# ZryOxidation

This class incorporates correlations for Zircaloy cladding oxidation through metal-water reactions. Calculated processes include outer oxide scale thickness growth and oxygen mass gain; the model is to be applied to the cladding waterside boundary. Current version covers LWR Zircaloy cladding only.

## Description

This material calculates corrosion oxide layer thickness and the oxygen mass gain at normal operating temperatures (temperature < 673K), and at high temperatures. The normal operating temperature available in this class are EPRI_KWU_CE and EPRI_SLI. The high temperature models available are based on correlations by LEISTIKOW and by CATHCART.

Zirconium alloy cladding can have an exothermic reaction with coolant water which converts metal to oxide at the cladding outer surface: (1) Such an oxidation process, which is referred to as water-side corrosion, is a fundamental aspect of LWR fuel performance. The resultant oxide film on the outer surface of cladding can affect both the thermal and mechanical properties of cladding. Because of the lower thermal conductivity of zirconium oxide in comparison with zirconium alloys, the oxidation of the cladding adds to thermal resistance to heat transfer from the fuel to the coolant.

Zirconium oxide is a brittle material and can be easily cracked. Thus it is expected that the mechanical strength of cladding is mainly determined by the metallic wall, which is thinned after corrosion. Concurrent to the oxidation process, a fraction of hydrogen can be absorbed into the metal and can diffuse under the influences of both temperature and stress.

## Zirconium Alloy at Normal Operating Temperatures

Low temperature (250 C/ 523 K to 400 C/ 673 K) oxidation is calculated considering that cladding oxidation under normal LWR conditions occurs in two stages: a pre-transition oxidation process that follows a cubic time dependence up to a transition oxide thickness, and a post-transition process that follows a linear time dependence. The transition between the two stages typically occurs at 2 microns.

For the pre-transition period, the corrosion rate is given by an Arrhenius equation (Ritchie, 1998): (2) For the post-transition period, the corrosion rate is given by (Ritchie, 1998): (3) where is the oxide thickness, is the metal-oxide interface temperature, is the rate constant for pre-transition oxidation, is the activation energy for pre-transition oxidation, is the rate constant for post-transition oxidation, is the activation energy for post-transition oxidation, is the universal gas constant, and is the transition oxide thickness.

The metal-oxide interface temperature, , is calculated assuming steady-state heat conduction across the oxide thickness as: (4) where is the outer surface (waterside) oxide temperature and is thermal conductivity of zirconium oxide. For a discussion of the metal-oxide interface temperature calculation, see the theoretical discussion in Zry Cladding Corrosion.

## Normal Operating Temperature Models

### EPRI KWU CE Model

For normal operating temperatures below 673 K, the EPRI/KWU/C-E oxidation model (Garzarolli et al., 1982; Garzarolli and Garzarolli, 2012) is used as the default corrosion model. The formulation is analogous to that described in Eq. 2 and Eq. 3, with the following values for the expressions shown in Table 1.

Table 1: Parameters used in the EPRI KWU CE Coolant Model (Garzarolli et al., 1982; Garzarolli and Garzarolli, 2012)

Model ExpressionParameter Value
m/day
K
m/day
K

where is the fast neutron flux in n/cms. accounts for the irradiation enhancement to corrosion.

### EPRI SLI Model

The EPRI/SLI model is also implemented in Bison code for modeling of the corrosion of PWR fuel cladding materials. This model uses enhancement factors on and . For the pre-transition period, is multiplied by two factors, one related to the lithium concentration in the coolant and the other related to the iron concentration in the cladding. These factors are given by Gilmore et al. (December 1995) as (5) where = lithium concentration (ppm) in the coolant, and = fraction of iron particles dissolved (%) for a given initial particle size distribution. The parameters used in above equations are given in Table 2.

Table 2: Parameters used in the EPRI SLI Li Concentration Model (Gilmore et al., December 1995)

Model ExpressionParameter Value
/day
cal/mol

The post-transition coefficient C, is multiplied by several enhancement coefficients as follows: (6) where C = 7.619$\times$ 10 The coolant chemistry (LiOH) enhancement factor is given by: (7) The cladding tin content enhancement factor is given by: (8) where Sn is tin content of cladding in (wt%). The heat flux normalization factor is given by: (9) where Q/A (W/cm) is the heat flux at cladding outer surface. The hydrogen redistribution enhancement factor is: (10) where H = cold side hydrogen content in the cladding metal-oxide interface. The fast neutron flux enhancement factor is: (11) where = fast flux (E 1 MeV, n/cm-s), C = 1.2 10 (n/cm-s), and P = 0.24. The iron enhancement factor is defined by Gilmore et al. (December 1995) as (12) Activation energy in the post-transition period is found to be dependent on hydrogen content (Cheng et al., 1996): (13) where = hydrogen enhancement factor at hydride rim ( = 18811.25 ppm), = 24825 cal/mol, and = 9135.6 cal/mol.

