def LN2evaporationFlow(vaporPressure, massFlow, T_incoming, P_incoming,
incomingGas):
T = CoolProp.CoolProp.PropsSI('T', 'P', vaporPressure, 'Q', 0, 'Nitrogen')
latentHeat = CoolProp.CoolProp.PropsSI(
'H', 'P', vaporPressure,
'Q', 1, 'Nitrogen') - CoolProp.CoolProp.PropsSI(
'H', 'P', vaporPressure, 'Q', 0, 'Nitrogen')
if incomingGas == 'He4':
enthalpyDifference = hepak.HeCalc(
'H', 0, 'T', T_incoming, 'P', P_incoming, 1) - hepak.HeCalc(
'H', 0, 'T', T, 'P', P_incoming, 1)
elif incomingGas == 'He3':
incomingDensity = he3pak.He3Density(P_incoming, T_incoming)
coldDensity = he3pak.He3Density(P_incoming, T)
enthalpyDifference = he3pak.He3Prop(6, incomingDensity,
T_incoming) - he3pak.He3Prop(
6, coldDensity, T)
elif incomingGas == 'He':
enthalpyDifference = CoolProp.CoolProp.PropsSI(
'enthalpy', 'T', T_incoming, 'P',
P_incoming, 'Helium') - CoolProp.CoolProp.PropsSI(
'enthalpy', 'T', T, 'P', P_incoming, 'Helium')
else:
raise NameError('Unknow gas ' + gas + '!')
heatLoad = massFlow * enthalpyDifference
return heatLoad / latentHeat
def He3CoolingLoad(flow, pressure, inletTemperature, outletTemperature):
inletDensity = he3pak.He3Density(pressure, inletTemperature)
inletEnthalpy = he3pak.He3Prop(6, inletDensity, inletTemperature)
outletDensity = he3pak.He3Density(pressure, outletTemperature)
outletEnthalpy = he3pak.He3Prop(6, outletDensity, outletTemperature)
return flow * (
inletEnthalpy - outletEnthalpy
) # heat load on 1K pot = He3 gas flow * He3 enthalpy difference
def He3Flow(inletTemperature, inletPressure, temperature, heatLoad):
inletDensity = he3pak.He3Density(inletPressure, inletTemperature)
inletEnthalpy = he3pak.He3Prop(6, inletDensity, inletTemperature)
vaporEnthalpy = he3pak.He3SaturatedVaporProp(6, temperature)
liquidEnthalpy = he3pak.He3SaturatedLiquidProp(6, temperature)
liquidFraction = (inletEnthalpy - vaporEnthalpy) / (liquidEnthalpy -
vaporEnthalpy)
latentHeat = he3pak.He3SaturatedLiquidProp(13, temperature)
liquidFlow = heatLoad / latentHeat
return liquidFlow / liquidFraction
def velocity(massFlow, ID, OD, T, P, gas):
if gas == 'He4':
density = hepak.HeCalc('D', 0, 'T', T, 'P', P, 1)
elif gas == 'He3':
density = he3pak.He3Density(P, T)
elif gas == 'N2':
density = CoolProp.CoolProp.PropsSI('D', 'T', T, 'P', P, 'Nitrogen')
elif gas == 'He':
density = CoolProp.CoolProp.PropsSI('D', 'T', T, 'P', P, 'Helium')
else:
raise NameError('Unknow gas ' + gas + '!')
crossSection = (OD**2 - ID**2) * math.pi / 4
return massFlow / density / crossSection
def dTdx2(massFlow, ID, OD, T, T_innerWall, T_outerWall, P, roughness, gas):
if gas == 'He4':
cP = hepak.HeCalc(14, 0, 'T', T, 'P', P, 1)
elif gas == 'He3':
density = he3pak.He3Density(P, T)
cP = he3pak.He3Prop(9, density, T)
elif gas == 'N2':
cP = CoolProp.CoolProp.PropsSI('Cpmass', 'T', T, 'P', P, 'Nitrogen')
elif gas == 'He':
cP = CoolProp.CoolProp.PropsSI('Cpmass', 'T', T, 'P', P, 'Helium')
else:
raise NameError('Unknow gas ' + gas + '!')
return dQdx2(massFlow, ID, OD, T, T_innerWall, T_outerWall, P, roughness,
gas) / cP / massFlow
def reynoldsNumber(massFlow, ID, OD, T, P, gas):
crossSection = (OD**2 - ID**2) * math.pi / 4.
hydraulicDiameter = OD - ID
if gas == 'He4':
viscosity = hepak.HeCalc(25, 0, 'T', T, 'P', P, 1)
elif gas == 'He3':
density = he3pak.He3Density(P, T)
viscosity = he3pak.He3Prop(29, density, T)
elif gas == 'N2':
viscosity = CoolProp.CoolProp.PropsSI('viscosity', 'T', T, 'P', P,
'Nitrogen')
elif gas == 'He':
viscosity = CoolProp.CoolProp.PropsSI('viscosity', 'T', T, 'P', P,
'Helium')
else:
raise NameError('Unknow gas ' + gas + '!')
