Draft-report on the RTOP-code simulations in the FUMEX-3 exercises.

Transcription

1 Draft-report on the RTOP-code simulations in the FUMEX-3 exercises. Institute Code Country Name of chief scientific investigator RTOP Russian Federation Mr. V. Likhanskii SRC RF TRINITI Troitsk Institute for Innovation and Fusion Research TABLE 1. The RTOP- CODE STRUCTURE AND MODELS (SIMPLIFIED RESPONSES) Code Investigator Based Mechanics Contact Failure on Code structure Fuel Clad Failure model Damage accumulation Stress corrosion cracking Sliding (non zero contact force) Stick Ridging Corrosion Solid Shell Plain strain Solid Cracked pellet Plain stress Plain strain Finite difference Finite element Axial symmetry RTOP Likhanskii TABLE 2. The RTOP- CODE STRUCTURE AND MODELS (SIMPLIFIED RESPONSES) (cont.) Code Investigator Burnup dependence Fission gas release models Code usage Code application Interim storage Accident conditions Normal operating conditions QA Licensing Development R&D Empirical High Burnup structure Grain growth He adsorption & release Integrated swelling model Percolation Grain sweeping Diffusion Melting point (fuel) Mechanical properties (fuel) Densification and swelling Failure mechanism Rim effect Thermal conductivity RTOP Likhanskii

2 TABLE 3. DETAILED MODELLING OF HIGH BURNUP Code Country/ Affiliation RTOP SRC RF TRINITI Porosity limited Interlinkage small FGR from rim High burnup fuel pellet rim Burnup degradation of λ limited/ reduced Matrix Swelling limited/ reduced Full porosity contribution to swelling Temperature limit for rim formation Influence of stress and/or grain size on rim formation Separate treatment of transition zone SRC RF TRINITI = State Research Centre of Russian Federation, Troitsk Institute for Innovation and Fusion Research (TRINITI) TABLE 4. DETAILED MODELLING OF HIGH BURNUP (cont.) Code High BU Fission Gas Release Diffusion coefficient for FGR Xe concentration limit Main contribution to high BU FGR Rim Transition Thermal From zone Interior zone rim BU enhancement of thermal diffusion coefficient BU enhancement of athermal diffusion coefficient phase transition of diffusion coefficient RTOP model - - Depend on conditions TABLE 5. DETAILED MODELLING OF HIGH BURNUP (cont.) Code Re-solution Radial power Other mechanisms From transition zone From pellet interior Depend on conditions Local BU for start of rim Restructuring (MWd/kgU) Intragranular Intergranular Inter/intra dep. On BU Inter/intra dep. on Temperature Pu build up Bubble drift, percolation+mechanics, (I, Cs) nuclides behavior optional. RTOP

3 CASES HAVE ANALYSED BY THE RTOP-code. Experiment Base FGR Base geom. Change Transient T Transient FGR Transient grain growth Transient PCMI Priority cases Risø3 II Risø3 II Risø3 GE OSIRIS H09 ± US PWR 16x16 ± Ginna X03 ± Interramp 20G AREVA idealized case Risø3 GE2, GE4, GE6, GE7, AN3, AN8 Extra Superramp BK7/ Validation done ± - Partial validation - Validation not done 3

4 Description of the RTOP-code. The RTOP-code is used for prediction of the following main parameters of a fuel rod during irradiation: internal gas pressure in fuel rods mechanical stresses in cladding and fuel pellets due to PCMI. Simulation of fuel behavior by the RTOP-code is based on various physical models. 1. Thermal models. 2. Evolution of Burnup and Pu distribution in the fuel rod during irradiation. 3. Fission gas release models. 4. Models of microstructure evolution of the fuel. 5. Mechanical stresses models and models for description of plastic deformations of fuel and cladding. 1. Fuel thermal conductivity model. Fuel temperature is the main parameter controlling the fission gas diffusion coefficients in different areas of the fuel column as well as the mechanical properties of fuel and cladding [1]. The state-ofthe-art correlation for fresh fuel [2] is used as the basic model of fuel heat conductivity in the RTOP code which comprises a term proportional to the burnup and responsible for defect and fission product accumulation as well as the dependence on the porosity [3]: λ 100 = + T + T + T Bu, exp T T λ = λ ( [ ]) 95 1 sw Here λ is fuel heat conductivity, W/(m K); λ 95 - heat conductivity of fuel with the density 95 % of the theoretical value; T fuel temperature, K; Bu fuel burnup, MWd/kgUO 2, sw volume fraction of porosity in fuel. The fuel heat conductivity at high burnups considerably depends on the fuel porosity, in particular, on the quantity of fission gas atoms at the inter-granular boundaries and the width of the rim-layer. The degradation of heat conductivity with the burnup is very important both under nominal conditions and at transients. The RTOP code models the behavior of high burnup fuel under nominal and transient conditions in a self-consistent way, considering the mutual effect of the temperature field in the pellet, fission gas behavior, fuel microstructure and changes in the geometrical parameters of the pellet and cladding

