FeCrAl Thermal Properties

Computes the specific heat and thermal conductivity for FeCrAl alloys.

Description

The ThermalFeCrAl model computes the specific heat and thermal conductivity for a variety of FeCrAl alloys. The alloys to available include the commercial alloys Special Metals Incoloy MA956, Plansee PM2000, Kanthal APMT, Resistalloy International Fecralloy, and Oak Ridge National Laboratory alloys C06M, C35M, and C36M.

The recent FeCrAl Handbook (Field et al., 2018) contains temperature dependent correlations for thermal conductivity and specific heat of four of the alloys listed above: Kanthal APMT, C06M, C35M, and C36M. The thermal conductivity is given as:

k=A1T2+A2T+A3 k = A_1T^2 + A_2T + A_3(1) where A1A_1, A2A_2, and A3A_3 are fitting constants tabulated in Table 1, and TT is the temperature in K. Note, the mean values provided in the handbook are tabulated.

Table 1: Coefficients used in the polynomial fit for thermal conductivity of select FeCrAl alloys

AlloyA1_1 (×10−7\times 10^{-7})A2_2 (×10−2\times 10^{-2})A3_3
Kanthal APMT-7.2231.56286.569
C06M6.7621.0329.956
C35M-19.861.5378.502
C36M-9.1841.3688.187

The specific heat capacity correlations provided in the handbook are divided into two temperature regimes. Below the Curie Temperature (TcT_c) the specific heat correlation is given by:

Cp=AT+BT2+CT3C_p = AT + BT^2 + CT^3 where AA, BB, and CC are fitting constants, CpC_p is the specific heat capacity in J/kg-K and TT is the temperature in K. The fitting constants as well as the Curie temperature for the alloys are summarized in Table 2. It should be mentioned that the units provided for these coefficients here are different than the handbook. It appears that the handbook was incorrectly assuming TT in units of K−1^{-1} when deriving the units of the coefficients.

Table 2: Coefficients used in the polynomial fit for specific heat of select alloys below the Curie temperature

AlloyA (J/kg-K2^{2})B (J/kg-K3^{3} ×10−3\times 10^{-3})C (J/kg-K4^{4} ×10−6\times 10^{-6})Tc_c (K)
Kanthal APMT2.540-4.3112.982852
C06M2.430-3.9572.656888
C35M2.450-4.0022.720870
C36M2.995-5.9534.516771

Above the Curie temperature the coefficients have additional terms to capture the larger increase in specific heat in the 750-900 K range. This increase is attributed to a phase change in the alloys from ferromagnetic to paramagnetic. The correlation is given by:

Cp=AT+BT2+CT3+DT+Eln⁡(∣(T−Tc)∣Tc)C_p = AT + BT^2 + CT^3 + \frac{D}{T} + E \ln \left( \frac{\left | \left(T - T_c\right) \right |}{T_c} \right) where DD and EE are additional fitting constants. The fitting constants in this temperature regime are summarized in Table 3.

Table 3: Coefficients used in the polynomial fit for specific heat of select alloys above the Curie temperature

AlloyA (J/kg-K2^{2})B (J/kg-K3^{3} ×10−3\times 10^{-3})C (J/kg-K4^{4} ×10−6\times 10^{-6})D (J/kg ×103\times 10^{3})E (J/kg-K)
Kanthal APMT1.840-1.8430.643-5.712-50.38
C06M1.827-1.8070.6134-9.419-54.54
C35M1.946-2.0020.698-1.652-53.93
C36M1.456-1.2960.43826.45-46.89

For the commercial alloys Special Metals MA956 and Plansee PM2000 the temperature dependent thermal conductivity and specific heat capacity are given in tabular form in their data sheets. Since no additional information is given about the behavior as a function of temperature, the material properties are linearly interpolated between the values provided in the table. For temperatures outside of the range provided in the table the thermal conductivity or specific heat is taken as the closest known value to avoid extrapolation into areas where no data is known.

The tabulated data for MA956 (Corporation, 2004) and PM2000 (MatWeb, 2014) are reproduced in Table 4 and Table 5 respectively. The thermal conductivity and specific heat capacity of Fecralloy are given as constant values of 16.0 W/m-K and 460 J/kg-K respectively (MatWeb, 2014).

