NUCLEAR REACTOR THERMAL HYDRAULICS AND OTHER APPLICATIONS Edited by Donna Post Guillen Nuclear Reactor Thermal Hydraulics and Other Applications http://dx.doi.org/10.5772/45830 Edited by Donna Post Guillen Contributors Alois Hoeld, Weidong Huang, Osama Abd-Elkawi, Ten-See Wang, Sergey Karabasov, Alex Obabko, Paul Fischer, Tim Tautges, Vasily Goloviznin, Mihail Zaitsev, Vladimir Chudanov, Valerii Pervichko, Anna Aksenova, Hernan Tinoco Published by InTech Janeza Trdine 9, 51000 Rijeka, Croatia Copyright © 2013 InTech All chapters are Open Access distributed under the Creative Commons Attribution 3.0 license, which allows users to download, copy and build upon published articles even for commercial purposes, as long as the author and publisher are properly credited, which ensures maximum dissemination and a wider impact of our publications After this work has been published by InTech, authors have the right to republish it, in whole or part, in any publication of which they are the author, and to make other personal use of the work Any republication, referencing or personal use of the work must explicitly identify the original source Notice Statements and opinions expressed in the chapters are these of the individual contributors and not necessarily those of the editors or publisher No responsibility is accepted for the accuracy of information contained in the published chapters The publisher assumes no responsibility for any damage or injury to persons or property arising out of the use of any materials, instructions, methods or ideas contained in the book Publishing Process Manager Iva Simcic Technical Editor InTech DTP team Cover InTech Design team First published February, 2013 Printed in Croatia A free online edition of this book is available at www.intechopen.com Additional hard copies can be obtained from orders@intechopen.com Nuclear Reactor Thermal Hydraulics and Other Applications, Edited by Donna Post Guillen p cm ISBN 978-953-51-0987-7 free online editions of InTech Books and Journals can be found at www.intechopen.com Contents Preface VII Section CFD Applications for Nuclear Reactor Safety Chapter The Coolant Channel Module CCM — A Basic Element for the Construction of Thermal-Hydraulic Models and Codes Alois Hoeld Chapter Large Eddy Simulation of Thermo-Hydraulic Mixing in a T-Junction 45 Aleksandr V Obabko, Paul F Fischer, Timothy J Tautges, Vasily M Goloviznin, Mikhail A Zaytsev, Vladimir V Chudanov, Valeriy A Pervichko, Anna E Aksenova and Sergey A Karabasov Chapter CFD as a Tool for the Analysis of the Mechanical Integrity of Light Water Nuclear Reactors 71 Hernan Tinoco Section General Thermal Hydraulic Applications Chapter Thermal Hydraulics Design and Analysis Methodology for a Solid-Core Nuclear Thermal Rocket Engine Thrust Chamber 107 Ten-See Wang, Francisco Canabal, Yen-Sen Chen, Gary Cheng and Yasushi Ito Chapter CFD Simulation of Flows in Stirred Tank Reactors Through Prediction of Momentum Source 135 Weidong Huang and Kun Li Chapter Hydrodynamic and Heat Transfer Simulation of Fluidized Bed Using CFD 155 Osama Sayed Abd El Kawi Ali 105 Preface This book covers a range of thermal hydraulic topics related, but not limited, to nuclear re‐ actors The purpose is to present research from around the globe that serves to advance our knowledge of nuclear reactor thermal hydraulics and related areas The focus is on comput‐ er code developments and applications to predict fluid flow and heat transfer, with an em‐ phasis on computational fluid dynamic (CFD) methods This book is divided into two sections The first section consists of three chapters concerning computational codes and methods applied to nuclear reactor safety The second section consists of four chapters cov‐ ering general thermal hydraulic applications The overarching theme of the first section of this book is thermal hydraulic models and co‐ des to address safety behaviour of nuclear power plants Accurate predictions of heat trans‐ fer and fluid flow are required to ensure effective heat removal under all conditions The section begins with a chapter discussing the theoretical development of thermal-hydraulic approaches to coolant channel analysis These traditional methods are widely used in sys‐ tem codes to evaluate nuclear power plant performance and safety The second chapter ex‐ amines several fully unsteady computational models in the framework of large eddy simulations