5 2. Fission gas release models. The RTOP-code includes following FGR models. Accumulation of gas atoms according to power distribution. Gas atoms diffusion in spherical grains. Recoil release. Gas bubbles formation in grains, on grain boundaries and grain edges. Drift of gas bubbles in temperature gradients. Grain growth and sweeping of gas atoms and gas bubbles by moving grain boundaries. Gas bubbles resolution and growth due to diffusion of gas atoms Percolation thresholds for inter-granular bubbles and edge bubbles. Interlikage of gases through large pores and cracks in fuel pellets with taking into account for mechanical stresses. The calculations show that if temperature in fuel does not exceed 1200 C the effect of grain boundary radiation blocking becomes important. The radiation blocking model implemented in the RTOP code was described in [4]. The model is based on an assumption of quasi-steady-state gas concentration close to the grain boundary, determined by the equality of diffusion flow on the grain boundary and the effect of radiation resolution of gas from the boundary into the fuel matrix. Such an approach makes it possible to state correctly the boundary condition for the diffusion equation in the grain and adequately describe the fission gas release to the grain boundary during the irradiation at nominal and reduced power. 3. High burnup models. The high burnup fuel possesses a number of specific physical features that need to be considered at its modeling. These features include: A high content of fission gas in the fuel matrix, intragranular and intergranular porosity; Rim-structure formation at the fuel pellet periphery; Fuel swelling and irradiation-induced cladding creep; Degradation of UO 2 fuel heat conductivity and mechanical properties of the fuel rod cladding. At present there is no theoretical model that allows explaining in detail all the observed behavior of fuel restructuring at high burnups and fission gas release out of the rim-area into the fuel rod free volume. The detail computational and theoretical models try to consider a large number of physical processes. As a rule, there are a lot of governing parameters in these models whose values are not experimentally established. Besides, the detail models require time-consuming 5

6 calculations that result in feasible correlations for the parameters of the emerging rim-structure. So actually in all the commercial fuel codes a correlation approach is used to consider the rim-effect. The dimensions of the rim zone depend on the burnup and temperature at the boundary of the fuel pellets. In the RTOP-code the value of the local burnup Bu = 70.1 MWd/kgU, which is equal to about 7.48% FIMA can be assumed as the threshold of rim-layer formation at the periphery of the fuel pellet in accordance with the experimental data of HBRP Project [5]. A close value of the threshold burnup is assumed in TRANSURANUS code [6]. The local burnup is calculated by the RTOP subprogram, which calculates the non-uniform distributions over the pellet for Pu production, power peaking, fission rate and burnup. According to the same data of HBRP Project [5], the limiting temperature before which the rim layer is formed is C. At higher temperature values the rim-layer is not formed due to effective annealing of the radiation defects. The value of 1000 C is assumed as the threshold temperature in the RTOP code. According to the model used in the code the porosity in the rim-layer area after the threshold has been reached increases linearly with the burnup until the maximum value of about 15% is reached. The calculations of the high-burnup fuel behavior at irradiation in nominal and transient conditions made by the RTOP code agree well with the experimental data from FUMEX Models for fuel rod mechanical behavior. Modeling of the pellet-cladding mechanical interaction in the RTOP-code is possible to carry out in the axially symmetric 1.5D and in the 3D geometries. The thermal-mechanical behavior of a fuel rod for the conditions of quasi-steady-state power is described using the 1.5D geometry. For fast power changes the program allows calculating in detail the evolution of stress-strain state of fuel rod in the 3D geometry. To accelerate the calculations in 3D geometry the current version of the RTOP code use of the CUDA technology that uses parallel computations on graphics processing units (GPU). The analysis of stresses in fuel rod cladding is carried out with the account for local non-uniformities of the mechanical stress fields in 3D geometry. More detailed information was published in [7]. 5. Mutual effects of fuel rod thermal-mechanical behavior and fission gas release. In case of fuel pellet-to-cladding interaction resulting from power increase the latter can experience significant tensile stresses. The value of stresses increases with the fuel burnup due to pellet swelling and the fuel-to-cladding gap closure. The loads in the cladding considerably increase 6