return massFlow * hydraulicDiameter / viscosity / crossSection
def heatTransferCoeff(massFlow, ID, OD, T, T_wall, P, roughness, gas):
Nu = nusseltNumber(massFlow, ID, OD, T, T_wall, P, roughness, gas)
thermalConductivity = 0.
if gas == 'He4':
thermalConductivity = hepak.HeCalc(26, 0, 'T', T, 'P', P, 1)
elif gas == 'He3':
density = he3pak.He3Density(P, T)
thermalConductivity = he3pak.He3Prop(28, density, T)
elif gas == 'N2':
thermalConductivity = CoolProp.CoolProp.PropsSI(
'conductivity', 'T', T, 'P', P, 'Nitrogen')
elif gas == 'He':
thermalConductivity = CoolProp.CoolProp.PropsSI(
'conductivity', 'T', T, 'P', P, 'Helium')
else:
raise NameError('Unknow gas ' + gas + '!')
return Nu * thermalConductivity / (OD - ID)
def nusseltNumber(massFlow, ID, OD, T, T_wall, P, roughness, gas):
Re = reynoldsNumber(massFlow, ID, OD, T, P, gas)
if Re < 1000: # laminar flow
return 4.36
if gas == 'He4':
prandtlNumber = hepak.HeCalc(27, 0, 'T', T, 'P', P, 1)
viscosity = hepak.HeCalc(25, 0, 'T', T, 'P', P, 1)
viscosity_wall = hepak.HeCalc(25, 0, 'T', T_wall, 'P', P, 1)
elif gas == 'He3':
density = he3pak.He3Density(P, T)
prandtlNumber = he3pak.He3Prop(32, density, T)
viscosity = he3pak.He3Prop(29, density, T)
viscosity_wall = he3pak.He3Prop(29, density, T_wall)
elif gas == 'N2':
prandtlNumber = CoolProp.CoolProp.PropsSI('Prandtl', 'T', T, 'P', P,
'Nitrogen')
viscosity = CoolProp.CoolProp.PropsSI('viscosity', 'T', T, 'P', P,
'Nitrogen')
viscosity_wall = CoolProp.CoolProp.PropsSI('viscosity', 'T', T_wall,
'P', P, 'Nitrogen')
elif gas == 'He':
prandtlNumber = CoolProp.CoolProp.PropsSI('Prandtl', 'T', T, 'P', P,
'Helium')
viscosity = CoolProp.CoolProp.PropsSI('viscosity', 'T', T, 'P', P,
'Helium')
viscosity_wall = CoolProp.CoolProp.PropsSI('viscosity', 'T', T_wall,
'P', P, 'Helium')
else:
raise NameError('Unknow gas ' + gas + '!')
# if Re > 10000.:
# if not 0.7 <= prandtlNumber <= 16700.:
# print('Prandtl number {0} outside valid range for Sieder-Tate correlation'.format(prandtlNumber))
return 0.023 * Re**0.8 * prandtlNumber**(1. / 3.) * (
viscosity / viscosity_wall)**0.14 # Sieder-Tate correlation
import hepak
import he3pak
print('He4 Standard density:', hepak.HeCalc('D', 0, 'P', 101300, 'T', 273.15,
1))
print(hepak.HeValidate(1, 2),
hepak.HeMsg(hepak.HeCalc(-1, 0, 'P', 101300, 'T', 273.15, 1)))
print('\nList of HEPAK properties and their units:')
for p in range(40):
print(p, hepak.HeProperty(p), [hepak.HeUnit(p, u) for u in range(1, 5)])
print('\nList of HEPAK constants:')
for p in range(1, 16):
print(p, hepak.HeConst(p))
print('\n')
print('He3 standard density:', he3pak.He3Density(101300, 273.15), 'kg/m3')
print('He3 saturated density at 3K: {0} kg/m3 (liquid), {1} kg/m3 (vapor)'.
