def dTdx(x, T):
if heatLoad == 0:
return 0.
if T[0] < hepak.HeConst(3):
print('T_4He {0:.3g} outside HEPAK range!'.format(T[0]))
return 0.
if conductivityModel == 'HEPAK':
k = hepak.HeCalc(38, 0, 'P', pressure, 'T', T[0],
1) # heat conductivity from HEPAK
if k > 0:
return (heatLoad / A)**3 / k
else:
print('HEPAK conductivity <= 0!')
return 0.
elif conductivityModel == 'VanSciver':
g_lambda = hepak.HeCalc(
'D', 0, 'P', pressure, 'T', T[0],
1)**2 * 1559.**4 * hepak.HeConst(9)**3 / 1450.
f_inverse = g_lambda * ((T[0] / hepak.HeConst(9))**5.7 *
(1 - (T[0] / hepak.HeConst(9))**5.7)
)**3 # heat conductivity from vanSciver
return (heatLoad / A)**3 / f_inverse
else:
raise 'Invalid Gorter-Mellink model!'
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 HeReservoirEvaporation(He3Flow, He3Pressure, He3InletTemperature, IPFlow,
IPPressure, IPInletTemperature, staticLoad,
reservoirPressure):
reservoirTemperature = hepak.HeCalc('T', 0, 'P', reservoirPressure, 'SV',
0., 1)
He3HeatLoad = He3CoolingLoad(He3Flow, He3Pressure, He3InletTemperature,
reservoirTemperature)
IPHeatLoad = HeCoolingLoad(IPFlow, IPPressure, IPInletTemperature,
reservoirTemperature)
return (He3HeatLoad + IPHeatLoad + staticLoad) / hepak.HeCalc(
7, 0, 'P', reservoirPressure, 'SL', 0.,
1) # evaporation flow = heatLoad/latent heat
def segmentedVaporTemperature(T_low, T_high, lengths):
dTdx = (T_high - T_low)/sum(lengths)
pressure = hepak.HeCalc('P', 0, 'T', T_low, 'SV', 0, 1)
x = 0.
fermiPotentials = []
for length in lengths:
x2 = x + length
meanDensity = scipy.integrate.quad(lambda y: hepak.HeCalc('D', 0, 'T', T_low + y*dTdx, 'P', pressure, 1), x, x2)[0]/length
meanTemperature = T_low + (dTdx*x2 + dTdx*x)/2.
meanLifetime = scipy.integrate.quad(lambda y: vaporLifetime(T_low + dTdx*y, pressure), x, x2)[0]/length
fermiImag = imaginaryFermiPotential(meanLifetime)
fermiPotentials.append( (realFermiPotential(meanDensity), fermiImag) )
print('{0:.2f}m: {1:.3f}K, {2:.1f}s'.format(x + length/2., meanTemperature, meanLifetime))
x = x2
return fermiPotentials
def equationSet(x, parameters):
heatLoad = parameters['Beam heating'] + parameters[
'Isopure static heat'] + HeCoolingLoad(
parameters['Isopure He flow'], parameters['Isopure He pressure'],
x[1], x[2])
T_He3 = He3Temperature(x[0], parameters['3He pressure drop'])
flow = He3Flow(x[1], parameters['3He inlet pressure'], T_He3, heatLoad)
reservoirTemperature = hepak.HeCalc('T', 0, 'P',
parameters['He reservoir pressure'],
'SV', 0., 1)
OneKPotFlow = OneKPotEvaporation(x[0], parameters['3He inlet pressure'], parameters['HEX4 exit temperature'], \
parameters['Isopure He flow'], parameters['Isopure He pressure'], reservoirTemperature, \
parameters['He reservoir pressure'], parameters['HEX5 exit temperature'], parameters['1K pot static load'], x[1])
T_1Kpot = OneKPotTemperature(OneKPotFlow, parameters['He pressure drop'])
T_HEX1_low = HEX1TemperatureLow(T_He3, parameters['HEX1 length'],
parameters['Channel diameter'],
parameters['HEX1 surface'], heatLoad)
