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Validation of the fuel rod performance analysis code FRIPAC
Nuclear Engineering and Technology 51 (2019) 1596e1609
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Original Article
Validation of the fuel rod performance analysis code FRIPAC Yong-Jun Deng, Jun Wei*, Yang Wang, Bin Zhang China Nuclear Power Technology Research Institute Co. Ltd, Shang-Bu Middle Road, Shen-Zhen, PR China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 14 February 2019 Received in revised form 29 April 2019 Accepted 2 May 2019 Available online 3 May 2019
The fuel rod performance has great importance for the safety and economy of an operating reactor. The fuel rod performance analysis code, which considers the thermal-mechanical response and irradiation effects of fuel rod, is usually developed in order to predict fuel rod performance accurately. The FRIPAC (Fuel Rod Integral Performance Analysis Code) is such a fuel rod performance analysis code that has been developed recently by China Nuclear Power Technology Research Institute Co. Ltd. The code aims at the computational simulation of the Pressurized Water Reactor fuel rod behavior for both steady-state and power ramp condition. A brief overview of FRIPAC is presented including the computational framework and the main behavioral models. Validation of the code is also presented and it focuses on the fuel rod behavior including fuel center temperature, fission gas release, rod internal pressure/internal void volume, cladding outer diameter and cladding corrosion thickness. The validation is based on experimental data from several international projects. The validation results indicate that FRIPAC is an accurate and reliable fuel rod performance analysis code because of the satisfactory comparison results between the experimental measurements and the code predictions. © 2019 Korean Nuclear Society, Published by Elsevier Korea LLC. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Keywords: FRIPAC Fuel behavior Model Validation
1. Introduction The nuclear fuel is the basic element of a nuclear reactor, providing the material for generating the energy which is used for the production of electricity or process heat. The fuel rod is the principal confinement of the nuclear fuel and the first safety barrier in the reactor core [1]. It is essential to predict the fuel rod behavior accurately for both safe and economic fuel usage. However, it is a difficult work due to the fuel rod suffers the combine effects of thermal, mechanical and neutronic impact during operation. Most related organizations chose to develop and apply fuel rod performance analysis codes to achieve this purpose. FRIPAC (Fuel Rod Integral Performance Analysis Code) is an efficient fuel rod performance analysis code which has been developed by China Nuclear Power Technology Research Institute Co. Ltd (CNPRI) recently. It has the ability to simulate thermalmechanical response of Pressurized Water Reactor (PWR) fuel rods during both steady-state and power ramp condition. It takes into consideration many physical phenomena of the fuel rod in-pile such as heat transfer throughout the fuel rod and coolant, deformation of fuel rod, fuel-cladding mechanical interaction, fission gas
* Corresponding author. E-mail address: [email protected] (J. Wei).
release (FGR), rod internal pressure, cladding oxidation and hydriding, etc. The structure and the main behavioral models of FRIPAC will be briefly introduced in this paper. To ensure the accuracy and reliability of a code, assessment or validation is absolutely necessary. Generally, the validation of a fuel rod performance code is implemented by comparing the code predictions to the related experimental data, e.g. FRAPCON [2], COPERNIC [3] and TRANSURANUS [4,5]. The validation of FRIPAC adopts the similar method as well, and the experimental data used in this paper come from several international projects. 2. Code overview FRIPAC is a 1.5-dimensional code which adopts the axial symmetry simplification. The code is programmed in Cþþ language by applying object-oriented programming (OOP) and structured programming method, which makes the possible optimization of the code quite convenient in the future. It has the ability to simulate the PWR fuel rod behaviors even in high duty and high burnup domains. The applicable fuel types in FRIPAC include uranium dioxide (UO2), mixed oxide fuel (MOX) and urania-gadolinia (UO2-Gd2O3), while the applicable cladding types include Zircaloy-4 and M5. In FRIPAC, the fuel rod is subdivided into discrete axial slices. These slices are then further subdivided into discrete radial concentric rings. The slices and rings composite form the numerical
https://doi.org/10.1016/j.net.2019.05.003 1738-5733/© 2019 Korean Nuclear Society, Published by Elsevier Korea LLC. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).
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framework (1.5-dimensional) for the mathematical analyses. The axial slices are individually analyzed for each time step. When all of the slices have been analyzed, they are coupled and quantities such as internal pressure are then determined. This general mathematical calculation sequence, which is performed at each time step, ensures that the fuel rod predictions can accurately simulate fuel rod behavior. The time-dependent parameters (linear power, fast flux, thermal data, etc.) are described by the user for each time step. Each time step is divided by the code into additional micro-time steps which are used for actual computation. The quantity is calculated by linear interpolation from the data of two successive time steps. The computational flowchart of FIRPAC is shown in Fig. 1. It contains two basic cycles and two iteration loops. The purpose of these two basic cycles is to achieve time discretization and spatial discretization respectively, while the purpose of the iteration loops is to analyze the coupling of thermal-mechanical behavior and improve the calculation accuracy. For given fuel rod manufacturing characteristics and irradiation conditions, FRIPAC offers detailed fuel rod behavior information of every slice and every time step after computation, including fuel rod temperature distribution, fuel-cladding gap size, contact pressure, rod internal pressure, fission gas release, cladding stress and strain, cladding corrosion and hydriding.
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3. Main behavioral models The main behavioral models of the FRIPAC code can be sorted into five categories d thermal models, mechanical models, FGR model, internal pressure model and cladding corrosion model. They will be briefly introduced as follows.
3.1. Thermal models The main function of the thermal models is to calculate the temperature distribution throughout the fuel rod which is the foundation for mechanical response calculation. The thermal models used in FRIPAC for the fuel rod temperature calculations assume a cylindrical fuel pellet located symmetrically within a cylindrical fuel rod surrounded by coolant. The coolant bulk temperature is calculated by using the axial linear heat generation rate and coolant boundary conditions (coolant inlet temperature, coolant mass flux, etc.). The film temperature rise is then calculated from the coolant to the outer surface of the cladding by using Dittus-Boelter equation [6] (for forced convection) or JensLottes equation [7] (for sub-cooled nucleated boiling) which depends on the status of coolant. The cladding inner surface temperature is achieved by calculating the temperature rise through the oxide and cladding. Here, the cladding temperature rise is confirmed ring by ring (the cladding is subdivided into several concentric rings) using Newton-Raphson iteration due to the adopted thermal conductivity of cladding is a cubic polynomial. The thermal conductivity for the zircaloy cladding used in FRIPAC is [8].
lclad ¼ 7:51 þ 2:09 102 T 1:45 102 T 2 þ 7:67 109 T 3 (1) Where,
lclad represents the thermal conductivity of zircaloy in W/m/K; T represents the cladding temperature in degree Kelvin (K). The temperature rise from the inner cladding surface to the fuel surface is determined by gap conductance model. The fuel-cladding gap conductance is the sum of the conductance due to radiant heat transfer [9], the conduction through gas in gap [10] and the conduction through regions of solid-solid contact [11]. Details of the three components of gap conductance can be found in corresponding references. As the gap size is influenced by the solution of the mechanical response and the mechanical response depends on the temperature distribution, iteration is needed in every time step for each axial layer in order to determine the gap conductance. Finally, the temperature distribution in the fuel is calculated with the Halden project fuel thermal conductivity model [12] by using the fuel surface temperature and it is assumed symmetry at the centerline as boundary conditions. This conductivity model can be applicable to UO2, UO2-Gd2O3 and MOX fuel as follows
l95 ¼
C1 C2 þ2:475 104 ð1 0:00333 BuUO2 Þ minðTc ;1650Þ
þ 0:0132 e0:00188Tc (2) C1 ¼
Fig. 1. Simplified computational flowchart of the FRIPAC Code.
Where,
1; for UO2 and UO2 Gd2 O3 0:92; for MOX fuel
fuel
(3)
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C2 ¼
0:1148 þ 0:011599 Gd þ 0:0040 BuUO2 ; for UO2 and UO2 Gd2 O3 fuel 0:1148 þ 0:011599 Pu þ 0:0040 BuUO2 ; for MOX fuel
l95 represents the thermal conductivity in W/m-K, at 95% theoretical density; BuUO2 represents the burnup of UO2 in MWd/kgU; Tc represents the temperature in degree Celsius ( C); Gd represents the weight fraction of gadolinia in %; Pu represents the weight fraction of Pu in MOX fuel in %. The above thermal conductivity is adjusted for as-fabricated fuel pellet density using the Lucuta recommendation for sphericalshaped pores [13]. The radial power distribution of fuel in FRIPAC applies interpolation method with a series of preset arrays of power, which consider the effects of burnup and fuel enrichment. The radial power distribution can also be input by users. The validation for FRIPAC below takes account of the effects of gadolinia doping, MOX fuel and UO2 fuel with a relatively high enrichment by applying the relating radial power distribution arrays due to the mentioned effects have significant influence on calculating the fuel temperature.
The mechanical models compute the stresses, strains and the corresponding deformations of fuel and cladding, the solutions of which bonded with that of thermal models deeply. In FRIPAC, the deformation analysis consists of small displacement analyses including stresses, strains, and displacements in the fuel and cladding for the entire fuel rod. The analyses assume that the cladding retains cylindrical shape during deformation. In general, the temperature distribution in fuel rod is calculated assuming a given geometry firstly. The analysis is followed by the calculations of mechanical models considering the temperature distribution calculated previously. The result is a new geometry and this whole process has to be continued until convergence criteria are fulfilled. 3.2.1. Pellet deformations The fuel pellet is considered to be rigid, and the deformations are mainly caused by thermal expansion, swelling, densification and relocation. a) Thermal expansion The fuel thermal expansion equations of UO2, UO2-Gd2O3 and PuO2 have the same form
R
¼ K1 T K2 þ K3 e
E D kT
by combining the contribution from each constituent of UO2 and PuO2 in proportion to its weight fraction. b) Swelling The fuel swelling is caused by the buildup of solid and gaseous fission products during irradiation. In FRIPAC, empirical relations are used to calculate the fuel swelling [8]. The swelling due to solid fission products is expressed as a simple linear function of burnup
Ssolid ¼ 2:5 1029 Bs
(6)
Where, Ssolid represents the fractional volume change due to solid fission products; Bs represents the burnup during a time step in fissions/m3. The swelling due to gaseous fission products when the fuel temperature is below 2800 K is
3.2. Mechanical models
DR
(4)
(5)
Where,
Sgaseous ¼ 8:8 1056 ð2800 TÞ11:73 e0:0162ð2800TÞ8:010
For MOX fuel, the thermal expansion of the solid is determined
B
Bs
(7) Where, Sgaseous represents the fractional volume change due to gaseous fission products; T represents the temperature in K; Bs represents the burnup during a time step in fissions/m3; B represents the total burnup of fuel in fissions/m3. For temperatures greater than 2800 K, Sgaseous is zero because the gas that causes swelling is assumed to have been released. c) Densification The fuel densification caused by irradiation in FRIPAC is calculated as a function of fuel burnup and initial density which is proposed by U. S. Nuclear Regulatory Commission (NRC) [14].