implemented for a thermal hydraulic transport problem relevant to the design of nuclear power plant piping systems A comparison of experimental data from a classic benchmark problem with the numerical results from three simulation codes is given The third chapter addresses the issue of properly modeling thermal mixing in Light Water Nu‐ clear Reactors A CFD approach is advocated, which allows the flow structures to develop and properly capture the mixing properties of turbulence The second section of this book includes chapters focusing on the application of CFD to crosscutting thermal hydraulic phenomena In line with best practices for CFD, the simula‐ tions are supported by relevant experimental data The section begins with a chapter de‐ scribing a thermal hydraulic design and analysis methodology for a nuclear thermal propulsion development effort Modern computational fluid dynamics and heat transfer methods are used to predict thermal, fluid, and hydrogen environments of a hypothetical solid-core, nuclear thermal engine designed in the 1960s The second chapter in this section investigates the applicability of several CFD approaches to modeling mixing and agitation in a stirred tank reactor The results are compared with experimentally-obtained velocity and turbulence parameters to determine the most appropriate methodology The third chap‐ ter in this section presents the results of CFD simulations used to study the hydrodynamics and heat transfer processes in a two-dimensional gas fluidized bed The final chapter uses CFD to predict the thermal hydraulics surrounding the design of a spallation target system for an Accelerator Driven System VIII Preface Our ability to simulate larger problems with greater fidelity has vastly expanded over the past decade The collection of material presented in this book is but a small contribution to the important topic of thermal hydraulics The contents of this book will interest researchers, scientists, engineers and graduate students Dr Donna Post Guillen Group Lead, Advanced Process and Decision Systems Department, Idaho National Laboratory, USA Section CFD Applications for Nuclear Reactor Safety Nuclear Reactor Thermal Hydraulics and Other Applications 0.8 dp=200 dp=300 dp=400 dp=500 0.78 m m m m eg 0.76 0.74 0.72 0.7 12 16 20 Time,(s) Figure Effect of particle diameter on gas volume fraction (B-type) 1300 dp=200 dp=300 dp=400 dp=500 rsus,(kg/m3) 1200 m m m m 1100 1000 900 800 12 16 20 Time,(s) Figure Effect of particle diameter on suspension density (B-type) dp=200 dp=300 dp=400 dp=500 1.6 m m m m 1.2 vg,(m/s) 178 0.8 0.4 0 12 Time,(s) Figure Effect of particle diameter on vertical gas velocity (B-type) 16 20 Hydrodynamic and Heat Transfer Simulation of Fluidized Bed Using CFD http://dx.doi.org/10.5772/52072 0.6 dp=200 dp=300 dp=400 dp=500 m m m m vs,(m/s) 0.4 0.2 -0.2 12 16 20 Time,(s) Figure Effect of change particle diameter on vertical particle velocity (B-type) dp=200 dp=300 dp=400 dp=500 0.004 m m m m us,(m/s) -0.004 -0.008 12 16 20 Time,(s) Figure 10 Effect of particle diameter on horizontal particle velocity (B-type) 0.005 dp=200 dp=300 dp=400 dp=500 0.004 m m m m ug,(m/s) 0.003 0.002 0.001 0 12 Time,(s) Figure 11 Effect of particle diameter on horizontal gas velocity (B-Type) 16 20 179 Nuclear Reactor Thermal Hydraulics and Other Applications 160 dp=200 dp=300 dp=400 dp=500 m m m m Tg(°C) 120 80 40 0 12 16 20 Time,(s) Figure 12 Effect of particle diameter on gas temperature (B-type) 200 12 16 20 200 dp=200 dp=300 dp=400 dp=500 m m m m Ts,(°C) 160 160 120 120 80 40 80 40 12 16 20 Time,(s) Figure 13 Effect of particle diameter on particle temperature (B-type) 0.84 dp=700 m dp=800 m dp=900 m dp=1000 m 0.8 eg 180 0.76 0.72 0.68 12 Time,(s) Figure 14 Effect of particle diameter on gas volume fraction (D-type) 16 20 Hydrodynamic and Heat Transfer Simulation of Fluidized Bed Using CFD http://dx.doi.org/10.5772/52072 1400 dp=700 m dp=800 m dp=900 m dp=1000 m rsus,(kg/m3) 1200 1000 800 12 16 20 Time,(s) Figure 15 Effect of particle diameter on suspension density (D-type) dp=700 m dp=800 m dp=900 m dp=1000 m vg,(m/s) 0 12 16 20 Time,(s) Figure 16 Effect of particle diameter on vertical gas velocity (D-type) dp=700 m dp=800 m dp=900 m dp=1000 m 1.5 vs,(m/s) 0.5 -0.5 12 16 20 Time,(s) Figure 17 Effect of change particle diameter on vertical particle velocity (D-Type) 181 Nuclear Reactor Thermal Hydraulics and Other Applications 