media and unconventional reservoirs - Explains analytical solutions and approaches as well as applications to modeling verification for today's reservoir problems, such as evaluating saturation and pressure profiles and recovery factors or displacement efficiency - Utilize practical codes and programs featured from online companion website

Multiphase Flow Dynamics 3

Author : Nikolay Ivanov Kolev
Publisher : Springer Science & Business Media
ISBN 13 : 354071443X
Total Pages : 314 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Multiphase Flow Dynamics 3 by : Nikolay Ivanov Kolev

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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .