Introduction to Fuel Behaviour Modelling

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2 1 Introduction to Fuel Behaviour Modelling Wolfgang Wiesenack OECD Halden Reactor Project, Norway Joint ICTP-IAEA Advanced Workshop on Multi-Scale Modelling for Characterization and Basic Understanding of Radiation Damage Mechanisms in Materials Trieste, April 12-23,

3 Overview Purpose and application of fuel modelling codes Main components 1. temperature calculations 2. fission gas release 3. dimensional changes and mechanical loads Code structure Basic measurements for in-core experiments Overview of codes 2 IAEA-ICTP 2010

4 Application of Fuel Performance Codes Calculate the behaviour of a fuel rod during irradiation steady state irradiation transients radiological source terms for accident analysis Applications include: R & D purposes design of new fuels and fuel cycles prove that operational limitations and safety criteria are obeyed (safety case submission) 3 IAEA-ICTP 2010

5 Ideally we want to predict... oxide thickness temperature distribution stored heat clad diameter fuel diameter PCMI ridging? (crack distribution) porosity distribution grain size distribution FGR, 131 I inventory rod pressure did it fail? 4 IAEA-ICTP 2010

6 Typical code structure Input Data Define calculating geometry Determine length of next timestep Determine power distribution fuel/clad mechanics PCMI Iteration loop Clad-fuel temperature distribution Failure probability Fission Gas Release Radioactive gap inventory Rod internal pressure 5 IAEA-ICTP 2010

7 ... but it may be more complicated 6 IAEA-ICTP 2010

8 Fuel behaviour codes must address and untangle interactions that become more and more complex as fuel burnup increases Fissions & fission products Time Enrichment Rim formation Conductivity degradation Fission gas release Rod pressure Fuel swelling Fuel temperature Fuel-clad bonding Gd high B fuel high Li Coolant chemistry CRUD AOA Clad lift-off Stored heat PCMI corrosion RIA 7 IAEA-ICTP 2010 LOCA

9 1. Fuel rod temperature distribution Many properties are exponentially dependent on temperature. Therefore, accurate temperature estimates are important. The fuel temperature is strongly linked to stored energy that must be removed in LOCA thermal expansion of the fuel pellet as strong contribution to pellet-clad mechanical interaction and rod failure fission gas release and thus rod pressure The fuel temperature distribution depends on design parameters, materials properties and on many phenomena which develop during irradiation. The fuel temperature is important for many safety criteria 8 IAEA-ICTP 2010

10 2. Fission gas release Fission products are responsible for fuel swelling and PCMI (solid fission products) stress corrosion cracking and failure (iodine) pressure build-up in the fuel rod (xenon, krypton) feedback on gap conductance and fuel temperature rod overpressure and clad lift-off driving force for ballooning during LOCA pressure build-up in the fuel pores fuel fragmentation and expulsion during RIA and LOCA gaseous swelling and PCMI (failure) Rod pressure is limited by safety criteria and must therefore be calculated for the safety case 9 IAEA-ICTP 2010

11 3. Dimensional changes and mechanical loads Reversible Elastic deformation Thermal expansion Partly reversible Cracking Fragment relocation Permanent Plastic deformation Creep Fission product swelling Densification Thermal expansion of the pellet in a temperature gradient causes ridging at the pellet-pellet interfaces (also called wheatsheafing, hour glassing) 10 IAEA-ICTP 2010

12 Treatment in fuel behaviour modelling 1 ½ D codes axi-symmetric 1D model (radial dependence only) axial length (z direction) is divided into nodes 2D 3D codes more rigorous description of the geometry, but... restricted to a few pellets (2D: axi-symmetric r-z) Axial coupling usually no axial heat flow released fission gas is distributed, same pressure everywhere mechanical coupling is complicated codes must consider relative movement between pellet and cladding: no contact, frictional sliding, sticking many 1 ½ D codes reduce the problem to no contact and sticking, thus avoiding the complications of axial coupling (a reasonable approximation valid for many situations, but not always) 11 IAEA-ICTP 2010

13 How accurate can fuel modelling be? Experimental Temperature ( o C ) % Predicted Temperature ( o C ) + 10 % FUMEX-I started with blind predictions of HRP experiments The codes showed considerable variation even if the input was the same temperature prediction fission gas release Very few codes were able to reproduce the mechanical response 12 IAEA-ICTP 2010

14 Useful Reading Donald R. Olander Fundamental Aspects of Nuclear Reactor Fuel Elements (Although from 1976, the fundamentals of most phenomena described in the book are unchanged. Look out for a new edition currently being prepared by Prof. Olander and a team of co-authors) SCDAP/RELAP5-3D Code Development Team MATPRO - A Library of Materials Properties for Light-Water- Reactor Accident Analysis (Contains correlations for many nuclear fuel materials properties, discussion of the underlying data and how the correlations were derived. Latest edition is from The link is the 1993 edition: ) 13 IAEA-ICTP 2010

15 HRP fuel performance data base Experimental data since 1970 Numerous experiments measuring fuel temperature rod pressure clad strain (axial and circumferential) Separate effect studies fission gas release (steady state, transient) fuel conductivity rod overpressure Various fuel types: standard and modified UO 2 MOX and inert matrix fuel UO 2 with gadolinia VVER fuel Burnup range 0 90 (-150) MWd/kg 14 IAEA-ICTP 2010

16 What can be measured on a fuel rod and to what fuel performance issue does the measurement relate? 1. Fuel Temperature Heat transfer (fuel thermal conductivity, gap conductance) 2. Rod Internal Pressure Change Fission gas release, fuel densification & swelling 3. Fuel Stack Length Change Fuel densification & swelling 4. Fuel Cladding Length Change PCMI, (or when no PCMI, surface heat transfer, growth) 5. Fuel Rod Outer Diameter Change PCMI, (or when no PCMI, creep & growth, corrosion) 15 IAEA-ICTP 2010

17 1. Fuel Temperature A good prediction of fuel temperature is an essential requirement for any fuel performance code Fuel centreline temperature is measure at a single point in an annular fuel pellet with a thermocouple along the length of an annular fuel stack (average fuel centreline temperature) with an expansion thermometer Fuel centreline temperature measurements enable modellers to test their code predictions with respect to: Fuel thermal conductivity and its degradation with burn-up Gap conductance / gas composition (fission gas release) Gap width (fuel densification & swelling, cladding creep) Fuel pellet surface roughness Eccentricity in the fuel stack 16 IAEA-ICTP 2010

18 Measuring Fuel Temperature with a Thermocouple High temperature thermocouples suitable for measuring inside a fuel stack are: W / Re Nicrosil / Nisil Strengths of thermocouples Reliable measurement: up to C, thermocouples can last several years and will even manage a few hours at 2000 C Accurate measurement: easy to calculate from measured to solid fuel pellet temperature Weaknesses of thermocouples Tendency to premature failure at high fuel temperatures or in failed rods Need to account for decalibration due to transmutation at high fluence 17 IAEA-ICTP 2010

19 Measuring Fuel Temperature with a Thermocouple In core connector Thermocouple end plug Instrument base plug Thermocouple Molybdenum tube Pre-irradiated fuel rod segment Both fresh and irradiated fuel pellets in a stack can be drilled to allow insertion of a thermocouple Neutron radiography shows exactly where the thermocouple tip (hot junction) is positioned Instrument base plug Pressure transducer end plug 18 IAEA-ICTP 2010

20 Measuring Fuel Temperature with an Expansion Thermometer Test rig structure (grid plate) Fuel rod upper end plug Plenum spring Fuel pellets (annular) Tungsten rod (dia. 1,5mm) Cladding Fuel rod lower end plug Core holder Ferritic core Linear voltage differential transformer (LVDT) Test rig structure (grid plate) A thin tungsten rod is inserted through a centre hole drilled in the entire fuel stack One end of W-rod fixed to fuel rod end-plug, other end is free and fitted with a magnetic core, movement of core sensed by an LVDT (Linear Voltage Differential Transformer) Average centreline temperature in fuel stack derived from measured axial expansion of tungsten rod 19 IAEA-ICTP 2010

21 Linear Variable Differential Transformer (LVDT) a c d Developed for measuring fuel rod pressure, temperature, fuel stack and cladding elongation Primary coil with two secondary coils connected in opposition. Movable magnetic core concentrically located inside coil system Core movement affects the balance of the secondary coils and generates the signal output b g f e a: b: c: d: e: f: g: Test rod end plug assembly Primary coil Secondary coils Ferritic core Twin-lead signal cables Body Housing 20 IAEA-ICTP 2010

22 2. Fuel Rod Internal Pressure Change Measuring changes in rod internal pressure provides data on Fission gas release (FGR) Fuel stack densification and swelling (in absence of FGR) Understanding or being able to adequately model fission gas release mechanisms is important especially for development of new fuel types for better fuel performance Rod pressure measurements often combined with fuel temperature measurements e.g. investigating threshold temperature for FGR onset Fuel rod internal pressure is a key issue for extending the discharge burn-up of fuel for power reactors - most licensing bodies limit allowable fuel rod internal pressure 21 IAEA-ICTP 2010

23 Measuring Fuel Rod Internal Pressure Change Gas connection to test rod Bellows support Bellows End plug Support for ferritic core Ferritic core Linear voltage differential transformer (LVDT) Small stainless steel or Inconel sealed bellows unit inserted in a fuel rod endplug Gas pressure in fuel rod acts on bellows One end of bellows fixed to end-plug, other end is free and fitted with a magnetic core, movement of core sensed by an LVDT In-pile calibration at start of life (know rod pressure), then subsequent signal gives change in rod pressure Different bellows used for different expected measuring ranges: up to 15, 30 or 70 bar ΔP 22 IAEA-ICTP 2010

24 3. Fuel Stack Length Change Measuring changes in fuel stack length provides data on Fuel densification and swelling (fuel-clad gap open) Fuel densification and swelling are of interest because of the way they affect the development of the fuel-clad gap e.g. as fresh fuel densifies initially, the gap size increases inducing an increase in the fuel temperature Dimensional stability behaviour varies between different fuel types and this is something that fuel models need to capture Fuel density Pellet shape (flat ended versus dished, hollow versus solid) MOX fuel, Gd-doped fuel, other additive fuels 23 IAEA-ICTP 2010

