# Copyright 2019 TerraPower, LLC
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
"""
Uranium metal.
Much info is from [AAAFuels]_.
.. [AAAFuels] Kim, Y S, and Hofman, G L. AAA fuels handbook.. United States: N. p., 2003. Web. doi:10.2172/822554. .
"""
from numpy import interp
from armi import runLog
from armi.materials.material import FuelMaterial
from armi.nucDirectory import nuclideBases as nb
from armi.utils.units import getTk
[docs]class Uranium(FuelMaterial):
enrichedNuclide = "U235"
materialIntro = ""
propertyNotes = {"thermal conductivity": ""}
propertyRawData = {"thermal conductivity": ""}
propertyUnits = {"thermal conductivity": "W/m-K", "heat capacity": "J/kg-K"}
propertyEquation = {
"thermal conductivity": "21.73 + 0.01591T + 5.907×10<super>-6</super>T<super>2</super>"
}
_heatCapacityTableK = [
298,
300,
400,
500,
600,
700,
800,
900,
941.9,
942,
1000,
1048.9,
1049,
1100,
1200,
1300,
1400,
1407.9,
1408,
1500,
1600,
1700,
1800,
1900,
2000,
2100,
2200,
2400,
]
_heatCapacityTable = [
27.665,
27.700,
29.684,
31.997,
34.762,
38.021,
41.791,
46.081,
48.038,
42.928,
42.928,
42.928,
38.284,
38.284,
38.284,
38.284,
38.284,
38.284,
48.660,
48.660,
48.660,
48.660,
48.660,
48.660,
48.660,
48.660,
48.660,
48.660,
] # J/K/mol
_densityTableK = [
293,
400,
500,
600,
700,
800,
900,
940.9,
941,
1000,
1047.9,
1048,
1100,
1200,
1400,
1407.9,
1408,
1500,
1600,
]
_densityTable = [
19.07,
18.98,
18.89,
18.79,
18.68,
18.55,
18.41,
18.39,
18.16,
18.11,
18.07,
17.94,
17.88,
17.76,
17.53,
17.52,
16.95,
16.84,
16.71,
] # g/cc
_linearExpansionPercent = [
0.000,
0.157,
0.315,
0.494,
0.697,
0.924,
1.186,
1.300,
1.635,
1.737,
1.820,
2.050,
2.168,
2.398,
2.855,
2.866,
4.006,
4.232,
4.502,
] # %
_linearExpansionTable = [
13.9,
15.2,
16.9,
19.0,
21.4,
24.3,
27.7,
29.1,
17.3,
17.3,
17.3,
22.9,
22.9,
22.9,
22.9,
22.9,
25.5,
25.5,
25.5,
] # 1e6/K
propertyValidTemperature = {
"thermal conductivity": ((255.4, 1173.2), "K"),
"heat capacity": ((_heatCapacityTableK[0], _heatCapacityTableK[-1]), "K"),
"density": ((_densityTableK[0], _densityTableK[-1]), "K"),
"linear expansion": ((_densityTableK[0], _densityTableK[-1]), "K"),
"linear expansion percent": ((_densityTableK[0], _densityTableK[-1]), "K"),
}
references = {
"thermal conductivity": [
"AAA Fuels Handbook by YS Kim and G.L. Hofman, ANL, Section 6.1.1"
],
"heat capacity": ["AAA Fuels Handbook by YS Kim and GL Hofman, Table 2-14"],
"melting point": ["AAA Fuels Handbook by YS Kim and GL Hofman, Table 2-13"],
"density": ["Metallic Fuels Handbook, ANL-NSE-3, Table B.3.3-1"],
"linear expansion": ["Metallic Fuels Handbook, ANL-NSE-3, Table B.3.3-1"],
"linear expansion percent": [
"Metallic Fuels Handbook, ANL-NSE-3, Table B.3.3-1"
],
}
refDens = 19.07 # the value corresponding to linearExpansionPercent = 0
[docs] def thermalConductivity(self, Tk: float = None, Tc: float = None) -> float:
"""The thermal conductivity of pure U in W-m/K."""
Tk = getTk(Tc, Tk)
self.checkPropertyTempRange("thermal conductivity", Tk)
kU = 21.73 + (0.01591 * Tk) + (0.000005907 * Tk**2)
return kU
[docs] def heatCapacity(self, Tk: float = None, Tc: float = None) -> float:
"""Heat capacity in J/kg-K."""
Tk = getTk(Tc, Tk)
self.checkPropertyTempRange("heat capacity", Tk)
return interp(Tk, self._heatCapacityTableK, self._heatCapacityTable)
[docs] def setDefaultMassFracs(self) -> None:
u235 = nb.byLabel["U235"]
u238 = nb.byLabel["U238"]
u238Abundance = (
1.0 - u235.abundance
) # neglect U234 and keep U235 at natural level
gramsIn1Mol = u235.abundance * u235.weight + u238Abundance * u238.weight
self.setMassFrac("U235", u235.weight * u235.abundance / gramsIn1Mol)
self.setMassFrac("U238", u238.weight * u238Abundance / gramsIn1Mol)
[docs] def meltingPoint(self):
"""Melting point in K."""
return 1408
[docs] def density(self, Tk: float = None, Tc: float = None) -> float:
"""Density in g/cc."""
Tk = getTk(Tc, Tk)
self.checkPropertyTempRange("density", Tk)
return interp(Tk, self._densityTableK, self._densityTable) * self.getTD()
[docs] def pseudoDensity(self, Tk: float = None, Tc: float = None) -> float:
"""2D-expanded density in g/cc."""
return super().pseudoDensity(Tk=Tk, Tc=Tc) * self.getTD()
[docs] def linearExpansion(self, Tk: float = None, Tc: float = None) -> float:
"""Linear expansion coefficient in 1/K."""
Tk = getTk(Tc, Tk)
self.checkPropertyTempRange("linear expansion", Tk)
return interp(Tk, self._densityTableK, self._linearExpansionTable) / 1e6
[docs] def linearExpansionPercent(self, Tk: float = None, Tc: float = None) -> float:
"""Linear expansion percent."""
Tk = getTk(Tc, Tk)
self.checkPropertyTempRange("linear expansion percent", Tk)
return interp(Tk, self._densityTableK, self._linearExpansionPercent)