A Probabilistic Physics-of-Failure Approach to Assessment of Frequency of In-Vessel Steam Generator Tube Rupture Accident in SMRs

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A Probabilistic Physics-of-Failure Approach to Assessment of Frequency of In-Vessel Steam Generator Tube Rupture Accident in SMRs Mohammad Modarres Professor of Nuclear Engineering

1 A Probabilistic Physics-of-Failure Approach to Assessment of Frequency of In-Vessel Steam Generator Tube Rupture Accident in SMRs Mohammad Modarres Professor of Nuclear Engineering Center for Risk and Reliability Department of Mechanical Engineering College Park PRESENTED AT THE NUCLEAR SCIENCE AND ENGINEERING MIT OCTOBER 17, 2011 Copyright 2012 by M. Modarres 1

2 Topics Covered SMR Steam Generator: Overview Issues Related to SGTR Frequency of SMRs Overview of the Probabilistic Physics-of-Failure Approach Used Application Example and Results Conclusions 2

3 Acknowledgements The work is part of the PhD research of one my current students: Mr. Kaushik Chaterjee The SG example shown is a scaled version of the actual SGs used Collaborative efforts with NuScale Power and input from NuScale Power, Inc. is greatly appreciated Crack growth rate data and Alloy 690 samples were provided by Dr. Bill Shack and Dr. Bogdan Alexandreanu of Argonne National Laboratory 3

Natural Convection for Cooling Inherently safe natural circulation of water over the fuel driven by gravity No pumps, no need for emergency generators

4 Natural Convection for Cooling Inherently safe natural circulation of water over the fuel driven by gravity No pumps, no need for emergency generators Simple and Small Reactor is 1/20 th the size of large reactors Integrated reactor design, no large-locas NuScale Reactor Courtesy of NuScale Power, Inc. 4

Decay Heat Removal System Using Steam Generators Two independent single-failureproof trains Closed loop system Two-phase natural circulation operation DHRS heat

5 Decay Heat Removal System Using Steam Generators Two independent single-failureproof trains Closed loop system Two-phase natural circulation operation DHRS heat exchangers nominally full of water Primary coolant natural circulation is maintained Pool provides a 3 day cooling supply for decay heat removal Courtesy of NuScale Power, Inc. 5

Decay heat removal using the containment Provides a means of removing core decay heat and limits containment pressure by: Steam Condensation Convective Heat Transfer Heat Conduction Sump

6 Decay heat removal using the containment Provides a means of removing core decay heat and limits containment pressure by: Steam Condensation Convective Heat Transfer Heat Conduction Sump Recirculation Reactor Vessel steam is vented through the reactor vent valves (flow limiter) Steam condenses on containment Condensate collects in lower containment region Reactor Recirculation Valves open to provide recirculation path through the core Provides +30 day cooling followed by indefinite period of air cooling. Courtesy of NuScale Power, Inc. 6

7 Stable Long Term Cooling Reactor and nuclear fuel cooled indefinitely without pumps or power WATER COOLING BOILING AIR COOLING Courtesy of NuScale Power, Inc. 7

Steam Generator Tube Rupture (SGTR) SGTR one of the most significant safety issues in PWRs.

Bypasses the plant s containment structure, resulting in direct release of radioactivity into atmosphere.

There have been 10 large scale SGTR occurrences in US between 1975 and 2000.

8 Steam Generator Tube Rupture (SGTR) SGTR one of the most significant safety issues in PWRs. Leads to loss of primary coolant inventory, primary side de-pressurization and potential reactor core meltdown. Bypasses the plant s containment structure, resulting in direct release of radioactivity into atmosphere. Frequency of SGTR in required in Probabilistic Risk Assessments (PRAs) of PWRs. There have been 10 large scale SGTR occurrences in US between 1975 and Several other reported cases of SG tube leakages and low scale ruptures (100,000 plugging as per US NRC). An example of SGTR event (US NRC, LER, 1990): (IAEA, 2007) SGTR event occurred at McGuire Unit 1 PWR near Charlotte, NC on March 7, Cause of this SGTR was stress corrosion cracking under normal operating conditions. 8

9 Estimation of SGTR Frequency Historical SGTR data Different SG geometry environmental and operating conditions. Non-homogeneous historical data are combined. Example (NUREG-1829, 2005/ NUREG-5750, 1999): SGTR data from a database for a 15-year time period between 1987 and 2002 were queried. 4 SGTR events that had leak rates greater than 100 GPM were identified. Power plant Year Degradation mechanism Tube Material Cumulative PWR reactor years of operation (15 yrs) SGTR frequency/ yr North Anna, VA McGuire, NC Palo Verde, AZ Indian Point, NY 1987 Fatigue Alloy Stress corrosion cracking Alloy Stress corrosion cracking Alloy Stress corrosion cracking Alloy x

