Single and Two-Phase Flow Thermal Hydraulics

Summary of the Course onSingle and Two-Phase Flow Thermal Hydraulicsheld at University of Pisa from June 19 to 30, 2006Teacher: Prof. Walter AmbrosiniExercises by Dr. Nicola ForgioneOrganisation of LecturesThe Course has been subdivided into 8 Teaching Units which are presented with the aid of shortnotes in Word Format given to the students before the lectures and projected during teaching.In addition, five units (from E1 to E5) were used for worked out exercises, applications anddemonstrations. The number of pages of documentation and the content for each lecture unit isreported hereafter.Unit 1 – Fluids and Balance Equations (31 pages)• Basic Concepts about Fluids• Fluid Models and Flow Regimes (single-phase)• Balance Equations for Single-Phase Fluidso General Conceptso Useful Mathematical Relationshipso Level of Detail in Balance Equationso Integral Lumped Parameter Equationso Partial Differential Balance Equationso Need for Closure LawsUnit 2 – Laminar Flow, Navier-Stokes Equations and Boundary Layer Phenomena (34 pages)• Basic Concepts about Laminar Flowo Newtonian and Non-Newtonian Fluidso Short Overview on Non-Newtonian Fluids• Laminar Flow of Newtonian Fluidso Navier-Stokes Equationso Dimensional Analysis of Navier-Stokes Equations• Typical Applications of Navier-Stokes Equations• Few Concepts about Rotational and Irrotational Flows• Boundary Layer Phenomena and EquationsUnit 3 – Heat Transfer in Laminar Flow (24 pages)• Few Basic Remarks on Heat Transfer Mechanisms• Thermal Energy Balance in Terms of Temperature• Heat Transfer Problems in Laminar Flowo Thermal Boundary Layer over a Flat Plateo Heat transfer in a circular pipe with laminar flowUnit 4 – Momentum and Heat Transfer in Turbulent Flow (40 pages)• General Remarks on Turbulent Flow• Statistical Treatment of Turbulent Flow• Momentum Transfer in Turbulent Flowo Eddy Viscosityo Velocity distribution in turbulent flow1/5

o Distributed Pressure Drops and Friction Factors in Turbulent Flowo Singular Pressure Dropso Few remarks on Pump Characteristics• Heat Transfer in Turbulent Flowo Eddy Diffusivityo Reynolds Analogy for Flow on a Flat Plateo Heat Transfer in Ducts with Forced Convectiono Remarks on Heat Transfer in Free ConvectionUnit 5a – Natural Circulation in Single-Phase Flow (9 pages)Unit 5b – Notes on Compressible Single-Phase Flow (14 pages)Unit 5c – More on Turbulence (20 pages)• Length Scales in Turbulence• Direct Numerical Simulation• Large Eddy Simulation• Reynolds Averaged Navier-Stokes Equationso Algebraic Modelso One-Equation Modelso Two-Equation ModelsUnit 6 – Two-Phase Flow: General Definitions, Flow Regime Maps and Balance Equations(52 pages)• General Definitions• Flow Regimeso Main Observed Phenomenao Flow Regime Mapso Flow Regime Transition Criteria• Balance Equations for Two-Phase Flowo General Remarkso One-Dimensional Homogeneous Equilibrium Modelo One-Dimensional Two-Fluid Modelo Remarks on Balance Equations for Two-Phase Flowo Semi-empirical Approaches for Mixture Modelso Mathematical Character of Balance Equations for Two-Phase FlowUnit 7 – Pressure Drops and Heat Transfer in Two-Phase Flow (58 pages)• Pressure Drops in Two-Phase Flowo General Definitionso The Homogeneous Equilibrium modelo The Lockhart and Martinelli Modelo The Martinelli-Nelson Modelo Other Modelso Codes and Two-Phase Pressure Drops• Boiling Heat Transfero Conditions for the Occurrence of Boilingo Phenomenological Description of Pool Boilingo Quantitative Evaluation of Pool Boiling Phenomenao Phenomenological Description of Flow Boilingo Quantitative Evaluation of Flow Boiling Phenomena2/5

• Condensationo General Remarkso Flmwise Condensationo Effect of Noncondensable Gaseso The analogy between Heat and Mass Transfero Superposition of latent and convective heat transfer during condensationo Two-Phase Heat Transfer in CodesUnit 8 – Some Specific Phenomena in Two-Phase Flow: Critical Flow, Flooding and BoilingChannel Instabilities (30 pages)• Critical Flowo General Description of the Phenomenono Importance of the Phenomenon for Nuclear Technologyo Mathematical Explanation of the Phenomenono Reminder of Critical Flow for a Perfect Gaso Two-Phase Critical Flow Models• Floodingo Phenomenological Descriptiono Quantitative Prediction• Boiling Channel Instabilitieso Classification of Instabilitieso Static Instabilitieso Dynamic Instabilitieso Tools for Predicting Boiling InstabilitiesOrganisation of Exercises and ApplicationsExercises were proposed all along the Course subdivided into Units E1 to E5, including:1) CLASSICAL NUCLEAR REACTOR PLANT CALCULATIONSo Energy Balances and Temperature Distributions in PWRs (E3)o Energy Balances and Temperature Distributions in BWRs (E3)o Application of lumped parameter equations for large capacities in two-phase flow (E2)o Manual and automatic calculation (via a specific FORTRAN code developed by theteacher for teaching purposes) of the first pressure peak in a nuclear reactor drycontainment (E2)o Demonstration of results obtained by the ECART non equilibrium model for thedynamics of the pressurizer and a PWR blowdown. (E2)2) MATLAB and manual calculationso Steady-state and transient heat conduction calculation in a fuel rod (E1)o Steady and transient heat conduction in a flat plate (E1)o Steady heat conduction in a 2D rectangular domain (E1)3) FLUENT and other CFD codes applicationso Laminar flow and comparison with closed form solutions (E4)Plane Poiseuille flowCircular duct Poiseuille flowo Corresponding turbulent cases and comparison with power law profiles (E4)o Flow patterns in a PWR downcomer and lower plenum (E4)o Condensation in a situation similar to the CONAN apparatus installed in Pisa (E4)o General presentation of supercritical reactor concepts and demonstration of CFDcalculation for heat transfer in supercritical CO2 (E4).3/5

