A study on the effect of creep on strength of nuclear reactor vessel during severe accident

MINISTRY OF EDUCATION AND TRAINING HANOI UNIVERSITY OF SCIENCE AND TECHNOLOGY - NGUYEN VAN THANH A STUDY ON THE EFFECT OF CREEP ON STRENGTH OF NUCLEAR REACTOR VESSEL DURING SEVERE ACCIDENT Field: ENGINEERING MECHANICS MASTER OF SCIENCE THESIS ENGINEERING MECHANICS Scientific Supervisor Asso, Pro, NGUYEN VIET HUNG HA NOI - 2014 Master of Science Thesis Hanoi University of Science and Technology Table of contents Table of contents i Acknowledgement iii Declaration iv Nomenclature v List of acronyms vii List of figures viii List of tables x Abstract xi Chapter 1: Introduction 1.1 Motivation 1.2 Severe accident in a Light Water Reactor 1.2.1 Basics of Light Water Reactor nuclear reactor .2 1.2.2 In-vessel accident progression and phenomena 1.2.3 Melt pool in the lower head and Reactor Pressure Vessel failure 1.3 Objectives of thesis work .8 Chapter 2: Thermal hydraulic calculation of homogeneous melt pool 10 2.1 Basics of natural convection heat transfer 10 2.2 Heat transfer simulation of homogeneous melt pool 15 2.2.1 Modeling of natural convection 15 2.2.2 Temperature results and discussion .19 Chapter 3: Numerical creep modeling of reactor pressure vessel lower head 22 3.1 Creep mechanism theory 22 3.1.1 Background on creep 22 Nguyen Van Thanh Page i Master of Science Thesis Hanoi University of Science and Technology 3.1.2 Creep equation and hardening theory 24 3.2 Linking a Time-hardening creep model to ANSYS 29 3.2.1 Creep calculation in ANSYS .29 3.3.2 The use of User Programmable Features 33 3.2.3 Linking a Time-hardening creep model into ANSYS 34 3.3 Creep simulation of reactor pressure vessel .40 3.3.1 SA533B1 material properties 40 3.3.2 Geometry model and Mesh 41 3.3.3 Boundary condition .42 3.3.4 The results and discussion 45 Chapter 4: Summary and outlook .49 References .51 Appendix .52 A1 Usercreep.F routine 52 A2 Compiling and linking UPFs procedures 55 A3 SA533B1 temperature - dependent properties 59 Nguyen Van Thanh Page ii Master of Science Thesis Hanoi University of Science and Technology Acknowledgement I would like to express great thank to Associate Professor Nguyen Viet Hung - the director of International Computational Science and Engineering Institute - Hanoi University of Science and Technology (ICSE, HUST), for his supervision during the time of implementing this thesis work My special thanks go to MSc Le Anh Tuan and other colleagues in the ICSE for their support and assistance throughout the duration of this thesis I would like to take this opportunity to thank Advanced Technology Joint Stock Company (http://advantech.vn/) for providing the licensed ANSYS software and other relative documents Lastly, I would also like to thank my family and friends for their encouragement throughout the time of taking Master course and doing this thesis as well Hanoi, November 2014 Nguyen Van Thanh Nguyen Van Thanh Page iii Master of Science Thesis Hanoi University of Science and Technology Declaration I, the undersigned, Nguyen Van Thanh, hereby declare that the work entitled “A study on the effect of creep on strength of nuclear reactor vessel during severe accident” is my original work under the supervision of Associate Professor Nguyen Viet Hung I not copy from any other sources except where due reference or acknowledgement is made explicitly in the text, nor any part is written for me by another person Hanoi, November 2014 Nguyen Van Thanh Nguyen Van Thanh Page iv Master of Science Thesis Hanoi University of Science and Technology Nomenclature E Elastic modulus, Mpa  Equivalent stress, MPa  Equivalent strain, %  cr Equivalent creep strain, %  pl Equivalent plastic strain, %  th Equivalent thermal strain, %  Poisson ratio t Time, hour t Time increment T Temperature, K R Boltzmann gas constant k Coefficient of thermal conductivity, W/m.K h Film coefficient in natural