25 Measuring Fuel Stack Length Change Linear voltage differential transformer (LVDT) Magnetic core Support for magnetic core End plug Spring Fuel stack Magnetic core holder fitted in fuel rod end-plug and spring loaded against fuel stack end Axial densification / swelling of the fuel stack acts on spring so magnetic core holder position moves Core movement sensed by LVDT In-pile calibration at start of life (zero point), then subsequent signal gives change in fuel stack length Stops being relevant once fuel-clad gap closes Because of connection between fuel dimensional changes and fuel temperature, fuel thermocouple often inserted at other end of same fuel rod 24 IAEA-ICTP 2010

26 4. Fuel Cladding Length Change Measuring changes in fuel cladding length can provide data on cladding strain from fuel pellet to cladding mechanical interaction (PCMI) under different conditions which can be used for model development predicting the outcome of situations where clad integrity may be jeopardised When there is no PCMI, measurements provide data on Heat transfer properties of surface layers (oxide, crud) Irradiation growth of cladding Onset of dry-out (in dry-out testing) 25 IAEA-ICTP 2010

27 Measuring Fuel Cladding Length Change Test rig structure (grid plate) Fuel rod upper end plug Plenum spring Fuel pellets Cladding Fuel rod lower end plug Core holder Ferritic core Linear voltage differential transformer (LVDT) Test rig structure (grid plate) Upper end of fuel rod fixed to test rig structure Magnetic core holder fitted to end-plug at lower (free) end of fuel rod Change in fuel cladding length causes core holder position to move relative to an LVDT In-pile calibration at start of life (zero point), then subsequent signal gives change in cladding length 26 IAEA-ICTP 2010

28 5. Fuel Rod Outer Diameter Change Measuring fuel cladding outer diameter changes can provide data on PCMI during power transients (continuous measurement) Cladding creep (measurement made once a week) Oxide / crud build-up on a fuel rod (measurement made once a month) Monitoring diametral in addition to the axial components of PCMI enables better understanding of what occurs during power transients Most fuel performance codes contain models for cladding creep as this affects the development of the fuel-clad gap as well as influences a fuel rod s PCMI behaviour Discharge burn-ups are often limited by the corrosion behaviour of the fuel rod cladding so knowing how different claddings behave in different water chemistries in-pile is a vital part of alloy development 27 IAEA-ICTP 2010

29 Measuring Fuel Rod Outer Diameter b a a b c Instrument based on the LVDT principle f a: Primary coil b: Secondary coil c: Ferritic bobbin e d g d: Ferritic armature e: Cross spring suspension f: Feelers g: Fuel rod Transformer body connected to armature via a pivot point Feelers on opposite sides of the fuel rod trace the fuel rod outer diameter profile Unit is driven along the fuel rod by a hydraulic system Position sensor used to sense axial position of DG along the rod Calibration steps machined into the fuel rod end-plug surface 28 IAEA-ICTP 2010

30 Methods (secondary measurements) Gas flow through a fuel stack (hydraulic diameter) Gas flushing plus gamma spectroscopy (fission gas release) Noise analysis Fuel temperature response to scram 29 IAEA-ICTP 2010

31 Secondary measurements Hydraulic diameter measurements determine the resistance that the fuel stack offers against gas flow and is applied to map changes of the fuel-clad gap with increasing burnup determine loosening of the fuel column in clad lift-off tests find the resistance of the fuel stack against axial gas transport (e.g. in LOCA or from local fission gas release). Gamma spectrometry (fission gas release) allows assessing low temperature fission gas release, recoil component, microstructural properties such as the surface-to-volume ratio Fuel time constant can be derived through evaluation of rapid power changes (reactor scram) noise analysis (fuel thermocouples + fast response ND) 30 IAEA-ICTP 2010

32 Origin and characteristics of codes (Fumex) Code BACO ELESIM EIMUS Organization Country CNEA Argentina AECL Canada CRIEPI Japan Based on Use Special feature BACO PHWR UO2 & MOX ELESIM CANDU ANS5.4 fission product release FEMAXI- 3 Evaluation BWR PWR HBWR ENIGMA BE, BNFL, UK PWR CAGR (BE) MOX (BNFL) ridging, 131 I release ENIGMA VTT Finland ENIGMA (UK) WWER E110 clad properties FAIR BARC India Ni-1 PHWR AHWR 2D capability clad failure model UO2 & MOX FRAPCON USNRC BWR, PWR Licensing benchmark FRAPCON (VO) CIAE China US version design, operation and clad failure model trans. code input safety evaluation FUDA BARC India design & licensing ridging clad failure model 31 IAEA-ICTP 2010

33 Origin and characteristics of codes (Fumex) Code Organization Country Based on Use Special feature PIN-micro REZ Czech Rep GT-2 PIN LWR WWER PIN-W RezCzech Rep PIN-micro WWER licensing PROFESS BARC India PIE analysis UO 2 & MOX ROFEM 1B INR Romania FEMAXI-3 PHWR CANDU START-3 IIM Russia fuel behaviour R&D Fuel failure calc. TRUST NFD Japan R&D Fuel design TRANSURANUS ITU Germany URANUS Fuel behaviour R&D MOX, UC, UN fast reactor, Monte Carlo TRANSURANUS PSI Switzerland ITU version Fuel behaviour R&D METEOR CEA France ITU code Fuel behaviour R&D COPERNIC FRAMATOME France TRANSUR BWR, PWR fuel design and licensing COMETHE-IV Belgo Nucleaire, Belgium BWR, PWR fuel design and licensing COSMOS KAERI South Korea Fuel performance analysis CYRANO-3 EDF France PWR licensing SIERRA Siemens PC BWR, PWR fuel design and licensing 32 IAEA-ICTP 2010

34 Origin and characteristics of codes (ANS Park City 2000) Code Organization Country Based on Use Special feature FRAPCON-2 USNRC GAPCON THERMAL-2 BWR, PWR FRAPCON-3 USNRC FRAPCON BWR, PWR -2 FRAPTRAN USNRC FRAPT-6 Transient analysis eg SCANAIR FRAS DRS/SEMAR France Kurchatov Institute, Russia LOCA and RIA Transient analysis eg LOCA and RIA Transient analysis eg RIA Licensing benchmark Licensing benchmark Fast transient capability Fast transient capability Fast transient capability 33 IAEA-ICTP 2010

35 The END 34 IAEA-ICTP 2010

36 2 Fuel Temperature Modelling and Phenomena (I) Cladding temperature and pellet-clad heat transfer Wolfgang Wiesenack OECD Halden Reactor Project, Norway Joint ICTP-IAEA Advanced Workshop on Multi-Scale Modelling for Characterization and Basic Understanding of Radiation Damage Mechanisms in Materials Trieste, April 12-23,

37 Overview Why temperature calculation? Coolant and cladding heat transfer Conductance through pellet-clad gap open gap, gas conduction closed gap, contact conductance geometrical changes influencing gap size Fuel temperature distribution Principal formulation fuel conductivity power distribution 2 IAEA-ICTP 2010

38 Fuel rod temperature distribution Many properties are exponentially dependent on temperature. Therefore, accurate temperature estimates are important. The fuel temperature is strongly linked to stored energy that must be removed in LOCA thermal expansion of the fuel pellet as strong contribution to pellet-clad mechanical interaction and rod failure fission gas release and thus rod pressure The fuel temperature distribution depends on design parameters, materials properties and on many phenomena which develop during irradiation. The fuel temperature is important for many safety criteria 3 IAEA-ICTP 2010

39 Practical influences and data The steady state temperature distribution can be calculated from outside to inside, starting from the fixed coolant temperature Knowledge of the conditions (material properties, temperature) inside is not required!!! In the following sections, the various influences will be visited one by one (from outside to inside) Their effect will be illustrated by experimental data where possible 4 IAEA-ICTP 2010

40 centreline Typical temperature distribution (20 kw/m) Heat flow resistances Pellet Gap Clad 840 C coolant 280 C 470 C 320 C 290 C 1. coolant cladding 2. oxide/crud layer 3. cladding wall 4. inner oxidation / bonding layer 5. fuel cladding gap numerous influences 6. fuel conductivity general porosity high burnup porous rim cracks 5 IAEA-ICTP 2010

41 1. Coolant clad heat transfer PWR conditions: Dittus - Boelter correlation h = * k/d E * Re 0.8 * Pr 0.4 k = water conductivity, D E = equivalent diameter, Re = Reynolds number, Nu = Nusselt number, ΔT C = q /(πd h) BWR conditions: Jens - Lottes correlation T wall T sat = 0.79 * exp(-p/62) * (q ) 0.25 p = pressure (bar); q = heat flux,w/m 2 typical ΔT C at 250 W/cm = 25 K for PWR 8 K for BWR 6 IAEA-ICTP 2010

42 2. Crud and oxide layer Outer oxide layer ΔT OX = q /(πd k OX /w OX ) k OX = 0.015±0.005 W/cm K; w OX = μm for PWR fuel at high burn-up (a factor of ~3 lower for BWR fuel). ΔT OX = C for q = 250 W/cm in PWR Crud layer constitutes a heat transfer barrier. the crud thickness is normally moderate (some tens of μm at most) conductivity is comparable to oxide conductivity. 7 IAEA-ICTP 2010

43 Cladding temperature / oxide layer Measurement of the cladding temperature is normally not within the scope of the HRP experimental programme. However, if PCMI can be eliminated, details of cladding elongation behaviour can be used to qualify Coolant-clad heat transfer coefficient (Jens-Lottes not satisfactory for low power) Zry-oxide conductivity Elongation of cladding with and without outer oxide layer 8 IAEA-ICTP 2010

44 3. Temperature increase in the cladding Conductivity, W/mK Q k clad ΔT Thermal conductivity of zircaloy Source: Matpro Temperature, C ΔT = 1 k k = average conductivity (W/m K) q = linear heat rating (W/m) R o, R i = outer, inner cladding radius (m) for typical wall thickness mm, the problem can also be approximated in 1 dimension k 17 W/m K (linear function of T) Example: ΔT for 0.6 mm thick cladding with R i = 4.2 mm at 20 kw/m? ΔT ~ 25 K q' R ln( 2π R o i ) 9 IAEA-ICTP 2010

45 4. Inner oxidation and bonding layer At burnup >35 MWd/kg, a bonding layer develops between fuel and cladding Fuel-cladding contact (pressure) is essential for the formation It consists of oxides of Zr and U and fission products (e.g. Cs) cladding bonding layer fuel The conductivity is similar to that of ZrO 2 and UO 2 The gap is effectively closed 20 μm 10 IAEA-ICTP 2010

