ZryThermal

Computes the thermal conductivity and the specific heat, under constant pressure, for zirconium alloy cladding based on either the MATPRO or IAEA models.

Description

The ZryThermal material model computes the thermal conductivity and specific heat capacity for zirconium alloy cladding. Two different sets of thermal properties models are available: one based on the MATPRO relations (Allison et al., 1993) and a second set based on IAEA relations (IAEA, 2006). The MATPRO models are the default behavior in BISON.

Thermal Conductivity

Both the MATPRO model and the IAEA model for thermal conductivity used experimental data from Zircaloy-2 and Zircaloy-4.

MATPRO Model

The correlation for thermal conductivity of zirconium alloy (Allison et al., 1993) is given by: k (W/m-K)=7.511+2.088×10−2T−1.450×10−5T2+7.668×10−9T3k\text{ (W/m-K)} = 7.511 + 2.088 \times 10^{-2} T - 1.450 \times 10^{-5} T^2 + 7.668 \times 10^{-9} T^3 where TT the temperature in Kelvin. This correlation is valid up to 2098 K.

IAEA Model

The IAEA thermal conductivity of zirconium alloy is (IAEA, 2006): k (W/m-K)=12.767−5.4348×10−4T+8.9818×10−6T2k\text{ (W/m-K)} = 12.767 - 5.4348\times 10{-4} T + 8.9818\times 10^{-6} T^2 where TT is the temperature in K. The IAEA model is valid for temperatures between 300K and 1800K.

Specific Heat Capacity

The MATPRO and the IAEA models for specific heat capacity for zirconium alloy are both based on experimental data for Zircaloy-2 and applied to Zircaloy-4; no information on the specific heat capacity of Zircaloy-4 is available in the open literature.

MATPRO Specific Heat Capacity Model

The specific heat capacity for Zircaloy alloys is based upon the tabulated data show in Table 1. Linear interpolation is used between the tabulated values.

Table 1: Temperature dependent specific heat capacity of Zircaloy (Allison et al., 1993)

Temperature (K)Specific Heat Capacity (J/kg-K)Temperature (K)Specific Heat Capacity (J/kg-K)
300.02811153.0719
400.03021173.0816
640.03311193.0770
1090.03751213.0619
1093.05021233.0469
1113.05901248.0356
1133.0615

IAEA Specific Heat Capacity Model

The IAEA model (IAEA, 2006) for specific heat capacity of zirconium alloy is a piece wise function that explicitly accounts for mixed α\alpha and β\beta phases as the zirconium alloy undergoes a phase transition with temperature. The piecewise function is constructed to weight the specific heat capacity calculation based on whether the α\alpha or β\beta phase is more previlant. cP={255.66+0.1024T for 273K<T<1100K255.66+0.1024T+1058.4exp⁡(−[T−1213.8]2719.61) for 1100<T<1214K597.1−0.4088T+1.565×10−4T2+1058.4exp⁡(−[T−1213.8]2719.61) for 1214<T<1320K597.1−0.4088T+1.565×10−4T2 for 1320<T<2000K c_P = \begin{cases} 255.66 + 0.1024 T & \text{ for } 273K < T < 1100 K \\ 255.66 + 0.1024 T + 1058.4 \exp{ \left( \frac{-\left[T-1213.8\right]^2}{719.61} \right)} & \text{ for } 1100 < T < 1214K \\ 597.1 - 0.4088 T + 1.565 \times10^{-4} T^2 + 1058.4 \exp{ \left( \frac{-\left[T-1213.8\right]^2}{719.61} \right)} & \text{ for } 1214 < T < 1320K \\ 597.1 - 0.4088 T + 1.565 \times 10^{-4} T^2 & \text{ for } 1320 < T < 2000K \end{cases}(1) where TT is the temperature in K, and the calculated specific heat capacity CpC_p has units of (J/kg-K). The IAEA heat capacity model is valid for temperatures between 273K and 2000K.

commentnote:Correction of Exponential Term

The ThermalZry model for heat capacity from the IAEA report, Eq. (1), includes two negative signs in the exponential terms, used to calculate the heat capacity for the mixed α\alpha and β\beta phases between 1100K and 1320K, which do not appear in the cited literature. This correction to the heat capacity equation is necessary to capture the Zircaloy-2 heat capacity data which demonstrates a local peak near 1200K. Without this correction the equation becomes asymptotic at 1200K.