convection heat transfer, W/m2.K Cp Specific heat, J/kg.K  Coefficient of volume expansion, 1/K As Heat transfer area, m2 Nu Nusselt number Ra L Rayleigh number Ra ' Modified Rayleigh number Pr Prandtl number Q Heat generation, W/m3 Nguyen Van Thanh Page v Master of Science Thesis Hanoi University of Science and Technology P Thermal power, W T Absolute temperature of the fluid sufficiently far from the surface, K Tm Melting point temperature, K TS Temperature of the surface, K  Density of the quiescent fluid sufficiently far from the surface, kg/m3 g Gravitational acceleration, m/s2 Lc Characteristic length of the geometry, m v Kinematic viscosity, m2/s  Thermal diffusivity, m2/s Nguyen Van Thanh Page vi Master of Science Thesis Hanoi University of Science and Technology List of acronyms LWR Light Water Reactor PWR Pressurized Water Reactor BWR Boiling Water Reactor RPV Reactor Pressure Vessel LOCA Loss of Cooling Accident CFD Computational Fluid Dynamic FEA FEA: Finite Element Analysis IAEA International Atomic Energy Agency SMART System-Integrated Modular Advanced Reactor Nguyen Van Thanh Page vii Master of Science Thesis Hanoi University of Science and Technology List of figures Figure 1.1 PWR reactor design Figure 1.2 BWR reactor design Figure 1.3 Physical phenomenon during the severe accident [IRSN and CEA-2007/83351] Figure 1.4 Core meltdown accident progression overview Figure 1.5 (a) Illustration of melt pool formation; (b) Layer separation of melt pool Figure 1.6 SMART PWR design reactor assembly Figure 1.7 Two considered hypothetical scenarios, (a) Scenario and (b) Scenario Figure 2.1 (a) Force acting on a differential control volume in natural convection; and (b) typical velocity and temperature profiles for natural convection flow over a hot vertical plate 11 Figure 2.2 Natural convection model induced by internal heating 15 Figure 2.3 (a) 2-D axisymmetric geometry of melt pool and vessel wall, (b) Mesh configuration 17 Figure 2.4 Temperature field in the whole of fluid volume and vessel wall at 6h in (a) scenario 1; and (b) scenario 19 Figure 2.5 Temperature field in vessel wall at 6h in (a) scenario 1; and (b) scenario .20 Figure 2.6 Temperature over time at the highest temperature point of vessel wall .20 Figure 3.1 Three stages of creep curve [1] 22 Figure 3.2 [1] Creep (a), and Stress relaxation (b) .23 Figure 3.3 Creep strain history prediction from Time Hardening theory [Kraus, 1980] .27 Figure 3.4 Creep strain history prediction from Strain Hardening theory [Kraus, 1980] .28 Figure 3.5 Step by step procedure to start working with UPFs on Window platform 34 Nguyen Van Thanh Page viii Master of Science Thesis Hanoi University of Science and Technology Figure 3.6 Experimental SA533B1 creep curve at T = 1150K and Stress = 26.5 MPa (J L Rempe, 1993, [1]) .35 Figure 3.7 Verification of usercreep.F routine .39 Figure 3.8 (a) 2-D axisymmetric geometry, (b) mesh with six layers of elements over wall thickness, (c) 2-D - Quad Plane 183 element geometry 41 Figure 3.9 Graph of mesh independent investigation 41 Figure 3.10 Process of importing temperature field from CFD to Mechanical APDL 43 Figure 3.11 Mechanical boundary conditions applied to both of scenarios 44 Figure 3.12 Graph of temperature distribution at internal surface of vessel wall at 4.3h .46 Figure 3.13 Equivalent creep strain at 4.3h in (a) scenario 1, and (b) scenario 47 Figure 3.14 Equivalent creep strain at 6h in (a) scenario 1, and (b) scenario 47 Figure 3.15 (a) equivalent creep strain at 4.3h with creep effect; (b) total mechanical and thermal strain at 4.3h without creep effect .48 Nguyen Van Thanh Page ix Master of Science Thesis Hanoi University of Science and Technology Figure 3.13 Equivalent creep strain at 4.3h in (a) scenario 1, and (b) scenario Figure 3.14 Equivalent creep strain at 6h in (a) scenario 1, and (b) scenario Nguyen Van Thanh Page 47 Master of Science Thesis Hanoi