4) RELAP5o Natural and gas-injection enhanced circulation (ENEA CIRCE facility and ScalbatraioLaboratory facility) (E5)o Boiling channel: stability conditions (E5)5) SHORT TOUR OF FACILITIES AT THE SCALBATRAIO LABORATORYProf. Ambrosini and Dr. Nicola Forgione mainly proposed the exercises. Ing. Medhat BashirSharabi proposed some remarks on the supercritical reactor concept and the application of CFD toexperiments concerning heat transfer on supercritical CO 2 . The responsibility of the content ofexercises, demonstrations and applications is fully retained by Prof. Ambrosini.Timetable of LecturesThe actual Timetable of Lectures can be found at the site:http://131.114.190.27/cgi-bin/virmap/regibo?registri:16897570;mainIn the overall, a total of 66 teaching hours have been delivered, including 49 hours of lectures and17 hours of applications.Educational Worth of the Course in the light of EMSNEThe Course (worth 6 ECTS credit units) has been delivered with the purpose of letting the studentsmaster basic concepts, equations and correlations in single and two-phase thermal-hydraulics, withmain reference to their use in nuclear reactor technology.The phenomena occurring or envisaged to occur in the nuclear reactor have been givenattention even while proposing fundamental concepts. In this aim, examples from the field ofNuclear Engineering have been continuously proposed during lectures as well as during exercisesand applications.After passing the Course, the students are supposed to possess all the basic backgroundneeded for understanding thermal-hydraulic plant behaviour during normal and accident conditions,as described in the Courses of Introduction to Nuclear Engineering, Nuclear Reactor Safety, etc..The demonstrations and the direct involvement of the students in the use of CFD and/orsystem codes was intended to let them be aware of the up-to-date techniques adopted in the analysisof nuclear reactor component thermal-hydraulic behaviour.Textbooks and SourcesIt must be remarked that the material provided by the teacher during the course can in no waysubstitute textbooks.It is intended that the students, after attending the lectures and reading the material proposedby the teacher, will use the suggested textbooks and the suggested readings for their preparation andformation of cultural background. Guidelines for preparing to the examination are provided by theteacher.The main suggested Textbook is:N.E. Todreas, M. S. Kazimi “Nuclear Systems I”, Taylor & Francis, 1990.Additional suggested readings have been proposed by the Teacher during the lectures. Among themthe following textbooks are quoted.4/5

For general treatments of single-phase fluid mechanic aspects• D.J. Tritton “Physical Fluid Dynamics”, Oxford Science Publications, 2 nd Edition, 1997.• R.L. Mott “Applied Fluid Mechanics”, Prentice Hall, 5 th Edition, 2000.• B.R. Munson, D.F. Young, T.H. Okiishi “Fundamentals of Fluid Mechanics”, 4 th Edition,Wiley, 2002, (with included CD-ROM).• R.B. Bird, W.E. Stuart, E.N. Lightfoot, “Transport Phenomena”, John Wiley & Sons, Inc.,1966.• W. F. Hughes and J. A. Brighton “Fluid Dynamics”, McGraw Hill, Schaum’s Outlines, 3 rdEdition, 1999.For specific single-phase heat transfer aspects• F.P. Incropera and D.P. DeWitt “Fundamentals of Heat and Mass Transfer”, 4 th Edition,1996.• Frank Kreith, Mark S. Bohn “Principles of Heat Transfer”, Thomson-Engineering, 2000.• J.H. Lienhard "A Heat Transfer Textbook", Prentice Hall, Englewood Cliffs, 1987.For summaries on turbulence modelling• D.C. Wilcox “Turbulence Modeling for CFD”, 2nd Edition, DCW Industries, 1998.• H.K. Veersteg and W. Malalasekera “An introduction to computational fluid dynamics”,Pearson, Prentice Hall, 1995.For two-phase flow and heat transfer• N.E. Todreas, M. S. Kazimi “Nuclear Systems II”, Taylor & Francis, 1990.• J. G. Collier and J.R. Thome “Convective Boiling and Condensation”, Oxford SciencePublications, 3 rd Edition, Clarendon Press, Oxford, 1999.• R.T. Lahey, Jr., F.J. Moody “The Thermal-Hydraulics of Boiling Water Nuclear Reactor”,American Nuclear Society, 2 nd Edition, 1993.• L.S. Tong, J. Weisman “Thermal Analysis of Pressurized Water Reactors”, AmericanNuclear Society, 3 rd Edition, 1996.For a better understanding basing on audiovisual tools• M. Van Dyke, “An Album of Fluid Motion”, The Parabolic Press, Stanford, CA, 1998.• CD-ROM attached to the text B.R. Munson, D.F. Young, T.H. Okiishi “Fundamentals ofFluid Mechanics”, 4 th Edition, Wiley, 2002,• Multimedia Fluid Mechanics, CD-ROM of Cambridge University Press.An old but still interesting general book on reactor safety and related phenomena:E.E. Lewis “Nuclear Power Reactor Safety”, John Wiley and Sons, 1977.5/5