Modeling of Multi-Physics Phenomena in Fast Reactors Design/Safety and Experimental Validation

Transcription

1 FR13, Paris FR13, Paris International Conference on Fast Reactors and Related Fuel Cycles (FR13) 4-7 March 2013, Paris, France Hisashi Ninokata, Hideki Kamide, Marco Pellegrini Marco Ricotti Modeling of Multi-Physics Phenomena in Fast Reactors Design/Safety and Experimental Validation Hisashi NINOKATA Politecnico di Milano Department of Energy CeSNEF-Nuclear Engineering Division Nuclear Reactors Group

2 Multi-physics phenomena of concern FR13, Paris Characterized by time-space scales Microscopic Mesoscopic Macroscopic Global scales Described by mass fields (components), flow fields, temperature fields Homogeneous mixture model Multi-fluid model or multi-fluid multi-field model Coupled with chemical reactions, structural mechanics, material sciences Chemical reactions Na burning, Na-H 2 O, Fluid-structure interactions chemical, mechanical, thermal Taking place when fast reactors are under S.S. full power operations: cavitation, erosion, corrosion, FP deposition, crud sedimentation, thermal striping/stratification, DHR conditions Transient conditions Accident conditions: fuel S/A degradation, core meltdown and relocation

3 Topics 1 Examples: 1. High cycle thermal fatigue in JSFR: Coupling of CFD and FEM 2. Sodium water reaction 3. Fuel S/A degradation and CDAs MULTI-PHYSICS PHENOMENA MODELING (NOTES ARE FROM OR BASED ON THE INFORMATION FROM JAEA)

4 High Cycle Thermal Fatigue at TOP Core Instrumentation Plate Thermal Fatigue caused by Thermal Mixing between - Hot Sodium from Fuel Subassemblies and - Cold sodium from Control Rod Channels and Blanket Fuel Subassemblies Upper Guide Tube Flow-hole 1st Baffle Plate (UIS) C/R Driving Rod Cold Sodium from C/R Electromagnet for SASS Core Instruments Plate (CIP) Hot Sodium Hot Sodium (Top view image around a control rod channel) Target Areas Concerning about Thermal Fatigue FS Primary Control Rod (PCR) Fuel Subassembly (FS) Backup Control Rod (BCR)

5 Numerical Estimation Method for Thermal Fatigue on CIP ~ Fluid-Structure Thermal Interaction Simulation ~ Japan Atomic Energy Agency 1Thermal-hydraulics in upper plenum by RANS - UIS external flow for blanket fuels - UIS internal flow for control rods Boundary conditions for local analysis 1Whole upper plenum analysis 2 Fluid-structure thermal interaction LES and heat conduction in structure simulation by MUGTHES in local areas around - Control rod (CR) channels - Blanket fuel (BF) subassemblies Temperature information in structure (for CRs) (for BFs) 2Local analysis 3Thermal stress analysis Local analysis around PCR of JSFR 3Estimation of structural integrity by thermal stress analysis (FINAS)

6 Numerical Simulations of Thermal Mixing in WATLON T-Pipe as Validation Japan Atomic Energy Agency Main pipe Branch pipe Inner Diameter: 0.15 m(=d m ) 0.05 m(=d b ) Inlet Temperature: 48 (=T m ) 33 (=T b ) Mean Velocity: (Impinging jet case) 0.26 m/s(=w m ) 1.0m/s(=V b ) (Wall jet case) 1.46 m/s(=w m ) 1.0m/s(=V b ) 4,000 data at 1kHz sampling during last 4 seconds in 10 seconds transient calculation Branch pipe flow 262,632 cells Main pipe flow (High Main Flow: Wall Jet) (Low Main Flow: Impinging Jet) Mm (kg.m/s2) Mr = Mm/Mb 0.35<Mr<1.35 ( :Deflecting jet) Mr < 0.35 ( :Impinging jet) M b (kg.m/s 2 ) Mr > 1.35 ( :Wall jet) Flow-pattern map 6 D b Mm m D m Mm b b 噴流の向き M m b b VW b Jet direction m M m m D b Main pipe flow: M m m Branch pipe flow: U 2 D D W m M D b b b W m 2 V b 2 4 b m