0.0002 dp=700 m dp=800 m dp=900 m dp=1000 m us,(m/s) -0.0002 -0.0004 -0.0006 12 16 20 Time,(s) Figure 18 Effect of particle diameter on horizontal particle velocity (D-type) 0.001 dp=700 m dp=800 m dp=900 m dp=1000 m 0.0008 ug,(m/s) 0.0006 0.0004 0.0002 0 12 16 20 Time,(s) Figure 19 Effect of particle diameter on horizontal gas particle velocity (D-type) 70 dp=700 m dp=800 m dp=900 m dp=1000 m 60 Tg(°C) 182 50 40 30 12 Time,(s) Figure 20 Effect of particle diameter on gas temperature (D-type) 16 20 Hydrodynamic and Heat Transfer Simulation of Fluidized Bed Using CFD http://dx.doi.org/10.5772/52072 200 dp=700 m dp=800 m dp=900 m dp=1000 m Ts(°C) 160 120 80 40 12 16 20 Time,(s) Figure 21 Effect of particle diameter on particle temperature (D-type) 8.2 Effect of input gas velocity In this section the input gas velocity is changed from one to nine times minimum fluidized velocity for 500 μm sand particles to study the the effect of this parameter on fluidization behavior Input gas velocity has an effective role in thermal performance of the fluidized bed In order to illustrate its effect, the relation between Nusselt number and flow number is described in figure (22) It is clear from this figure that with increase in flow numbers, the Nusselt number increases until reached an optimum flow number where the Nusselt number reaches its maximum value After this optimum value the increase in flow number is associated with a decrease in Nusselt number This decrease in Nusselt number may be due to the increase of input gas velocity toward the terminal velocity, consequently the bed goes to be empty bed Figure (23) shows the variation of Nusselt number with velocity number Also the relation between Nusselt number and velocity number has the same trend as the Nusselt number with flow number This confirms the result from figure (22) This means that there is an optimum input gas velocity to yield the best heat transfer characteristics This velocity is the target of the fluidized bed designer The value of this velocity depends on the fluidized gas properties, the fluidized material, particle diameter, and bed geometry 8.3 Effect of fluidized material type Type of fluidized material controls hydrodynamic and thermal performance of fluidized bed.It affects on the different parameters of fluidization such as gas volume fraction, suspension density, gas velocity distribution and particle velocity distribution, gas phase temperature and particle phase temperature In this section different types of materials such as sand, marble, lead, copper, aluminum and steel of particle diameters 1mm are used to study the effect of fluidized materials on the bed performance Figure (24) shows the change of gas volume fraction with time for different types of fluidized materials The figure shows that the gas volume fraction of copper is the highest value 183 Nuclear Reactor Thermal Hydraulics and Other Applications 8.4 Sand particles dp= 500 mm 8.2 Nu 7.8 7.6 0.1 0.2 0.3 0.4 0.5 0.6 fl Figure 22 Variation of Nusselt number with flow number 8.3 Sand particles dp= 500 mm 8.2 8.1 Nu 184 7.9 7.8 0.5 1.5 W1/3 2.5 Figure 23 Variation of Nusselt number with velocity number followed by lead and steel Gas volume fraction of sand, marble and aluminum are at the same level The change of suspension density with time for several types of fluidized materials is shown in Figure (25) It is clear that the highest suspension density lies with the material of the highest density Figures (26) to (29) show the effect of change of fluidized material type on horizontal and vertical velocities of gas and particle Figures (30) and (40) illustrate the effect of change of fluidized material type on particle and gas temperatures Hydrodynamic and Heat Transfer Simulation of Fluidized Bed Using CFD http://dx.doi.org/10.5772/52072 0.88 Sand Particles Aluminum Particles Marble Particles Steel Particles Lead Particles Copper Particles 0.84 eg 0.8 0.76 0.72 0.68 12 16 20 Time,(s) Figure 24 Effect of fluidized material type on gas volume fraction 8000 Sand Particles Aluminum Particles Marble Particles Steel Particles Lead Particles Copper Particles rsus,(kg/m3) 6000 4000 2000 0 12 16 20 Time,(s) Figure 25 Effect of fluidized material type on suspension density Sand Particles Aluminum Particles Marble Particles Steel Particles Lead Particles Copper Particles vs,(m/s) -2 12 Time,(s) Figure 26 Effect of fluidized material type on