## Zirconium Alloy at High Temperatures

In the high temperature range (e.g., accident situations) the coolant has become steam, and oxidation proceeds much more rapidly than at normal LWR operating temperatures. Under these conditions, the kinetics of oxide scale growth and oxygen mass gain in the cladding can be described by a parabolic law, with the reaction rate constant defined as a function of the temperature through an Arrhenius relation (Schanz, 2003) (14) where is either the oxide scale thickness, = S (m), or the oxygen mass, = g (kgm), is the metal-oxide interface temperature (K), is the oxidation rate constant (m or kgm), is the activation energy (J/mol), and is the universal gas constant (J/mol-K).

Following the recommendations in Schanz (2003), the Bison model includes correlations for oxide scale growth and oxygen mass gain rates in Zircaloy-2/4 appropriate to different temperature ranges. In particular, the following approach is adopted:

• For metal-oxide interface temperatures from 673 K up to 1800 K, the Leistikov (Leistikow et al., 1983) correlation is used. The Cathcart-Pawel correlation (Cathcart et al., 1977) is also available and can be chosen as an option. The Leistikov correlation has been selected as reference in view of the larger underlying database, the availability of experimentally determined mass gain for all tests, and the better fit for lower temperature relative to the Cathcart-Pawel correlation (Schanz, 2003).

• Between 1800 and 1900 K, a linear interpolation is made. Linear interpolation between two correlations of Arrhenius type is obtained by a third correlation of the same type (Schanz, 2003).

• Above 1900 K, the Prater-Courtright correlation (Prater and Courtright, 1987) is used.

The values of the parameters in Eq. 14 relative to the different correlations are given in Table 3.

Table 3: Parameters of the correlations for oxide scale (S) and oxygen mass gain (g) at high temperature (Schanz, 2003)

Correlation (ms) (K) (kgm) (K)
Leistikov
Cathcart-Pawel
Prater-Courtright

## Example Input Syntax


[./oxidation_zry]
type = ZryOxidation
boundary = 1
clad_inner_radius = 0.004650
clad_outer_radius = 0.005375
normal_operating_temperature_model = epri_kwu_ce
high_temperature_model = leistikow
temperature = temp
fast_neutron_flux = fast_neutron_flux
[../]
(test/tests/tensor_mechanics/zry_oxidation_cladding/oxidation_cladding_zry_tm.i)

## Input Parameters

• clad_inner_radiusInner cladding radius (m)

C++ Type:double

Description:Inner cladding radius (m)

• temperatureCladding outer surface temperature (K)

C++ Type:std::vector

Description:Cladding outer surface temperature (K)

• clad_outer_radiusOuter cladding radius (m)

C++ Type:double

Description:Outer cladding radius (m)

### Required Parameters

• oxidation_scale_factor1Scaling factor for oxidation

Default:1

C++ Type:double

Description:Scaling factor for oxidation

• computeTrueWhen false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the Material via MaterialPropertyInterface::getMaterial(). Non-computed Materials are not sorted for dependencies.

Default:True

C++ Type:bool

Description:When false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the Material via MaterialPropertyInterface::getMaterial(). Non-computed Materials are not sorted for dependencies.

• oxygen_weight_fraction_initial0.0012As-fabricated oxygen weight fraction in cladding

Default:0.0012

C++ Type:double

Description:As-fabricated oxygen weight fraction in cladding

• fraction_iron_particles0the fraction of iron particles disolve for a given initial particle size distribution, used in the EPRI_SLI model

Default:0

C++ Type:double

Description:the fraction of iron particles disolve for a given initial particle size distribution, used in the EPRI_SLI model

• normal_operating_temperature_modelepri_kwu_ceType of zircaloy corrosion model to use under normal operating temperatures. Choices are: epri_kwu_ce epri_sli

Default:epri_kwu_ce

C++ Type:MooseEnum

Description:Type of zircaloy corrosion model to use under normal operating temperatures. Choices are: epri_kwu_ce epri_sli

• interface_hydrogen_content0the cold side hydrogen content in the cladding metal-oxide interface

Default:0

C++ Type:double

Description:the cold side hydrogen content in the cladding metal-oxide interface

• tin_content1.38tin content (weight percent)

Default:1.38

C++ Type:double

Description:tin content (weight percent)

• high_temperature_modelleistikowType of zircaloy corrosion model to in accident condition high temperatures. Choices are: leistikow cathcart

Default:leistikow

C++ Type:MooseEnum

Description:Type of zircaloy corrosion model to in accident condition high temperatures. Choices are: leistikow cathcart