format(he3pak.He3SaturatedLiquidProp(3, 0.8),
he3pak.He3SaturatedVaporProp(3, 0.8)))
print('He3 temperature at saturated vapor pressure of 1 atm:',
he3pak.He3SaturatedTemperature(101300), 'K')
def plotTubeInTubeHEX(sol, innerMassFlow, innerID, innerOD, innerGas,
outerMassFlow, outerID, outerOD, outerGas, N2ID, N2OD,
roughness):
fig, axes = plt.subplots(3, 2, figsize=(9.6, 10.8))
fig.set_tight_layout(True)
axes[0][0].plot(sol.x, sol.y[0], color='tab:red')
axes[0][0].plot(sol.x, sol.y[1], color='tab:blue')
y = numpy.array([Twall(innerMassFlow, innerID, innerOD, T_He, P_He, innerGas, outerMassFlow, outerID, outerOD, T_He3, P_He3, outerGas, roughness) \
for T_He, T_He3, P_He, P_He3 in zip(sol.y[0], sol.y[1], sol.y[2], sol.y[3])])
axes[0][0].plot(sol.x, y, color='tab:brown')
if len(sol.y) > 4:
N2massFlow = LN2evaporationFlow(sol.y[5][0], He3MassFlow, sol.y[1][0],
sol.y[3][0], outerGas)
axes[0][0].plot(sol.x, sol.y[4], color='tab:green')
y = numpy.array([Twall(innerMassFlow, innerID, innerOD, T_He, P_He, outerGas, N2massFlow, 0., N2OD, T_N2, P_N2, 'N2', roughness) \
for T_N2, T_He, P_N2, P_He in zip(sol.y[0], sol.y[4], sol.y[2], sol.y[5])])
axes[0][0].plot(sol.x, y, color='tab:purple')
axes[0][0].set_yscale('log')
axes[0][0].set_ylabel('Temperature (K)')
axes[0][0].grid(True, 'both')
y = numpy.array([
reynoldsNumber(innerMassFlow, innerID, innerOD, T, P, innerGas)
for T, P in zip(sol.y[0], sol.y[2])
])
axes[0][1].plot(sol.x, y, color='tab:red')
y = numpy.array([
reynoldsNumber(outerMassFlow, outerID, outerOD, T, P, outerGas)
for T, P in zip(sol.y[1], sol.y[3])
])
axes[0][1].plot(sol.x, y, color='tab:blue')
if len(sol.y) > 4:
y = numpy.array([
reynoldsNumber(N2massFlow, 0., N2OD, T, P, 'N2')
for T, P in zip(sol.y[4], sol.y[5])
])
axes[0][1].plot(sol.x, y, color='tab:green')
y = numpy.array([nusseltNumber(outerMassFlow, outerID, outerOD, T_outer, Twall(innerMassFlow, innerID, innerOD, T_inner, P_inner, innerGas, outerMassFlow, outerID, outerOD, T_outer, P_outer, outerGas, roughness), P_outer, roughness, outerGas) \
for T_inner, P_inner, T_outer, P_outer in zip(sol.y[0], sol.y[2], sol.y[1], sol.y[3])])
axes[0][1].plot(sol.x, y, color='tab:cyan')
axes[0][1].set_yscale('log')
axes[0][1].set_ylabel('Reynolds number')
axes[0][1].grid(True, 'both')
#y = numpy.array([hepak.HeCalc('D', 0, 'P', P_He, 'T', T, 1) for T, P_He in zip(sol.y[0], sol.y[2])])
#axes[1][0].plot(sol.x, y, color = 'tab:red')
y = numpy.array(
[he3pak.He3Density(P_He3, T) for T, P_He3 in zip(sol.y[1], sol.y[3])])
axes[1][0].plot(sol.x, y, color='tab:blue')
axes[1][0].set_ylabel('Density (kg/m3)')
axes[1][0].grid(True, 'both')
y = numpy.array([
velocity(innerMassFlow, innerID, innerOD, T, P, innerGas)
for T, P in zip(sol.y[0], sol.y[2])
])
axes[1][1].plot(sol.x, y, color='tab:red')
y = numpy.array([
velocity(outerMassFlow, outerID, outerOD, T, P, innerGas)
for T, P in zip(sol.y[1], sol.y[3])
])
axes[1][1].plot(sol.x, y, color='tab:blue')
if len(sol.y) > 4:
y = numpy.array([
velocity(N2massFlow, N2ID, N2OD, T, P, 'N2')
for T, P in zip(sol.y[4], sol.y[5])
])
axes[1][1].plot(sol.x, y, color='tab:green')
axes[1][1].set_yscale('log')
axes[1][1].set_ylabel('Velocity (m/s)')
axes[1][1].grid(True, 'both')
axes[2][0].plot(sol.x, sol.y[2], color='tab:red')
axes[2][0].plot(sol.x, sol.y[3], color='tab:blue')
if len(sol.y) > 4:
axes[2][0].plot(sol.x, sol.y[5], color='tab:green')
axes[2][0].set_ylabel('Pressure (Pa)')
axes[2][0].grid(True, 'both')
while True:
try:
plt.savefig(
'HEX7_{0:.4g}K_{1:.4g}K_{2:.4g}gs_{3:.4g}gs.pdf'.format(
sol.y[0][0], sol.y[1][-1], innerMassFlow, outerMassFlow))
except PermissionError:
input(
'Could not save plots. If the target file is still opened in another application please close it. Press ENTER to try again.'
)
else:
break
plt.close()