7 Typical Numerical Results of Fluid Temperature Distributions at Impinging Jet and Wall Jet Cases in WATLON Japan Atomic Energy Agency Impinging jet case y /Dm Experiment, (T-Tb)/dT b LES(Cs=0.14), (T -T b )/dt Experiment, T'/dT 0.0 LES(Cs=0.14), T' /dt Wall jet case temperature large-scale eddy structure (T -T b )/dt, T'/dT Experiment, (T-Tb)/dT b LES(Cs=0.14), (T-Tb)/dT b Experiment, T'/dT LES(Cs=0.14), T'/dT 0.6 y /Dm (T -T b )/dt, T'/dT

8 Topics 2 Examples: 1. High cycle thermal fatigue in JSFR 2. Sodium water reaction: wastage, failure propagation 3. Fuel S/A degradation and CDAs MULTI-PHYSICS PHENOMENA MODELING (NOTES ARE FROM OR BASED ON THE INFORMATION FROM JAEA)

9 Sodium-Water Reaction (SWR) Accident Safety assessment of steam generator (SG) in sodium-cooled fast reactor Na Water, vapor Reacting jet Failed tube Adjacent tube Sodium-water reaction Wastage Over-heating rupture Erosion FAC Combination Strength degradation Secondary failure (failure propagation) Progression of damage SG (evaporator) in Monju Water side: about 15 MPa Shell side: 0.2 MPa Evaluation of possibility of propagation most important issue Multi-physics nature: thermal hydraulics, multiphase flow, chemical reaction, structure, material complex 9

10 Evaluation of Failure Propagation Final goal is to evaluate wastage environment wastage rate possibility of failure propagation Evaluation for SG in prototype FR A large number of mock-up tests Evaluation for SG in commercial FR Numerical analysis and minimal mock-up test Analytical evaluation system (1) SERAPHIM Analysis of compressive multicomponent multiphase flow with SWR B.C. (2) TACT Analysis of target tube heat transfer and stress, evaluation of wastage rate and failure propagation Wastage environment B.C. (3) RELAP5 Analysis of boiling two-phase flow 10

11 Numerical Methods in SERAPHIM Basis Finite difference method 3D Cartesian coordinate (x, y, z), 2D cylindrical coordinate (r, z) Compressible multiphase flow model Multi-fluid model (water, liquid sodium and multi-component gas) HSMAC method (modified for compressible multiphase flow) Phase change model EOS: Modified Benedict-Webb-Rubin equation Sodium-water chemical reaction model Surface reaction model (gas-liquid reaction) Gas-phase reaction model (gas-gas reaction) 11

12 Surface Reaction Model Surface reaction = Chemical reaction at interface between water vapor and liquid sodium Model assumptions Na(liquid) Na(l) + H 2 O(g) NaOH(l) + 1/2H 2 (g) H 2 Infinite reaction rate (progress of chemical reaction is limited by mass flow rate of reactant gas toward interface) NaOH H 2 O Mass flow rate Reaction products move to gas phase sf Dmj sf b 1 H gl j Sh gyja j Le Yja l C Reaction heat is added to gas phase pg Interface Multicomponent gas: H 2 O, Na(gas), NaOH(aerosol), NaOH(gas), H 2 12

13 Numerical results for the SWAT-1R test Cylindrical vessel filled with liquid sodium Diameter: 0.4 m Height: 1.8 m Gas phase goes upward (weight averaged) (measured) 43 tubes Water vapor leaks from the lowest tube and goes upward [ o C] Conditions of water vapor: 17.0 MPa, 352 o C Conditions of sodium: 0.2 MPa, 470 o C Computational Domain Void fraction Calculation Temperature Field Experiment High temperature region expands to upper left both in the experimental result and the numerical result.

14 Topics 3 Examples: 1. High cycle thermal fatigue in JSFR 2. Sodium water reaction 3. Fuel S/A degradation and CDAs: calculation quality depends on the physical models MULTI-PHYSICS PHENOMENA MODELING (NOTES ARE FROM OR BASED ON THE INFORMATION FROM JAEA; AND TOKYO INSTITUTE OF TECHNOLOGY R&D RESULTS)