• fast_neutron_fluxFast neutron flux (n/m^2-sec)

C++ Type:std::vector

Description:Fast neutron flux (n/m^2-sec)

• boundaryThe list of boundary IDs from the mesh where this boundary condition applies

C++ Type:std::vector

Description:The list of boundary IDs from the mesh where this boundary condition applies

• lithium_concentration0lithium concentration (ppm)

Default:0

C++ Type:double

Description:lithium concentration (ppm)

• show_debug_outputFalseflag to save and output additional information to aid in debugging

Default:False

C++ Type:bool

Description:flag to save and output additional information to aid in debugging

• use_coolant_channelFalseCoolant channel model is used

Default:False

C++ Type:bool

Description:Coolant channel model is used

• blockThe list of block ids (SubdomainID) that this object will be applied

C++ Type:std::vector

Description:The list of block ids (SubdomainID) that this object will be applied

### Optional Parameters

• enableTrueSet the enabled status of the MooseObject.

Default:True

C++ Type:bool

Description:Set the enabled status of the MooseObject.

• use_displaced_meshFalseWhether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.

Default:False

C++ Type:bool

Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.

• control_tagsAdds user-defined labels for accessing object parameters via control logic.

C++ Type:std::vector

Description:Adds user-defined labels for accessing object parameters via control logic.

• seed0The seed for the master random number generator

Default:0

C++ Type:unsigned int

Description:The seed for the master random number generator

• implicitTrueDetermines whether this object is calculated using an implicit or explicit form

Default:True

C++ Type:bool

Description:Determines whether this object is calculated using an implicit or explicit form

• constant_onNONEWhen ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeSubdomainProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped

Default:NONE

C++ Type:MooseEnum

Description:When ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeSubdomainProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped

### Advanced Parameters

• output_propertiesList of material properties, from this material, to output (outputs must also be defined to an output type)

C++ Type:std::vector

Description:List of material properties, from this material, to output (outputs must also be defined to an output type)

• outputsnone Vector of output names were you would like to restrict the output of variables(s) associated with this object

Default:none

C++ Type:std::vector

Description:Vector of output names were you would like to restrict the output of variables(s) associated with this object

## References

1. J. V. Cathcart, R. E. Pawel, R. A. McKee, R. E. Druschel, G. J. Yurek, J. J. Campbell, and S. H. Jury. Zirconium metal-water oxidation kinetics, IV. reaction rate studies. Technical Report ORNL/NUREG-17, Oak Ridge National Laboratory, 1977.[BibTeX]
2. B. Cheng, P. M. Gilmore, and H. H. Klepfer. PWR zircaloy fuel cladding corrosion performance, mechanisms, and modeling. In Zirconium in the Nuclear Industry: Eleventh International Symposium, 137–160. ASTM STP 1295, American Society for Testing and Materials, 1996, 1996.[BibTeX]
3. F. Garzarolli and M. Garzarolli. PWR Zr alloy cladding water side corrosion. Technical Report ANT International, ANT International, 2012.[BibTeX]
4. F. Garzarolli, W. Jung, H. Shoenfeld, A. M. Garde, G. W. Parray, and P.G. Smerd. Review of PWR fuel rod waterside corrosion behavior. Technical Report EPRI NP-2789 Project 1250 Final Report, Kraftwerk Union A.G. and Combustion Engineering Inc., 1982.[BibTeX]
5. P. M. Gilmore, H. H. Klepfer, and J. M. Sorensen. EPRI PWR fuel cladding corrosion (PFCC) model volume 1: theory and user's manual. Technical Report TR-105387-V1, EPRI, December 1995.[BibTeX]
6. S. Leistikow, G. Schanz, H. v. Berg, and A.E. Aly. Comprehensive presentation of extended Zircaloy-4/steam oxidation results 600-1600 C. In CSNI/IAEA specialists meeting on water reactor fuel safety and fission product release in off-normal and accident conditions. Riso Nat. Lab., Denmark, 1983.[BibTeX]
7. J. T. Prater and E. L. Courtright. Zircaloy-4 oxidation at 1300 to 2400 C. Technical Report NUREG/CR-4889, PNL-6166, Pacific Northwest Lab, 1987.[BibTeX]
8. I. G. Ritchie. Waterside corrosion of zirconium alloys in nuclear power plants. Technical Report IAEA TECDOC 996, IAEA, 1998.[BibTeX]
9. G. Schanz. Recommendations and supporting information on the choice of zirconium oxidation models in severe accident codes. Technical Report FZKA 6827, SAM-COLOSS-P043, Institut fÃ¼r Materialforschung, 2003.[BibTeX]