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radiative_loads.py
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radiative_loads.py
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#!/usr/bin/env python
# encoding: utf-8
"""
mli_conductivity.py
Created by Zigmund Kermish on 2014-01-20. Heavily copy/pasted from Jon Gudmundsson's Matlab code, which was based
on Bill Jones' IDL code
"""
import sys
import os
import areas
import numpy as np
import mli_keller
#Stefan-Boltzmann constant
sigma = 5.6704E-12 #[J/s*cm^2*K^4]
def toy_filter_load(T_SFT, T_MT, T_VCS1, T_VCS2, T_Shell, config='TNG', insNum = 1.0):
if config == 'TNG':
# filter diameter taken from Galitzki's thesis
d_filter_VCS2 = 4.5 * 2.54 # cm
d_filter_VCS1 = 4.5 * 2.54 # cm
d_filter_MT = 4.125 * 2.54 # cm
effi_filter_VCS2 = 0.9
effi_filter_VCS1 = 0.9
effi_filter_MT = 0.9
window_VCS2 = sigma*(1-effi_filter_VCS2)*(np.pi*d_filter_VCS2**2/4)*(T_Shell**4-T_VCS2**4)
window_VCS1 = sigma*(1-effi_filter_VCS1)*(np.pi*d_filter_VCS1**2/4)*(T_VCS2**4-T_VCS1**4)
window_MT = sigma*(1-effi_filter_MT)*(np.pi*d_filter_MT**2/4)*(T_VCS1**4-T_MT**4)
return window_MT, window_VCS1, window_VCS2
def mli_rad_keller(T_SFT, T_MT, T_VCS1, T_VCS2, T_Shell,
p_ins1=1e-3, p_ins2=1e-3, e_Al=0.15, alpha=0.15, beta=4.0e-3, config='theo', insNum = 6.0
):
'''returns the radiative loads INCLUDING all conductive and gas effects in MLI.
MLI is only used on VCS1 and VCS2 as gas loading would dmake MT MLI ineffective'''
SFT_Area, MT_Area, VCS1_Area, VCS2_Area = areas.load_areas(config=config, insNum = insNum)
if config == 'TNG':
# number of layers, from Galitzki thesis
N1 = 15
N2 = 25
NMT = 5
# layers per cm
N1_s = 20
N2_s = 20
NMT_s = 5
Rad_VCS1 = VCS1_Area*1e-4* mli_keller.P_tot(p_ins1, N1, N1_s, T_VCS2, T_VCS1, e_r = e_Al)
Rad_VCS2 = VCS2_Area*1e-4* mli_keller.P_tot(p_ins2, N2, N2_s, T_Shell, T_VCS2, e_r = e_Al)
Rad_SFTtoMT = sigma*e_Al*(SFT_Area)*(T_MT**4-T_SFT**4)
RadSFTtoVCS1 = 0.
# for main tank, keller might no longer be accurate because:
# 1. temp is lower then the lowest in keller
# 2. conduction is dominating at lower temp thus we can use dense MLI
# 3. keller did not test with wide gap MLI
p_mt = 1e-6 #low pressure due to cryogenics pumping at He temp
Rad_MT = MT_Area*1e-4* mli_keller.P_tot(p_mt, NMT, NMT_s, T_VCS1, T_MT, e_r = e_Al)
# Rad_MT = sigma*MT_Area*(T_VCS1**4-T_MT**4)/sum(1./effectEmiss(np.hstack((e_Al*0.8,
# MLIEmiss(T_MT,T_VCS1,NMT,alpha,beta), e_Al*0.9))))
else:
#Thickness of mli sheets
t1 = 2.00 #[cm]
t2 = 3.81 #[cm]
#number of layers
N1 = 16
N2 = 52
N1_s = N1 / t1
N2_s = N2 / t2
Rad_VCS1 = VCS1_Area*1e-4*mli_keller.P_tot(p_ins1, N1, N1_s, T_VCS2, T_VCS1, e_r = e_Al)
Rad_VCS2 = VCS2_Area*1e-4*mli_keller.P_tot(p_ins2, N2, N2_s, T_Shell, T_VCS2, e_r = e_Al)
Rad_SFTtoMT = sigma*e_Al*(SFT_Area/2)*(T_MT**4-T_SFT**4)
RadSFTtoVCS1 = sigma*e_Al*(SFT_Area/2)*(T_VCS1**4-T_SFT**4)
Rad_MT = sigma*MT_Area*(T_VCS1**4-T_MT**4)/sum(1./effectEmiss(np.hstack((e_Al*0.8,
MLIEmiss(T_MT,T_VCS1,0,alpha,beta), e_Al*0.9))))
return Rad_SFTtoMT, RadSFTtoVCS1, Rad_MT, Rad_VCS1, Rad_VCS2
def mli_cond(T_VCS1,T_VCS2,T_Shell,Lambda = 1.0e-6, config='theo', insNum = 6.0):
'''Temperatures in Kelvin