15 Computational model SAS/SIMMER code system for CDAs since 1970 s KAMUI for fuel S/A degradation by subchannel analysis Multi-component multi-phase flow Multi-component multi-field formulation In case of fuel S/A degradation: 3 components, 3-phases and 2- or 3-velocity fields (mixture velocity fields): [ex] Liquid-phase and solid-phase assigned to one field and gas-phase to the other; Mixture fields required mixture material properties (viscosity, heat capacity, conductivity,.. etc.) Phase interfaces --- topology Lumped modeling of heat, momentum and mass transfers at the phase interfaces among all components; all from experiment Component Solid-phase Liquid-phase Vapor-phase Fuel X X X Steel X X X Sodium X X (2velocity fields) Mixture velocity field Gas-phase v

16 In-Pile Experiment CABRI SCARABEE TREAT EBR-II IGR-EAGLE (Experimental Acquisition of Generalized Logic to Eliminate criticalities) 16

17 CDA Evaluation Methods & Mitigation Measures - IGR (Impulse Graphite Reactor) in EAGLE Project - CEC Control rod channel PERFORMANCE Max. thermal neutron flux density: Max. thermal neutron fluence: Min. half-width of pulse: Max. energy release: Central Experimental Channel (CEC): Cooling water n/cm 2 s cavity n/cm s 5.2 GJ φ228mm L3825mm Cross-section of IGR core (NNC in Kazakhstan) 17 Reactor core

18 CDA Evaluation Methods & Mitigation Measures - Upward Discharge Experiment in EAGLE Project - Discharge path SA can wall Core Sodium Discharge path Simulated upper plenum Inner duct Closed end Cross section IGR core Simulated core part Fuel pins to be molten FAIDUS option (reference for JSFR) Test section for upward discharge Insertion of test section into IGR core 18

19 Validation of subassembly degradation and core meltdown_relocation models CABRI hodo-scope data SCARABEE TIB temperature flow data TREAT/SLSF ACRR Coolant Fuel pin Wall Fissile length 60cm Flow blockage at the start of transient

20 flow Flow rate rate (m3/h /h) temperature Temperature (C) ( ) temperature Temperature (C) ( ) Multi-component multi-field model validation for SCARABEE-BE+2 Experiments -2 (TIB) Computation tcool(4,9) tcool(4,10) tcool(4,11) Coolant T (S/A peripheral) Time 12(sec) tim e (sec) tclad(1,9) tclad(1,10) tclad(1,11) Cladding T (S/A center) Time 12(sec) tim e(sec) B E+2 outflow Exit flow Time 12(sec) tim e (sec)

21 Multi-component multi-field model validation for SCARABEE-BE+2 Experiments -3 (TIB) S/A Centerline Good agreement for the onset timings of sodium boiling and cladding melting-relocation Fuel Clad S/A wall Fuel Clad Vapor Vapor Steel Blockage BLiquid ESteel Liquid Sodium Liquid Sodium 5s 7s

22 Multi-component multi-field model validation for SCARABEE-BE+2 Experiments -4 (TIB) S/A center fuel melting_relocation. S/A peripheral fuels no melting agreement with the experiment Fuel Clad Vapor Fuel Particle Liquid Sodium Liquid Steel Steel Blockage 15s

23 Multi-component multi-field model validation for SCARABEE-BE+2 Experiments -5 Subchannel analysis results KAMUI BE+2 KAMUI APL

24 Agreement? Excellent, good, fair, poor? Trend agreement is important but meaningless if the users don t try to catch physics To minimize subjective judgment on modeling multiphysics, we need: Identification and estimation of uncertainties Only visual comparisons are not sufficient

25 How do you catch physics? I. In case of DNS or LES So much information from DNS or LES Many new phenomena, detailed turbulent structure through visualization Done by visualization thanks to rapid progresses in CG technology. Fancy -- but it s a subjective approach Objective education techniques, to avoid possible controversy and to identify nature and significance of the structure Ex. Proper Orthogonal Decomposition Technique Oct H. Ninokata and E.

26 POD: Proper Orthogonal Decomposition To identify the motions which contain the most energy. Lumley (1967) Berkooz, Holmes & Lumley (1993), Holmes et al, (1996) Based on the Karhunen-Loeve expansion, a basic tool in pattern recognition; DNS (or LES) data: <U(x)>+u(x,t); Energy: u 2 Principle: Expand u(x,t) by the orthogonal functions; u(x,t) ~ Sa n (t)j n (x) Maximize u 2 : Orthogonal functions as a weighting function; The process reduced to an Eigen-value problem (l 1 >l 2 >l 3, >l N >...); Higher order terms can be curtailed: a partial sum is sufficient Therefore the maximization problem automatically selects the decomposition that contains the highest amount of energy in the first few modes. It allows us to truncate the expansion at low values of N Oct H. Ninokata and E.

