In its fifth extended edition the successful monograph package “Multiphase Flow Dynamics” contains theory, methods and practical experience for describing complex transient multi-phase processes in arbitrary geometrical configurations, providing a systematic presentation of the theory and practice of numerical multi-phase fluid dynamics. In the present first volume the local volume and time averaging is used to derive a complete set of conservation equations for three fluids each of them having multi components as constituents. Large parts of the book are devoted on the design of successful numerical methods for solving the obtained system of partial differential equations. Finally the analysis is repeated for boundary fitted curvilinear coordinate systems designing methods applicable for interconnected multi-blocks. This fifth edition includes various updates, extensions, improvements and corrections, as well as a completely new chapter containing the basic physics describing the multi-phase flow in turbines, compressors, pumps and other rotating hydraulic machines.

This 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. Therefore the book presents a complete coverage of the modern Nuclear Thermal Hydrodynamics. This present third edition includes various updates, extensions, improvements and corrections.

In its fifth extended edition the successful monograph package "Multiphase Flow Dynamics" contains theory, methods and practical experience for describing complex transient multi-phase processes in arbitrary geometrical configurations, providing a systematic presentation of the theory and practice of numerical multi-phase fluid dynamics. In the present first volume the local volume and time averaging is used to derive a complete set of conservation equations for three fluids each of them having multi components as constituents. Large parts of the book are devoted on the design of successful numerical methods for solving the obtained system of partial differential equations. Finally the analysis is repeated for boundary fitted curvilinear coordinate systems designing methods applicable for interconnected multi-blocks. This fifth edition includes various updates, extensions, improvements and corrections, as well as a completely new chapter containing the basic physics describing the multi-phase flow in turbines, compressors, pumps and other rotating hydraulic machines.

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.

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 fourth extended edition the successful monograph package "Multiphase Flow Daynmics" contains theory, methods and practical experience for describing complex transient multi-phase processes in arbitrary geometrical configurations, providing a systematic presentation of the theory and practice of numerical multi-phase fluid dynamics. In the present second volume the methods for describing the mechanical interactions in multiphase dynamics are provided. This fourth edition includes various updates, extensions, improvements and corrections. "The literature in the field of multiphase flows is numerous. Therefore, it is very important to have a comprehensive and systematic overview including useful numerical methods. The volumes have the character of a handbook and accomplish this function excellently. The models are described in detail and a great number of comprehensive examples and some cases useful for testing numerical solutions are included. These two volumes are very useful for scientists and practicing engineers in the fields of technical thermodynamics, chemical engineering, fluid mechanics, and for mathematicians with interest in technical problems. Besides, they can give a good overview of the dynamically developing, complex field of knowledge to students. This monograph is highly recommended," BERND PLATZER, ZAAM In the present second volume the methods for describing the mechanical interactions in multiphase dynamics are provided. This fourth edition includes various updates, extensions, improvements and corrections. "The literature in the field of multiphase flows is numerous. Therefore, it is very important to have a comprehensive and systematic overview including useful numerical methods. The volumes have the character of a handbook and accomplish this function excellently. The models are described in detail and a great number of comprehensive examples and some cases useful for testing numerical solutions are included. These two volumes are very useful for scientists and practicing engineers in the fields of technical thermodynamics, chemical engineering, fluid mechanics, and for mathematicians with interest in technical problems. Besides, they can give a good overview of the dynamically developing, complex field of knowledge to students. This monograph is highly recommended," BERND PLATZER, ZAAM "The literature in the field of multiphase flows is numerous. Therefore, it is very important to have a comprehensive and systematic overview including useful numerical methods. The volumes have the character of a handbook and accomplish this function excellently. The models are described in detail and a great number of comprehensive examples and some cases useful for testing numerical solutions are included. These two volumes are very useful for scientists and practicing engineers in the fields of technical thermodynamics, chemical engineering, fluid mechanics, and for mathematicians with interest in technical problems. Besides, they can give a good overview of the dynamically developing, complex field of knowledge to students. This monograph is highly recommended," BERND PLATZER, ZAAM

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.

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.

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

This 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. Therefore the book presents a complete coverage of the modern Nuclear Thermal Hydrodynamics. This present third edition includes various updates, extensions, improvements and corrections.