8 0; Bu Bumin > > > > > > N,lg ðBu=Bu Þ,0:5 min 10 DL < ; Bu 100 , Bumin ¼ 3,½DEN N,lg10 ðBu=Bumin Þ,0:5 > L > > > N > > ; Bu > 100 , Bumin : 3,ðDEN NÞ (8)
DR represents the linear strain caused by thermal expansion R
(equal to zero at 300 K); T represents the temperature in K; ED represents the energy of formation of a defect in Joule; k represents the Boltzmann’s constant; K1 , K2 and K3 are contants which are different for UO2 and PuO2.
27
Bumin ¼ Where,
20; 5;
absðNÞ 4 absðNÞ > 4
(9)
DL represents the fuel dimension change (percent); L
Bumin represents the minimum burnup in NRC model (MWd/ tU);
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N represents the resinter density change comparing theoretical density (percent); DEN represents the ratio of actual density and theoretical density. d) Relocation Fuel relocation models the effect of fuel cracking on gap width. Thermal gradients in a fuel pellet result in corresponding stress gradients that exceed the fuel fracture stress, causing radial cracks. The free surfaces of the crack result in an overall increase of fuel pellet diameter. This effect can be modeled by applying a radial strain to the fuel pellet. This strain is similar to a volumetric strain, but only in the radial direction. The relocation model applied in FRIPAC is the function of local power and burnup which is also incorporated in FRAPCON 4.0 [15].
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The cladding elastic strain is mainly caused by difference between the external and internal pressure. The generalized plane strain hypothesis (one-dimensional radial solution and uniform axial strain) is used for the model. The cladding deformation due to elasticity satisfies three basic equations d equilibrium, strain compatibility and stress-strain equations. According to these, the Euler equation can be deduced
d2 u 1 du u ¼0 þ dr2 r dr r 2
(12)
With boundary conditions
sr jr¼Ro ¼ Po ; sr jr¼Ri ¼ Pi
(13)
Where,
DG G
¼
0:055; Bu < 0:0937GWd=tU 0:055 þ min½reloc; reloc , ð0:5795 þ 0:2447 , lnðBuÞÞ; Bu 0:0937GWd = tU
(10)
uðrÞ represents the cladding displacement expression;
sr represents the radial stress at the position of radius r; 8 P < 20 < 0:345; reloc ¼ 0:345 þ ðP 20Þ=200; 20 P 40 : 0:445; P > 40
(11)
Where,
Ro represents the cladding outer radius; Ri represents the cladding inner radius; Po represents the external pressure on cladding; Pi represents the internal pressure on cladding. b) Thermal expansion The cladding strain caused by thermal expansion [8] for zircaloy used in FRIPAC is
8 300 < T < 1083K 1:485 103 þ 4:95 106 , T; > > > > > > < T 1083 , p 103 ; 1083 T < 1244K 2:77763 þ 1:09822 , cos εth;R ¼ > 161 > > > > > : 1:04 102 þ 9:7 106 , T; 1244 T 2098K 8 3 5 > 300 < T < 1083K > > 3:78 10 þ 1:26 10 , T; > > > > < T 1083 , p 103 ; 1083 T < 1244K 8:76758 þ 1:09822 , cos εth;L ¼ 161 > > > > > > > :ε 3 þ 9:7 106 , T; 1244 T 2098K th;L ¼ 4:4 10
(14)
DG represents the fraction of as fabricated gap closure due to G
pellet relocation; P represents the local power in kW/ft; Bu represents the local burnup in GWd/tU.
3.2.2. Cladding deformations Cladding deformations can be mainly divided into several parts, including elastic strain, thermal expansion, irradiation growth and creep.
Where, εth;R represents the circumferential thermal expansion (m/m); εth;L represents the axial thermal expansion (m/m); T represents the temperature (K). The basal plane symmetry is assumed here, which meaning the circumferential thermal expansion equals to the radial thermal expansion. c) Irradiation growth
a) Elastic strain
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Irradiation growth is caused by the radiation damage due to fast neutrons. The irradiation growth model of zircaloy [16] used in FRIPAC is
ax ¼ A,FB
(15)
Where, ax represents the axial growth increment (m/m);
F represents the fast neutron fluence (n/m2); A and B are constants which are different for different kinds of zircaloy cladding. d) Creep The cladding creep strain rate is used in FRIPAC, and the model is described as
ε_ tot ¼ C ð_εH þ ε_ irr Þ ε_ H ¼
52,εsp ,ð_εth þ ε_ irr Þ1=2 2,t 1=2
(16) pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi exp 52, ð_εth þ ε_ irr Þ,t þ ð_εth
þ ε_ irr Þ Where,
(17)
ε_ tot represents the total strain rate (m/m/h); ε_ H represents the total thermal strain rate (m/m/h); ε_ th represents the thermal strain rate (m/m/h); ε_ irr represents the irradiation strain rate (m/m/h); εsp represents the saturated primary hoop strain (m/m); t represents the time (hours). C represents a constant in the model.
In FRIPAC, the Peng-Robinson equation of state (EOS) is applied to compute the rod internal pressure [24].
R,T ai p ¼ V i 2 i b V i ni þ 2b Vi b2
3.3. Fission gas release model
ni
The rod internal pressure of the gas in the fuel rod is computed after the fuel rod temperature distribution and deformation calculations have been completed. The temperature distribution, the void volume and the gas inventory in fuel rod are required to calculate the internal pressure. The temperature distribution is provided by thermal models. The void volume is derived from the geometry information calculated by the mechanical models. And the gas inventory is provided by the fission gas release and the initial filled gas. The gaseous fission products (primarily Xenon and Krypton) generated from fuel pellets release into rod internal void volume. This process is known as fission gas release. The various mechanisms affecting the fission gas behavior in fuel are presented and discussed in detail in Ref. [17]. As we know, most fission gas release models are based on the theory for diffusion from a sphere which was firstly proposed by Booth [18]. The Forsberg-Massih model [19,20] is a typically approved FGR model which is developed from the Booth sphere diffusion model
Where, r represents the radial position in grain; t represents the time; Cðr; tÞ represents the gas concentration;
The derivation and calculation process of the Forsberg-Massih model were described in detail in Ref. [21]. The fission gas release described by Forsberg-Massih model is a two-stage approach. The first stage computes diffusion of fission gas atoms from within the fuel grains to the grain boundaries by solving the relevant diffusion equation in spherical co-ordinates numerically. An effective diffusion coefficient is employed, which accounts for gas atom resolution from and trapping into intragranular bubbles. The second stage of the model utilizes time-dependent boundary conditions to determine grain boundary gas accumulation as inter-granular lenticular bubbles, resolution, saturation, and release. Fission gas release from the grain boundaries is controlled using a grain boundary saturation criterion that involves a threshold concentration of gas at the grain boundaries. The Forsberg-Massih model is incorporated in FRIPAC as default FGR model. The code validation below is based on it. It is worth noting that the Forsberg-Massih model is developed for UO2 pellets, while the FGR of MOX pellets is treated by applying different diffusion coefficient. The Forsberg-Massih model is also applied to UO2-Gd2O3 pellets in the FRIPAC code, since the FGR model for UO2 pellets is suitable to UO2-Gd2O3 pellets according to the observation conducted by Delorme et al. [22] and Arana et al. [23]. Both of their researches demonstrated that the FGR of UO2Gd2O3 fuel were consistent with that of UO2 fuel under similar burnup and power levels. 3.4. Internal pressure model
Details of the creep strain model can be found in Ref. [15].
" # vCðr; tÞ v2 2 v ¼ DðtÞ Cðr; tÞ þ bðtÞ þ vt vr 2 r vr
DðtÞ represents the diffusion coefficient;
bðtÞ represents the gas production.
(18)
(19)
ni
Where, p represents the fuel rod internal gas pressure; R represents the universal gas constant; Vi represents i-th internal void volume; ni represents number of moles in the Vi void volume; Ti represents the gas temperature in the Vi void volume; ai represents the cohesion parameter; b represents the covolume parameter. ai and b are both affected by the critical temperature and critical pressure of gas, while ai is also affected by the function of the acentric factor. More details of the Peng-Robinson EOS can be found in Ref. [24]. The void volume in the fuel rod consists of pellet dish volume, pellet chamfer volume, pellet crack volume, fuel-cladding gap volume, open porosity volume, surface roughness and chip volume, upper and lower plenum volume, fuel central hole volume (if present). The plenum volume is calculated from initial cladding, fuel and spring dimensions after accounting for temperature and irradiation effects (such as cladding growth, fuel densification/ swelling). The dish volume is calculated at any given power and time by applying the appropriate thermal expansion and fuel densification/swelling to all radial rings, recalculating the shape of the pellet, and then summing up the volume at the pellet end face. The gap volume is calculated by subtracting a pellet cross-sectional area based on radial expansion due to fuel densification/swelling and thermal expansion from a cladding inner cross-sectional area
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which includes the effects of elastic and plastic cladding deformation. The radial crack volume is the difference between the linear and the areal calculation of the pellet thermal expansion. The chip volume is calculated by a user defined factor which is usually obtained from large number of measurements on unirradiated production pellets. The roughness volume is calculated by an empirical equation considering the pellet diameter and geometric fuel volume. The open porosity volume is calculated as a function of initial fuel density and fuel temperature at corresponding power. The void volumes mentioned above are assumed to be interconnected and the pressure is assumed to be uniformly distributed over these volumes. It is notable that these various volume components, moles of gas and corresponding temperatures change with time, and they will be computed continuously until the rod internal pressure is convergent. The Peng-Robinson EOS is believed to be more accurate than the ideal gas EOS for predicting mixture gas pressures in high temperature and high pressure environment. However, the pressure predictions from Peng-Robinson EOS is quite similar to those from the ideal gas EOS in the environment of PWR fuel rods according to practical calculations. The ideal gas EOS and other commonly used EOS correlations are also incorporated in FRIPAC for contrast, while the PengRobinson EOS is used as default option and adopted in the validation below. 3.5. Cladding corrosion model The FRIPAC code incorporates an approved and reliable cladding corrosion model from Ref. [8], which has already been applied in the FRAPCON code. For Zircaloy-4 cladding, the cubic rate law is applied for corrosion-layer thickness as a function of time until a transition thickness is attained. After the transition thickness is attained, a flux-dependent linear rate law is applied, with the rate constant being an Arrhenius function of oxide-metal interface temperature. More details of the corrosion model can be found in Ref. [8].