46 5. Temperature step in the pellet-cladding gap Heat transfer routes: 1. h rad by radiation 2. h cont through areas of contact 3. h gas through the gas gap the pellet is usually eccentrically located in the cladding tube treatment in one dimension with effective heat transfer coefficient h eff = h rad + f(h cont, h gas ) proper averaging (f) of contact and gas conductance is important for good results model details depend on numerous properties and results from other parts of a fuel modelling code 11 IAEA-ICTP 2010

47 ... and interactions may be quite complicated 12 IAEA-ICTP 2010

48 Gap conductance Gap conductance models usually contain a number of parameters that are experimentally accessible. Halden reactor separate effects experiments include: Systematic variation of gap size ( μm) Variation of surface roughness of fuel and cladding Assessment of effect of eccentric pellet location Different initial fill gases (He, Ar, Xe) and their mixtures Variation of gap gas composition in-pile Determination of gap size by different techniques The associated data are indispensable for the verification of correct modelling of basic phenomena in fuel-clad gap heat transfer 13 IAEA-ICTP 2010

49 5.1 Radiative heat transfer Stefan-Boltzmann constant ( W/m 2 K) h rad σ ( T = Fuel & clad emissivities )( T ( 1/ ε ) + ( 1/ ε ) 1 typical emissivities: ε f = x10-5 T (= 0.8 at 500 C) ε c = 0.3 (shiny metal) 0.8 (oxidised) 2 f f + no dependence on gap size since ratio of inner and outer radii is practically 1 (small gap) Small contribution in normal operation 1-2 % of total heat transfer T 2 c Surface temperature fuel & cladding (K) f c + T c ) 14 IAEA-ICTP 2010

50 5.2 Contact conductance Roughness Fuel Cladding δ k f k c Areas of contact Interfacial pressure P i h cont Occurs even for open gaps due to eccentric location of pellets Several theories mostly based on circles of contact whose number or area increases with interfacial pressure A typical equation has the form: β 2k k f c = k f + k 1/ 2 c δ Const Pi H Fitted to data Meyer hardness 15 IAEA-ICTP 2010

51 5.3 Gas conductance through the gap Fuel d thermal Effective gap clad g ΔT gap Energy transfer (conductance) through a gas is independent of gas pressure if the mean free path is small compared to the conduction path. This is not the case for the pellet-clad gap. Imperfect heat transport across the solidgas interface leads to the concept of the Temperature Jump Distance (g) which effectively increases the gap size: h gas = δ + d k gas thermal + 2g surface roughness thermal gap temperature jump distance 16 IAEA-ICTP 2010

52 k gas gas conductivity Gases are bad heat conductors (good insulation) k gas = A 4 10 T 0.79 thermal conductivity (W/mK) Helium Krypton Xenon temperature (C) k gas (W/mK) and T(K) A = 15.8 He 1.15 Kr 0.72 Xe Note: independent of pressure For a gas mixture: x He and (1-x) Xe k mix = ( k He ) x ( k Xe ) (1 x) (von Ubisch rule, more complicated formulations exist) 17 IAEA-ICTP 2010

53 In-core effect of fill gas composition The initial fuel rod fill gas (helium) is diluted by released fission gas resulting in decreased gap conductance The effect and the feedback on temperatures and further gas release needs accurate modelling A number of experiments were conducted in the past where xenon or argon were added to simulate various degrees of fission gas release Fuel centre temperature, o C kw/m 20 kw/m initial Xenon content, % Influence of fill gas on fuel temperature 18 IAEA-ICTP 2010

54 2g temperature jump distance The Halden FTEMP code uses this empirical expression: x g m (10 9* ) Xe 2 ( μ ) = p x Xe = fraction of Xe in He p = gas pressure (bar) This equates to 2g values at STP (1 bar) of: ~10. μm He ~1.0 μm Xe 19 IAEA-ICTP 2010

55 2g in-core effect of temperature jump distance Gap conductance models employ the concept of extrapolation length to account for imperfect heat transfer between gas and solid The correction depends on pressure (and temperature) The effect has been assessed experimentally It is stronger than calculated with 2g in the gap only and includes fuel cracks (a heat flow resistance as well) It shows some burnup dependence, possibly due to changes in number of fuel cracks temperature change (K) 0,00-5,00-10,00-15,00-20,00-25,00-30,00-35,00-40,00 TF2 Ar TF2 He TF6 Ar TF6 He TF8 Ar TF8 He 0,00 0,25 0,50 0,75 1,00 inverse pressure 1/p (1/bar) 20 IAEA-ICTP 2010

56 δ surface roughness Surface roughness is a parameter in gap conductance models effective gap width contact conductance The parameter was investigated in IFA Although an effect could be identified, it was not as clear and pronounced as predicted 21 IAEA-ICTP 2010

57 ... and the gap (d thermal )? The phenomena and properties mentioned before (with complexity of description ranging from constants and empirical equations to formulations based on first principles) are important parts of gap heat transfer modelling. However the most important quantity is the pellet-clad gap. It depends on 1. differential thermal expansion of fuel and cladding 2. fuel cracking and relocation 3. distribution of open and closed gap 4. fuel densification and swelling 5. clad creep-down Many of these phenomena are stochastic and cannot be calculated exactly depend in complicated ways on other phenomena The calculation of the heat transfer between pellet and cladding remains a source of uncertainty 22 IAEA-ICTP 2010

58 5.3.1 Differential thermal expansion MATPRO recommendations for Zry and UO 2 ε ε ε clad, circ clad, axial uriania = = = T T T e 5000 / T Uranium oxide expands more than Zircaloy (circumferentially) The fuel gets much hotter than the cladding the gap closes due to thermal expansion expansion (-) 0,025 0,02 0,015 0,01 0,005 0 Zry circumf. Zry axial uranium oxide temperature, C 23 IAEA-ICTP 2010

59 5.3.2 Fuel cracking and relocation A fuel pellet will start cracking at W/cm due to thermal stresses induced by the temp. gradient Cracks are irregular, but with a predominantly radial direction hollow pellets tend to develop nice radial cracks The fuel fragments are assumed to relocate slightly evidence is essentially indirect through temperature meas. Fuel modelling codes employ the relocation concept to improve fuel temperature predictions by decreasing the thermally effective gap size 24 IAEA-ICTP 2010

60 Extent of relocation Relocation can be regarded as a parameter to bring about agreement between measured and calculated fuel centre temperatures As a modelling concept, it is thus not independent of other models and correlations employed in a code Typical values (code dependent) 20-40% reduction of cold gap slight increase with power slight increase with burnup It is reasonable to assume that a fragment can be found anywhere in the available relocation space 50% reduction of hot gap on average effective circumferential crack component (heat flow resistance in the fuel) should reduce the overall conductance improvement 25 IAEA-ICTP 2010

61 5.3.3 Modelling alternative: Distribution of open and closed gap Instead of reducing the thermal gap, it can also be assumed that a certain fraction of the fragments is in contact with the cladding while the rest keeps a maximum separation Such a concept, the contact area function, is employed in the Halden Project s temperature analysis code FTEMP In ENIGMA, gap conductance is improved by a contact component that is always present δ 2 CA = 1 ( ) 1.5 ε δ CA = contact area function δ = diametral gap (hot) ε = contact fration 1,2 1 0,8 0,6 0,4 0,2 eccentricity parameter 0 Contact Area Function hot diametral gap, micro m 26 IAEA-ICTP 2010

62 Average heat transfer coefficient A 1-D treatment requires a proper averaging to derive an effective heat transfer coefficient from the components: heat source R fuel R fuel heat source R fuel h eff = h rad + f(h cont, h gas ) Various concepts for f are employed i fuel modelling codes R cont R gas coolant R eff coolant The Halden Project FTEMP uses the electrical analogy of parallel resistances between a common potential difference R h eff eff = R = 1/ R fuel eff CA + R cont + 1 CA R + R fuel gas 1 R fuel 27 IAEA-ICTP 2010

63 Effect of eccentrically located pellet on fuel centre temperature Fuel pellets assume an eccentric position in the cladding tube. The asymmetric heat transfer should lead to overall lower average fuel temperatures compared to the ideal concentric case. The effect was investigated in HBWR experiments which provided some corroboration of the expected outcome. The nonlinear relation of temperature vs. power is typical of Xe or fission gas filled rods. Fuel centre temperature, o C Xenon, concentric Xenon, eccentric Helium data local power, kw/m Effect of eccentric pellets on temperature 28 IAEA-ICTP 2010

64 The pellet-clad gap is opened by fuel densification cladding creep (if overpressure)... closed by cladding creep fuel swelling More about these in lecture on dimensional changes and pellet-clad interaction 29 IAEA-ICTP 2010

65 Variation of gap size The gap between fuel and cladding is a design parameter and in addition changes with exposure Numerous HRP experiments provide an extensive data base for assessing the basic influence of gap size on gap conductance The general trend is summarised in the graph on the right for Helium and Xenon as fill gas Fuel centre temperature, o C Xenon 20 kw/m As fabricated gap, mm Helium 30 kw/m Helium 20 kw/m Influence of gap on fuel temperature 30 IAEA-ICTP 2010

66 Gap size determination The size of the gap between fuel pellet and cladding can be assessed by different direct and indirect techniques: Clad squeezing (mechanical in-core device) Hydraulic diameter measurements Evaluation of onset of pellet-clad mechanical interaction Gas exchange and effect on fuel temperature 31 IAEA-ICTP 2010

67 Clad squeezing technique Clad squeezing was used to determine the fuel-clad gap at power. A discrepancy between calculated thermal expansion and measured gap is apparent. 32 IAEA-ICTP 2010

68 Hydraulic diameter measurements Hydraulic diameter (μm) initial gap gap closure with 0.7 ΔV/V swelling per 10 MWd/kgU Burnup (MWd/kg UO 2 ) Change of hydraulic diameter (free fuel column volume) The hydraulic diameter reflects the free volume in the fuel column. Normal changes are: initial pellet cracking and fragment relocation solid fission product fuel swelling development of a minimal HD as fuel and cladding accommodate to each other 33 IAEA-ICTP 2010

69 Hydraulic diameter measurements At zero power, high burnup fuel typically has a gap size reflecting thermal contraction from the accommodation power level When the accommodation power level is approached, the hydraulic diameter decreases at a higher rate, similar to the onset of PCMI Regular measurements in a number of HBWR experiments connected to the gas flow system High burnup fuel example The hydraulic diameter measurements show a linear decrease of gap size with increasing power 34 IAEA-ICTP 2010