University of Science and Technology Figure 3.15 (a) equivalent creep strain at 4.3h with creep effect; (b) total mechanical and thermal strain at 4.3h without creep effect Nguyen Van Thanh Page 48 Master of Science Thesis Hanoi University of Science and Technology Chapter 4: Summary and outlook The present thesis work address the theoretical background for numerical simulation of some main phenomena during a core meltdown hypothetical accident in a Pressurized Water Reactor The main objective of this thesis is to basically understand the effect of creep on the strength of nuclear reactor vessel during severe accident To support the main objective, the convection heat transfer simulation by mean of ANSYS Fluent is conducted to provide the temperature fields, which is used as the thermal boundary condition in creep simulation Furthermore, the User Programmable Features is proposed to compile and link the user defined creep model into ANSYS The scope of Chapter is to give the basic of Light Water Reactor and its two types as well as the hypothetical severe accident scenarios Melt pool in Pressurized Water Reactor in a core meltdown accident and its phenomena is discussed in detail In Chapter 2, thermal hydraulic calculation of homogeneous melt pool is performed The first part discusses the physical mechanism of natural convection The remains of this chapter basically describes the model of natural convection of homogeneous melt pool used in the CFD simulation The results of temperature field within the vessel wall in two scenarios are then imported as the thermal boundary condition in the creep simulation in Chapter Chapter presents the numerical creep simulation of vessel wall This is also the main section of this thesis work Firstly, the basic of creep mechanics in metal materials is given to provide the understanding of hardening creep theories and creep models which can be used in numerical simulation The User Programmable Features is applied to compile and link a Time hardening creep model into ANSYS for modeling of the creep behavior of vessel wall The results of this chapter is the important factor to evaluate the significant of temperature on the creep behavior of vessel wall material and the strong effect of creep to the strength of reactor vessel lower head in a hypothetical core meltdown accident The results of this chapter also prove the huge positive effect of water flooding outside of reactor vessel in case of accident Nguyen Van Thanh Page 49 Master of Science Thesis Hanoi University of Science and Technology Based on the results of this thesis work, it is possible to state that the creep process of vessel wall material is only initiated by the simultaneous occurrence of high temperatures (>6000C) and pressure (>1MPa) If the creep process is initiated, the weakest region is the hot-focused area, where the highest local creep strain rate occurs This leads to wall thinning, which accelerates the creep geometrically Failure of vessel wall lower head may occurs at the position of highest temperatures after the time of reaching the tertiary creep stage In next research, it is needed to make some uncertainties clear in the thermal hydraulic analysis, such as the layered melt pool instead of assumed homogeneous melt pool, the solidification phenomenon in the thin layer of melt pool which adjacent to the internal vessel wall, the effect of air gap to the conduction heat transfer between the melt pool and internal vessel wall Besides, in the numerical creep modeling The creep model provided by future creep test data can be used by means of User Programmable in ANSYS to more accurate predict the vessel wall behavior As a whole, the present thesis work has demonstrated a close connection between numerical simulation by means of ANSYS tools and the phenomena in experiments, boosting the predictive capability of using numerical method in the nuclear engineering safety