T_HEX1_high = HEX1TemperatureHigh(T_HEX1_low, parameters['HEX1 length'],
heatLoad)
T_HeII_low = HeIITemperatureLow(T_HEX1_high, parameters['HEX1 length'],
parameters['Channel diameter'], heatLoad)
return [flow - x[0], T_1Kpot - x[1], T_HeII_low - x[2]]
def printSegmentedTemperature(T_low, pressure, heatLoad, channelDiameter, channelLength, conductivityModel, segmentLength, YoshikiParameter):
profile = UCNsource.GorterMellink(T_low, pressure, heatLoad, channelDiameter, channelLength, conductivityModel)
A = math.pi/4.*channelDiameter**2
bottleVolume = 0.034
temperatureVolumeIntegral = scipy.integrate.quad(lambda x: profile(x)[0], 0., channelLength)[0]*A + profile(channelLength)[0]*bottleVolume
meanTemperature = temperatureVolumeIntegral/(channelLength*A + bottleVolume)
lifetimeVolumeIntegral = scipy.integrate.quad(lambda x: liquidLifetime(profile(x)[0], YoshikiParameter), 0., channelLength)[0]*A + liquidLifetime(profile(channelLength)[0], YoshikiParameter)*bottleVolume
meanLifetime = lifetimeVolumeIntegral/(channelLength*A + bottleVolume)
print('Mean: {0:.3f} K, {1:.1f} s'.format(meanTemperature, meanLifetime))
with open('{0:.3f}K_{1:.2f}W_{2}_{3:.3f}.csv'.format(T_low, heatLoad, conductivityModel, YoshikiParameter), 'w', newline = '') as csvfile:
csvWriter = csv.writer(csvfile)
csvWriter.writerow(['Position (m)', 'Mean temperature (K)'])
x = 0.
fermiPotentials = []
while x < channelLength:
meanDensity = scipy.integrate.quad(lambda y: hepak.HeCalc('D', 0, 'T', profile(y)[0], 'P', pressure, 1), x, x + segmentLength)[0]/segmentLength
meanTemperature = scipy.integrate.quad(lambda y: profile(y)[0], x, x + segmentLength)[0]/segmentLength
meanLifetime = scipy.integrate.quad(lambda y: liquidLifetime(profile(y)[0], YoshikiParameter), x, x + segmentLength)[0]/segmentLength
fermiPotentials.append( (realFermiPotential(meanDensity), imaginaryFermiPotential(meanLifetime)) )
print('{0:.2f}m: {1:.3f}K, {2:.1f}s'.format(x + segmentLength/2.,meanTemperature, meanLifetime))
csvWriter.writerow([x + segmentLength/2., meanTemperature])
x = x + segmentLength
return profile, fermiPotentials
def dydx(x, y):
H = y[0]
P = max(100., y[1])
density = hepak.HeCalc('D', 0, 'P', P, 'H', H, 1)
dHdx = heatLoad / massFlow + pressureDrop / density
dPdx = -pressureDrop
if x < verticalDrop:
dHdx = dHdx + 9.81
dPdx = dPdx + density * 9.81
return [dHdx, dPdx]
def OneKPotEvaporation(He3Flow, He3Pressure, He3InletTemperature, IPFlow,
IPPressure, IPInletTemperature, HeInletPressure,
HeInletTemperature, staticLoad, OneKPotTemperature):
He3HeatLoad = He3CoolingLoad(He3Flow, He3Pressure, He3InletTemperature,
OneKPotTemperature)
IPHeatLoad = HeCoolingLoad(IPFlow, IPPressure, IPInletTemperature,
OneKPotTemperature)
HeInletEnthalpy = hepak.HeCalc('H', 0, 'T', HeInletTemperature, 'P',
HeInletPressure, 1)
HeVaporEnthalpy = hepak.HeCalc('H', 0, 'T', OneKPotTemperature, 'SV', 0.,
1)
HeLiquidEnthalpy = hepak.HeCalc('H', 0, 'T', OneKPotTemperature, 'SL', 0.,
1)
liquidFraction = (HeInletEnthalpy - HeVaporEnthalpy) / (HeLiquidEnthalpy -
HeVaporEnthalpy)