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4. Code validation 4.1. Validation cases overview The validation of the FRIPAC code are implemented by applying well-characterized experimental fuel rods from several irradiation experiment projects, including OECD Halden Reactor Project, Risoe3, GAIN, Super-Ramp, US-PWR 16x16, Beznau-1, Balfour BR-3, ATR WG-MOX, Gravelines-4, FUGEN, B&W Studsvik, BNFL BR-3, Oconee. These projects provided reliable experimental data with measurements reflecting different kinds of fuel rod behaviors. The power histories, fuel rod manufacturing characteristics and system parameters were derived from relevant experiment documents to make the input profiles for the FRIPAC code. The experimental fuel rods were irradiated in PWR and Boiling Water Reactor (BWR) coolant conditions (including the research and commercial reactors). The preferred experimental measurements in the validation of a fuel rod performance analysis code are fuel center temperature, fission gas release, internal pressure, cladding outer diameter and cladding corrosion thickness. These experimental measurements are compared to corresponding predictions by the code. Then the accuracy and reliability of the code can be concluded from these comparison results. The specific validation processes and results of each characteristic parameter for FRIPAC are presented as follows by comparing the code predictions to the corresponding measurements from experimental data. This validation method and corresponding validation matrix have been adopted by many other fuel rod performance codes. The overview of the main experimental fuel rods used for the validation of the FRIPAC code is shown in Table 1. Details of these experimental fuel rods are described in corresponding references, including the fuel enrichment, fuel grain size range and fuel rod geometry. 4.2. Validation of the fuel center temperatures The accurate prediction of the fuel temperatures is most
Table 1 The overview of the main experimental data used for the validation of the FRIPAC code. Experiment
Number of rods
Fuel typea
Fuel enrichment
Cladding type
Rod burnup (GWd/tHM)
Reference
HALDEN
14
UO2
~3e13% U235
Zr-2/Zr-4
4e88
HALDEN
3
UO2-Gd2O3
Zr-2
25e60
HALDEN
9
MOX
Zr-4
20e68
Risoe-3 Super-Ramp Super-Ramp
12 12 4
UO2 UO2 UO2-Gd2O3
Zr-2/Zr-4 Zr-4 Zr-4
42 30e45 34
[33,34,35] [36,37] [38] [39] [39]
US-PWR 16x16 GAIN
16 4
UO2 UO2-Gd2O3
Zr-4 Zr-4
36e58 39
[40] [41]
Balfour BR-3 Oconee PWR HBEP ATR WG-MOX
5 1 1 6
UO2 UO2 UO2 MOX
Zr-4 Zr-4 Zr-4 Zr-4
13e61 50 25 30e50
[42] [43] [44] [45]
B&W Studsvik FUGEN
1 3
UO2 MOX
Zr-4 Zr-2
62 30e42
[46] [45]
Gravelines-4
3
MOX
Zr-4
48e57
[47]
Beznau-1
8
MOX
~4e13% U235 ~8% Gd2O3 ~0.3% U235 ~4e8% Pu ~3% U235 ~3e6% U235 ~3% U235 ~4% Gd2O3 ~3.5% U235 ~3.5% U235 ~3e7% Gd2O3 ~5e8.5% U235 ~3% U235 ~3% U235 ~0.3% U235 ~5% Pu ~3% U235 ~0.7% U235 ~5% Pu ~0.2% U235 ~5% Pu ~0.3% U235 ~3e5.5% Pu
[25,26,27] [28,29,30] [31,32]
Zr-4
35e58
[48,49,50]
a The validation cases contain the fuel pellets with different kinds of manufacturing methods including ammonium diuranate (ADU) and ammonium uranyl carbonate (AUC) for UO2, short binderless route (SBR) and integrated dry route (IDR) for MOX.
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Fig. 2. Rod average LHGR versus Rod average burnup for fuel center temperature validation cases from HALDEN project.
Fig. 3. Comparison of measured fuel center temperatures with those predicted by FRIPAC with upper and lower bound lines (dashed lines).
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Fig. 4. Predicted minus measured divided by measured center temperature as a function of burnup.
essential for any fuel rod performance codes. Many temperaturedependent physical phenomena are strongly affected by the accuracy of their predictions, such as thermal expansion, fission gas diffusion and release, creep, etc. Large amount of convincing experimental fuel center temperature data have been measured in associated projects worldwide so far. Therefore, fuel center temperature is taken as one of the validation parameters for the FRIPAC code. The experimental fuel center temperature data for the validation of FRIPAC are derived from 23 fuel rods consist of 15 UO2 fuel rods, 5 MOX fuel rods and 3 UO2-Gd2O3 rods. These experimental fuel rods were mainly measured in OECD Halden Reactor project. Fig. 2 shows the rod average linear heat generation rate (LHGR) as a function of rod average burnup for the validation cases of fuel center temperatures. This figure indicates that these 23 fuel center temperature validation cases cover a wide range of burnup and LHGR. The rod average burnup of UO2, MOX and UO2-Gd2O3 validation cases range up to 88 GWd/tHM, 32 GWd/tHM and 71 GWd/ tHM respectively. And the rod average LHGR of all fuel center temperature validation cases range up to 44 kW/m. It is desirable to include more validation cases, especially the MOX fuel cases with high burnup. Comparison of the measurements from experimental data and the corresponding predictions by the FRIPAC code for all fuel center temperature validation cases is shown in Fig. 3. These data are also shown in terms of relative bias in Fig. 4 as a function of burnup. The predicted to measured (P/M) mean value is 1.002 and the standard deviation is 0.110 according to statistic calculation. This standard deviation is reasonable given the uncertainty in the thermocouple data and the calculated rod power. As shown in Figs. 3 and 4, most data points are located near around the P ¼ M line. The discrepancy
remains within the bound lines up to a temperature of about 1500 K and increases beyond this temperature, which is largely due to the overpredictions for IFA-432R2 and underpredictions for IFA513R6. Both of these two experimental rods may lack accuracy of measurement slightly, due to the same problems were shown in the assessment of the code FRAPCON [2]. After ignoring these two rods, it can be concluded that FRIPAC gives satisfactory predictions of fuel center temperature for UO2, MOX and UO2-Gd2O3 fuel rods. 4.3. Validation of the fission gas release Fission gas release (FGR) is another key phenomenon that must be considered in a fuel performance code. The fission gas released from fuel pellet contributes to the increase of the fuel rod internal pressure, with the associated risks of fuel thermal degradation and even cladding failure. The accurate prediction of FGR is important for fuel performance code due to two reasons: firstly, it has a significant impact on the prediction of gap conductance and fuel temperatures, and secondly, it is also necessary for the calculation of rod internal pressures which affect end-of-life rod pressures. The validation of the FRIPAC code here is based on the FGR model proposed by Forsberg and Massih which has been described above. The ability of the FRIPAC code to predict FGR has been validated based on comparisons to experimental FGR data from 54 UO2 fuel rods, 26 MOX fuel rods and 8 UO2-Gd2O3 fuel rods respectively. Both steady-state and transient FGR cases are included. The experimental FGR data are commonly inferred from rod puncture test, or estimated from rod pressure data at end of irradiation. Fig. 5 shows the rod average LHGR as a function of rod average burnup for the validation cases of FGR. It demonstrates that the FGR validation cases cover a wide range of burnup and LHGR.
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Fig. 5. Rod average LHGR versus Rod average burnup for FGR validation cases from HALDEN, US-PWR 16x16, Riseo-3, Super-Ramp, Balfour BR-3, Oconee PWR, B&W Studsvik, HBEP, GAIN, ATR WG-MOX, FUGEN, Gravelines-4 and Beznau-1 projects.
can be concluded that FRIPAC provides satisfactory predictions of FGR for UO2, MOX and UO2-Gd2O3 validation cases basing on this information. It should be note that FRIPAC provides underpredictions for several cases with less than 5% FGR, which are very hard to predict accurately for most FGR models nowadays. It is to be noted that the limiting rods have released above 10% FGR at end of life in today’s nuclear power plant (particularly for power uprated plants). Because of this, only the fuel rod cases with greater than 5% FGR were selected in the integral assessment of the code FRAPCON [2].
4.4. Validation of the rod internal pressure and internal void volume
Fig. 6. Comparison of fission gas release predicted by the FRIPAC code and corresponding experimental data with a factor of 2 error bound (dash lines).
The comparisons of the measured FGR values with the corresponding FRIPAC predictions are summarized in Fig. 6. Due to the inherent uncertainties of fission gas behavior modeling, a deviation of code predictions from the experimental data within a factor of about 2 up and down is generally regarded as satisfactory [51]. It
The internal pressure and internal void volume within a fuel rod will change continuously during operation. The rod internal void volume varies with burnup due to combined effects of the temperature distribution and the deformations in rod primarily. The rod internal void volume is one of the most significant factors for the accurate prediction of the rod internal pressure. These two parameters are closely connected to each other. As we know, rod internal pressure is a design criterion for fuel rod design. Therefore, it is necessary to ensure that the internal gas pressure and internal void volume predictions are accurate. The ability of FRIPAC to predict internal pressure and internal void volume are validated against 7 and 15 well-characterized fuel rods respectively. The internal pressure data points are obtained
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Fig. 7. Rod average LHGR versus Rod average burnup for internal pressure and void volume validation cases from HALDEN, US-PWR 16x16, GAIN and Beznau-1 projects.
Fig. 8. The comparison of measured and predicted rod internal pressures for 7 validation cases with ±2s error bounds (dash lines).
from the pressure transducers in the rods that provide on-line values, and the internal void volume data points are obtained from post-irradiation examination. Fig. 7 shows the rod average LHGR as a function of rod average burnup for the internal pressure and internal void volume validation cases. The rod average burnup of the internal pressure validation cases range up to 33 GWd/tHM while that of the internal void volume cases range up to 60 GWd/ tHM. The rod average LHGR range over 40 kW/m for both kinds of cases. It is desirable to include more validation cases, especially
internal pressure cases with high burnup, but no more fuel rods with reliable measured data have been achieved presently. Fig. 8 presents the comparison between the measured and FRIPAC calculated rod internal pressures. The P/M mean value is 1.042 and the standard deviation is 0.201 according to statistic calculation. It indicates that FRIPAC predicts the internal pressures satisfactorily. Most data points are located nearly around the P ¼ M line and between the ±2s error bound lines (s is the standard deviation of (P-M) values). The predictions for IFA-513R2 case are a
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Fig. 9. The comparison of measured and predicted rod internal void volume at end of irradiation for 15 validation cases with ±2s error bounds (dash lines).
Fig. 10. Rod average LHGR versus Rod average burnup for cladding outer diameter validation cases from US-PWR 16x16, GAIN, Riseo-3 and Beznau-1 projects.