10 Estimation of SGTR Frequency Large Scale PWRs vs. SMRs Large scale PWRs designs: U shaped or straight tubes Tubes subjected to tensile stresses Tube material susceptible to corrosion Stress corrosion cracking is the primary degradation mechanism Some SMR Designs: Helical shaped tubes Advanced tube material resistant to corrosion Compressive stresses Negligible risk from stress corrosion cracking Historical data-based SGTR frequency Based on non-homogeneous data Not reactor specific Actual reactor operating (boundary) conditions not taken into account Tube material properties or geometry not taken into account Chatterjee, K. and Modarres, M., A probabilistic physics-of-failure approach to prediction of steam generator tube rupture frequency, Nuclear Science and Engineering, Volume 170, Issue 2,

11 PPoF Estimation of SGTR Frequency Probabilistic Physics-of-Failure (PPoF) is a structured mechanistic-based approach with consideration of uncertainties. Why mechanistic? Considers underlying degradation and processes that lead to failure. Why probabilistic? Considers uncertainties associated with unknown or partially known factors such as material properties, manufacturing methods, model uncertainties, and measurement errors. Research objective: Develop a PPoF-based approach to SGTR frequency prediction. Develop mechanistic models of applicable primary failure mechanisms under normal operating conditions. Develop a Bayesian approach to estimate and characterize the epistemic and aleatory uncertainties. Develop an approach to estimate the stress agents acting on tubes. Develop a probabilistic reliability simulation and prediction approach. 11

12 PPoF-Based Approach for SGTR Frequency Prediction Identify SG tube geometry and material properties Identify underlying operating conditions Identify underlying degradation conditions Identify probable degradation mechanisms Experimental degradation data Formulate mechanistic models Finite element analysis Assess stress agents Characterize epistemic and aleatory uncertainties Initial flaw severity Estimate SGTR frequency through MATLAB simulation 12

13 SG Tube Primary Failure Mechanisms Stress corrosion cracking Fatigue SGTR Pitting corrosion Fretting wear Alloy 690 (higher corrosion resistance) used in modern steam generators. Risk of tube failure from SCC and pitting corrosion considerably reduced *. Susceptible to failure mechanisms: fatigue and fretting wear caused by flow-induced tube vibration. *Berge, P. et al., Materials requirements for pressurized water reactor steam generator tubing, Nuclear Technology, Vol. 55, October

14 Probabilistic Fatigue Model da dn c(1 0.82R) 2.2 ( K) p (0, ) Random Variables c p Estimation Process Bayesian regression Bayesian regression a i Literature data ΔS Finite element analysis da / dn = crack growth rate; DK = stress intensity factor range; R = stress ratio; a f = final crack size; c & p = model parameters; Y = crack geometry factor; t m = mean life of steam generator; a i = initial crack size; DS = stress range for the applied loading 14

15 Uncertainty Characterization of Fatigue Model Bayesian Regression Approach Crack growth rate (m/cycle) E-08 1E-09 1E-10 1E Stress intensity factor range, MPa.m^1/2 Bayesian regression da dn c(1 0.82R) g(c, p) 2.2 Parameter uncertainty (epistemic) ( K) p (0, ) g(ε) Model error Epistemic Aleatory CGR Data: Curtsey of Dr. Bill Shack, ANL PoF model Prior distribution of c and p Likelihood function Fatigue crack growth data for Alloy 690 Bayesian Inference Posterior distribution of c and p 15

16 Bayesian Regression and Uncertainty Characterization of Fatigue Model Parameter Estimation Crack growth rate (m/cycle) E-08 1E-09 1E-10 1E-11 Bayesian regression Parameters Values estimated through Bayesian regression μ p, σ p 3.75, μ c, σ c μ σ, σ σ 2.72E-13, 5.00E E-8, 2.36E Stress intensity factor range, MPa.m^1/2 Bayesian Regression using WinBUGS based on a Markov Chain Monte Carlo sampling Parameter, c Parameter, p Parameter, σ 16

17 Fatigue Model Epistemic Uncertainties p p c q( p, c) e ( c c z p 1 c 2 1 z ( p ) p 2 ( p )( c ) p c ) c 2 V pc p c 6 x Joint Probability Density Parameter, p Parameter, c x

Probabilistic Fretting Wear Model d 1 dl kf 2 dt R l 1 cos2 dt Input variable distribution sampling Initial flaw size, h i Random Variables Estimation Process/ Source Wear force and rate of change of

18 Probabilistic Fretting Wear Model d 1 dl kf 2 dt R l 1 cos2 dt Input variable distribution sampling Initial flaw size, h i Random Variables Estimation Process/ Source Wear force and rate of change of sliding distance with time Wear volume growth analysis k Bayesian regression Wear rate prediction Update wear depth, h i+1 k h wear wear coefficient; depth; L α contact sliding angle; 18 Repeat simulation distance; l R tube n=n+1 Yes radius; Yes support F h i+1 h critical No t f mean life normal No effective length force