return (He3HeatLoad + IPHeatLoad + staticLoad) / hepak.HeCalc(
7, 0, 'T', OneKPotTemperature, 'SL', 0., 1
) / liquidFraction # He mass flow = heat load / latent heat(T) / (1 - vapor mass fraction(H,T))
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 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
def OneKPotTemperature(HeFlow, pumpingPressureDrop):
HeFlow = max(0., min(HeFlow, 0.1))
# inletPressure = scipy.optimize.root_scalar(lambda P: hepak.HeCalc(5, 0, 'P', P, 'T', pumpInletTemperature, 0)*gasFlow*hepak.HeConst(4)*inletTemperature/(pumpingSpeed/3600) - P, bracket = (1., 1e5)) # He pressure = Z(P, T)*dm/dt*R_s*T/(dV/dt)
# if not inletPressure.converged:
# print('Could not determine pump inlet pressure')
# pumpInletPressure = HeFlow*hepak.HeConst(4)*pumpInletTemperature/(pumpingSpeed/3600) # P = dm/dt R_s T / (dV/dt)
pumpInletPressure = scipy.optimize.root_scalar(
lambda P: pumpData(P) / 0.75 - HeFlow, bracket=(15., 12000.)
) # find inlet pressure for given flow in pump data for He3 (divide by 0.75 to scale to He4)
if not pumpInletPressure.converged:
print("Could not calculate He4 pump inlet pressure!")
T = hepak.HeCalc('T', 0, 'P', pumpInletPressure.root + pumpingPressureDrop,
'SL', 0., 1) # T_sat(P + dP)
return T
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 HeCoolingFlow(heatLoad, pressure, inletTemperature, outletTemperature):
return heatLoad / (
hepak.HeCalc('H', 0, 'P', pressure, 'T', outletTemperature, 1) -
hepak.HeCalc('H', 0, 'P', pressure, 'T', inletTemperature, 1))
'HEX1 surface': 1.67,
'HeII overfill': 0.05,
'He reservoir pressure': 1.2e5,
'Isopure He flow': 0.,
#'Isopure He flow': 0.00014/3, # isopure condensation
'Isopure He pressure': 100e2,
'20K shield temperature': 20.,
'100K shield temperature': 100.,
}
result = UCNsource.calcUCNSource(parameters)
print('3He flow: {0:.4g} g/s'.format(result['3He flow']*1000))
print('He reservoir evaporation: {0:.4g} g/s'.format(result['He reservoir flow']*1000))
print('1K pot: {0:.4} K, {1:.4g} g/s'.format(result['1K pot temperature'], result['1K pot flow']*1000))
print('He consumption: {0:.3g} L/h'.format((max(result['He reservoir flow'], result['20K shield flow'], result['100K shield flow']) + result['1K pot flow'])/hepak.HeCalc('D', 0, 'P', 1013e2, 'SL', 0., 1)*1000*3600))
print('Required shield flows: {0:.3g} g/s, {1:.3g} g/s'.format(result['20K shield flow']*1000, result['100K shield flow']*1000))
print('He-II pressure: {0:.4g} + {1:.4g} Pa'.format(result['HeII vapor pressure'], result['HeII pressure head']))
print('T: {0:.4g} -> {1:.4g} -> {2:.4g} -> {3:.4g} -> {4[0]:.4g} to {4[1]:.4g} K'.format(result['T_3He'], result['T_HEX1_low'], result['T_HEX1_high'], result['T_HeII_low'], result['T_HeII_high']))
it = 0
for T_low, heatLoad, GorterMellink, yoshikiParameter in zip([1.023, 0.9, 1.1, 0.8, 1.0, 1.023, 1.023, 1.023],\
[9.6, 9.6, 9.6, 0.2, 0.2, 9.6, 9.6, 9.6],\
['VanSciver', 'VanSciver', 'VanSciver', 'VanSciver', 'VanSciver', 'HEPAK', 'VanSciver', 'VanSciver'],\
[0.016, 0.016, 0.016, 0.016, 0.016, 0.016, 0.008, 0.024]):