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 fourth extended edition the successful monograph package Multiphase Flow Daynmics contains theory, methods and practical experience for describing complex transient multi-phase processes in arbitrary geometrical configurations, providing a systematic presentation of the theory and practice of numerical multi-phase fluid dynamics.

In the present third volume methods for describing of the thermal interactions in multiphase dynamics are provided. In addition a large number of valuable experiments is collected and predicted using the methods introduced in this monograph. In this way the accuracy of the methods is revealed to the reader.

This fourth edition includes various updates, extensions, improvements and corrections.

"The literature in the field of multiphase flows is numerous. Therefore, it is very important to have a comprehensive and systematic overview including useful numerical methods. The volumes have the character of a handbook and accomplish this function excellently. The models are described in detail and a great number of comprehensive examples and some cases useful for testing numerical solutions are included. These two volumes are very useful for scientists and practicing engineers in the fields of technical thermodynamics, chemical engineering, fluid mechanics, and for mathematicians with interest in technical problems. Besides, they can give a good overview of the dynamically developing, complex field of knowledge to students. This monograph is highly recommended,

BERND PLATZER, ZAAM

In the present third volume methods for describing of the thermal interactions in multiphase dynamics are provided. In addition a large number of valuable experiments is collected and predicted using the methods introduced in this monograph. In this way the accuracy of the methods is revealed to the reader.

This fourth edition includes various updates, extensions, improvements and corrections.

"The literature in the field of multiphase flows is numerous. Therefore, it is very important to have a comprehensive and systematic overview including useful numerical methods. The volumes have the character of a handbook and accomplish this function excellently. The models are described in detail and a great number of comprehensive examples and some cases useful for testing numerical solutions are included. These two volumes are very useful for scientists and practicing engineers in the fields of technical thermodynamics, chemical engineering, fluid mechanics, and for mathematicians with interest in technical problems. Besides, they can give a good overview of the dynamically developing, complex field of knowledge to students. This monograph is highly recommended,

BERND PLATZER, ZAAM

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 fourth extended edition the successful monograph package Multiphase Flow Daynmics contains theory, methods and practical experience for describing complex transient multi-phase processes in arbitrary geometrical configurations, providing a systematic presentation of the theory and practice of numerical multi-phase fluid dynamics.

In the present second volume the methods for describing the mechanical interactions in multiphase dynamics are provided. This fourth edition includes various updates, extensions, improvements and corrections.

"The literature in the field of multiphase flows is numerous. Therefore, it is very important to have a comprehensive and systematic overview including useful numerical methods. The volumes have the character of a handbook and accomplish this function excellently. The models are described in detail and a great number of comprehensive examples and some cases useful for testing numerical solutions are included. These two volumes are very useful for scientists and practicing engineers in the fields of technical thermodynamics, chemical engineering, fluid mechanics, and for mathematicians with interest in technical problems. Besides, they can give a good overview of the dynamically developing, complex field of knowledge to students. This monograph is highly recommended,

BERND PLATZER, ZAAM

In the present second volume the methods for describing the mechanical interactions in multiphase dynamics are provided. This fourth edition includes various updates, extensions, improvements and corrections.

"The literature in the field of multiphase flows is numerous. Therefore, it is very important to have a comprehensive and systematic overview including useful numerical methods. The volumes have the character of a handbook and accomplish this function excellently. The models are described in detail and a great number of comprehensive examples and some cases useful for testing numerical solutions are included. These two volumes are very useful for scientists and practicing engineers in the fields of technical thermodynamics, chemical engineering, fluid mechanics, and for mathematicians with interest in technical problems. Besides, they can give a good overview of the dynamically developing, complex field of knowledge to students. This monograph is highly recommended,

BERND PLATZER, ZAAM

"The literature in the field of multiphase flows is numerous. Therefore, it is very important to have a comprehensive and systematic overview including useful numerical methods. The volumes have the character of a handbook and accomplish this function excellently. The models are described in detail and a great number of comprehensive examples and some cases useful for testing numerical solutions are included. These two volumes are very useful for scientists and practicing engineers in the fields of technical thermodynamics, chemical engineering, fluid mechanics, and for mathematicians with interest in technical problems. Besides, they can give a good overview of the dynamically developing, complex field of knowledge to students. This monograph is highly recommended,

BERND PLATZER, ZAAM