70 Gap size - onset of PCMI Clad elongation (mm) Calc. thermal expansion Measured elongation Rating (kw/m) Cladding elongation of ex-pwr fuel (57 MWd/kgU) during several start-up / shut-down sequences Pellet-clad mechanical interaction undergoes various phases. When the cracked fuel has accommodated to the cladding, the onset of appreciable PCMI indicates gap closure. The high burnup fuel example illustrates: cladding elongation deviates little from free thermal expansion onset of interaction occurs at previously reached maximum power (14-16 kw/m) 35 IAEA-ICTP 2010

71 Gas exchange in irradiated fuel rods Experimental rigs with gas lines provide for a change of fill gas during in-core service This feature allows assessing the dependence of gap conductance on fill gas composition Other influences on gap conductance are (practically) unchanged relocation fuel cracking pattern 36 IAEA-ICTP 2010

72 Change of fill gas and temperature response Fuel temperatures with He and Ar fill gas The difference between Ar and He fill gas is small, reflecting an essentially closed gap The comparison with code calculations is satisfactory, but details differ: the calculated temperature curve bends upwards, while the measured data are best rendered by a straight or slightly downward bending curve Such subtle differences may indicate a different distribution of the thermal resistances (solid fuel, fuel cracks, fuelclad gap) than commonly assumed in fuel modelling codes 37 IAEA-ICTP 2010

73 The END 38 IAEA-ICTP 2010

74 3 Fuel Temperature Modelling and Phenomena (II) - fuel temperature distribution - Wolfgang Wiesenack OECD Halden Reactor Project, Norway Joint ICTP-IAEA Advanced Workshop on Multi-Scale Modelling for Characterization and Basic Understanding of Radiation Damage Mechanisms in Materials Trieste, April 12-23,

75 Overview Why temperature calculation? Coolant and cladding heat transfer Conductance through pellet-clad gap open gap, gas conduction closed gap, contact conductance geometrical changes influencing gap size Fuel temperature distribution principal formulation fuel conductivity power distribution 2 IAEA-ICTP 2010

76 centreline Typical temperature distribution (20 kw/m) Heat flow resistances Pellet Gap Clad 840 C coolant 280 C 470 C 320 C 290 C 1. coolant cladding 2. oxide/crud layer 3. cladding wall 4. inner oxidation / bonding layer 5. fuel cladding gap numerous influences 6. fuel conductivity general porosity high burnup porous rim cracks 3 IAEA-ICTP 2010

77 P 6. Fuel temperature distribution - general formulation - v Heat balance T div q = cpρ t Heat conduction q = λ grad T P v q c p ρ T t power density heat flux heat capacity density temperature time W/m 3 W/m 2 J/g K g/m 3 C s λ conductivity W/m K P v Heat equation T + div( λ gradt ) = cpρ t Valid in general for steady state and transient conditions 4 IAEA-ICTP 2010

78 Simplified formulation A fuel rod is a cylinder and most easily described in cylinder coordinates. Simplifications are possible: A fuel rod (pellet) is basically axi-symmetric T = 0 No heat flow in the circumferential direction ϕ In the axial direction - no cooling at the ends - stack interrupted by pellet-pellet interfaces - much longer axially than radially T = 0 No heat flow in the axial direction z The fuel time constant, 5-10 s, is small compared to speed of most power/temperature changes T = 0 No consideration of time dependence t 5 IAEA-ICTP 2010

79 Some useful equations and numbers P v + 1 r d d r ( λ( T, r) r dt ) d r = 0 Simplified basic equation, radial dependence only T ( r) = T R Pv ( R λ 2 r 2 ) Solved for P v = const and λ = const; R = pellet radius The basic temperature distribution is parabolic T 0 = T R + 1 4πR 2 q' R λ 2 Centre temp. expressed with linear heat rating q (W/m) The centre temperature T o is independent of radius R kw/m (UO2 per kw/m (UO 30K 2 ) ) Power to melting (ca 2800 C) Centre temperature increase 6 IAEA-ICTP 2010

80 ... but we need some more details 1. Thermal conductivity of the fuel temperature dependence burnup dependence influence of additives (e.g. Gd) 2. Influence of porosity on fuel (UO 2 ) conductivity densification (removal of pores) Fuel thermal conductivity, W/mK Burnup B MWd/kgUO 2 25 generation of new porosity by fission gas 3. Influence of fuel cracking Radial power distribution changes due to burnup and Pu generation burnable poisons λ = 4040/(464 + a*b + ( *B)*T) *e T W/m/K fresh fuel a = 16 a = 15 (-1 σ) a = 17 (+1 σ) Temperature, o C 7 IAEA-ICTP 2010

81 6.1 Thermal conductivity (UO 2 ) Data for UO 2 with 95% theoretical density UO 2 (a ceramic) is a poor heat conductor. The thermal energy is transported by lattice vibrations travelling through the lattice as waves, also known as phonons. The data have ±5% spread in K range of practical interest. 8 IAEA-ICTP 2010

82 Thermal conductivity contributions λ = λ λ phonon phonon + λ electronic 1 = A + B T λ electronic = E1 exp( E2 T ) In addition, λ depends on porosity burn-up stoichiometry 9 IAEA-ICTP 2010

83 Influence of impurities The phonon travelling is disturbed by scattering sites The intrinsic scattering sites are increased by additives such as Gd (burnable poison) accumulation of fission products in the matrix irradiation induced defects λ phonon A = A A A Gd bu d = = A = 0 c c = + c d Gd bu 1 A + B T A + A Gd bu bu Gd bu + A Gd = gadolinia concentr. bu = burnup d 10 IAEA-ICTP 2010

84 Thermal Conductivity, Degradation Development of temperature in UO 2 and (U,Gd)O 2 fuel Fuel Centre Temperature ( o C) (U,Gd)O Rod Burnup (MWd/kgUO 2 ) UO 2 The comparative irradiation shows the conductivity difference of the two types of fuel as well as the change of conductivity with burnup. Measured fuel centre-line temperatures are linked to the thermal conductivity of the fuel. The linear increase of the measured temperature with burnup implies a modification of the phonon term with a linear burnup dependent term in the denominator: A bu = c bu bu 11 IAEA-ICTP 2010

85 6 Fuel thermal conductivity, W/mK Burnup B MWd/kgUO λ = 4040/(464 + a*b + ( *B)*T) *e T W/m/K fresh fuel a = 16 a = 15 (-1 σ) a = 17 (+1 σ) Temperature, o C Change of UO 2 thermal conductivity derived from Halden reactor fuel temperature measurements 12 IAEA-ICTP 2010

86 Laser flash conductivity measurement The fuel sample is heated up to the test temperature The response to a laser flash can be evaluated regarding thermal conductivity For irradiated fuel, a marked difference between going up and down in temperature indicates annealing of phonon scattering sites Little is yet known about the kinetics of this effect and its dependence on in-core temperature changes 13 IAEA-ICTP 2010

87 6.2 Influence of porosity on fuel (UO 2 ) conductivity Maximum achievable density by sintering is about 98% th.d. (10.96 g/cm 3 for UO 2 ) Some porosity (3-5%) is desirable and achieved through adding pore formers to the powder before sintering The porosity changes during irradiation destruction/removal of pores by fission spikes (densification) formation of fission gas bubbles intragranular intergranular on grain edges and faces 14 IAEA-ICTP 2010

88 Porosity correction factors For fuel with porosity P, the conductivity is modified with: λ P = f(p) λ 0 Various formulations for f(p): f = 1 2.5P f = (1-P)/(1+0.5P) f = (1 P) 2 f = (1-P 1 )(1-P 2 ) 2.5 (1-P 3 ) 3.5 P 1 = coarse spherical pores P 2 = fine spherical pores P 3 = grain face pores (Loeb) (Maxwell) (Schulz) (Harding) correction (-) 1 0,95 0,9 0,85 0,8 0,75 0,7 0,65 0,6 Porosity correction Loeb Maxwell Schulz 0 0,05 0,1 0,15 porosity (-) 15 IAEA-ICTP 2010

89 Beware! Conductivity is sometimes given for 100% dense fuel. This means that a certain correction was applied to the data obtained with less dense fuel (often 94-96% th.d.) When applying a different porosity correction, the conductivity data should also be transformed back to the original density correction (-) 1,125 1,075 1,025 0,975 0,925 0,875 0,825 0,775 0,725 Porosity correction normalised to 95% th.d. Loeb Maxwell Schulz 0 0,05 0,1 0,15 porosity (-) 16 IAEA-ICTP 2010

90 6.3 Influence of fuel cracking Cracking of the UO 2 fuel pellets reduces the effective fuel thermal conductivity This effect may be approximated by appropriately chosen ''crack factors'' that reduce the solid- UO 2 thermal conductivity introduction of cracks in the geometry and modelling of the temperature increase across the crack in a way similar to that for the fuel-cladding gap Circumferential cracks are most efficient, but they only develop at cool-down after long periods at high power In general, the cracking pattern is not known and may even be influenced by the introduction of a TC 17 IAEA-ICTP 2010

91 Examples of fuel cracking Heat flow resistances are introduced by circumferential cracks cracks deviating from the radial direction transversal cracks deviating from the plane normal to the axial direction 18 IAEA-ICTP 2010

92 Consequences The temperature calculation in fuel modelling codes is linked to measured fuel centre temperature data Since a codes must stay tuned to the data base, the assumption of reduced fuel conductivity results in a reduction of the fuel stored energy, regardless of the modelling approach Accounting for fuel cracking leads to lower calculated peak clad temperatures obtained in some loss-of-coolant accident simulations temperature Fuel temperature distribution cracked solid 0 0,5 1 relative radius 19 IAEA-ICTP 2010

93 6.4 Radial power distribution Thermal neutrons are absorbed in the fuel (mostly causing fission) These neutrons are not replaced locally (fission neutrons have high energies) The net result is a neutron flux depression that depends on geometry (radius) and enrichment Over time, Pu will build up in the pellet periphery due to U-238 neutron absorption resonances in the epithermal energy region, resulting in a strongly edge-peaked radial power distribution 20 IAEA-ICTP 2010

94 Power distribution in high burnup fuel The TUBRNP model was developed to calculate the radial power and burnup distribution, taking into account the Pu build-up. Alternatively, more sophisticated lattice codes can be used, but differences are small. 21 IAEA-ICTP 2010