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outer diameter changes in comparison to the initial values) are calculated, and the absolute deviation between the predicted and measured cladding deformations are within acceptable ranges (the maximum absolute deviation is about 0.11 mm which is also discovered in D10 case). Hence, it can be concluded that FRIPAC provides reasonable predictions of cladding outer diameters. 4.6. Validation of the cladding corrosion thickness
Fig. 11. The comparison of measured and predicted cladding outer diameters for 14 validation cases with ±2s error bounds (dash lines).
bit more overpredicted and this is probably due to overpredicting the FGR for this rod. Fig. 9 presents the measured and FRIPAC calculated rod internal void volume at end of irradiation for these 15 fuel rods. These calculations were set as room temperature and atmospheric pressure at final two time steps because it is approximate to the environment at which the data were collected. The P/M mean value is 1.089 and the standard deviation is 0.246 according to statistic calculation. It indicated that the FRIPAC code does a good job of predicting the rod internal void volumes while most data points locate between the ±2s error bound lines (s is the standard deviation of (P-M) values). Only TSQ053 case is a little overpredicted with comparatively large deviation. 4.5. Validation of the cladding outer diameter Accurate simulation of the mechanical behavior of fuel rod is important because the heat transfer coefficient across the fuelcladding gap is closely related to the effective gap size or the contact pressure. The prediction of cladding outer diameter reflects the accuracy of mechanical models for both fuel and cladding generally. The cladding outer diameter is dominated by creep at early life during operation. However, at higher burnups, following fuelcladding contact, the cladding dimension deformation is mainly controlled by mechanical behavior of the fuel. The ability of FRIPAC to predict cladding outer diameter is validated against 14 well-characterized fuel rod. The measurements were made post irradiation in hot cell, including both base irradiation and power ramp situations. The cladding type of all validation cases is Zircaloy-4. Fig. 10 shows the rod average LHGR as a function of rod average burnup for the cladding outer diameter validation cases. The rod average burnup ranges up to 60 GWd/tHM and the rod average LHGR ranges up to 40 kW/m as shown in Fig. 10. The measured and predicted cladding outer diameters of all the 14 validation cases are summarized in Fig. 11. The P/M mean value is 1.007 and the standard deviation is 0.005 according to statistic calculation. Most data points are located between the ±2s error bounds as shown in Fig. 11 (s is the standard deviation of (P-M) values). However, the predictions of some validation cases are a bit overpredicted with acceptable deviations (the maximum relative deviation is about 1.3% which is discovered in D10 case). Furthermore, the predicted and measured cladding deformations (cladding
The oxidation phenomenon produces oxide layers on fuel rod cladding, which degrades the heat transfer and mechanical property of cladding. The cladding oxide layer thickness is also a design criterion which indicates its importance. It is necessary to validate FRIPAC’s ability to accurately predict the cladding corrosion thickness. 8 well-characterized fuel rods were selected to demonstrate the capability of FRIPAC to accurately calculate fuel rod waterside oxidation. The cladding type of these fuel rods is Zircaloy-4. The FRIPAC code also has the ability to predict corrosion behavior of the fuel rods with M5 alloy, but the experimental fuel rods with known power histories and end-of-life measured oxide thickness for M5 alloy are very limited for us at present. Fig. 12 shows the rod average LHGR as a function of rod average burnup for the cladding corrosion thickness validation cases. The rod average burnup levels of these rods range up to 60 GWd/tHM and the rod average LHGR range up to 25 kW/m. The predicted and the measured end-of-life oxide layer thickness of Zircaloy-4 claddings are compared in Fig. 13 The P/M mean value is 1.161 and the standard deviation is 0.297 according to statistic calculation. As shown in Fig. 13, the model in FRIPAC overpredicts for the relatively low values of oxide thickness, up to about 20 microns. Beyond this value, a number of cases with underprediction seem to systematically grow slightly. This is a little confused, but there are only 8 cases and about 100 data points totally which are deficient for the validation of a corrosion model. The comparison indicates that FRIPAC has a tendency to overpredict the cladding oxide layer thickness in general for current cases. The results seem to be reasonably conservative. However, more cases for the validation of the corrosion thickness are needed to make the validation more comprehensive. 5. Summary The fuel rod performance analysis code FRIPAC is an advanced computer programme for the predictions of PWR fuel rod behaviors that has been developed by CNPRI. It is designed with excellent structure applying OOP and structured programming method, which make the optimization convenient. Basic analysis process and the main behavioral models of the FRIPAC code are briefly introduced. In the validation study, FRIPAC has been validated against a set of pre-selected experimental data from 102 well-characterized fuel rods which are sorted from several international projects. These validation cases cover a wide range of operating conditions. Overall, FRIPAC gives satisfactory and reasonable predictions on fuel center temperature, FGR, rod internal pressure, internal void volume, cladding outer diameter and cladding corrosion thickness for current validation cases. No major shortcoming was discovered during validation. It can be demonstrated that FRIPAC is a reliable and accurate fuel performance code which has the potential to be used for predicting the PWR fuel rod behaviors in engineering design. In future, more experimental cases are required to make the validation of FRIAPC more extensive and creditable. Besides, we also planned to incorporate a series of acknowledged behavioral models for BWR. New material models and corresponding
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Fig. 12. Rod average LHGR versus Rod average burnup for cladding corrosion thickness validation cases from US-PWR 16x16 and Super-Ramp projects.
Fig. 13. The comparison of measured and predicted oxide layer thickness of Zircaloy-4 cladding for 8 fuel rods with ±2s error bounds (dash lines).
uncertainties are planned to be developed and determined according to new obtained experimental data. The Graphical User Interface (GUI) for FRIPAC is also under development which makes the preparation of inputs and the treatment of outputs much more convenient for users. Acknowledgements The authors wish to thank the National Science and Technology Major Project of the People’s Republic of China (No. 2016ZX06004002) for financial support to this research. References [1] D.G. Cacuci, Handbook of Nuclear Engineering [M], Springer, New York, 2010.
[2] K.J. Geelhood, W.G. Luscher, FRAPCON-4.0: Integral Assessment, PNNL, U.S. Department of Energy, 2015. PNNL-19418. [3] J.L. Jacoud, Ph Vesco, Despription and Qualification of the COPERNIC/TRANSURANS (Update of May 2000) Fuel Rod Design Code, Framatome Nuclear Fuel, 2000, p. TFJCDC1556. [4] K. Lassmann, H. Blank, Modeling of fuel rod behavior and recent advances of the TRANSURANUS code, Nucl. Eng. Des. 106 (1988) 291e313. [5] P.V. Uffelen, A. Schubert, J. van de Laar, et al., Verification of the TRANSURANUS fuel performance code - an overview, in: 7th International Conference on WWER Fuel Performance, Albena, Bulgaria, 2007. [6] F.W. Dittus, L.M.K. Boelter, Heat transfer in automobile radiators of the tubular type, Int. Commun. Heat Mass Transf. 12 (1985) 3e22. [7] W.H. Jens, P.A. Lottes, Analysis of Heat Transfer, Burnout, Pressure Drop and Density Data for High-Pressure Water, Argonne National Laboratory, 1951. ANL-4627. [8] L.J. Siefken, E.W. Coryell, E.A. Harvego, J.K. Hohorst, SCDAP/RELAP5/MOD 3.1 Code Manual: MATPRO, A Library of Materials Properties for Light-WaterReactor Accident Analysis, vol. 4, Idaho National Engineering and Environmental Laboratory, 2001. INEL-96/0422, NUREG/CR-6150. [9] F. Kreith, R.M. Manglik, M. Bohn, Principles of Heat Transfer, seventh ed., Cengage Learning, 2011. [10] C.E. Beyer, C.R. Hann, D.D. Lanning, F.E. Panisko, L.J. Parchen, GAPCONTHERMAL-2: A Computer Program for Calculating the Thermal Behavior of an Oxide Fuel Rod, Battelle Northwest Laboratory, 1975. BNWL-1898. [11] G. Jacobs, N. Todreas, Thermal contact conductance in reactor fuel elements, Nucl. Sci. Eng. 50 (1973) 283e290. [12] D.D. Lanning, C.E. Beyer, K.J. Geelhood, FRAPCON-3 Updates, Including MixedOxide Fuel Properties, vol. 4, Pacific Northwest National Laboratory, 2005. PNNL-11513, NUREG/CR-6534. [13] P.G. Lucuta, H.S. Matzke, I.J. Hastings, A pragmatic approach to modeling thermal conductivity of irradiated UO2 fuel: review and recommendations, J. Nucl. Mater. 232 (1996) 166e180. [14] U.S. Nuclear Regulatory Commission, An Acceptable Model and Related Statistical Methods for the Analysis of Fuel Densification, Office of Standards Development, 1978, p. 126. Regulatory Guide 1. [15] K.J. Geelhood, W.G. Luscher, P.A. Raynaud, I.E. Porter, FRAPCON-4.0: A Computer Code for the Calculation of Steady-State, Thermal-Mechanical Behavior of Oxide Fuel Rods for High Burnup, Pacific Northwest National Laboratory, 2015. PNNL-19418, Vol.1, Rev.2. [16] W.G. Luscher, K.J. Geelhood, Material Property Correlations: Comparisons between FRAPCON-3.4, FRAPTRAN 1.4, and MATPRO, Pacific Northwest National Laboratory, 2011. PNNL-19417, NUREG/CR-7024. [17] P.V. Uffelen, Contribution to the Modelling of Fission Gas Release in Light Water Reactor Fuel, PhD Thesis, Nuclear Engineering, University of Liege, 2002. [18] A.H. Booth, A Method of Calculating Fission Gas Diffusion from UO2 Fuel and its Application to the X-2 Loop Test, Atomic Energy of Canada, Ltd., Chalk River Project, 1957. CRDC-721.