Lambda is the effective MLI conductivity, given in microWatts/cm/K
'''
SFT_Area, MT_Area, VCS1_Area, VCS2_Area = areas.load_areas(config=config, insNum = insNum)
#Thickness of mli sheets
t1 = 2.00 #[cm]
t2 = 3.81 #[cm]
lambda1 = 0.8*Lambda
lambda2 = 1.2*Lambda
mli_load_VCS1 = lambda1 * ( VCS1_Area / t1 ) * (T_VCS2-T_VCS1)
mli_load_VCS2 = lambda2 * ( VCS2_Area / t2 ) * (T_Shell-T_VCS2)
return mli_load_VCS1, mli_load_VCS2
def effectEmiss(eVector):
L = len(eVector)
if L < 2:
print('emissivty vector input does not have enough elements')
exit()
eV1 = eVector[0:L-1]
eV2 = eVector[1:L]
EffEmm = (eV1*eV2)/(eV1+eV2-eV1*eV2)
return EffEmm
def MLIEmiss(Tc, Th, N, alpha, beta):
'''Assume a linear dependence of MLI layers on temperature and
calculate array of emissivities with temperature dependence'''
if N == 0:
emissivities = np.array([])
else:
if Tc != Th:
T = np.linspace(Tc, Th, N)
emissivities = alpha + beta*T**0.5
elif Tc == Th and N == 1:
emissivities = alpha+beta*Tc**0.5
else:
emissivities = 0
return emissivities
def rad_load(T_SFT, T_MT, T_VCS1,T_VCS2,T_Shell, e_Al=0.15, alpha=0.15, beta=4.0e-3, config = 'theo', insNum = 6.0):
if config == 'TNG':
N1 = 0 #MLI layers around SFT
N2 = 5
N3 = 15
N4 = 25
SFT_Area, MT_Area, VCS1_Area, VCS2_Area = areas.load_areas(config=config, insNum = insNum)
#Radiative heat fluxess
Rad_SFTtoMT = sigma*e_Al*SFT_Area*(T_MT**4-T_SFT**4)
RadSFTtoVCS1 = 0.
Rad_MT = sigma*MT_Area*(T_VCS1**4-T_MT**4)/sum(1./effectEmiss(np.hstack((e_Al*0.8,
MLIEmiss(T_MT,T_VCS1,N2,alpha,beta), e_Al*0.9))))
Rad_VCS1 = sigma*VCS1_Area*(T_VCS2**4-T_VCS1**4)/sum(1./effectEmiss(np.hstack((e_Al*0.9,
MLIEmiss(T_VCS1,T_VCS2,N3,alpha,beta), e_Al))))
Rad_VCS2 = sigma*VCS2_Area*(T_Shell**4-T_VCS2**4)/sum(1./effectEmiss(np.hstack((e_Al,
MLIEmiss(T_VCS2,T_Shell,N4,alpha,beta), e_Al*1.1))))
else:
N1 = 2 #MLI layers around SFT
N2 = 0
N3 = 16
N4 = 52
SFT_Area, MT_Area, VCS1_Area, VCS2_Area = areas.load_areas(config=config, insNum = insNum)
#Radiative heat fluxess
if config == 'lloro':
RadSFTtoVCS1 = sigma*SFT_Area/2*(T_VCS1**4-T_SFT**4)/sum(1./effectEmiss(np.hstack((e_Al,
MLIEmiss(T_SFT,T_VCS1,N1,alpha,beta), e_Al))))
Rad_SFTtoMT = sigma*SFT_Area/2*(T_MT**4-T_SFT**4)/sum(1./effectEmiss(np.hstack((e_Al,
MLIEmiss(T_SFT,T_MT,N1,alpha,beta), e_Al))))
else:
Rad_SFTtoMT = sigma*e_Al*SFT_Area/2*(T_MT**4-T_SFT**4)
RadSFTtoVCS1 = sigma*e_Al*SFT_Area/2*(T_VCS1**4-T_SFT**4)
Rad_MT = sigma*MT_Area*(T_VCS1**4-T_MT**4)/sum(1./effectEmiss(np.hstack((e_Al*0.8,
MLIEmiss(T_MT,T_VCS1,N2,alpha,beta), e_Al*0.9))))
Rad_VCS1 = sigma*VCS1_Area*(T_VCS2**4-T_VCS1**4)/sum(1./effectEmiss(np.hstack((e_Al*0.9,
MLIEmiss(T_VCS1,T_VCS2,N3,alpha,beta), e_Al))))
Rad_VCS2 = sigma*VCS2_Area*(T_Shell**4-T_VCS2**4)/sum(1./effectEmiss(np.hstack((e_Al,
MLIEmiss(T_VCS2,T_Shell,N4,alpha,beta), e_Al*1.1))))
return Rad_SFTtoMT, RadSFTtoVCS1, Rad_MT, Rad_VCS1, Rad_VCS2
def main():
mli_load_VCS1, mli_load_VCS2 = mli_cond(49.17, 170.31, 300)
print('VCS1: %s W' % mli_load_VCS1)
print('VCS2: %s W' % mli_load_VCS2)
Rad_SFTtoMT, RadSFTtoVCS1, Rad_MT, Rad_VCS1, Rad_VCS2 = rad_load(T_SFT ,T_MT , T_VCS1 , T_VCS2, T_Shell,
e_Al, alpha,beta)
Rad_SFT = Rad_SFTtoMT+RadSFTtoVCS1
if __name__ == '__main__':
main()