Example Input Syntax

[Materials]
  [thermal_clad]
    type = ZryThermal
    temperature = T
    zry_thermal_properties_model = IAEA
  []
[]
(test/tests/thermalZry/thermal_test_IAEA.i)

Input Parameters

  • temperatureCoupled temperature

    C++ Type:std::vector<VariableName>

    Unit:(no unit assumed)

    Controllable:No

    Description:Coupled temperature

Required Parameters

  • base_nameOptional parameter that allows the user to define multiple material systems on the same block, e.g. for multiple phases.

    C++ Type:std::string

    Controllable:No

    Description:Optional parameter that allows the user to define multiple material systems on the same block, e.g. for multiple phases.

  • blockThe list of blocks (ids or names) that this object will be applied

    C++ Type:std::vector<SubdomainName>

    Controllable:No

    Description:The list of blocks (ids or names) that this object will be applied

  • boundaryThe list of boundaries (ids or names) from the mesh where this object applies

    C++ Type:std::vector<BoundaryName>

    Controllable:No

    Description:The list of boundaries (ids or names) from the mesh where this object applies

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

    Default:True

    C++ Type:bool

    Controllable:No

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

  • 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 computeQpProperties() 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

    Options:NONE, ELEMENT, SUBDOMAIN

    Controllable:No

    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 computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped

  • declare_suffixAn optional suffix parameter that can be appended to any declared properties. The suffix will be prepended with a '_' character.

    C++ Type:MaterialPropertyName

    Unit:(no unit assumed)

    Controllable:No

    Description:An optional suffix parameter that can be appended to any declared properties. The suffix will be prepended with a '_' character.

  • zry_thermal_properties_modelMATPROReference source for the set of thermal property calculations to use: MATPRO IAEA

    Default:MATPRO

    C++ Type:MooseEnum

    Options:MATPRO, IAEA

    Controllable:No

    Description:Reference source for the set of thermal property calculations to use: MATPRO IAEA

Optional Parameters

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

    C++ Type:std::vector<std::string>

    Controllable:No

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

  • enableTrueSet the enabled status of the MooseObject.

    Default:True

    C++ Type:bool

    Controllable:Yes

    Description:Set the enabled status of the MooseObject.

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

    Default:True

    C++ Type:bool

    Controllable:No

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

  • seed0The seed for the master random number generator

    Default:0

    C++ Type:unsigned int

    Controllable:No

    Description:The seed for the master random number generator

  • 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

    Controllable:No

    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.

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<std::string>

    Controllable:No

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

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

    Default:none

    C++ Type:std::vector<OutputName>

    Controllable:No

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

Outputs Parameters

  • prop_getter_suffixAn optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.

    C++ Type:MaterialPropertyName

    Unit:(no unit assumed)

    Controllable:No

    Description:An optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.

  • use_interpolated_stateFalseFor the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.

    Default:False

    C++ Type:bool

    Controllable:No

    Description:For the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.

Material Property Retrieval Parameters

  • specific_heat_scale_factor1The scaling factor on the specific heat.

    Default:1

    C++ Type:double

    Unit:(no unit assumed)

    Controllable:No

    Description:The scaling factor on the specific heat.

  • thermal_conductivity_scale_factor1The scaling factor on the thermal conductivity.

    Default:1

    C++ Type:double

    Unit:(no unit assumed)

    Controllable:No

    Description:The scaling factor on the thermal conductivity.

Advanced: Scaling Factors Parameters

Input Files

References

  1. C. M. Allison, G. A. Berna, R. Chambers, E. W. Coryell, K. L. Davis, D. L. Hagrman, D. T. Hagrman, N. L. Hampton, J. K. Hohorst, R. E. Mason, M. L. McComas, K. A. McNeil, R. L. Miller, C. S. Olsen, G. A. Reymann, and L. J. Siefken. SCDAP/RELAP5/MOD3.1 code manual, volume IV: MATPRO-A library of materials properties for light-water-reactor accident analysis. Technical Report NUREG/CR-6150, EGG-2720, Idaho National Engineering Laboratory, 1993.[BibTeX]
  2. IAEA. Thermophysical properties database of materials for light water reactors and heavy water reactors: final report of a coordinated research project 1999-2005. Technical Report IAEA-TECDOC-1496, IAEA, 2006.[BibTeX]