27 How do you catch physics? II. In case of multi-physics simulation As more multi-physics involved, more complex calculation system with so many physical models representing the interactions Physical models are based on known knowledge and a result of assumptions, approximations, compromises With the CV sizes larger, more uncertainties Comparisons must be done with experiment (and theory if any), Done by visualization Not sufficient Needs to identify modeling uncertainties, to avoid possible controversy and to identify nature and significance of the structure An attempt to quantify uncertainty Oct H. Ninokata and E.

28 Uncertainty identification in physical modeling -1 Erroneous example: stratification in sodium flow turbulence heat flux model should take into account the gravity We would like to know how erroneous the predictions are when the turbulent heat flux is modeled w/ or w/o gravity effects We follow the Bayesian rule P(B A)={P(A B)*P(B)}/P(A) Prior probability P(B) [calculation] can be updated to P(B A) with P(A), probability of A by experimentation, where P(A B) a likelihood function; Noted that the likelihood P(A B) is given a priori but subjective; should be improved by optimal estimation-control theories

29 Uncertainty identification in physical modeling -2 Assume a degree of being subjective for a certain model, P(B), P(B) could be updated based on a direct comparison of the model prediction with experiment, to P(B A) By carrying out as many as calculations as possible with different model parameter values, we obtain P(B A) P(B A) accounts also for the uncertainty in the experimental results P(A) and provides statistical information on the mean value, standard deviation, tolerance limits,..

30 Uncertainty identification in physical modeling -3 A Simple Example: Suppose the model for the turbulent heat flux in a CFD code is expressed in terms of velocity gradient (C1) and the gravity effect (C3) Run as many cases for C1 and C3 as possible (Monte Carlo or economical Latin Hypercube Sampling) to construct a response surface Mean value of C1 and C3 represent optimal values while the standard deviation could be interpreted as a subjective degree of belief in C1 and C3 model parameters. C1 trustable; C3 questionable.. Note: this is just an example

31 Final Comments Focused on the current practices of numerical modeling and simulations of thermal hydraulic phenomena in sodium-cooled fast reactor systems All these multi-physics simulation models have been subject to on-going validation programs In practice, validation of engineering multi-physics phenomena is likely to be made on rather qualitative basis, often relying on many subjective judgments in comparison with the results from large-scale integral tests or mock-up experiments In validation processes, although an eventual subjective judgment cannot be ruled out but should be made minimal. To make it more quantitative and rational, a proposal has been made of the identification of errors and/or uncertainties inherent in computations based on the Bayesian rule

32 END Thank you! Hisashi NINOKATA Politecnico di Milano Department of Energy CeSNEF-Nuclear Engineering Division Nuclear Reactors Group

33 Modeling wall friction; Interfacial friction n F C 1/2 2 WL, Z, 1/2 f il W f h n 1 G 2 f 4 D 2 L b ( Cf) W a, m Re Re f G f Dh / f f : two phase flow pressure drop multiplier Fluid mixture wall friction factor f : mixture viscosity 1 n 1/ 2 n n 1 n 1 n 1 n 1 I, z C f G wg w L wg w L 1/2 n 1/2 FIL, z il,, 2, A 1/2 I z Iz n n 1/2 n 1/2 FIG, z AI, z Iz, il, 1/2 A I,z :Interfacial area concentration; ρ G :vapor density; C f :Interfacial friction factor (Wallis) ; w: axial velocity A I,z : α > 0.6 annular flow model 0.6 > α > 0.4 Ishii & Chawla for slug flows 0.4 > α Ishii & Chawla for bubbly flow model

34 Heat transfers Between solid wall and liquid (sodium, liquid phase of steel, MOX fuels) HT correlations for liquid metals Between solid wall and vapor-gas Dittus-Boelter etc. Between fluid and different fluid (sodium/molten steel, sodium/molten fuel, molten fuel/molten steel, etc) Between liquid and vapor-gas (Interfacial heat transfer and heat transfer with interfacial mass transfer) Radiation heat transfer