95 Burnup distribution and rim structure The periphery-peaked power generation causes a similar burnup distribution and the formation of the so-called rim structure as fabricated grains subdivide into very small grains (<0.1μm) generation of spherical pores containing fission gas at high pressure The fuel shown to the right has undergone considerable changes: loss of defined grains up to 100 μm into the fuel development of spherical porosity reaching about 500 μm into the fuel bonding layer between fuel and cladding The conductivity of rim material is presently being determined (laser flash method) porous rim SEM image 67 MWd/kg 22 IAEA-ICTP 2010

96 Estimation of rim porosity Extra porosity is produced when the local burnup exceeds 70 MWd/kgU (full rim structure formation) The porosity increases linearly with burnup in excess of rim formation burnup 0.5% extra porosity is generated per 1 MWd/kgU beyond rim formation burnup Burnup distribution calculated with the TUBRNP model 23 IAEA-ICTP 2010

97 Thermal behaviour of high burnup fuel - combined effects - Fuel centre temperature ( o C) fresh fuel, 30μm gap TUBRNP power distrib. 1 + cond. par. a= rim porosity 3 + cond. par. a=16 measured data Local heat rate (kw/m) 67 MWd/kg fuel reinstrumented with fuel thermocouple Appreciable difference to temperatures of fresh fuel Important factors: - conductivity degradation - power distribution - rim porosity The model for UO 2 conductivity degradation derived from in-core temperature data is suitable for explaining the differences 24 IAEA-ICTP 2010

98 Power distribution in fuel with burnable poison (Gd) Relative power 2,5 2,0 1,5 1,0 0,5 BU=0 MWd/kgOx BU=4.00 MWd/kgOx BU=18.18 MWd/kgOx 8% Gd BU=2.01 MWd/kgOx BU=10.27 MWd/kgOx The evolution of the radial power distribution in fuels with burnable poison is a complicated function of neutron fluence and spectrum 0, Radius (mm) Helios calculated radial power distribution in Gd-bearing fuel (Halden IFA 681) Fuel modelling codes would take such distributions as input 25 IAEA-ICTP 2010

99 Time dependent temperature distribution 20 Required for fast power changes 15 reactivity insertion accidents (RIA) OI-11, ms OI-10 BWR power oscillation ms reactor scrams 0 (loss-of-coolant accident) Time (ms) Many fuel modelling codes do not treat non-steady state temperatures Some divide the problem into steady state and transient treatment (e.g. Frapcon/Fraptran) Some implement rigorous solutions Enigma, Transuranus... For proper rendering of measured data, the thermocouple response should be included in the solution NSRR power (GW) IAEA-ICTP 2010

100 Time dependent temperature distribution (for temperature independent conductivity and constant heat gen.) Increasing time T 1 d dr A Cp dt r 0 ρ 1 + = = r dr dt k k dt K Solution: r ( 2 2 a r ) A0 2A0 = k ak n= 4 1 n 1 e 2 n K α t dt dt diffusivity Bessel functions J0( rα n) 3 α J ( aα ) n Because of the space dependence of the heat generation and the thermal properties, the problem is usually solved numerically on the differential equation level. 27 IAEA-ICTP 2010

101 Temperature response to reactor scram T ( t) T T T 0 The response can be described with cool cool T τ τ cool TC F = Aexp( t / τ TC ) + = coolant temperature = thermocouple time constant = fuel time constant B exp( t / τ F ) 28 IAEA-ICTP 2010

102 Properties of the fuel time constant The simplified time dependent solution identifies the basic influences of geometry and material parameters on the major fuel time constant Changes over time occur due to conductivity degradation (λ) fission gas release (h) τ = R a J 1 0, 1 2 λ a = ρ c 2 1 = pellet radius R J 0( a1) = h λ J ( a ) J R 1 p 1 Bessel functions 29 IAEA-ICTP 2010

103 Application to real data A scram of the Halden reactor triggers a fast data logging system which saves all temperature data every 0.5s The function coefficients (e.g. time constants) are determined with a least squares fitting procedure These data, when collected over longer periods, provide supplementary information on fuel conductivity changes fission gas release (gap cond.) 30 IAEA-ICTP 2010

104 Long-term development Fuel diameter 8.09 mm gap size mm fill gas helium no fission gas release Fuel diameter mm gap size mm fill gas helium FGR after 17.5 MWd/kg 31 IAEA-ICTP 2010

105 Typical time constants The thermocouple time constant represents a delayed registration of the actual fuel temperature typical values are s values depend on the thickness of the TC (mass) and the heat transfer from the TC to the fuel (fuel TC gap) The major fuel time constant depends on geometry and heat transfer properties values range from 3s (small diameter fuel, R<3mm) to about 10s (test rods filled with Xe) typical values for standard geometry are 4 8s Temperatures associated with power changes occurring over minutes or longer can be treated with steady state calculation Evaluation by noise analysis results in similar values; differences reflect response at different locations (centre, periphery, fuel average) 32 IAEA-ICTP 2010

106 Summary fuel temperatures Fuel temperatures and their development with burnup are influenced by many phenomena which interact in complicated ways First principal models as well as empirical data and correlations are employed in solving the problem The Halden reactor experimental data constitute a solid basis for model development and verification However, due to the nature of the problem, knowledge on many details will be deficient or lacking, and considerable uncertainties associated with fuel temperature calculations must be expected 33 IAEA-ICTP 2010

107 The END 34 IAEA-ICTP 2010

108 4 Fission gas release Wolfgang Wiesenack OECD Halden Reactor Project, Norway Joint ICTP-IAEA Advanced Workshop on Multi-Scale Modelling for Characterization and Basic Understanding of Radiation Damage Mechanisms in Materials Trieste, April 12-23,

109 Overview Why fission gas release calculation? safety criteria interaction with other phenomena Basic mechanisms Experimental data 2 IAEA-ICTP 2010

110 ... but it may be more complicated 3 IAEA-ICTP 2010

111 Fuel behaviour codes must address and untangle interactions that become more and more complex as fuel burnup increases Fissions & fission products Time Enrichment Rim formation Conductivity degradation Fission gas release Rod pressure Fuel swelling Fuel temperature Fuel-clad bonding Gd high B fuel high Li Coolant chemistry CRUD AOA Clad lift-off Stored heat PCMI corrosion RIA 4 IAEA-ICTP 2010 LOCA

112 Fission products Kr Xe The fission products range in mass from around 72 to 161 (U-235) with peaks in the yield distribution close to the elements krypton and xenon The overall yield of these so-called fission gases is approximately 28 atoms per 100 fissions About 85% are Xe atoms, about 15% are Kr atoms (Kr yield is lower for Pu fiss.) Xe and Kr are noble gases with low solubility in the fuel matrix 5 IAEA-ICTP 2010

113 There is no ideal place for fission gases If released, they can lead to thermal runaway (gap cond.) rod-overpressure restricted by safety criteria If retained, they can lead to large fission gas swelling and thus pellet-clad interaction grain boundary embrittlement and porosity with high pressure, both contributing to fuel fragmentation under accident conditions (RIA, LOCA) Safe reactor operation therefore requires a thorough understanding of the behaviour of fission gas 6 IAEA-ICTP 2010

114 Fission gas release and safety criteria Fission gas generation is about 28 cm 3 /MWd A fraction is released from the fuel matrix to the free rod volume, increasing the rod pressure all gas released rod pressure bar at room T Rod pressure is limited by safety criteria and must therefore be calculated for the safety case Regulation differs from country to country and may prescribe: rod pressure must not exceed system pressure a pressure limit which is above system pressure (e. g. Belgium, 184 bar) pressure may exceed system pressure, but must not lead to gap opening (no lift-off causing thermal feed-back) 7 IAEA-ICTP 2010

115 Rod pressure increase For rod pressure calculation, fuel modelling codes have to take into account generated fission gas (easy) released fission gas (hard) change of free volume fuel densification and swelling clad creep and growth temperature of free volume plenum rod pressure at room T, bar for 100% release 7% free vol. 10% free vol. 13% free vol. dishing, centre hole pellet-cladding gap, chamfer open fuel vol. (pores, cracks) burnup, MWd/kg 8 IAEA-ICTP 2010

116 Fission gas release - basic mechanisms - 1. Fission gas atoms diffuse from within the fuel grain to the grain surface (temperature driven) 2. The fission gas atoms accumulate at the grain surface in gas bubbles 3. When the surface is saturated with bubbles, they interlink and the gas is released out of the fuel matrix FGR depends on temperature and burn-up (time) FGR is <1% for temperatures below ~ o C and ~10-20% at ~1500 o C 9 IAEA-ICTP 2010

117 Fission gas release - phenomena involved - 1. Recoil 2. Knock-out & sputtering 3. Lattice diffusion 4. Trapping 5. Irradiation re-solution 6. Thermal re-solution 7. Densification 8. Thermal diffusion 9. Grain boundary diffusion 10. Grain boundary sweeping 11. Bubble migration 12. Bubble interconnection 13. Sublimation or vaporisation 10 IAEA-ICTP 2010

118 Recoil R recoil Surface / volume When a fission fragment is close enough to a free surface (< 6-9 μm), it can directly escape from the fuel due to its high kinetic energy ( MeV) It only affects the geometric outer layer of the fuel R recoil ~ Fis.rate Surface/Volume It is an athermal mechanism (independent of temperature and temperature gradient) Domain of application is for T<1000 C 11 IAEA-ICTP 2010

119 Knock-out Knock-out and sputtering The interaction of a fission fragment, a collision cascade or a fission spike with a stationary gas atom close enough to the surface can cause the latter to be ejected Sputtering A fission fragment travelling through oxide looses energy by interactions with UO 2 at a rate ~1keV/Å high local heat pulse when it leaves the free UO 2 surface, the heated zone will evaporate or sputter Affect outer layer and open surfaces: (S/V) total Athermal; independent of T and temp. gradient Release/Birth ~ (Surface/Volume) total 12 IAEA-ICTP 2010

120 Lattice diffusion, diffusion coefficient D = D + D + Thermal coefficient (T>1400 o C) exp ΔH Da = D0 RT Intermediate D b = F& exp T Athermal coefficient (T<1000 o C) = A F & Dc a b D The release rate is enhanced by deviation from stoichiometry (UO 2+x ) and by impurities simulating non-stoichiometry c cf. Turnbull et al 13 IAEA-ICTP 2010