analysis Nguyen Van Thanh Page 50 Master of Science Thesis Hanoi University of Science and Technology References [1] ANSYS®, Inc ANSYS 14.5 Help and User’s Manual, 2014 [2] J L Rempe, S A Chavez, G L Thinnes, C M Allison, G E Korth Light Water Reactor Lower Head Failure Analysis EG&G Idaho, Inc Idaho Falls, ID 83415 [3] Viet Nam Atomic Energy Institute VINATOM-KAERI Training Courses (2012): “Severe Accident Research” [4] M M Pilch, Y R Rashid, J S Ludwigsen and T Y Chu Creep Failure of a Reactor Pressure Vessel Lower Head Under Severer Accident Conditions Sandia National Laboratories P.O.Box 5800-1139 [5] Chi Thanh TRAN’s doctoral thesis The Effective Convectivity Model for Simulation and Analysis of Melt Pool Heat Transfer in a Light Water Reactor Pressure Vessel Lower Head [6] Yunus A CenGel Heat Transfer, A Practical Approach Second Edition [7] R.K Penny, D.L Marriott Design For Creep Second edition [8] H.-G Willschutz, E Altstadt, B.R Sehgal, F.-P Weiss Coupled thermal structural analysis of LWR vessel creep failure experiments ELSEVIER, Nuclear Engineering and Design 208 (2001) 265-282 [9] Walter Villanueva, Chi-Thanh Tran, Pavel Kudinov (2011) Coupled themomechanical creep analysis for boiling water reactor pressure vessel lower head ELSEVIER, Nuclear Engineering and Design 249 (2011) 146-153 [10] Nguyen Van Thanh, Le Anh Tuan, Nguyen Viet Hung A study on the effect of creep on strength of nuclear reactor vessel during severe accident Hội nghị Cơ học kỹ thuật toàn quốc kỷ niệm 35 năm thành lập Viện Cơ học, Hà Nội tháng 4, 2014 [11] Le Anh Tuan, Nguyen Van Thanh, Nguyen Viet Hung, Nguyen Phu Khanh Integrating an User Programmable Feature into ANSYS software to study the integrity of nuclear reactor vessel during severe accident The 2nd AUN/SEED-Net Natural Disaster Conference (ANDC), MYANMA, Sept 2014 Nguyen Van Thanh Page 51 Master of Science Thesis Hanoi University of Science and Technology Appendix A1 Usercreep.F routine SUBROUTINE usercreep (impflg, ldstep, isubst, matId , & elemId, kDInPt, kLayer, kSecPt, nstatv, nprop, & prop , time , dtime , temp , dtemp , & toffst, Ustatev, creqv , pres , seqv , & delcr , dcrda) c************************************************************************* c *** primary function *** c Define creep law corresponding to the "Constitutive Creep Law" of SA533B1 TMI-2 creep rupture test results c when creep table options are TB,CREEP with TBOPT=100 (user defined creep) c Creep equation is c creqv := C1/(C3+1))*seqv**C2*t**(C3+1); (time hardening form) c dotcreq := C1*seqv**C2*t**C3; c seqv is equivalent effective stress (Von-Mises stress) c creqv is equivalent effective creep strain (Von-Mises creep strain) c C1, C2, C3 are materials constants, (strain hardening form) c************************************************************************* c input arguments c =============== c impflg (in ,sc ,i) c Explicit/implicit integration flag (currently not used) c ldstep (in ,sc ,i) Current load step c isubst (in ,sc ,i) Current sub step c matId (in ,sc ,i) number of material index c elemId (in ,sc ,i) Element number c kDInPt (in ,sc ,i) Material integration point c kLayer (in ,sc ,i) Layer number c kSecPt (in ,sc ,i) Section point c nstatv (in ,sc ,i) Number of state variables c nprop (in ,sc ,i) size of mat properties array c prop (dp ,ar(*),i) mat properties array c This array is passed all the creep c constants defined by command c TBDATA associated with TB,CREEP c (do not use prop(13), as it is used c elsewhere) Nguyen Van Thanh Page 52 Master of Science Thesis c Hanoi University of Science and Technology at temperature temp c time Current time c dtime Current time increment c temp Current temperature c dtemp Current temperature increment c toffst (dp, sc, i) temperature offset from absolute zero c seqv equivalent effective stress c creqv (dp ,sc , i) c pres (dp ,sc , i) equivalent effective creep strain (dp ,sc , i) hydrostatic pressure