vaporPressure = hepak.HeCalc('P', 0, 'T', T_low, 'SV', 0, 1)
liquidPressure = vaporPressure + hepak.HeCalc('D', 0, 'T', T_low, 'SL', 0., 1)*9.81*parameters['HeII overfill']
profile, liquidPotentials = printSegmentedTemperature(T_low, liquidPressure, heatLoad, parameters['Channel diameter'], parameters['Channel length'], GorterMellink, segmentLength, yoshikiParameter)
fig, ax = plt.subplots()
xdata = numpy.linspace(0., parameters['Channel length'], int(parameters['Channel length']/segmentLength), endpoint = True)
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')
y7 = []
y72 = []
y8 = []
y9 = []
y9_2 = []
for j in range(datapoints):
value = parameters[p]['range'][0] + float(j) / (datapoints - 1) * (
parameters[p]['range'][1] - parameters[p]['range'][0])
tempParameters[p] = value
res = UCNsource.calcUCNSource(tempParameters)
if res:
print('{0:.3g} {1}: {2:.1f} L/h'.format(
value, parameters[p]['unit'],
(max(res['He reservoir flow'], res['20K shield flow'],
res['100K shield flow']) + res['1K pot flow']) /
hepak.HeCalc('D', 0, 'P', 1013e2, 'SL', 0., 1) * 1000 * 3600))
x.append(value)
y.append(res['He reservoir flow'] * 1000)
y2.append(res['T_HeII_high'][0])
y2_2.append(res['T_HeII_high'][1])
y3.append(res['T_3He'])
y4.append(res['T_HeII_low'])
y5.append(res['3He flow'] * 1000)
y6.append(res['1K pot flow'] * 1000)
y7.append(res['20K shield flow'] * 1000)
y72.append(res['100K shield flow'] * 1000)
y8.append(res['1K pot temperature'])
y9.append(res['T_HEX1_low'])
y9_2.append(res['T_HEX1_high'])
ax = axes[i % plotRows][int(i / plotRows)]
axes[0][0].get_shared_y_axes().join(axes[0][0], ax)
def dydx(x, y):
H = y[0]
P = max(100., y[1])
density = hepak.HeCalc('D', 0, 'P', P, 'H', H, 1)
dHdx = heatLoad / massFlow + pressureDrop / density
dPdx = -pressureDrop
if x < verticalDrop:
dHdx = dHdx + 9.81
dPdx = dPdx + density * 9.81
return [dHdx, dPdx]
result = scipy.integrate.solve_ivp(dydx, (0, length), [
hepak.HeCalc('H', 0, 'P', inletPressure, 'SL', 0, 1),
inletPressure - valvePressureDrop
],
max_step=1.)
exitEnthalpy = result.y[0][-1]
exitPressure = result.y[1][-1]
exitDensity = hepak.HeCalc('D', 0, 'P', exitPressure, 'H', exitEnthalpy, 1)
exitLiquidDensity = hepak.HeCalc('D', 0, 'P', exitPressure, 'SL', 0, 1)
exitVaporDensity = hepak.HeCalc('D', 0, 'P', exitPressure, 'SV', 0, 1)
exitVaporMassFraction = hepak.HeCalc('X', 0, 'H', exitEnthalpy, 'P',
exitPressure, 1)
exitVaporVolumeFraction = exitVaporMassFraction / exitVaporDensity * exitDensity
fullLiquidVelocity = massFlow / exitLiquidDensity / crossSection
def HeCoolingLoad(flow, pressure, inletTemperature, outletTemperature):
outletTemperature = max(hepak.HeConst(3), outletTemperature)
return flow * (
hepak.HeCalc('H', 0, 'P', pressure, 'T', inletTemperature, 1) -
hepak.HeCalc('H', 0, 'P', pressure, 'T', outletTemperature, 1))
def calcUCNSource(parameters):
sol = scipy.optimize.root(equationSet,
x0=[0.0008, 1.8, 1.],
args=parameters,
method='hybr')
if not sol.success:
print('Solution did not converge!')