121 Fission gas release - basic diffusion model - Fission gas release was observed very early on and explained by diffusion out of the fuel grains (Booth) Assumptions for (simple) model: c atomic diffusion in hypothetical sphere grain boundary = perfect sink gas at grain boundary immediately released (?) constant conditions of temperature and fission rate = D Δ C + S t ( gr t) C R, = 0 c = 0 r r= 0 C R,0 = 0 ( gr ) Solution (Booth diffusion, release rate) f ( t) = 4 π Dt R 3 2 Dt 2 2 gr R gr 14 IAEA-ICTP 2010

122 Observation: incubation threshold Central temperature ( C) Original 1% data Siemens 2% data New 1% data Empirical Halden threshold high gas release > 1% low gas release < 1% Burnup (MWd/kgUO2) 15 IAEA-ICTP 2010

123 Explains incubation and onset of (stable) fission gas release during normal operation due to increase of open surface (open tunnel network) Explains burst release (micro-cracking) during abrupt power variations requires precise knowledge of local stress Fission gas release - Bubble interconnection - 16 IAEA-ICTP 2010

124 Classification of models Empirical calibrated with specific data-base Mechanistic many unknown parameters limited application range lack of detailed experimental data excellent performance inexpensive in use efficient tool for fuel design Focus on speed, robustness, precision physical description of phenomena wide range of application possible to extend range Focus on (physical) understanding 17 IAEA-ICTP 2010

125 Fission Gas Release models Large number of models Improvements numerical techniques new mechanisms Various applications: conditions, reactor types, Large uncertainties (mechanistic) model parameters diffusion coefficient resolution,... input parameters: temperatures hydrostatic stress, IAEA-ICTP 2010

126 A simple model (in use at Halden) A simple, yet fairly successful model is in use at Halden which considers the basic influences and observations. Athermal release, always present Three-stage diffusion driven release process 1. intergranular diffusion to the grain boundary, Booth model 2. accumulation of gas atoms on the grain surface to a concentration of cm -1 (not released to the free volume) 3. reaching the limit concentration signifies bubble interlinkage, and from then on fission gas atoms arriving at the grain surface are assumed to be released to the free volume Special procedure to apply the Booth solutions (which are for constant conditions) to varying powers and temperatures 19 IAEA-ICTP 2010

127 Comparison with FG release data An important result from the Halden Programme is the 1% FGR threshold established for UO 2 up to ~30 MWd/kgUO 2 The simple model is able to reproduce the observations in the low burnup range using a three-term diffusion coefficient and fission gas accumulation on grain boundaries For higher burnup, a burnup dependent diffusion coefficient is required to maintain good agreement with the experimental data Centre Temperature (C) Threshold for 1% FGR Code calcs for 1% FGR Experimental 1% data Burn-up (MWd/kgUO 2 ) Comparison of simple fission gas release model with empirically derived release threshold and experimental data at high burnup 20 IAEA-ICTP 2010

128 Experimental Measurements: (see introductory lecture) Rod pressure Gamma spectroscopy Rod puncturing and gas analysis Observations Release onset Interlinkage ( release onset) Release kinetics Grain size effect Gas mixing 21 IAEA-ICTP 2010

129 Fission gas release onset Irradiation of fresh and high burnup fuel (segments from LWRs) lnstrumentation: - fuel thermocouple - rod pressure sensor Stepwise power / temp. increase to establish onset of fission gas release Simultaneous measurement of fuel temperature (most important parameter) and pressure Fuel Temperature ( o C) Pressure (bar) Centre Temperature (C) Threshold for 1% FGR Code calcs for 1% FGR Experimental 1% data Burn-up (MWd/kgUO 2 ) Measured Temperature Peak Temperature. Release onset new point 44 Full Power Days Temperature history and measured rod pressure (fission gas release) 22 IAEA-ICTP 2010

130 Gas flow system (radioactive fission product analysis) To off gas system Gas flow path Flow meter P215 He Ar Cold trap bank Rods 7,8,9,10 UO 2 11,12 MOX γ Detector P IAEA-ICTP 2010

131 Gas flow analysis Evaluation method Isotopic release rate from γ- spectrometry Isotopic birth rate from fission yield calculations R B = S V D Surface area to volume ratio * square root of diffusion coefficient α + λ R B recoil Recoil release to birth rate Square root of precursor enhancement factor / decay constant In start-up diffusivity analysis S/V fixed In first cycle analysis D fixed 24 IAEA-ICTP 2010

132 Diffusion coefficient, m 2 /s 1.E-18 1.E-19 1.E-20 1.E-21 1.E-22 1.E-23 Gas flow analysis Assume S/V and derive diffusion coefficient IFA-563 IFA-558 IFA-504 IFA-655 large grain UO2 IFA-655 standard grain UO2 IFA-655 heterogeneous MOX IFA-655 homogeneous MOX S/V = 70 cm -1 temperatures varied by changing power and fill gas / Fuel temperature, K W/gHM 80 W/gHM 10 W/gHM 25 IAEA-ICTP 2010

133 Gas flow analysis Assume diffusion coefficient and derive S/V Rod 7 (standard grain UO2) Rod 8 (large grain UO2) Rod 9 (standard grain UO2) Rod 10 (large grain UO2) Rod 11 (homogeneous MOX) Rod 12 (heterogeneous MOX) S/V, cm Rod average burnup, MWd/kgOxide 26 IAEA-ICTP 2010

134 Through-life gas flow measurements No change in recoil R/B as HBS is formed Interlinkage due to temperature excursion 27 IAEA-ICTP 2010

135 Fission gas release kinetics Temperature and FGR history Steady state power (temperature) for longterm kinetics For high burnup fuel, power dips are necessary in order to obtain communication with the plenum (tight fuel column) Envelope of release curve indicates diffusion controlled release 28 IAEA-ICTP 2010

136 Influence of grain size on gas release (I) According to diffusion models, an increased grain size will in general result in reduced fission gas release The onset of fission gas release occurs at about the same time since the inner (grain) surface varies with 1/R grain and thus compensates for fewer atoms arriving at the grain surface Larger grains are produced by using additives which may influence (increase) the diffusion coefficient Concerning gas release properties, the effect of increased diffusion length (lower FGR) therefore competes with the effect of increased diffusion coefficient (higher FGR) 29 IAEA-ICTP 2010

137 Influence of grains size on gas release (II) Grain size increase is less effective at higher power and FGR >10% high burnup Satisfactory prediction with diffusion-based FGR model (Turnbull) fission gas release, % grain 22 μm grain 8.5 μm predicted grain size 8.5 μm grain size 22 μm Burn-up (MWd/kgUO 2 ) Measured and predicted FGR for UO 2 fuel with different grain sizes 30 IAEA-ICTP 2010

138 Gas mixing in a fuel rod (I) Released fission gas has to move (diffuse) to the rod plenum A temporary strong dilution of the fill gas in the fuel column may result... and cause increased fuel temperatures and positive feedback on fission gas release. Gas mixing behaviour and feedback has been investigated in different ways: Injection of argon at one end and tracing the equilibration Cause FGR and monitor the temperature response 31 IAEA-ICTP 2010

139 Gas mixing in a fuel rod (II) Argon injected in lower plenum Diffusion to upper plenum, equilibration Temperature response measured 32 IAEA-ICTP 2010

140 Related: gas flow through the fuel column - hydraulic diameter measurements η L R T D H = 4 = π D ( 2 2 p p ) D = mean fuel diameter D H = hydraulic diameter p 1 = gas pressure supply side (high pressure = rod pressure) p 2 = gas pressure return side (low pressure = rig pressure) Ha = Hagen number η = dynamic viscosity L = flow channel length R = universal gas constant T = gas temperature 1 2 n& Hydraulic diameter (μm) initial gap gap closure with 0.7 ΔV/V swelling per 10 MWd/kgU Burnup (MWd/kg UO 2 ) IAEA-ICTP 2010

141 Related: gas flow through the fuel column - delayed fission gas release Internal rod pressure (bar) steady state Average heat rate (kw/m) When the accommodation power level is approached, the hydraulic diameter decreases at a higher rate and the fuel column becomes very tight. The fuel column becomes permeable after a limited power reduction. The release of the inner overpressure to the fuel rod plenum is detected then. 34 IAEA-ICTP 2010

142 Delayed fission gas release Delayed fission gas release means that the rod pressure, as detected by a pressure transducer located in the rod plenum, increases when power is reduced and a path to the plenum is opened The phenomenon is regularly observed when fuel burnup exceeds MWd/kg It cannot be diffusion driven since the pressure step is also observed after a reactor scram (the fuel is cooled down by several hundred degrees within a few seconds, and any diffusion is effectively stopped) 35 IAEA-ICTP 2010

143 The END 36 IAEA-ICTP 2010

144 5 Dimensional Changes and Pellet-Clad Interaction Wolfgang Wiesenack OECD Halden Reactor Project, Norway Joint ICTP-IAEA Advanced Workshop on Multi-Scale Modelling for Characterization and Basic Understanding of Radiation Damage Mechanisms in Materials Trieste, April 12-23,

145 Overview Fuel and clad mechanics stresses and strains contact forces and interactions fuel size changes thermal expansion densification swelling Cladding creep Considerations for modelling 1D/2D/3D 2 IAEA-ICTP 2010

146 Introduction A purpose of fuel behaviour modelling is to predict mechanical loads in normal operation and transients does the fuel rod fail? Stresses and strains are responsible for failure and occur because of temperature gradients in the materials different thermal expansion of fuel and cladding in contact with each other irradiation induced geometry changes clad creep-down, creep-out, growth fuel densification and swelling Modelling in 1/1.5 D and 2/3 D (FEM) 3 IAEA-ICTP 2010

147 Fuel & Clad Mechanics Practical approaches to Fuel & Clad Mechanics are governed by complexity of the problem many highly non-linear phenomena complicated fuel-clad mechanical interaction need for discretisation incomplete knowledge on the state of the fuel computer power limitations Whole rod usually treated in 1.5D Early attempts to apply FE techniques limited to a few pellets (FEMAXI 1976) 4 IAEA-ICTP 2010

148 5 IAEA-ICTP 2010 Some equations for stresses and strains equilibrium condition compatibility condition materials law (generalised Hooke s law) = = = = = = = + pl z cr z i pl t cr t i pl r cr r i z t r z t r r E C z w r u r u z r r ε ε ε ε ε ε ε ε ε σ σ σ ν ν ν ν ν ν ε ε ε ε ε ε σ σ σ σ z t r z t r (plain strain) 0 0 1/1.5D fuel modelling codes typically employ an axi-symmetric plain strain formulation. It is better fulfilled for the cladding than the fuel.

