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Henryk Anglart Thermal- Hydraulics in Nuclear Systems Henryk Anglart Thermal-Hydraulics in Nuclear Systems 2010 Henryk Anglart All rights reserved i his textbook is intended to be an introduction to selected thermal-hydraulic topics for students of energy engineering and applied sciences as well as for professionals working in the nuclear engineering field. The basic aspects of T thermal-hydraulics in nuclear systems are presented with a goal to demonstrate how to solve practical problems. This ‘hands-on’ approach is supported with numerous examples and exercises provided throughout the book. In addition, the book is accompanied with computational software, I C O N K E Y implemented in the Scilab ( www.scilab.org ) environment. The software is available for download at Note Corner www.reactor.sci.kth.se/downloads and is shortly described Examples in Appendices C and D. Computer Program More Reading The textbook is organized into five chapters and each of them is divided into several sections. Parts in the book of special interest are designed with icons, as indicated in the table to the left. The “Note Corner” icon indicates a section with additional relevant information, not directly related to the topics covered by the book, but which could be of interest to the reader. All examples are marked with a pen icon. Special icons are also used to mark sections with computer programs and with suggested more reading. The first chapter is concerned with various introductory topics in nuclear reactor thermal-hydraulics. The second chapter deals with the rudiments of thermodynamics, at the level which is necessary to understand the material presented in Chapter 3 (fluid mechanics) and Chapter 4 (heat transfer). The last chapter contains analyses of several applications of practical concern such as stationary and transient flows in channels and vessels with particular attention to prediction of reaction forces. It also contains more detailed analysis of selected nuclear power plant components. The table below shows the workload in a classroom envisaged in the course “Thermal- Hydraulics in Nuclear Energy Systems” given at the Royal Institute of Technology. In total, the course covers 24 hours of lectures and 24 hours of exercises performed with a teacher assistance in a classroom. In addition, students should spend about 110 hours studying at home and performing home assignments. Nr Topic Lecture and exercise hours 1 Introduction to thermodynamics 1a Laws of thermodynamics 1 h lect. + 1 h exerc. 1b Thermodynamic processes 1 h lect. + 1 h exerc. 2 Introduction to fluid mechanics 2a Governing equations for single phase flows 1 h lect. + 1 h exerc. 2b Single-phase flows in channels; friction losses; 2 h lect. + 2 h exerc. local losses 2c Governing equations and models for two-phase 2 h lect. + 2 h exerc. 3 flows 2d Void fraction prediction 1 h lect. + 1 h exerc. 2e Pressure drops; friction, local losses, gravity, 2 h lect. + 2 h exerc. acceleration 3 Heat transfer 3a Heat conduction 1 h lect. + 1 h exerc. 3b Single-phase convection 2 h lect. + 2 h exerc. 3c Radiative heat transfer 1 h lect. + 1 h exerc. 3d Boiling heat transfer; pool boiling, convective 2 h lect. + 2 h exerc. boiling 3e Critical Heat Flux (CHF) and post-CHF heat 2 h lect. + 2 h exerc. transfer 4 Selected applications 4a Compressible flows 1 h lect. + 1 h exerc. 4b Single- and two-phase critical flows 1 h lect. + 1 h exerc. 4c Fluid structure interactions; reaction forces; 1 h lect. + 1 h exerc. transients in elastic channels; flow induced vibrations 4d Thermal-hydraulic analysis of selected plant 3 h lect. + 3 h exerc. components Total 24 h lect. + 24 h exerc. 4 CONTENTS 1. INTRODUCTION ............................................................................ 9 1.1 Thermal-Hydraulic Processes in Nuclear Reactors .....................................................10 1.2 Power Generation in Nuclear Reactors ........................................................................12 2. THERMODYNAMICS ....................................................................17 2.1 Laws of Thermodynamics ..............................................................................................18 2.1.1 Zero-th Law of Thermodynamics ..............................................................................18 2.1.2 First Law of Thermodynamics ...................................................................................19 2.1.3 Second Law of Thermodynamics ...............................................................................22 2.1.4 Maximum Work and Exergy ......................................................................................23 2.2 Thermodynamic Processes ............................................................................................24 2.2.1 Ideal Gas ....................................................................................................................24 2.2.2 van der Waals Equation .............................................................................................28 2.2.3 Gas Mixtures ..............................................................................................................29 2.2.4 Gas Processes .............................................................................................................30 2.2.5 Carnot Cycle ..............................................................................................................34 2.2.6 Rankine Cycle ............................................................................................................35 2.2.7 Brayton Cycle ............................................................................................................36 2.2.8 Phase Change .............................................................................................................37 3. FLUID MECHANICS .....................................................................39 3.1 Mathematical Tools ........................................................................................................39 3.1.1 Coordinate System .....................................................................................................39 3.1.2 Scalars, Vectors and Tensors .....................................................................................41 3.1.3 Differential Operators ................................................................................................43 3.1.4 Substantial Time Derivative .......................................................................................44 3.1.5 Integral Theorems ......................................................................................................44 3.2 Field Equations for Single-Phase Flows .......................................................................46 3.2.1 Mass Conservation .....................................................................................................46 3.2.2 Momentum Conservation ...........................................................................................47 3.2.3 Energy Conservation ..................................................................................................50 3.2.4 Constitutive Equations ...............................................................................................53 3.2.5 Conservation Equations for Ideal Fluids ....................................................................54 3.2.6 Conservation Equations for Ideal Gas ........................................................................55 3.2.7 Turbulence in Incompressible Flows .........................................................................55 3.3 Field Equations for Multi-Phase Flows ........................................................................59 3.3.1 Local Instantaneous Conservation Equations.............................................................59 3.3.2 Time-Averaged Conservation Equations ...................................................................61 3.4 Single-Phase Flows in Channels ....................................................................................69 3.4.1 Mass Conservation Equation......................................................................................70 3.4.2 Momentum Conservation Equation ...........................................................................71 3.4.3 Energy Conservation Equation ..................................................................................76 3.4.4 Wall Shear Stress in Laminar Flows ..........................................................................82 3.4.5 Wall Shear Stress in Turbulent Flows ........................................................................84 3.4.6 Local Pressure Losses ................................................................................................85 5 3.4.7 Total Pressure Drop ................................................................................................... 88 3.5 Multi-phase Flows in Channels .................................................................................... 88 3.5.1 Area-Averaged Conservation Equations ................................................................... 88 3.5.2 Void Fraction and Quality in Multiphase Flows ....................................................... 97 3.5.3 Homogeneous Equilibrium Model ............................................................................ 99 3.5.4 Drift Flux Model ..................................................................................................... 100 3.5.5 Pressure
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