return
result = {}
result['3He flow'] = sol.x[0]
result['1K pot temperature'] = sol.x[1]
result['T_HeII_low'] = sol.x[2]
result['He reservoir temperature'] = hepak.HeCalc(
'T', 0, 'P', parameters['He reservoir pressure'], 'SV', 0., 1)
result['1K pot flow'] = OneKPotEvaporation(result['3He flow'], parameters['3He inlet pressure'], parameters['HEX4 exit temperature'], \
parameters['Isopure He flow'], parameters['Isopure He pressure'], result['He reservoir temperature'], \
parameters['He reservoir pressure'], parameters['HEX5 exit temperature'], parameters['1K pot static load'], result['1K pot temperature'])
result['He reservoir flow'] = HeReservoirEvaporation(result['3He flow'], parameters['3He inlet pressure'], parameters['He reservoir inlet temperature'], \
parameters['Isopure He flow'], parameters['Isopure He pressure'], parameters['20K shield temperature'], \
parameters['He reservoir static load'], parameters['He reservoir pressure'])
result['He consumption'] = (
result['He reservoir flow'] + result['1K pot flow']) / hepak.HeCalc(
'D', 0, 'P', 1013e2, 'SL', 0., 1) * 1000 * 3600
result['20K shield flow'], result['100K shield flow'] = shieldFlow(parameters['20K shield temperature'], parameters['100K shield temperature'], result['He reservoir temperature'] + 0.1, \
parameters['20K shield temperature'], parameters['Isopure He flow'], parameters['Isopure He pressure'])
result['Shield consumption'] = max(
result['20K shield flow'], result['100K shield flow']) / hepak.HeCalc(
'D', 0, 'P', 1013e2, 'SL', 0., 1) * 1000 * 3600
result['T_3He'] = He3Temperature(result['3He flow'],
parameters['3He pressure drop'])
heatLoad = parameters['Beam heating'] + parameters[
'Isopure static heat'] + HeCoolingLoad(
parameters['Isopure He flow'], parameters['Isopure He pressure'],
result['1K pot temperature'], result['T_HeII_low'])
result['T_HEX1_low'] = HEX1TemperatureLow(result['T_3He'],
parameters['HEX1 length'],
parameters['Channel diameter'],
parameters['HEX1 surface'],
heatLoad)
result['T_HEX1_high'] = HEX1TemperatureHigh(result['T_HEX1_low'],
parameters['HEX1 length'],
heatLoad)
result['HeII vapor pressure'] = 0.
result['HeII pressure head'] = 0.
result['T_HeII_high'] = result['T_HeII_low'], result['T_HeII_low']
if parameters['Beam heating'] > 0. and result[
'T_HeII_low'] > hepak.HeConst(3):
result['HeII vapor pressure'] = hepak.HeCalc('P', 0, 'T',
result['T_HeII_low'],
'SL', 0., 1)
result['HeII pressure head'] = hepak.HeCalc(
'D', 0, 'T', result['T_HeII_low'], 'SL', 0.,
1) * 9.81 * parameters['HeII overfill']
result['T_HeII_high'] = HeIItemperatureHigh(
parameters['Channel length'], result['T_HeII_low'],
result['HeII vapor pressure'] + result['HeII pressure head'],
parameters['Beam heating'], parameters['Channel diameter'])
return result