vertical particle velocity 16 20 185 Nuclear Reactor Thermal Hydraulics and Other Applications 0.002 Sand Particles Aluminum Particles Marble Particles Steel Particles Lead Particles Copper Particles us,(m/s) -0.002 -0.004 12 16 20 Time,(s) Figure 27 Effect of fluidized material type on horizontal particle velocity 10 12 16 20 10 Sand Particles Aluminum Particles Marble Particles Steel Particles Lead Particles Copper Particles 8 4 2 vg,(m/s) 0 12 16 20 Time,(s) Figure 28 Effect of fluidized material type on vertical gas velocity 0.0016 Sand Particles Aluminum Particles Marble Particles Steel Particles Lead Particles Copper Particles 0.0012 ug,(m/s) 186 0.0008 0.0004 0 12 Time,(s) Figure 29 Effect of fluidized material type on horizontal gas velocity 16 20 Hydrodynamic and Heat Transfer Simulation of Fluidized Bed Using CFD http://dx.doi.org/10.5772/52072 200 Sand Particles Aluminum Particles Marble Particles Steel Particles Lead Particles Copper Particles o Ts,( C) 160 120 80 40 12 16 20 Time,(s) Figure 30 Effect of fluidized material type on particle temperature 55 Sand Particles Aluminum Particles Marble Particles Steel Particles Lead Particles Copper Particles 50 o Tg,( C) 45 40 35 30 12 16 20 Time,(s) Figure 31 Effect of fluidized material type on gas temperature 8.4 Effect of heat generation by particles The aluminum particles of mm diameter are fluidized with different value of heat generated in particles (0, 500,1000,1500,2000 and 3000 Watt), the effect of change of heat generated in particles is studied With the increase of heat generated by particles the gas phase tempera‐ ture increases as shown in Figure (32) The value of the increase in gas temperature is approximately in range of °C Figure (33) shows that the particle phase temperature increases with the increase of heat generated by particles The range of increase is about 45°C It is clear that the rate of increase in particle temperature is more than the rate of increase in gas temperature, consequently the temperature difference between the two phases increase Figure (34) illustrates the relation between average heat transfer coefficient and heat generated by particles The results of the present work shows that the average heat transfer coeffi‐ cient dos not depend on heat generated by particles and all heat generated by particles converts to temperature difference between the two phases This result agrees with that of reference [9] 187 Nuclear Reactor Thermal Hydraulics and Other Applications 8.5 Terminal velocity effect Figure (35) shows the relation between terminal velocity and average heat transfer coefficient It is clear from the figure that with the increase in terminal velocity the average heat transfer coefficient decreases 8.6 Minimum fluidized velocity effect Minimum fluidized velocity is the most important parameter in study of fluidization This velocity distinguishes the fluidized bed from a packed bed and is an indicator that fluidization is occurred Figure (36) shows the variation of average heat transfer coefficient with minimum fluidized velocity The average heat transfer coefficient decreases with the increase of mini‐ mum fluidized velocity 55 50 Tg,(°C) 45 40 q= q= q= q= q= q= 35 30 12 w/m 500 w/m 1000 w/m 1500 w/m 2000 w/m 3000 w/m 16 20 Time,(s) Figure 32 Effect of particle heat generation on gas temperature 200 q = w/m q = 500 w/m q= 1000 w/m q= 1500 w/m q= 2000 w/m q= 3000 w/m 160 Ts,(°C) 188 120 80 40 12 Time,(s) Figure 33 Effect of particle heat generation in particle temperature 16 20 Hydrodynamic and Heat Transfer Simulation of Fluidized Bed Using CFD http://dx.doi.org/10.5772/52072 400 hav,(W/m2K) 300 200 Refernce [6] P resent W ork 100 1000 2000 3000 Heat Generated by Particles,(W/m3) Figure 34 Effect of particle heat generation on average heat transfer coefficient 1000 hav,(w/m2K) 800 600 400 200 Particle Terminal Velocity,(m/s) Figure 35 Effect of terminal velocity on average heat transfer coefficient 1000 hav,(w/m2K) 800 600 400 200 0.2 0.4 Minimum Fluidized Velocity,(m/s) Figure 36 Effect of Minimum Velocity on Average Heat Transfer Coefficient 0.6 189 190 Nuclear Reactor Thermal Hydraulics and Other Applications Nomenclature gdp ρg (ρs − ρg ) Ar Archimedes number, Ar = Cd Drag coefficient, Cd = 0.63 + ( μg 4.8 Re0.5 ) Cp,g Specific heat of fluidizing gas at constant pressure J/kg.K Cp,s Specific heat of solid particles J/kg.K dg Residue of the gas continuity