7 close to the stress concentrators: areas opposite to radial cracks in the pellet and to the pellet-topellet interfaces. The peaked stresses in the cladding can lead to the fuel rod failure. One of the main considered failure mechanisms is iodine stress corrosion cracking of the cladding. Gas swelling of fuel can considerably increase pellet pressure on the cladding. It is also necessary to consider the feedback effects: the effect of mechanical stresses on the processes of gas release out of the fuel column. Fuel microcracking model. The RTOP code contains a separate module to describe the intergranular microcracking of fuel over the grain boundaries. The mechanical strength at the grain boundaries is lower than inside the grain volume. Therefore, as a result of sharp increase in the nonuniform temperature field and gas pressure in the bubbles can lead to cracking along the grain boundaries. If the cracks along the intergranular boundaries become sufficiently large, the effect of irradiation-induced resolution of the intergranular gas into the fuel matrix stops and the intragranular gas is released into the crack faster. The model of cracking along the grain boundaries described in [8]. There exist two modes of intergranular bubble behavior. The first mode under a quick heating can lead to fuel cracking along the grain boundaries. This case is realized when the effective tensile stress exceeds the critical value. The second mode is observed at a slow temperature rise. In this case the other mechanism of pressure decrease in the bubbles is an increase in their volume due to a diffusion flow of vacancies leading to reduction in the mechanical stresses and increase in the intergranular porosity. If the temperature change is small, the pressure in the bubbles decreases and the criterion for cracking might not be reached. At present the model of microcracking undergoes the stage of additional verification. Fuel swelling and percolation threshold. It is commonly assumed, that the percolation limit for the bubbles at the grain boundaries is reached when the fraction of grain surface area occupied with bubbles is equal to some definite value (usually 0.5). The relation of threshold concentration of gas at the grain boundary at which the percolation takes place to the hydrostatic pressure in fuel deserves being determined. It is reasonable to assume that the number of bubbles on the grain boundaries weakly depends on the external pressure and therefore the percolation condition can be stated based on the bubble size r = r c. The critical size of bubble r c definitely depends on other parameters, such as fuel temperature. The form of dependence of gas threshold concentration at the grain boundary on pressure in fuel: c ( P ) c (0) P cr ext cr ext As the fuel contacts with cladding compressive stresses arise over the radius and the length of the 7

8 fuel column. They increase the threshold concentration of gas needed to reach the percolation and thus slow down the gas release into the fuel rod plenum. At power drop the condition of percolation is met and an accelerated gas release into the plenum takes place. Gas release from the intergranular boundaries into the fuel rod free volume might not occur in case when there are significant deformations in the pellet that block the channels connecting the intergranular porosity and the plenum (cracks in fuel, fuel-to-cladding gap). The solution of the problem of gas flow in a porous medium of UO 2 fuel is sufficiently complex, considering a high sensitivity of such a model to the parameters that are difficult to verify experimentally (for example, the dynamics of growth and healing of cracks between the fuel fragments). The following approach to description of the gas blocked in the macroporosity and cracks of UO 2 fuel has been implemented in the RTOP code. The blocked fission gas can be assumed to situate mainly in radial cracks and radially-oriented pores. It is confined by the angular component of stress tensor σ θθ. With the quantity of gas blocked in the porosity known, its volume can be found from the equation of state: ( ) = NkT V Nb, σ θθ here the overline implies the averaging over the pellet radius. To determine the conditions under which gas is blocked in cracks and the microporosity, a following assumption can be made: gas is released via the channels that are located parallel to the pellet circumference and that are blocked upon radial compression. Then the condition of gas blocking is given by a characteristic parameter that defines the value of elastic radial deformations in the pellet: Here E is the Young modulus of fuel. z = σ / E, If parameter z is negative, the channels are not blocked and neither is the gas. Otherwise the fraction of gas flowing out of the intergranular porosity that is blocked in cracks and micropores at the present moment of time amounts to: rr 1 z z δ = 1 + erf 2 2z Here z 0 and z 1 are the critical parameters that have meaning of the average parameter of blockage and its dispersion correspondingly and erf is the function of error integral. Respectively, the fraction of fission gas flow directed to the plenum is 1 δ. The above effects of increasing the percolation threshold in the intergranular bubbles due to the pressure in fuel and fission gas atom blockage in fuel bring about a slowdown in gas release into the fuel rod plenum under transient power increases. At that, porosity volume increases and the load