19 Uncertainty Characterization of Fretting Wear Model Bayesian Regression Approach (μmm 3 /s) Wear rate Bayesian regression V = kfl dv dt = k d(fl) = k dw dt dt V = kw +e(0,s) Work rate, mw Data From: Lee, Y. et al., A study on wear coefficients and mechanisms of steam generator tube materials, Wear, Vol. 250, Issues 1-12, pp: , 2001 PoF model g(k) Parameter uncertainty (epistemic) g(ε) Model error Epistemic Aleatory Prior distribution of k Likelihood function Fretting wear data for Alloy 690 Bayesian Inference Posterior distribution of k 19

20 Uncertainty Characterization of Fretting Wear Model Parameter Estimation 800 (μmm 3 /s) Wear rate Bayesian regression Parameters μ k, σ k μ σ, σ σ Values estimated through Bayesian regression 3.0E-11, 4.1E E-13, 2.0E Work rate, mw 2.0E E E E Parameter, k E E E E E Parameter, s σ E E-13 20

21 Approach for Considering Parameter Uncertainties in Estimating SGTR Frequency r random samples from joint distribution of parameters, e.g., p and c Distribution of SGTR frequency p 1 & c 1 p 2 & c 2 p 3 & c 3 p 4 & c p r & c r Weighted distribution of SGTR frequency Example : weighted ( SGTR) i r 2 i 1 Pi ( SGTR1 SGTR SGTR ) r 21

22 Application of PPoF-Based Approach to A New Design of Helically-Coiled SG 22

23 SG Design Parameters SG coil is a once-through heat exchanger with many helically coiled tubes intertwined like DNA structure. Helical tubes are made of Alloy 690. Compressive forces. Primary coolant flows downward through the tube bundle by natural circulation. Helical tubes are subjected to liquid cross-flow externally and multi-phase flow internally. Cr Fe C Si Mn S Co Ni Alloy <0.15 <0.5 <1 <0.015 <0.1 Balance (>72) Alloy <0.05 <0.5 <0.5 <0.015 <0.1 Balance (>58) 23

24 Identification of Underlying Operating Conditions Vibration excitation mechanisms Occurrence conditions Effects Fluid-elastic instability High gap flow velocities High amplitude vibration and failure in quick time Vortex shedding Medium gap flow velocities High amplitude vibration and failure in quick time Turbulence excitation Low gap flow velocities Low amplitude vibration causing long-term damage, e.g., fatigue, fretting wear The high amplitude vibration excitation mechanisms should not occur for normal operating conditions in steam generators. Ref: Connors, H.J., Flow-induced vibration and wear of steam generator tubes, Nuclear Technology, Vol. 55, pp: ,

25 Critical Failure Mechanisms Failure mechanisms Degradation conditions Conditions in helical SG design Stress corrosion cracking Constant tensile stresses, corrosion susceptible material, corrosive environment Compressive stresses, Alloy 690 tube material (high corrosion resistance) Pitting corrosion Corrosive environment, corrosion susceptible material Alloy 690 tube material (high corrosion resistance) Fatigue Alternating stresses, localized degradation Alternating stresses due to turbulence induced tube vibration, manufacturing flaws Fretting wear Oscillatory small amplitude sliding motion between contacting components Relative fretting motion between tube and support plates due to turbulence induced tube vibration Alloy 690 helical tubes with pre-existing flaws are susceptible to fatigue and fretting wear failure mechanisms under turbulent flow-induced tube vibration. 25

Assessing Stresses Random Vibration Analysis Approach The approach developed in this research for determining the dynamic response of SG tubes to the turbulent

26 Assessing Stresses Random Vibration Analysis Approach The approach developed in this research for determining the dynamic response of SG tubes to the turbulent flow-induced forces is as shown in the flowchart. The approach uses finite element methods to determine the turbulence induced random vibration amplitudes and stresses. 26

27 Assessing Stress Agents Turbulence Induced Random Vibration Net lateral turbulent force acting on tube per unit length, Tube cross-section y z F y 2 0 p x,, t cosrddx The partial differential equation of motion of a uniform rod responding to this force is, 2 z, t Yz, t 4 Y EI m F y z, t 4 2 z t p(x,ө,t) ө R Fig: Turbulent primary fluid pressures Where, E isthe modulus of elasticity, m is the mass per unit length, I is the second moment of inertia, p(x,θ,t) is turbulent primary fluid pressure, R is outer radius of t is time. tube, Fig: Net lateral turbulent force Blevins, R.D., Flow-induced Vibration, Van Nostrand Reinhold, New York,