equation Kg/m3 s dp Mean particle diameter M G Acceleration due to gravity m/s2 Fgx Total gas phase force in x direction per unit volume N /m3 Fgy Total gas phase force in y direction per unit volume N /m3 Fsx Total particle phase force in x direction per unit volume N /m3 Fsy Total particle phase force in y direction per unit volume N /m3 fl Flow number , fl = hgp Heat transfer coefficient between gas phase and particle phase hv Volumetric heat transfer coefficient , h v = H Total height of the bed and freeboard M Hmf Minimum fluidized head of the bed M H1 Expansion head of bed at the input velocity M kg Thermal conductivity of gas phase W/m.K ks Thermal conductivity of particle phase W/m.K L Width of the bed M Nu Nusselt number based on particle diameter, (Nu= hgpdp/kg) V g ,in ut 6(1 − εg )h gp dp W/m2.K W/m3.K Pg Gas pressure Pr Prandtl number , Pr= μgCpg/kg Pa q • Rate of heat generated within particle phase W/m3 ug Gas phase velocity in x direction m/s Ugin Input gas velocity to the bed in x direction m/s us Particle phase velocity in x direction m/s ut Particle terminal velocity m/s Ur Relative velocity between two phases m/s Hydrodynamic and Heat Transfer Simulation of Fluidized Bed Using CFD http://dx.doi.org/10.5772/52072 → εg ρg dp | U r | μg Re Reynolds number, Re = S Stability function T Time s Tg Gas phase temperature C◦ Ts Particle phase temperature C◦ TFM Two fluid model vg gas phase velocity in y direction m/s Vg,mf Gas minimum fluidized velocity m/s Vg,in Input gas velocity to the bed in y direction m/s vs Particle phase velocity in y direction m/s Greek Letters ΔPB Total Pressure drop across the bed Pa Δt Time step s Δx Length of cell in the computational grid m Δy height of cell in the computational grid m ∈g Gas phase volume fraction ∈g,mf Gas phase volume fraction at minimum fluidization ∈in Gas volume fraction at the input velocity ∈s Particle phase volume fraction ρg Density of gas phase Kg/m3 ρs Density of particle phase Kg/m3 ρsus Suspension density Kg/m3 μg Viscosity of gas Pa.s δ Small positive value = 5X10-3 Author details Osama Sayed Abd El Kawi Ali1,2 Egyptian Nuclear Research Center, Egypt Faculty of Engineering – Al Baha University, Saudi Arabia 191 192 Nuclear Reactor Thermal Hydraulics and Other Applications References [1] Farhang Sefidvash ‘Fluidized Bed Nuclear Reactor“ from internet (2000) www.regg.ufrgs.br/fbnr_ing.htm, [2] John, D and Jr Anderson, ”Computational Fluid Dynamics”,McGraw-Hill,Inc, (1995) [3] Gibilaro, L G Fluidization Dynamics”, BUTTER WORTH-HEINEMANN, Oxford, (2001) [4] Kodikal, J Nilesh Kodikal and H Bhavnani Sushil,” A Computer Simulation of Hy‐ drodynamics and Heat Transfer at Immersed Surfaces in a Fluidized Bed”, Paper Proceedings of the 15th International Conference on Fluidized Bed Combustion, May 16-19, Savannah, Georgia, Copyright by ASME,(1999) (FBC99-0077), 99-0077 [5] Hans Enwald and Eric PeiranoGemini: A Cartesian Multiblock Finite Differ‐ ence”,Code for Simulation of Gas-Particle Flows", Department of Thermo and Fluid Dynamics, Chalmers University of Technology, 412 96 Goteborg, Sweden,(1997) [6] Martin RhodesIntroduction to Particle Technology", Published by John Wiley &sons, London, (1998) [7] Asit KumarDesign, construction,and Operation of 30.5 cm Square Fluidized Bed for Heat Transfer Study”, master of technology,Indian institute of technology, Mad‐ ras,Indian, (1986) [8] Paola LettieriLuca CammarataGiorgi, D M Micale and John Yates, " CFD Simula‐ tions of Gas Fluidized Beds Using Alternative Eulerian-Eulerian Modelling Ap‐ proaches ",International Journal Of Chemical Reactor Engineering, Article 5, (2003) , [9] Osama Sayed Abd ElkawiStudy of Heat Transfer in Fluidized Bed Heat Exchangers”, M.Sc thesis, Mechanical power department, Faculty of engineering, University of Mansoura, Egypt, (2001) ... combined with other sets of algebraic equations and ODE-s coming from additional parts of 37 38 Nuclear Reactor Thermal Hydraulics and Other Applications such a complex model (heat transfer or nuclear. .. coolant channel with its cross section A) are demanded to 10 Nuclear Reactor Thermal Hydraulics and Other Applications be known (See also sections 2.2.4 and 3.5) They are assumed to be directed into... at BC entrance PBEIN and outlet PBAIN These three parameters are needed for steady state considerations (and partially 21 22 Nuclear Reactor Thermal Hydraulics and Other Applications used for