149 Symbols used r, t, z directions (radial, circumferential, axial) σ -stress ε -strain ν - Poisson s number u - radial displacement w - axial displacement cr-creep pl - plastic i - isotropic (ε i = ε thermal + ε swelling + ε densification ) 6 IAEA-ICTP 2010

150 Fuel stresses cracking Ceramic fuels crack easily due to the strong stresses caused by the (radial) temperature gradient The stress-strain equations are kept approximately valid by introducing crack strains (e.g. Transuranus) setting stresses to zero (e.g. Frapcon) If the fuel is cracked both radially and axially, the fuel displacement u is essentially free thermal expansion plus the contributions of swelling and densification 7 IAEA-ICTP 2010

151 Contact situations Many fuel modelling codes simplify by assuming either no contact (open fuel-clad gap) or hard contact (closed gap) Stress concentration in the cladding opposite of fuel cracks is not included in this matrix 8 IAEA-ICTP 2010

152 Modelling Considerations (I) The pellet configuration is quickly affected by pellet cracking and fuel fragment relocation (see also lecture on temperature calculations) This should make the calculation of interaction(s) even more complicated, but on the other hand to calculate the slope of a pile of sand (or coal or boulders or ) with some accuracy, we do not have to calculate and determine the interaction between all grains Despite the differences, a single model describes the situation Can cracked fuel pellets within the cladding be treated like a pile of sand? 9 IAEA-ICTP 2010

153 Modelling Considerations (II) Williford et al. proposed a crack compliance model Fuel and cladding are always in contact with each other, as observed in experiments The surfaces with roughness d interact with each other via contact stresses σ 1 2 d erfc( ) R 2 σ = σ + H d = crack width, R = roughness, H = Meyer hardness The model allows a unified treatment of thermal and mechanical behaviour Suitable for the high burnup situation with bonded fuel 10 IAEA-ICTP 2010

154 PCMI in practice - experimental observations - Onset of interaction fresh fuel Random stacking Development of onset of interaction with burnup Axial racheting PCMI at high burnup, bonded fuel 11 IAEA-ICTP 2010

155 PCMI: Onset of interaction fresh fuel The experimental observations are difficult to reconcile with predictions of models assuming a concentric arrangement of fuel and cladding and a dividing gap: First power ramp: very early onset of interaction Following power ramps: shift of PCMI onset to higher power Relaxation of axial strain during power holds (sliding, densification, creep) Continuation of elongation when power increases (strong contact) 12 IAEA-ICTP 2010

156 Random stacking The fuel stack has no stability in itself. Pellets are eccentrically located, and some touch the cladding at one side. This random stacking causes PCMI from the beginning, even if the pelletclad gap is nominally open. Interaction due to random stacking depends on Pellet length (L/D) shorter pellets means more friction interfaces Hold-down spring force stronger friction force against alignment Stack length longer fuel columns are less randomly stacked which means weaker interaction 13 IAEA-ICTP 2010

157 PCMI: Development of onset of interaction Fuel-clad accommodation The onset of interaction moves to lower power with increasing burnup and decreasing power The accommodation of fuel and cladding to each other result in small interaction tails as long as power does not exceed previously reached levels. Consequences for conditioning/deconditioning of fuel, e.g. after stretch-out 14 IAEA-ICTP 2010

158 PCMI: Axial racheting Burnup MWd/kgUO The slight mismatch between release and onset of interaction causes axial ratcheting and elongation peaks 15 IAEA-ICTP 2010

159 PCMI: high burnup behaviour Elongation (mm) grain 22 μm grain 38 μm 0.75 % fuel swelling Burnup (MWd/kgUO 2 ) Cladding elongation response of re-instrumented PWR fuels (61 MWd/kgU) with different grain sizes during steady state periods. Permanent elongation Clad elongation increase reflects fuel swelling Ratcheting Elongation peaks associated with shut-down / start-up (release/onset mismatch) Relaxation Initial relaxation of high power elongation. Stress caused by ratcheting is relaxed by fuel creep within a few days 16 IAEA-ICTP 2010

160 Thermal expansion (equations see temperature lecture) Thermal expansion occurs instantaneously and is the main cause of PCMI in semi-rapid power changes, e.g. control rod withdrawal and reactor start-up very rapid power changes, e.g. reactivity insertion accidents Uranium oxide expands more than Zircaloy (circumferentially) The fuel gets much hotter than the cladding PCMI due to thermal expansion expansion (-) 0,025 0,02 0,015 0,01 0,005 0 Zry circumf. Zry axial uranium oxide temperature, C 17 IAEA-ICTP 2010

161 Fuel densification UO 2 pellets are produced by pressing of powder and sintering at high temperature ( C) The fuel pellets have a small amount of porosity (3-5%) after the sintering Some of the porosity is removed as a result of irradiation, leading to densification of the fuel This has led to problems in the early days, but is well under control in today s routine fuel fabrication Most research on densification from about H. Assmann, H. Stehle; Thermal and in-reactor densification of UO 2 : mechanisms and experimental results; NEaD 48 (1978) Densification affects the gap size and thus the fuel temperature 18 IAEA-ICTP 2010

162 Densification model UO 2 in-reactor densification and thermally activated sintering depend on: burnup density pore size distribution grain size temperature O/U-ratio ΔV V p p d 0,0 0, i i = p 0,0 (1 e a B ) = init. fine porosity fraction, diam. < 0.1μm = init. coarse porosity fract. i, diam. > 0.1 μm = diameter of coarse porosity class i ( d > 0.1) B = burnup; a, b = constants i p 0,1 (1 (1 b B ) d i 3 ) According to theory, mechanisms controlled by temperature are effective only for T >1300 C 19 IAEA-ICTP 2010

163 Fuel swelling Swelling is due to the inclusion of solid fission products in the matrix and accumulation of fission gas in pores (effective at high T) theoretically, the solid fission product swelling rate is 0.13% Δ V/V per fissions/m 3 (0.037% per MWd/kg) if the fuel completely utilized the vacancies created during irradiation 0.54% Δ V/V per fissions/m 3 (0.153% per MWd/kg) if none of the vacancies are used Swelling measured in-core is often between these values in the range %/10MWd/kg and includes the effect of gaseous fission products (Xe, Kr) 20 IAEA-ICTP 2010

164 Gaseous fuel swelling The fission products xenon and krypton (noble gases) are virtually insoluble in the UO 2 fuel matrix By diffusion, they accumulate in inter- and intra-granular bubbles Gas atoms in bubbles occupy more space than the atoms they originated from Consequently, the fuel volume is increased gaseous fuel swelling Correlations are highly empirical 21 IAEA-ICTP 2010

165 Gaseous fuel swelling - MATPRO ΔS g Θ = = min( T The potential for gaseous fuel swelling increases with burnup It is significant for temperatures >1500 C Reduced at very high T because of fission gas release Θ swelling fraction e Θ e 273, 2800) 0,25 0,2 0,15 0,1 0,05 0 temperature B ΔB burnup, MWd/kg 22 IAEA-ICTP 2010

166 Densification & swelling Numerous experiments address fuel densification and swelling. The primary instrument is the fuel stack elongation detector. Densification information can also be derived from rod pressure measurements. The data of the example stem from a disk fuel irradiation and show a dependence on grain size (small vs. large grain) irradiation temperature fuel fabrication (for MOX fuel) 23 IAEA-ICTP 2010

167 % ΔV/V o Fuel elongation, mm Densification and swelling as measured with a fuel stack elongation detector (EF) UO 2 fuel (EF1) Gd 2 O 3 fuel (EF2) Gd 2 O 3 (EF2 at HSB) UO 2 (EF1 at HSB) 0.5% dv/v / 10 MWd/kgUO Rod burnup, MWd/kgUO 2 Swelling of UO 2 and Gd-UO 2 fuel derived from fuel stack length change UO 2 and (U,Gd)O 2 fuel comparison Irradiation of production line UO 2 and Gd-UO 2 fuel, 8 w /o gadolinia No densification is observed for Gd-UO 2 fuel Both fuel types show a swelling rate of about 0.5% ΔV/V 24 IAEA-ICTP 2010

168 Clad creep-down In water cooled reactors, the cladding is initially in compressive state The resulting creep-down of the cladding contributes to closing the fuel-cladding gap A typical steady state creep equation has the form ε = f ( σ, φ, t) exp( Q / RT ) σ = stress; t = time φ = fast neutron flux 25 IAEA-ICTP 2010

169 Empirical steady state creep correlations m ε = A σ ε s s = A sinh CREEP Primary n φ exp( Q/RT) t P ( B σ ) ( φ t) exp( Q/RT) Steady state T 1 T 2 Time Tertiary σ A, B = constants m, n, p = constants (n, p 1; m > < 1) σ = stress φ = fast neutron flux T = temperature Q = activation Energy t = time 26 IAEA-ICTP 2010

170 Ridge formations from PCMI Ridges at pellet-pellet interfaces caused by the hour-glass shape of the fuel pellet under its temperature gradient Ridging reduced during hold periods at power due to fuel creep The figure shows data from rig with diameter gauge for measurement of cladding diameter change during power ramp 27 IAEA-ICTP 2010

171 y a d x General, with shear stresses and strains u = 2 1 Strain energy density (for improving failure predictions) F x Force F x acting on cube with length a, causing stress σ x =F x /a 2, (elastic) displacement d in x direction and strain ε x =d/a Work Strain energy Strain energy density W U = = U u= V 1 Fxd σ xa ε xa = 2 = σxε xa / a 3 1 σ xε xa = σxε x 2 ( σ ε + σ ε + σ ε + τ γ + τ γ + τ γ ) x x y y z z xy xy yz yz xz xz 28 IAEA-ICTP 2010

172 Critical strain energy density correlation The critical strain energy density (CSED) at which failure occurs, is claimed to be a material property In reality, it depends on a number of parameters The following correlation was developed by CIEMAT based on work by Rashid (Anatech/EPRI) and experimental results from the French PROMETRA program on irradiated Zry-4 cladding CSED = x -126ε& + x = oxide layer thickness, μm T = clad temperature, K = clad strain rate, s -1 ε& T [MPa] 29 IAEA-ICTP 2010