stress, -(Sxx+Syy+Szz)/3 c note that: constitutive consistency is not accounted for c if creep strains are function of pressure c input output arguments input desc c ====================== c Ustatev (dp,ar(*), i/o) / output desc ========== =========== user defined iinternal state variables at c time 't' / 't+dt' c This array will be passed in containing the c values of these variables at start of the c time increment They must be updated in this c subroutine to their values at the end of c time increment, if any of these internal c state variables are associated with the c creep behavior c output arguments c ================ c delcr (dp ,sc , o) c dcrda (dp,ar(*), o) incremental creep strain c output array dcrda(1) - derivitive of incremental creep c strain to effective stress c dcrda(2) - derivitive of incremental creep c strain to creep strain c local variables c =============== c c1,c2,c3 (dp, sc, l) temporary variables as creep constants c************************************************************************* c - parameters #include "impcom.inc" DOUBLE PRECISION ZERO PARAMETER (ZERO = 0.0d0) c - argument list Nguyen Van Thanh Page 53 Master of Science Thesis INTEGER Hanoi University of Science and Technology ldstep, isubst, matId , elemId, & kDInPt, kLayer, kSecPt, nstatv, & impflg, nprop DOUBLE PRECISION dtime , time , temp , dtemp , toffst, & creqv , seqv , pres DOUBLE PRECISION prop(*), dcrda(*), Ustatev(nstatv) c - local variables DOUBLE PRECISION c1, c2, c3, delcr c************************************************************************* c *** skip and move to 990 when stress and creep strain are all zero if (seqv.LE.ZERO.AND.creqv.LE.ZERO) GO TO 990 c *** Define "Constitutive Creep Law" constants c delcr := (C1/(C3+1))*seqv**C2*t**(C3+1) c1 = prop(1) c2 = prop(2) c3 = prop(3) c *** calculate incremental creep strain if (creqv le TINY) creqv = sqrt(TINY) delcr = ZERO IF(c1.gt.ZERO) delcr = (exp((c3*(log(c1)+c3*log(c3+1))/(c3+1)+ & c2*log(seqv)/(c3+1)+c3*log(creqv)/(c3+1))))*(dtime) c *** derivitive of incremental creep strain to effective stress dcrda(1)= (delcr*c2)/((c3+1)*seqv) c *** derivitive of incremental creep strain to effective creep strain dcrda(2)= (delcr*c3)/((c3+1)*creqv) c *** write the effective creep strain to last state variable if (nstatv gt 0) then Ustatev(nstatv) = creqv end if 990 continue return end Nguyen Van Thanh Page 54 Master of Science Thesis Hanoi University of Science and Technology A2 Compiling and linking UPFs procedures a) Installing the customization tools ANSYS Customization Files are not installed with the default installation Therefore, in order to access UPFs, users must select such an option during the installation procedure [1] b) Compilers requirements for Windows systems All ANSYS, Inc products are built and tested using the Visual Studio 2008 SP1 (including the MS C++ compiler) and Intel FORTRAN 11.1 compilers Visual Studio 2008 is required for linking user programmable features on Windows systems If your system does not have Visual Studio 2008, you can still link user programmable features into ANSYS by downloading Microsoft Windows SDK v7.0 from the following location: http://www.microsoft.com/en-us/download/details.aspx?id=3138 After installation of both Microsoft and Intel products, in that order, it is recommended to check if the IFORT_COMPILER11 environment variable is set properly In particular, it should be set in the following manner: IFORT_COMPILER11 = C:\Program Files (x86)\Intel\Compiler\11.1\065(*) For further verification, it is possible to check if the “path” of the shortcut Fortran Build Environment for applications running on Intel(R) 64 points to ifortvars.bat Only if strictly needed, this file should be edited and modified accordingly Nguyen Van Thanh Page 55 Master of Science Thesis Hanoi University of Science and Technology (*) the patch level, 065 in this case, may differ In Windows 7, environment