Y.-J. Deng et al. / Nuclear Engineering and Technology 51 (2019) 1596e1609 [19] K. Forsberg, A.R. Massih, Fission gas release under time-varying conditions, J. Nucl. Mater. 127 (1985) 141e145. [20] K. Forsberg, A.R. Massih, Diffusion theory of fission gas migration in irradiated nuclear fuel UO2, J. Nucl. Mater. 135 (1985) 140e148. [21] K. Lassmann, H. Benk, Numerical algorithms for intragranular fission gas release, J. Nucl. Mater. 280 (2000) 127e135. [22] R. Delorme, Ch Valot, L. Fayaette, X. Pujol, I. Aubrun, J. Lamontagne, T. Blay, B. Pasquet, P. Bienvenu, I. Roure, C. Pozo, G. Carlot, C. Sabathier, P. Martin, G. Trillon, V. Auret, S. Bouffard, Study of fission gas behaviour and fuel restructuration in irradited (U,Gd)O2 fuel, in: Transactions of the TopFuel 2012 Reactor Fuel Performance Conference, Manchester, UK, September 2-6, 2012. [23] I. Arana, C. Munoz-Reja, F. Culbebras, Post-irradiation examination of high burnup fuel rods from Vandellos II, in: Transactions of the TopFuel 2012 Reactor Fuel Performance Conference, Manchester, UK, September 2-6, 2012. [24] D. Peng, D.B. Robinson, A new two-constant equation of state, Ind. Eng. Chem. Fundam. 15 (1975) 59e64. [25] C. Nealley, D.D. Lanning, M.E. Cunningham, C.R. Hann, Post-irradiation Data Analysis for NRC/PNL Halden Assembly IFA-431, Pacific Northwest Laboratory, 1979. NCREG/CR-0797, PNL-2975. [26] D.D. Lanning, Irradiation History and Final Post-irradiation Data for IFA-432, Pacific Northwest Laboratory, 1986. NCREG/CR-4717, PNL-5971. [27] J.A. Turnbull, R.J. White, The Thermal Performance of the Gas Flow Rigs: A Review of Experiments and Their Analyses, OECD Halden Reactor Project, 2002. HWR-715. [28] I. Matsson, J.A. Turnbull, The Integral Fuel Rod Behaviour Test IFA-597.3: Analysis of the Measurements, OECD Halden Reactor Project, 1998. HWR-543. [29] P.M. Chantoin, E. Sartori, J.A. Turnbull, The compilation of a public domain database on nuclear fuel performance for the purpose of code development and validation, in: Proceedings of the ANS/ENS International Topical Meeting on Light Water Reactor Fuel Performance, Portland, Oregon, March 2-6, 1997. [30] C. Bagger, H. Carlson, P. Knudson, Details of Design Irradiation and Fission Gas Release for the Danish UO2-Zr Irradiation Test 022, Risø National Laboratory, 1978. RISO-M-2152. [31] T. Tverberg, M. Amaya, Study of Thermal Behavior of UO2 and (U,Gd)O2 to High Burnup (IFA-515), OECD Halden Reactor Project, 2001. HWR-671. [32] H. Ruhamann, W. Beere, B.H. Lee, Irradiation Performance of Commercial UO2 and (U,Gd)O2 Fuel; Update of the Test IFA-636.1, OECD Halden Reactor Project, 2001. HWR-672. [33] H. Koike, The MOX Fuel Behavior Test IFA-597.4/.5/.6/.7; Summary of In-Pile Fuel Thermal Temperature and Gas Release Data, OECD Halden Reactor Project, 2003. HWR-729. [34] L. Mertens, M. Lippens, J. Alvis, The FIGARO Programme: the Behaviour of Irradiated MOX Fuel Tested in the IFA-606 Experiment, Description of Results and Comparison with COMETHE Calculation, 1998. HPR 349/30 Halden Reactor Project. [35] R.J. White, The Re-irradiation of MIMAS MOX Fuel in IFA-629.1, OECD Halden
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Reactor Project, 1999. HWR-586. [36] B. Petiprez, Ramp Tests with Two High Burnup MOX Fuel Rods in IFA-629.3, OECD Halden Reactor Project, 2002. HWR-714. [37] P. Blair, J. Wright, The IMF/MOX Comparative Test, IFA-651.1: Result after Four Cycles of Irradiation, OECD Halden Reactor Project, 2004. HWR-763. [38] K.R. Merckx, L.F. Van Swam, G.L. Ritter, The Third Risoe Fission Gas Project (RISOE-III) Database, Risoe National Laboratory, 1995. NEA-1493 IFPE/RISOEIII. [39] S. Djurle, The Super-ramp Project, Final Report of the Super-ramp Project, Studsvik AB Atomenergi, 1984. STIR-32. [40] W.F. Lyon, US-PWR 16x16 LTA Extended Burnup Demonstration Program Database, EPRI, 2005. NEA-1738 IFPE/US-PWR-16x16LTA. [41] M. Boulanger, M. Lippens, Gadolinia Doped UO2 Fuel Behaviour Experiment Database, Belgonucleaire, 2002. NEA-1625 IFPE/GAIN. [42] M.G. Balfour, BR-3 High Burnup Fuel Rod Hot Cell Program, Final Report, Westinghouse Electric Corporation, 1982. WCAP 10238, DOE/ET/34073-1. [43] L.W. Newman, The Hot Cell Examination of Oconee-1 Fuel Rods after Five Cycles of Irradiation, Babcock and Wilcox Company, 1986. DOE/ET/34212-50, BAW-1874. [44] D.D. Lanning, M.E. Cunningham, J.O. Barner, E.R. Bradley, Qualification of Fission Gas Release Data from Task 2 Rods, HBEP 25, Final Report, Pacific Northwest Laboratory, 1987. [45] T. Ozawa, Performance of ATR MOX fuel assemblies irradiated to 40 GWd/tU, in: Proceedings of the 2004 International Meeting on LWR Fuel Performance, Orlando, Florida, September 19-22, 2004. [46] D.A. Wesley, K. Mori, S. Inoue, Mark BEB ramp testing program, in: Proceedings of the 1994 ANS/ENS International Topical Meeting on Light Water Reactor Fuel Performance, American Nuclear Society, West Palm Beach, Florida, 1994. [47] S. Beguin, The Lift-Off Experiment with MOX Fuel Rod in IFA-610.2 Initial Results, OECD Halden Reactor Project, 1999. HWR-603. [48] E. de Meulemeester, N. Hoppe, G. de Contenson, M. Watteau, Review of work carried out by BELGONUCLEAIRE and CEA on the improvement and verification of the COMETHE computer code with the aid of in-pile experimental results, in: BNES International Conference on Nuclear Fuel Performance, Paper ECS-EEC-73-595, London, UK, 1973. [49] R.J. White, S.B. Fisher, P.M.A. Cook, R. Stratton, C.T. Walker, I.D. Palmer, Measurement and analysis of fission gas release from BNFL’s SBR MOX fuel, J. Nucl. Mater. 288 (2001) 43e56. [50] P. Cook, E. Matthews, M. Barker, R. Foster, A. Donaldson, C. Ott, D. Papaioannou, C. Walker, Post-irradiation examination and testing of BNFL SBR MOX fuel, In: Proceedings of the 2004 International Meeting on LWR Fuel Performance, Orlando, Florida, September 19-22, 2004. [51] IAEA, Improvement of Computer Codes Used for Fuel Behaviour Simulation (FUMEX-III): Report of a Coordinated Research Project 2008-2012, International Atomic Energy Agency, 2013. Technical Report IAEA-TECDOC-1697.
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Nuclear Engineering and Technology journal homepage: www.elsevier.com/locate/net
Original Article
Validation of the fuel rod performance analysis code FRIPAC Yong-Jun Deng, Jun Wei*, Yang Wang, Bin Zhang China Nuclear Power Technology Research Institute Co. Ltd, Shang-Bu Middle Road, Shen-Zhen, PR China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 14 February 2019 Received in revised form 29 April 2019 Accepted 2 May 2019 Available online 3 May 2019
The fuel rod performance has great importance for the safety and economy of an operating reactor. The fuel rod performance analysis code, which considers the thermal-mechanical response and irradiation effects of fuel rod, is usually developed in order to predict fuel rod performance accurately. The FRIPAC (Fuel Rod Integral Performance Analysis Code) is such a fuel rod performance analysis code that has been developed recently by China Nuclear Power Technology Research Institute Co. Ltd. The code aims at the computational simulation of the Pressurized Water Reactor fuel rod behavior for both steady-state and power ramp condition. A brief overview of FRIPAC is presented including the computational framework and the main behavioral models. Validation of the code is also presented and it focuses on the fuel rod behavior including fuel center temperature, fission gas release, rod internal pressure/internal void volume, cladding outer diameter and cladding corrosion thickness. The validation is based on experimental data from several international projects. The validation results indicate that FRIPAC is an accurate and reliable fuel rod performance analysis code because of the satisfactory comparison results between the experimental measurements and the code predictions. © 2019 Korean Nuclear Society, Published by Elsevier Korea LLC. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Keywords: FRIPAC Fuel behavior Model Validation
1. Introduction The nuclear fuel is the basic element of a nuclear reactor, providing the material for generating the energy which is used for the production of electricity or process heat. The fuel rod is the principal confinement of the nuclear fuel and the first safety barrier in the reactor core [1]. It is essential to predict the fuel rod behavior accurately for both safe and economic fuel usage. However, it is a difficult work due to the fuel rod suffers the combine effects of thermal, mechanical and neutronic impact during operation. Most related organizations chose to develop and apply fuel rod performance analysis codes to achieve this purpose. FRIPAC (Fuel Rod Integral Performance Analysis Code) is an efficient fuel rod performance analysis code which has been developed by China Nuclear Power Technology Research Institute Co. Ltd (CNPRI) recently. It has the ability to simulate thermalmechanical response of Pressurized Water Reactor (PWR) fuel rods during both steady-state and power ramp condition. It takes into consideration many physical phenomena of the fuel rod in-pile such as heat transfer throughout the fuel rod and coolant, deformation of fuel rod, fuel-cladding mechanical interaction, fission gas
* Corresponding author. E-mail address: [email protected] (J. Wei).
release (FGR), rod internal pressure, cladding oxidation and hydriding, etc. The structure and the main behavioral models of FRIPAC will be briefly introduced in this paper. To ensure the accuracy and reliability of a code, assessment or validation is absolutely necessary. Generally, the validation of a fuel rod performance code is implemented by comparing the code predictions to the related experimental data, e.g. FRAPCON [2], COPERNIC [3] and TRANSURANUS [4,5]. The validation of FRIPAC adopts the similar method as well, and the experimental data used in this paper come from several international projects. 2. Code overview FRIPAC is a 1.5-dimensional code which adopts the axial symmetry simplification. The code is programmed in Cþþ language by applying object-oriented programming (OOP) and structured programming method, which makes the possible optimization of the code quite convenient in the future. It has the ability to simulate the PWR fuel rod behaviors even in high duty and high burnup domains. The applicable fuel types in FRIPAC include uranium dioxide (UO2), mixed oxide fuel (MOX) and urania-gadolinia (UO2-Gd2O3), while the applicable cladding types include Zircaloy-4 and M5. In FRIPAC, the fuel rod is subdivided into discrete axial slices. These slices are then further subdivided into discrete radial concentric rings. The slices and rings composite form the numerical
https://doi.org/10.1016/j.net.2019.05.003 1738-5733/© 2019 Korean Nuclear Society, Published by Elsevier Korea LLC. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).
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framework (1.5-dimensional) for the mathematical analyses. The axial slices are individually analyzed for each time step. When all of the slices have been analyzed, they are coupled and quantities such as internal pressure are then determined. This general mathematical calculation sequence, which is performed at each time step, ensures that the fuel rod predictions can accurately simulate fuel rod behavior. The time-dependent parameters (linear power, fast flux, thermal data, etc.) are described by the user for each time step. Each time step is divided by the code into additional micro-time steps which are used for actual computation. The quantity is calculated by linear interpolation from the data of two successive time steps. The computational flowchart of FIRPAC is shown in Fig. 1. It contains two basic cycles and two iteration loops. The purpose of these two basic cycles is to achieve time discretization and spatial discretization respectively, while the purpose of the iteration loops is to analyze the coupling of thermal-mechanical behavior and improve the calculation accuracy. For given fuel rod manufacturing characteristics and irradiation conditions, FRIPAC offers detailed fuel rod behavior information of every slice and every time step after computation, including fuel rod temperature distribution, fuel-cladding gap size, contact pressure, rod internal pressure, fission gas release, cladding stress and strain, cladding corrosion and hydriding.
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3. Main behavioral models The main behavioral models of the FRIPAC code can be sorted into five categories d thermal models, mechanical models, FGR model, internal pressure model and cladding corrosion model. They will be briefly introduced as follows.