Table 4: Temperature dependent thermal conductivity and specific heat capacity of MA956 alloy

Temperature (K)Thermal Conductivity (W/m-K)Specific Heat Capacity (J/kg-K)
293.1510.9469
373.1512.2491
473.1513.9519
573.1515.4547
673.1516.9575
773.1518.4608
873.1519.8630
973.1521.2658
1073.1522.6686
1173.1524.1714
1273.1525.5741
1373.1527769

 ~

Table 5: Temperature dependent thermal conductivity and specific heat capacity of PM2000 alloy

Temperature (K)Thermal Conductivity (W/m-K)Specific Heat Capacity (J/kg-K)
293.1510.9
373.15500
473.1516480
773.1521610
1073.1522680
1273.1525.5740
1473.1528

 ~

Range of Applicability and Uncertainty

All of the thermal conductivity and specific heat models have an associated range of temperature over which they are valid. The user is cautioned to examine their results when using the correlations or tabulated values outside their applicability ranges. The correlations for Kanthal APMT, C06M, C35M, and C36M are applicable from 300 K to ∼\sim1400 K. Recall that the specific heat correlation has two different equations depending upon whether the temperature is above or below the Curie temperature. For the MA956 and PM2000 alloys, which only have tabulated values, the closest known value is taken for thermal conductivity or specific heat for temperatures outside the available range to avoid unknown consequences of extrapolation. The correlations for MA956 are applicable from 293.15 K to 1373.15 K. For PM2000, the thermal conductivity correlation is applicable from 293.15 K to 1473.15 K whereas the specific heat correlation is applicable from 373.15 K to 1473.15 K.

The correlations for Kanthal APMT, C06M, C35M, and C36M from the FeCrAl handbook (Field et al., 2018) are fit to experimental data that has some associated uncertainty. For thermal conductivity, the correlations all have R2^2 values greater than 0.96 with the experimental data. Thus, the uncertainty on the experimental data is applied to the models for thermal conductivity. This uncertainty over the entire temperature range of applicability is 7%. For specific heat currently no uncertainty in the experimental data has been provided.

Example Input Syntax

[./fuel_thermalFeCrAl]
  type = ThermalFeCrAl
  block = 0
  material = APMT
  scale_factor_k = 1.0
  scale_factor_cp = 1.0
  temp = T
[../]
Copy
(test/tests/thermalFeCrAl/thermalFeCrAl_APMT.i)

Input Parameters

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

    C++ Type:std::vector

    Options:

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

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

    C++ Type:std::vector

    Options:

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

    Options:

    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 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

    Options:NONE ELEMENT SUBDOMAIN

    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

  • materialAPMTThe FeCrAl alloy being used for the cladding. Choices are: APMT C06M C35M C36M MA956 PM2000 FECRALLOY

    Default:APMT

    C++ Type:MooseEnum

    Options:APMT C06M C35M C36M MA956 PM2000 FECRALLOY

    Description:The FeCrAl alloy being used for the cladding. Choices are: APMT C06M C35M C36M MA956 PM2000 FECRALLOY

  • scale_factor_cp1Scale factor to be applied to the specific heat

    Default:1

    C++ Type:double

    Options:

    Description:Scale factor to be applied to the specific heat

  • scale_factor_k1Scale factor to be applied to the thermal conductivity

    Default:1

    C++ Type:double

    Options:

    Description:Scale factor to be applied to the thermal conductivity

  • tempCoupled Temperature

    C++ Type:std::vector

    Options:

    Description:Coupled Temperature

Optional Parameters

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

    C++ Type:std::vector

    Options:

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

  • enableTrueSet the enabled status of the MooseObject.

    Default:True

    C++ Type:bool

    Options:

    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

    Options:

    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

    Options:

    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

    Options:

    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

    Options:

    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

    Options:

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

Outputs Parameters

Input Files

References

  1. Special Metals Corporation. Special Metals Incoloy alloy MA956. www.specialmetals.com/documents/Incoloy, 2004.[BibTeX]
  2. K. G. Field, M. A. Snead, Y. Yamamoto, and K. A. Terrani. Handbook on the material properties of fecral alloys for nuclear power production applications. Technical Report ORNL/SPR-2018/905 Rev. 1, Oak Ridge National Laboratory, 2018.[BibTeX]
  3. MatWeb. Resistalloy International Fecralloy Electrical Resistance Steel. http://www.matweb.com/search/datasheet.aspx?MatGUID=c2427c6297594858bedac2a4e5981d2f, 2014.[BibTeX]
  4. MatWeb. Schwarzkopf Plansee PM 2000. http://www.matweb.com/search/datasheet.aspx?matguid=21e9ec9a0de24b47bcf69ab11c375567, 2014.[BibTeX]