variables can be set/edited here: Control Panel\System  Advanced System Settings  Advanced  Environment Variables c) Creating a custom ANSYS-executable There are two ways to create a custom executable of the ANSYS program: The ANSCUST.BAT procedure and The ANS_ADMIN utility The following is the ANSCUST.BAT step-by-step procedure to be used in order to include usercreep.F routine into a customized ansys.exe file Of course, it also can be completely done by using The ANS_ADMIN utility Copy the available usercreep.F file to be compiled from: C:\Program Files\ANSYS Inc\v145\ansys\customize\user Modify the usercreep.F file following all the aspects which are described in section 3.2.3; Paste the usercreep.F file to: C:\Program Files\ANSYS Inc\v145\ansys\custom\user\winx64 Open the Microsoft Windows SDK’s CMD shell: Nguyen Van Thanh Page 56 Master of Science Thesis Hanoi University of Science and Technology Start  All Programs  Microsoft Windows SDK v7.0  CMD Shell Change the path to: C:\Program Files\ANSYS Inc\v145\ansys\custom\user\winx64 Issue the command ANSCUST.BAT,  enter… … then press any key to continuous Consider linking the Wind Turbine Aeroelastic library with Mechanical APDL (“no” in this case): If the link is successful, then the following message appears When doing this procedure the first time, we need to answer “Y” to the following question: Nguyen Van Thanh Page 57 Master of Science Thesis Hanoi University of Science and Technology There should be 107 *dll files copied For subsequent links there is no need to copy the DLLs again Therefore the answer will be “N” 10 If the compiling/linking processes were correct then we should have the following additional files (including the customized ansys.exe): 11 Before simulation process, we need to specify working directory, job name, input and output files in the File Management tab as usual And importantly, we need to specify the location of the Custom ANSYS Executable in the Customization Preferences tab: To confirm that the news, customized version of ANSYS is running, check the Output window or Output File for the following line: Note - This ANSYS version was linked by Licensee Nguyen Van Thanh Page 58 Master of Science Thesis Hanoi University of Science and Technology We can then activate the user creep law via TB,CREEP,,,,100 , also define other inputs as usual A3 SA533B1 temperature - dependent properties Young Modulus Density Temp (K) E (Mpa) Temp (K) Density (kg/m^3) 200 220000 200 7850 300 220000 300 7850 400 215000 400 7825 500 205000 500 7790 600 185000 600 7750 700 155000 700 7710 800 123000 800 7685 900 90400 900 7640 1000 65000 1000 7610 1100 45000 1100 7650 1200 32000 1200 7610 1300 24000 1300 7560 1400 17000 1400 7510 1500 12500 1500 7480 1600 8880 1700 6500 1800 5100 Nguyen Van Thanh Page 59 Master of Science Thesis Hanoi University of Science and Technology Thermal conductivity Temp Thermal conductivity (K) (W/m.K) 300 47 Specific heat Temp (K) Specific heat (J/kg.K) 300 0.033 400 45 400 0.055 500 43 500 0.1 600 40 600 0.143 700 37 700 0.21 800 34 800 0.3 900 31 900 0.45 1000 29 1000 0.95 1100 27.5 1100 0.25 1200 27 1200 0.183 1300 27 1300 0.187 1400 28 1400 0.172 1500 28 Nguyen Van Thanh Page 60 Master of Science Thesis Hanoi University of Science and Technology The end Nguyen Van Thanh Page 61 ... transient melt pool heat transfer in the reactor lower head and numerical prediction of the creep failure of vessel wall are of paramount importance for severe accidents analysis in nuclear safety... Thanh, hereby declare that the work entitled ? ?A study on the effect of creep on strength of nuclear reactor vessel during severe accident? ?? is my original work under the supervision of Associate... University of Science and Technology 1.2 Severe accident in a Light Water Reactor According to the definition of IAEA, severe accident is the accident conditions more severe than a design basic accident