3.1. Thermal models The main function of the thermal models is to calculate the temperature distribution throughout the fuel rod which is the foundation for mechanical response calculation. The thermal models used in FRIPAC for the fuel rod temperature calculations assume a cylindrical fuel pellet located symmetrically within a cylindrical fuel rod surrounded by coolant. The coolant bulk temperature is calculated by using the axial linear heat generation rate and coolant boundary conditions (coolant inlet temperature, coolant mass flux, etc.). The film temperature rise is then calculated from the coolant to the outer surface of the cladding by using Dittus-Boelter equation [6] (for forced convection) or JensLottes equation [7] (for sub-cooled nucleated boiling) which depends on the status of coolant. The cladding inner surface temperature is achieved by calculating the temperature rise through the oxide and cladding. Here, the cladding temperature rise is confirmed ring by ring (the cladding is subdivided into several concentric rings) using Newton-Raphson iteration due to the adopted thermal conductivity of cladding is a cubic polynomial. The thermal conductivity for the zircaloy cladding used in FRIPAC is [8].
lclad ¼ 7:51 þ 2:09 102 T 1:45 102 T 2 þ 7:67 109 T 3 (1) Where,
lclad represents the thermal conductivity of zircaloy in W/m/K; T represents the cladding temperature in degree Kelvin (K). The temperature rise from the inner cladding surface to the fuel surface is determined by gap conductance model. The fuel-cladding gap conductance is the sum of the conductance due to radiant heat transfer [9], the conduction through gas in gap [10] and the conduction through regions of solid-solid contact [11]. Details of the three components of gap conductance can be found in corresponding references. As the gap size is influenced by the solution of the mechanical response and the mechanical response depends on the temperature distribution, iteration is needed in every time step for each axial layer in order to determine the gap conductance. Finally, the temperature distribution in the fuel is calculated with the Halden project fuel thermal conductivity model [12] by using the fuel surface temperature and it is assumed symmetry at the centerline as boundary conditions. This conductivity model can be applicable to UO2, UO2-Gd2O3 and MOX fuel as follows
l95 ¼
C1 C2 þ2:475 104 ð1 0:00333 BuUO2 Þ minðTc ;1650Þ
þ 0:0132 e0:00188Tc (2) C1 ¼
Fig. 1. Simplified computational flowchart of the FRIPAC Code.
Where,
1; for UO2 and UO2 Gd2 O3 0:92; for MOX fuel
fuel
(3)
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C2 ¼
0:1148 þ 0:011599 Gd þ 0:0040 BuUO2 ; for UO2 and UO2 Gd2 O3 fuel 0:1148 þ 0:011599 Pu þ 0:0040 BuUO2 ; for MOX fuel
l95 represents the thermal conductivity in W/m-K, at 95% theoretical density; BuUO2 represents the burnup of UO2 in MWd/kgU; Tc represents the temperature in degree Celsius ( C); Gd represents the weight fraction of gadolinia in %; Pu represents the weight fraction of Pu in MOX fuel in %. The above thermal conductivity is adjusted for as-fabricated fuel pellet density using the Lucuta recommendation for sphericalshaped pores [13]. The radial power distribution of fuel in FRIPAC applies interpolation method with a series of preset arrays of power, which consider the effects of burnup and fuel enrichment. The radial power distribution can also be input by users. The validation for FRIPAC below takes account of the effects of gadolinia doping, MOX fuel and UO2 fuel with a relatively high enrichment by applying the relating radial power distribution arrays due to the mentioned effects have significant influence on calculating the fuel temperature.
The mechanical models compute the stresses, strains and the corresponding deformations of fuel and cladding, the solutions of which bonded with that of thermal models deeply. In FRIPAC, the deformation analysis consists of small displacement analyses including stresses, strains, and displacements in the fuel and cladding for the entire fuel rod. The analyses assume that the cladding retains cylindrical shape during deformation. In general, the temperature distribution in fuel rod is calculated assuming a given geometry firstly. The analysis is followed by the calculations of mechanical models considering the temperature distribution calculated previously. The result is a new geometry and this whole process has to be continued until convergence criteria are fulfilled. 3.2.1. Pellet deformations The fuel pellet is considered to be rigid, and the deformations are mainly caused by thermal expansion, swelling, densification and relocation. a) Thermal expansion The fuel thermal expansion equations of UO2, UO2-Gd2O3 and PuO2 have the same form
R
¼ K1 T K2 þ K3 e
E D kT
by combining the contribution from each constituent of UO2 and PuO2 in proportion to its weight fraction. b) Swelling The fuel swelling is caused by the buildup of solid and gaseous fission products during irradiation. In FRIPAC, empirical relations are used to calculate the fuel swelling [8]. The swelling due to solid fission products is expressed as a simple linear function of burnup
Ssolid ¼ 2:5 1029 Bs
(6)
Where, Ssolid represents the fractional volume change due to solid fission products; Bs represents the burnup during a time step in fissions/m3. The swelling due to gaseous fission products when the fuel temperature is below 2800 K is
3.2. Mechanical models
DR
(4)
(5)
Where,
Sgaseous ¼ 8:8 1056 ð2800 TÞ11:73 e0:0162ð2800TÞ8:010
For MOX fuel, the thermal expansion of the solid is determined
B
Bs
(7) Where, Sgaseous represents the fractional volume change due to gaseous fission products; T represents the temperature in K; Bs represents the burnup during a time step in fissions/m3; B represents the total burnup of fuel in fissions/m3. For temperatures greater than 2800 K, Sgaseous is zero because the gas that causes swelling is assumed to have been released. c) Densification The fuel densification caused by irradiation in FRIPAC is calculated as a function of fuel burnup and initial density which is proposed by U. S. Nuclear Regulatory Commission (NRC) [14].
8 0; Bu Bumin > > > > > > N,lg ðBu=Bu Þ,0:5 min 10 DL < ; Bu 100 , Bumin ¼ 3,½DEN N,lg10 ðBu=Bumin Þ,0:5 > L > > > N > > ; Bu > 100 , Bumin : 3,ðDEN NÞ (8)
DR represents the linear strain caused by thermal expansion R
(equal to zero at 300 K); T represents the temperature in K; ED represents the energy of formation of a defect in Joule; k represents the Boltzmann’s constant; K1 , K2 and K3 are contants which are different for UO2 and PuO2.
27
Bumin ¼ Where,
20; 5;
absðNÞ 4 absðNÞ > 4
(9)
DL represents the fuel dimension change (percent); L
Bumin represents the minimum burnup in NRC model (MWd/ tU);
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N represents the resinter density change comparing theoretical density (percent); DEN represents the ratio of actual density and theoretical density. d) Relocation Fuel relocation models the effect of fuel cracking on gap width. Thermal gradients in a fuel pellet result in corresponding stress gradients that exceed the fuel fracture stress, causing radial cracks. The free surfaces of the crack result in an overall increase of fuel pellet diameter. This effect can be modeled by applying a radial strain to the fuel pellet. This strain is similar to a volumetric strain, but only in the radial direction. The relocation model applied in FRIPAC is the function of local power and burnup which is also incorporated in FRAPCON 4.0 [15].
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The cladding elastic strain is mainly caused by difference between the external and internal pressure. The generalized plane strain hypothesis (one-dimensional radial solution and uniform axial strain) is used for the model. The cladding deformation due to elasticity satisfies three basic equations d equilibrium, strain compatibility and stress-strain equations. According to these, the Euler equation can be deduced
d2 u 1 du u ¼0 þ dr2 r dr r 2
(12)
With boundary conditions
sr jr¼Ro ¼ Po ; sr jr¼Ri ¼ Pi
(13)
Where,
DG G
¼
0:055; Bu < 0:0937GWd=tU 0:055 þ min½reloc; reloc , ð0:5795 þ 0:2447 , lnðBuÞÞ; Bu 0:0937GWd = tU
(10)
uðrÞ represents the cladding displacement expression;
sr represents the radial stress at the position of radius r; 8 P < 20 < 0:345; reloc ¼ 0:345 þ ðP 20Þ=200; 20 P 40 : 0:445; P > 40
(11)
Where,
Ro represents the cladding outer radius; Ri represents the cladding inner radius; Po represents the external pressure on cladding; Pi represents the internal pressure on cladding. b) Thermal expansion The cladding strain caused by thermal expansion [8] for zircaloy used in FRIPAC is
8 300 < T < 1083K 1:485 103 þ 4:95 106 , T; > > > > > > < T 1083 , p 103 ; 1083 T < 1244K 2:77763 þ 1:09822 , cos εth;R ¼ > 161 > > > > > : 1:04 102 þ 9:7 106 , T; 1244 T 2098K 8 3 5 > 300 < T < 1083K > > 3:78 10 þ 1:26 10 , T; > > > > < T 1083 , p 103 ; 1083 T < 1244K 8:76758 þ 1:09822 , cos εth;L ¼ 161 > > > > > > > :ε 3 þ 9:7 106 , T; 1244 T 2098K th;L ¼ 4:4 10
(14)
DG represents the fraction of as fabricated gap closure due to G
pellet relocation; P represents the local power in kW/ft; Bu represents the local burnup in GWd/tU.
3.2.2. Cladding deformations Cladding deformations can be mainly divided into several parts, including elastic strain, thermal expansion, irradiation growth and creep.
Where, εth;R represents the circumferential thermal expansion (m/m); εth;L represents the axial thermal expansion (m/m); T represents the temperature (K). The basal plane symmetry is assumed here, which meaning the circumferential thermal expansion equals to the radial thermal expansion. c) Irradiation growth
a) Elastic strain
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Irradiation growth is caused by the radiation damage due to fast neutrons. The irradiation growth model of zircaloy [16] used in FRIPAC is
ax ¼ A,FB
(15)
Where, ax represents the axial growth increment (m/m);
F represents the fast neutron fluence (n/m2); A and B are constants which are different for different kinds of zircaloy cladding. d) Creep The cladding creep strain rate is used in FRIPAC, and the model is described as
ε_ tot ¼ C ð_εH þ ε_ irr Þ ε_ H ¼
52,εsp ,ð_εth þ ε_ irr Þ1=2 2,t 1=2
(16) pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi exp 52, ð_εth þ ε_ irr Þ,t þ ð_εth
þ ε_ irr Þ Where,
(17)
ε_ tot represents the total strain rate (m/m/h); ε_ H represents the total thermal strain rate (m/m/h); ε_ th represents the thermal strain rate (m/m/h); ε_ irr represents the irradiation strain rate (m/m/h); εsp represents the saturated primary hoop strain (m/m); t represents the time (hours). C represents a constant in the model.
In FRIPAC, the Peng-Robinson equation of state (EOS) is applied to compute the rod internal pressure [24].