28 Assessing Stress Agents Finite Element Model and Modal Analysis Model of one span of the helical SG tube developed using ANSYS v Simply supported boundary conditions used at each end of the helical span to simulate the support points. Modal analysis performed to obtain the natural frequencies and the modal stresses. Reduced method used for the eigenvalue and eigenvector extractions to calculate tube natural frequencies. 28

29 Assessment of Stresses Turbulence-Induced Force PSD Calculation 1 2 D S Auto spectral density of turbulence-induced force normal F ρu D Φ fd/u y to 2 the axis Uof a cylinder in single-phase cross flow in steam generators * : where, S Fy where, S Fy f i D / U 6 force normal 10 to the faxis id/uof ρ 1 2 fluid 410 fd/u dimensionless spectral shape 3function f D/U, Critical velocity was estimated using the following equation ** in order to ensure that there is no U average cross flow velocity through the fluid-elastic instability in the tube bundles for the velocity range of interest (obtained from 2-D thermal minimum hydraulic gap between analysis) tubes during turbulent flow: D tube ρu 4 auto 4spectral 10 fid/u density of, 0.01 turbulence fid/u induced density outside 2 D 2 diameter D Φ U fd/u , i a, cylinder 0.2 fin D/U cross 3flow 0.5 C VΦ fd/u dimensionless spectral shape function c, n 2 m ζ t t t C 2 mt fnd d ρ V c,n is S Fy ρ D Φ total the density d external U average cross flow velocity through the minimum gap between tubes tube damping fluid of fluidelastic auto spectral density of turbulence induced force normal to the axis of mass tube density diameter f i D / U outside critical ratio instability per external velocity unit 2 diameter length fluid a cylinder in cross flow for nth coefficient of tube free 4 i f i vibration **Connors, H.J., Flow-induced vibration and wear of steam generator tubes, Nuclear Technology, Vol. 55, pp: , *Axisa, F., et al., Random excitation of heat exchanger tubes by cross flow, Journal of Fluids and Structures, Vol. 4, Issue 3, pp: , D/U mode, f i D / U.5,

30 Assessing Stress Agents Random Vibration Analysis Results σrms,1, y rms,1 σrms,2, y rms,2 σrms,3, y rms,3 σrms,4, y rms,4 σrms,5, y rms,5 σ rms = rms bending stresses y rms = rms vibration amplitudes One span of a helical tube SGTR frequency assessment: Bending stresses were used in probabilistic fatigue model. Vibration amplitudes were used to calculate the normal force initiating wear and rate of change of sliding distance with time, which were used in probabilistic fretting wear model. 30

31 Assessing Stress Agents Force Initiating Fretting Wear Normal force initiating wear assuming F 0, clearance if y between g the tube and its supports: F F n n where, y rms normal component of rms tube displacement F n k 0, if Equivalent stiffness, k c assuming an equivalent linear spring acting in the direction k c equivalent stiffness of tube support combination 2 of motion as soon as impact occurs: g diametric clearance between a tube y rms c ( y normal normal k c rms y Eh 1.9 d where, g), if g rms contact force component 2 y between of rms h d g rms tube F where, F n normal contact force between tube and support plates k c equivalent stiffness of tube support combination g diametric clearance between a tube and its support and k c n n and k c ( y support rms Eh 1.9 its d support g), if rms plates h d y g tube displacement where, h tube thickness; d tube diameter; E Young' s modulus rms h tube thickness; d tube diameter; E Young' s modulus Au-Yang, M.K., Flow-induced vibration of power and process plant components, ASME Press, New York,

32 SGTR Frequency Predictions for the New Design of Helical SGs Using the Developed PPoF Models and Calculated Stress Agents 32

33 Uncertainty Representation of SGTR Frequency Due to Fatigue 33

34 Uncertainty Representation of SGTR Frequency Due to Fretting Wear 34

35 Uncertainty Representation of Total SGTR Frequency 35

36 Summary and Conclusions Historical failure data-based SGTR frequency estimates do not apply to SMRs Based on non-homogeneous data collected from varied PWRs. Not plant specific. Do not account for degradation conditions or tube material and geometry. A PPoF-based SGTR frequency prediction approach has been developed in this research. Accounts for underlying degradation conditions. Considers epistemic and aleatory uncertainties of models and data. An application of the PPoF approach has been successfully implemented. PPoF technique provides an effective tool for evaluating safety and reliability of new SGs and other passive systems and structures. 36

37 Future Direction More detailed 3-D thermal hydraulic analysis of the primary-side fluid-flow characteristics (e.g., gap turbulent flow velocities, fluid density) and secondary side in SG tube bundles during normal operating conditions in the SMRs. Better characterization of the initial flaw characteristics would be useful. 37

38 Thank you! 38

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