173 Modelling Considerations Codes must consider all the aspects, and more, shown in this presentation cladding fuel thermal expansion, creep, thermo elasticity, plasticity, growth,... thermal expansion, densification, cracking and relocation (contact force and crack pattern), fission product swelling, creep, gaseous swelling, fission gas release (PCI failure),... relative movement between pellet and cladding: no contact, frictional sliding, sticking additionally for PCI failure modelling (ramp tests, RIA) local stresses, crack initiation, fission product release, crack propagation (SCC) 30 IAEA-ICTP 2010

174 Modelling PCMI 1 ½ D codes axi-symmetric 1D model (radial dependence only) does not allow direct calculation of ridge formation axial length (z direction) is divided into nodes axial coupling of nodes 2D 3D codes more rigorous description of the geometry, but... restricted to a few pellets (2D: axi-symmetric r-z) special coupling elements Goals Calculation of dimensional changes during irradiation PCI failure probability / limits Operational constraints? 31 IAEA-ICTP 2010

175 The END 32 IAEA-ICTP 2010

176 6 Special Experiments and their Evaluation Wolfgang Wiesenack OECD Halden Reactor Project, Norway Joint ICTP-IAEA Advanced Workshop on Multi-Scale Modelling for Characterization and Basic Understanding of Radiation Damage Mechanisms in Materials Trieste, April 12-23,

177 Overview Fuel conductivity degradation Cladding creep Rod overpressure clad lift-off Hydraulic diameter & LOCA 2 IAEA-ICTP 2010

178 Fuel conductivity degradation - Ultra-high burnup test - Four UO 2 fuel rods irradiated to 77 MWd/kgUO 2 Instrumentation expansion thermometer rod pressure transducer Minimise gap conductance changes Small fuel-clad gap (100 μm) Temperature kept below fission gas release threshold 10 bar helium to further minimise effect of fission gas release 3 IAEA-ICTP 2010

179 Raw data: power / temperature history Temperatures follow power changes Gradually decreasing temperature due to fuel depletion Temperatures stay well below the FGR threshold 4 IAEA-ICTP 2010

180 Temperature at 0 and high burnup Although gap conductance must have improved due to gap closure... temperatures at 60 MWd/kg UO 2 and 17 kw/m are about 160 C higher than at first start-up Linear temperature/power relationship is typical of fuel with He-filled gap 5 IAEA-ICTP 2010

181 Normalising temperatures to constant power At constant power, a clear trend becomes visible for all rods: temperatures increase approximately linearly with burnup (temperature curves are offset by 100 K for clarity) 6 IAEA-ICTP 2010

182 6 Fuel thermal conductivity, W/mK Burnup B MWd/kgUO λ = 4040/(464 + a*b + ( *B)*T) *e T W/m/K fresh fuel a = 16 a = 15 (-1 σ) a = 17 (+1 σ) Temperature, o C Change of UO 2 thermal conductivity derived from Halden reactor fuel temperature measurements (see lecture on fuel temperature for more details) 7 IAEA-ICTP 2010

183 Gas lines Cladding creep - stress reversal experiment - Investigate creep behaviour following stress reversals, increments and decrements, generating data for use by fuel performance code modellers Test rods connected to high pressure gas system to control applied hoop stress PWR loop for system pressure and temperature Booster fuel rods for fast flux Contact scanning diameter gauge for monitoring change of rod outer diameter 8 IAEA-ICTP 2010

184 Background and Objectives Clad thermal and irradiation creep affects the fuelclad gap Fuel-clad gap affects thermal performance of fuel In-pile creep data needed to validate clad creep models in fuel performance codes for modern fuel clad materials under variable loading conditions Addressed in several creep studies in the Halden reactor using different cladding alloys exposed to BWR and PWR conditions (How) does primary creep recur after stress change? 9 IAEA-ICTP 2010

185 The diameter gauge is repeatedly run up and down the rod string Measurements Diameter traces are aligned at the calibration steps and compared to the reference trace taken at the beginning of a stress period end plug Gas line Zry-2 rod Cal. step mid plug Diam. gauge Cal. step Zry-2 rod end plug 10 IAEA-ICTP 2010

186 Goal: for a given material determine - primary creep increment - secondary creep rate Primary creep Secondary creep Strain (fractional diameter change) ε S ε P ε 0 dε/dt = έ s KEY ε 0 = Loading strain ε P = Total primary strain ε S = Total secondary strain ε c = Total creep strain έ s = Secondary creep rate ε c Stress applied Exposure time Stress removed 11 IAEA-ICTP 2010

187 Measurements evaluated for a stress period 12 IAEA-ICTP 2010

188 Entire set of measurements 13 IAEA-ICTP 2010

189 Secondary creep rate depends on stress level and is greater in tension than compression 14 IAEA-ICTP 2010

190 Primary creep Recurs with every stress change Depends on amount of stress change No difference in absolute value between tension and compression 15 IAEA-ICTP 2010

191 Rod overpressure clad lift-off Excessive fission gas release and the reduction of the free rod volume due to fuel swelling can cause the rod pressure to rise beyond system pressure. The consequences are investigated in a Halden Project experimental series to: establish the overpressure leading to onset of increasing fuel temperature investigate the temperature response at different overpressure levels assess different combinations of fuel and cladding High burnup instrumented fuel segments are used for these investigations 16 IAEA-ICTP 2010

192 HBWR irradiation rig Outlet thermocouple Gas line Fuel thermocouple Fuel rod Booster rods Gas line Inlet thermocouple Pressure flask Measurement Possibilities Fuel centreline temperature and its change as primary clad lift-off indicator Temperature response to fill gas change (argon versus helium) during operation Fission gas release by means of gamma-spectroscopy PCMI and fuel swelling by means of clad elongation measurements Hydraulic diameter Coherence between fast response neutron detector (power) and clad elongation 17 IAEA-ICTP 2010

193 Power and pressure history Rod power 1st cycle 15 kw/m average 2nd cycle 12 kw/m average Rod pressure Increased in steps of ca. 50 bar maximum 470 bar 18 IAEA-ICTP 2010

194 Response to fuel rod overpressure Normalised fuel temperature Shows clear response to level of overpressure and direct effect of pressure step 19 IAEA-ICTP 2010

195 Summary of measurements The rate of temperature increase is correlated with the overpressure The onset of thermal feedback occurs at about 138 bar overpressure This represents the lift-off threshold for the particular combination of fuel and cladding utilised in the test Below this threshold, any clad creep-out is sufficiently compensated, e.g. by fuel swelling, such that no net thermal feedback becomes apparent 20 IAEA-ICTP 2010

196 Data evaluation (I) Influence of conductivity degradation corrected according to Halden model ΔT degrad = 14 K Cladding creep based on evaluation of clad creep test and Franklin s model ΔD creep = Fuel swelling according to measurements in lift-off experiment ΔD swell = 9 μm t Fuel thermal conductivity, W/mK Burnup B MWd/kgUO 2 25 σ = 40μm Θ λ = 4040/(464 + a*b + ( *B)*T) *e T W/m/K fresh fuel a = 16 a = 15 (-1 σ) a = 17 (+1 σ) Temperature, o C Total diameter change (μm) Full power hours 21 IAEA-ICTP 2010

197 Data evaluation (II) About 60K of the observed temperature increase can be attributed to the combined effect of increasing space in the fuel and thermal conductivity degradation (14K) The Halden Project s thermal analysis code calculates a 60K temperature increase when the gap size is increased by 28μm This is close to the evaluated effective increase of 31 μm which is the difference between clad creep-out and fuel swelling The analysis confirms that the observed temperature change is reasonable The model for cladding creep plays a critical role in the analysis Different cladding types will exhibit individual sensitivities to lift-off 22 IAEA-ICTP 2010

198 Noise data - PCMI Coherence between rod power and cladding elongation The coherence between power (fast response neutron detector) and clad elongation increases slightly until the maximum overpressure is applied Then, it drops gradually until the end of irradiation Significance of coherence value: <0.05 PCMI free >0.20 PCMI developed Noise analysis supports the conclusion derived from steady state data that considerable fuel-clad contact is maintained also in the state of lift-off 23 IAEA-ICTP 2010

199 Modelling of clad lift-off Modelling must take into account and calculate: Instantaneous cladding distension (elastic, primarily in experiment) Primary and secondary creep of the cladding (response to both pressure steps and gradual pressure increase) Fuel swelling Relocation/redistribution of fuel fragments into available space as cladding creeps outwards Resulting temperature response Fission gas release Different types of measurement indicate that pellets and cladding keep contact and that the pellet fragments follow clad creep-out by swelling and relocation A fuel model where (solid) pellet and cladding are separated by a gap will have problems to explain all of the observations in a satisfactory way 24 IAEA-ICTP 2010

200 Hydraulic diameter & LOCA In a Loss-of-Coolant Accident (LOCA), the fuel rod balloons (and ruptures) for T > C The ballooning process is driven by the supply of gas from the fuel rod plenum However, the fuel column is a restriction between plenum and balloon and impedes axial gas transport The effect of restricted axial gas transport was investigated in the 70s using fresh or low burnup fuel It was found that gas supply is still sufficient under the investigated conditions But what about high burnup, bonded fuel? 25 IAEA-ICTP 2010

201 Three LOCA tests with high burnup fuel - observations visual inspection - 3. High burnup fuel (82 MWd/kg), clad failure by a small crack; relatively fast pressure drop 4. High burnup fuel (92 MWd/kg), ballooning, rupture and instantaneous loss of pressure 5. High burnup fuel (83 MWd/kg), small ballooning, rupture and very slow loss of pressure 26 IAEA-ICTP 2010

202 Pressure drop measurements 27 IAEA-ICTP 2010

203 Test #5 - cladding distension 13 12, ,5 diameter, mm 11 10,5 axial length, cm Strong contact at the upper half of the fuel segment impeded axial gas flow in test 5 28 IAEA-ICTP 2010

204 Hydraulic diameter measurements η L R T D H = 4 = π D ( 2 2 p p ) D = mean fuel diameter D H = hydraulic diameter p 1 = gas pressure supply side (high pressure = rod pressure) p 2 = gas pressure return side (low pressure = rig pressure) Ha = Hagen number η = dynamic viscosity L = flow channel length R = universal gas constant T = gas temperature 1 2 n& Hydraulic diameter (μm) initial gap gap closure with 0.7 ΔV/V swelling per 10 MWd/kgU Burnup (MWd/kg UO 2 ) IAEA-ICTP 2010

205 Application to LOCA experiment #5 30 IAEA-ICTP 2010