R,T ai p ¼ V i 2 i b V i ni þ 2b Vi b2
3.3. Fission gas release model
ni
The rod internal pressure of the gas in the fuel rod is computed after the fuel rod temperature distribution and deformation calculations have been completed. The temperature distribution, the void volume and the gas inventory in fuel rod are required to calculate the internal pressure. The temperature distribution is provided by thermal models. The void volume is derived from the geometry information calculated by the mechanical models. And the gas inventory is provided by the fission gas release and the initial filled gas. The gaseous fission products (primarily Xenon and Krypton) generated from fuel pellets release into rod internal void volume. This process is known as fission gas release. The various mechanisms affecting the fission gas behavior in fuel are presented and discussed in detail in Ref. [17]. As we know, most fission gas release models are based on the theory for diffusion from a sphere which was firstly proposed by Booth [18]. The Forsberg-Massih model [19,20] is a typically approved FGR model which is developed from the Booth sphere diffusion model
Where, r represents the radial position in grain; t represents the time; Cðr; tÞ represents the gas concentration;
The derivation and calculation process of the Forsberg-Massih model were described in detail in Ref. [21]. The fission gas release described by Forsberg-Massih model is a two-stage approach. The first stage computes diffusion of fission gas atoms from within the fuel grains to the grain boundaries by solving the relevant diffusion equation in spherical co-ordinates numerically. An effective diffusion coefficient is employed, which accounts for gas atom resolution from and trapping into intragranular bubbles. The second stage of the model utilizes time-dependent boundary conditions to determine grain boundary gas accumulation as inter-granular lenticular bubbles, resolution, saturation, and release. Fission gas release from the grain boundaries is controlled using a grain boundary saturation criterion that involves a threshold concentration of gas at the grain boundaries. The Forsberg-Massih model is incorporated in FRIPAC as default FGR model. The code validation below is based on it. It is worth noting that the Forsberg-Massih model is developed for UO2 pellets, while the FGR of MOX pellets is treated by applying different diffusion coefficient. The Forsberg-Massih model is also applied to UO2-Gd2O3 pellets in the FRIPAC code, since the FGR model for UO2 pellets is suitable to UO2-Gd2O3 pellets according to the observation conducted by Delorme et al. [22] and Arana et al. [23]. Both of their researches demonstrated that the FGR of UO2Gd2O3 fuel were consistent with that of UO2 fuel under similar burnup and power levels. 3.4. Internal pressure model
Details of the creep strain model can be found in Ref. [15].
" # vCðr; tÞ v2 2 v ¼ DðtÞ Cðr; tÞ þ bðtÞ þ vt vr 2 r vr
DðtÞ represents the diffusion coefficient;
bðtÞ represents the gas production.
(18)
(19)
ni
Where, p represents the fuel rod internal gas pressure; R represents the universal gas constant; Vi represents i-th internal void volume; ni represents number of moles in the Vi void volume; Ti represents the gas temperature in the Vi void volume; ai represents the cohesion parameter; b represents the covolume parameter. ai and b are both affected by the critical temperature and critical pressure of gas, while ai is also affected by the function of the acentric factor. More details of the Peng-Robinson EOS can be found in Ref. [24]. The void volume in the fuel rod consists of pellet dish volume, pellet chamfer volume, pellet crack volume, fuel-cladding gap volume, open porosity volume, surface roughness and chip volume, upper and lower plenum volume, fuel central hole volume (if present). The plenum volume is calculated from initial cladding, fuel and spring dimensions after accounting for temperature and irradiation effects (such as cladding growth, fuel densification/ swelling). The dish volume is calculated at any given power and time by applying the appropriate thermal expansion and fuel densification/swelling to all radial rings, recalculating the shape of the pellet, and then summing up the volume at the pellet end face. The gap volume is calculated by subtracting a pellet cross-sectional area based on radial expansion due to fuel densification/swelling and thermal expansion from a cladding inner cross-sectional area
Y.-J. Deng et al. / Nuclear Engineering and Technology 51 (2019) 1596e1609
which includes the effects of elastic and plastic cladding deformation. The radial crack volume is the difference between the linear and the areal calculation of the pellet thermal expansion. The chip volume is calculated by a user defined factor which is usually obtained from large number of measurements on unirradiated production pellets. The roughness volume is calculated by an empirical equation considering the pellet diameter and geometric fuel volume. The open porosity volume is calculated as a function of initial fuel density and fuel temperature at corresponding power. The void volumes mentioned above are assumed to be interconnected and the pressure is assumed to be uniformly distributed over these volumes. It is notable that these various volume components, moles of gas and corresponding temperatures change with time, and they will be computed continuously until the rod internal pressure is convergent. The Peng-Robinson EOS is believed to be more accurate than the ideal gas EOS for predicting mixture gas pressures in high temperature and high pressure environment. However, the pressure predictions from Peng-Robinson EOS is quite similar to those from the ideal gas EOS in the environment of PWR fuel rods according to practical calculations. The ideal gas EOS and other commonly used EOS correlations are also incorporated in FRIPAC for contrast, while the PengRobinson EOS is used as default option and adopted in the validation below. 3.5. Cladding corrosion model The FRIPAC code incorporates an approved and reliable cladding corrosion model from Ref. [8], which has already been applied in the FRAPCON code. For Zircaloy-4 cladding, the cubic rate law is applied for corrosion-layer thickness as a function of time until a transition thickness is attained. After the transition thickness is attained, a flux-dependent linear rate law is applied, with the rate constant being an Arrhenius function of oxide-metal interface temperature. More details of the corrosion model can be found in Ref. [8].
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4. Code validation 4.1. Validation cases overview The validation of the FRIPAC code are implemented by applying well-characterized experimental fuel rods from several irradiation experiment projects, including OECD Halden Reactor Project, Risoe3, GAIN, Super-Ramp, US-PWR 16x16, Beznau-1, Balfour BR-3, ATR WG-MOX, Gravelines-4, FUGEN, B&W Studsvik, BNFL BR-3, Oconee. These projects provided reliable experimental data with measurements reflecting different kinds of fuel rod behaviors. The power histories, fuel rod manufacturing characteristics and system parameters were derived from relevant experiment documents to make the input profiles for the FRIPAC code. The experimental fuel rods were irradiated in PWR and Boiling Water Reactor (BWR) coolant conditions (including the research and commercial reactors). The preferred experimental measurements in the validation of a fuel rod performance analysis code are fuel center temperature, fission gas release, internal pressure, cladding outer diameter and cladding corrosion thickness. These experimental measurements are compared to corresponding predictions by the code. Then the accuracy and reliability of the code can be concluded from these comparison results. The specific validation processes and results of each characteristic parameter for FRIPAC are presented as follows by comparing the code predictions to the corresponding measurements from experimental data. This validation method and corresponding validation matrix have been adopted by many other fuel rod performance codes. The overview of the main experimental fuel rods used for the validation of the FRIPAC code is shown in Table 1. Details of these experimental fuel rods are described in corresponding references, including the fuel enrichment, fuel grain size range and fuel rod geometry. 4.2. Validation of the fuel center temperatures The accurate prediction of the fuel temperatures is most
Table 1 The overview of the main experimental data used for the validation of the FRIPAC code. Experiment
Number of rods
Fuel typea
Fuel enrichment
Cladding type
Rod burnup (GWd/tHM)
Reference
HALDEN
14
UO2
~3e13% U235
Zr-2/Zr-4
4e88
HALDEN
3
UO2-Gd2O3
Zr-2
25e60
HALDEN
9
MOX
Zr-4
20e68
Risoe-3 Super-Ramp Super-Ramp
12 12 4
UO2 UO2 UO2-Gd2O3
Zr-2/Zr-4 Zr-4 Zr-4
42 30e45 34
[33,34,35] [36,37] [38] [39] [39]
US-PWR 16x16 GAIN
16 4
UO2 UO2-Gd2O3
Zr-4 Zr-4
36e58 39
[40] [41]
Balfour BR-3 Oconee PWR HBEP ATR WG-MOX
5 1 1 6
UO2 UO2 UO2 MOX
Zr-4 Zr-4 Zr-4 Zr-4
13e61 50 25 30e50
[42] [43] [44] [45]
B&W Studsvik FUGEN
1 3
UO2 MOX
Zr-4 Zr-2
62 30e42
[46] [45]
Gravelines-4
3
MOX
Zr-4
48e57
[47]
Beznau-1
8
MOX
~4e13% U235 ~8% Gd2O3 ~0.3% U235 ~4e8% Pu ~3% U235 ~3e6% U235 ~3% U235 ~4% Gd2O3 ~3.5% U235 ~3.5% U235 ~3e7% Gd2O3 ~5e8.5% U235 ~3% U235 ~3% U235 ~0.3% U235 ~5% Pu ~3% U235 ~0.7% U235 ~5% Pu ~0.2% U235 ~5% Pu ~0.3% U235 ~3e5.5% Pu
[25,26,27] [28,29,30] [31,32]
Zr-4
35e58
[48,49,50]
a The validation cases contain the fuel pellets with different kinds of manufacturing methods including ammonium diuranate (ADU) and ammonium uranyl carbonate (AUC) for UO2, short binderless route (SBR) and integrated dry route (IDR) for MOX.
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Fig. 2. Rod average LHGR versus Rod average burnup for fuel center temperature validation cases from HALDEN project.
Fig. 3. Comparison of measured fuel center temperatures with those predicted by FRIPAC with upper and lower bound lines (dashed lines).
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Fig. 4. Predicted minus measured divided by measured center temperature as a function of burnup.
essential for any fuel rod performance codes. Many temperaturedependent physical phenomena are strongly affected by the accuracy of their predictions, such as thermal expansion, fission gas diffusion and release, creep, etc. Large amount of convincing experimental fuel center temperature data have been measured in associated projects worldwide so far. Therefore, fuel center temperature is taken as one of the validation parameters for the FRIPAC code. The experimental fuel center temperature data for the validation of FRIPAC are derived from 23 fuel rods consist of 15 UO2 fuel rods, 5 MOX fuel rods and 3 UO2-Gd2O3 rods. These experimental fuel rods were mainly measured in OECD Halden Reactor project. Fig. 2 shows the rod average linear heat generation rate (LHGR) as a function of rod average burnup for the validation cases of fuel center temperatures. This figure indicates that these 23 fuel center temperature validation cases cover a wide range of burnup and LHGR. The rod average burnup of UO2, MOX and UO2-Gd2O3 validation cases range up to 88 GWd/tHM, 32 GWd/tHM and 71 GWd/ tHM respectively. And the rod average LHGR of all fuel center temperature validation cases range up to 44 kW/m. It is desirable to include more validation cases, especially the MOX fuel cases with high burnup. Comparison of the measurements from experimental data and the corresponding predictions by the FRIPAC code for all fuel center temperature validation cases is shown in Fig. 3. These data are also shown in terms of relative bias in Fig. 4 as a function of burnup. The predicted to measured (P/M) mean value is 1.002 and the standard deviation is 0.110 according to statistic calculation. This standard deviation is reasonable given the uncertainty in the thermocouple data and the calculated rod power. As shown in Figs. 3 and 4, most data points are located near around the P ¼ M line. The discrepancy
remains within the bound lines up to a temperature of about 1500 K and increases beyond this temperature, which is largely due to the overpredictions for IFA-432R2 and underpredictions for IFA513R6. Both of these two experimental rods may lack accuracy of measurement slightly, due to the same problems were shown in the assessment of the code FRAPCON [2]. After ignoring these two rods, it can be concluded that FRIPAC gives satisfactory predictions of fuel center temperature for UO2, MOX and UO2-Gd2O3 fuel rods. 4.3. Validation of the fission gas release Fission gas release (FGR) is another key phenomenon that must be considered in a fuel performance code. The fission gas released from fuel pellet contributes to the increase of the fuel rod internal pressure, with the associated risks of fuel thermal degradation and even cladding failure. The accurate prediction of FGR is important for fuel performance code due to two reasons: firstly, it has a significant impact on the prediction of gap conductance and fuel temperatures, and secondly, it is also necessary for the calculation of rod internal pressures which affect end-of-life rod pressures. The validation of the FRIPAC code here is based on the FGR model proposed by Forsberg and Massih which has been described above. The ability of the FRIPAC code to predict FGR has been validated based on comparisons to experimental FGR data from 54 UO2 fuel rods, 26 MOX fuel rods and 8 UO2-Gd2O3 fuel rods respectively. Both steady-state and transient FGR cases are included. The experimental FGR data are commonly inferred from rod puncture test, or estimated from rod pressure data at end of irradiation. Fig. 5 shows the rod average LHGR as a function of rod average burnup for the validation cases of FGR. It demonstrates that the FGR validation cases cover a wide range of burnup and LHGR.