9 on the cladding rises. After power drop the porosity opens up and gas pressure in the fuel rod quickly increases. The given phenomenon is observed in Risø3 tests. A comparison of the basic calculation without consideration of the models that slow down the fission gas release under transients, the calculation with the models included and the measured FGR versus the time shows that the implementation of these models in the RTOP code allows improving considerably the kinetics of FGR predicted by the code. In addition, the effect of porosity on the magnitude of fuel pellet pressure exerted on the fuel rod cladding. Porosity formation leads to an increase in fuel pressure on the cladding by about 25%. REFERENCIES 1. V.V. Likhanskii, T.N. Aliev, I.A. Evdokimov, V.G. Zborovskii, V.D. Kanukova, A.A. Sorokin. Models of high burnup UO 2 fuel. Nuclear physics and engineering, 2010, V.2, pp M.R. Billaux, F. Sontheimer, V.I. Arimescu, H. Landskron. Fuel and Cladding Properties at High Burnup, in Proceedings of the ANS Meeting Light Water Reactor Fuel Performance, Park Sity, Utah, April 2000, pp (poster session). 3. V.V. Likhanskii, T.N. Aliev, I.A. Evdokimov, V.G. Zborovskii, V.D. Kanukova, A.A. Sorokin. Models of high burnup UO 2 fuel. Nuclear physics and engineering, 2010, V.2, pp B.V. Dobrov, V.D. Kanukova, S.Yu. Kurchatov, V.V. Likhanskii, O.V. Khoruzhii. Simulation of radiation sealing of an intergranular boundary and the influence of this effect on the release of gaseous fission products from UO 2. Atomic energy, 2000, V.88, No.6, pp M.Kinoshita et al, High burnup rim project: (III) Properties of Rims-Structured Fuel, Proc. of the 2004 International Meeting on LWR Fuel Performance, Orlando, Florida, Sep , 2004, Paper K. Lassmann, C. Walker, J. Van de Laar, F. Lindstrom. Modelling the high burnup UO 2 structure in LWR fuel, J. of Nuclear Materials, v.226 (1995), p A.A Sorokin, V.V. Likhanskii, I.A. Evdokimov, V.G. Zborovskii, L.A. Maslova, N.A. Agapov, A.V. Kukushkin, A.S. Prokopenko, A.V. Trachenko. 3-D simulation of pelletcladding mechanical interaction in the RTOP code, submitted for the 9 th International Conference on WWER fuel performance, modelling and experimental support, Helena Resort, Bulgaria, V.V. Likhanskii, L.V. Matveev. Models of grain boundary cracking and diffusion growth of intergrain bubbles in rapidly heated irradiated fuel. Atomic energy, 1999, V.87, No.1, pp

10 Plant type MOX CANDU CNEA 5 rods 1 undoped BU15 LWR IFA PRIMO rod (BD8) Mechanical interaction Severe transients PCMI PCI LOCA RIA 2 low BU from Riso 2 GE-m and II- 3 IRDMR FIO-118; FIO-119 Riso3 GE7; + OSIRIS - 2 rod HO9 + for parametric study find failure threshold INTERRAMP 10G 20G SUPERRAMP PK6 and PW3 35G Load follow transients THE PRIORITY CASES WERE ANALYSED BY THE RTOP-code. + FIO 131 IFA FK1 and FK2 IFA 519.8/9 Rods DC and DK FGR; Temperature etc Transients IRDMR FIO-118; FIO-119 (7 rods in total 2+5) IFA535 5 rod 9 Riso 3 rod II5 52G WWER MIR Ramp rods Materials Gad/Nb GAIN Gd 701 and 301 Normal operation FGR Pitesti RO89 RO51 AECL NRU (one rod from each ring) US 16x16 PWR + TSQ002 TSQ022? AREVA idealised case + US 16x16 PWR TSQ022 Ginna XO3 segmented standard and annular pellets, nom gap, standard clad FUMEX2 10