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Fig. 5. Rod average LHGR versus Rod average burnup for FGR validation cases from HALDEN, US-PWR 16x16, Riseo-3, Super-Ramp, Balfour BR-3, Oconee PWR, B&W Studsvik, HBEP, GAIN, ATR WG-MOX, FUGEN, Gravelines-4 and Beznau-1 projects.
can be concluded that FRIPAC provides satisfactory predictions of FGR for UO2, MOX and UO2-Gd2O3 validation cases basing on this information. It should be note that FRIPAC provides underpredictions for several cases with less than 5% FGR, which are very hard to predict accurately for most FGR models nowadays. It is to be noted that the limiting rods have released above 10% FGR at end of life in today’s nuclear power plant (particularly for power uprated plants). Because of this, only the fuel rod cases with greater than 5% FGR were selected in the integral assessment of the code FRAPCON [2].
4.4. Validation of the rod internal pressure and internal void volume
Fig. 6. Comparison of fission gas release predicted by the FRIPAC code and corresponding experimental data with a factor of 2 error bound (dash lines).
The comparisons of the measured FGR values with the corresponding FRIPAC predictions are summarized in Fig. 6. Due to the inherent uncertainties of fission gas behavior modeling, a deviation of code predictions from the experimental data within a factor of about 2 up and down is generally regarded as satisfactory [51]. It
The internal pressure and internal void volume within a fuel rod will change continuously during operation. The rod internal void volume varies with burnup due to combined effects of the temperature distribution and the deformations in rod primarily. The rod internal void volume is one of the most significant factors for the accurate prediction of the rod internal pressure. These two parameters are closely connected to each other. As we know, rod internal pressure is a design criterion for fuel rod design. Therefore, it is necessary to ensure that the internal gas pressure and internal void volume predictions are accurate. The ability of FRIPAC to predict internal pressure and internal void volume are validated against 7 and 15 well-characterized fuel rods respectively. The internal pressure data points are obtained
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Fig. 7. Rod average LHGR versus Rod average burnup for internal pressure and void volume validation cases from HALDEN, US-PWR 16x16, GAIN and Beznau-1 projects.
Fig. 8. The comparison of measured and predicted rod internal pressures for 7 validation cases with ±2s error bounds (dash lines).
from the pressure transducers in the rods that provide on-line values, and the internal void volume data points are obtained from post-irradiation examination. Fig. 7 shows the rod average LHGR as a function of rod average burnup for the internal pressure and internal void volume validation cases. The rod average burnup of the internal pressure validation cases range up to 33 GWd/tHM while that of the internal void volume cases range up to 60 GWd/ tHM. The rod average LHGR range over 40 kW/m for both kinds of cases. It is desirable to include more validation cases, especially
internal pressure cases with high burnup, but no more fuel rods with reliable measured data have been achieved presently. Fig. 8 presents the comparison between the measured and FRIPAC calculated rod internal pressures. The P/M mean value is 1.042 and the standard deviation is 0.201 according to statistic calculation. It indicates that FRIPAC predicts the internal pressures satisfactorily. Most data points are located nearly around the P ¼ M line and between the ±2s error bound lines (s is the standard deviation of (P-M) values). The predictions for IFA-513R2 case are a
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Fig. 9. The comparison of measured and predicted rod internal void volume at end of irradiation for 15 validation cases with ±2s error bounds (dash lines).
Fig. 10. Rod average LHGR versus Rod average burnup for cladding outer diameter validation cases from US-PWR 16x16, GAIN, Riseo-3 and Beznau-1 projects.
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outer diameter changes in comparison to the initial values) are calculated, and the absolute deviation between the predicted and measured cladding deformations are within acceptable ranges (the maximum absolute deviation is about 0.11 mm which is also discovered in D10 case). Hence, it can be concluded that FRIPAC provides reasonable predictions of cladding outer diameters. 4.6. Validation of the cladding corrosion thickness
Fig. 11. The comparison of measured and predicted cladding outer diameters for 14 validation cases with ±2s error bounds (dash lines).
bit more overpredicted and this is probably due to overpredicting the FGR for this rod. Fig. 9 presents the measured and FRIPAC calculated rod internal void volume at end of irradiation for these 15 fuel rods. These calculations were set as room temperature and atmospheric pressure at final two time steps because it is approximate to the environment at which the data were collected. The P/M mean value is 1.089 and the standard deviation is 0.246 according to statistic calculation. It indicated that the FRIPAC code does a good job of predicting the rod internal void volumes while most data points locate between the ±2s error bound lines (s is the standard deviation of (P-M) values). Only TSQ053 case is a little overpredicted with comparatively large deviation. 4.5. Validation of the cladding outer diameter Accurate simulation of the mechanical behavior of fuel rod is important because the heat transfer coefficient across the fuelcladding gap is closely related to the effective gap size or the contact pressure. The prediction of cladding outer diameter reflects the accuracy of mechanical models for both fuel and cladding generally. The cladding outer diameter is dominated by creep at early life during operation. However, at higher burnups, following fuelcladding contact, the cladding dimension deformation is mainly controlled by mechanical behavior of the fuel. The ability of FRIPAC to predict cladding outer diameter is validated against 14 well-characterized fuel rod. The measurements were made post irradiation in hot cell, including both base irradiation and power ramp situations. The cladding type of all validation cases is Zircaloy-4. Fig. 10 shows the rod average LHGR as a function of rod average burnup for the cladding outer diameter validation cases. The rod average burnup ranges up to 60 GWd/tHM and the rod average LHGR ranges up to 40 kW/m as shown in Fig. 10. The measured and predicted cladding outer diameters of all the 14 validation cases are summarized in Fig. 11. The P/M mean value is 1.007 and the standard deviation is 0.005 according to statistic calculation. Most data points are located between the ±2s error bounds as shown in Fig. 11 (s is the standard deviation of (P-M) values). However, the predictions of some validation cases are a bit overpredicted with acceptable deviations (the maximum relative deviation is about 1.3% which is discovered in D10 case). Furthermore, the predicted and measured cladding deformations (cladding
The oxidation phenomenon produces oxide layers on fuel rod cladding, which degrades the heat transfer and mechanical property of cladding. The cladding oxide layer thickness is also a design criterion which indicates its importance. It is necessary to validate FRIPAC’s ability to accurately predict the cladding corrosion thickness. 8 well-characterized fuel rods were selected to demonstrate the capability of FRIPAC to accurately calculate fuel rod waterside oxidation. The cladding type of these fuel rods is Zircaloy-4. The FRIPAC code also has the ability to predict corrosion behavior of the fuel rods with M5 alloy, but the experimental fuel rods with known power histories and end-of-life measured oxide thickness for M5 alloy are very limited for us at present. Fig. 12 shows the rod average LHGR as a function of rod average burnup for the cladding corrosion thickness validation cases. The rod average burnup levels of these rods range up to 60 GWd/tHM and the rod average LHGR range up to 25 kW/m. The predicted and the measured end-of-life oxide layer thickness of Zircaloy-4 claddings are compared in Fig. 13 The P/M mean value is 1.161 and the standard deviation is 0.297 according to statistic calculation. As shown in Fig. 13, the model in FRIPAC overpredicts for the relatively low values of oxide thickness, up to about 20 microns. Beyond this value, a number of cases with underprediction seem to systematically grow slightly. This is a little confused, but there are only 8 cases and about 100 data points totally which are deficient for the validation of a corrosion model. The comparison indicates that FRIPAC has a tendency to overpredict the cladding oxide layer thickness in general for current cases. The results seem to be reasonably conservative. However, more cases for the validation of the corrosion thickness are needed to make the validation more comprehensive. 5. Summary The fuel rod performance analysis code FRIPAC is an advanced computer programme for the predictions of PWR fuel rod behaviors that has been developed by CNPRI. It is designed with excellent structure applying OOP and structured programming method, which make the optimization convenient. Basic analysis process and the main behavioral models of the FRIPAC code are briefly introduced. In the validation study, FRIPAC has been validated against a set of pre-selected experimental data from 102 well-characterized fuel rods which are sorted from several international projects. These validation cases cover a wide range of operating conditions. Overall, FRIPAC gives satisfactory and reasonable predictions on fuel center temperature, FGR, rod internal pressure, internal void volume, cladding outer diameter and cladding corrosion thickness for current validation cases. No major shortcoming was discovered during validation. It can be demonstrated that FRIPAC is a reliable and accurate fuel performance code which has the potential to be used for predicting the PWR fuel rod behaviors in engineering design. In future, more experimental cases are required to make the validation of FRIAPC more extensive and creditable. Besides, we also planned to incorporate a series of acknowledged behavioral models for BWR. New material models and corresponding
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Fig. 12. Rod average LHGR versus Rod average burnup for cladding corrosion thickness validation cases from US-PWR 16x16 and Super-Ramp projects.
Fig. 13. The comparison of measured and predicted oxide layer thickness of Zircaloy-4 cladding for 8 fuel rods with ±2s error bounds (dash lines).
uncertainties are planned to be developed and determined according to new obtained experimental data. The Graphical User Interface (GUI) for FRIPAC is also under development which makes the preparation of inputs and the treatment of outputs much more convenient for users. Acknowledgements The authors wish to thank the National Science and Technology Major Project of the People’s Republic of China (No. 2016ZX06004002) for financial support to this research. References [1] D.G. Cacuci, Handbook of Nuclear Engineering [M], Springer, New York, 2010.
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