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nitrogen_sys_calcs.py
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nitrogen_sys_calcs.py
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# This document contains 1-D calculations for the Refrigerator system using LN2.
import CoolProp
import CoolProp.CoolProp as CP
import numpy as np
from scipy.optimize import fixed_point
#Physical Parameters
D =.0254 #meter, Hydraulic diameter of 1.0" pipe/hose
epsilon_pipe = 0.0001 # meter, surface roughness of piping
epsilon_hose = 0.00635 # meter, referenced from Swagelok convoluted flex hoses
#Flow Parameters
m_dot = 0.400 # kg/second, NEEDS TO BE OPTIMIZED
T_operation = 90 # degree K, (-135 deg C)
X_max = 0.01 # Max allowable quality NEEDS TO BE VERIFIED BY EXPERIENCE OF DECAM
# Heat Loads
Q_camera = 540 # watt, total camera power consumption, including contingency for heaters
L_pipe = 80 # Meters of vacuum insulated hose
L_hose = 30 # Meters of vacuum insulated hose
loss_pipe = .452 # W/m, loss rate per unit length @ LN2 temps with 1.0" pipe. Ref: Technifab
loss_hose = .9 # W/m, estimate
Q_pipes = loss_pipe*L_pipe
Q_hose = loss_hose*L_hose
Q_valves = 25 # watt, Heat leak from valves throughout the system. Equal to value from DECAM
Q_pump = 150 # watt, 3X value from DECAM, assumes that we might need tripple the flow.
Q_net = Q_pipes + Q_hose + Q_camera + Q_pump + Q_valves
print "Q_net = ", '%.1f' % Q_net
# Compute the pressure drop from the maximum vertical rise in the system.
cam_height = 18.6 # meters, height difference from the utility room to the camera high spot
g = 9.81 # m/s^2, gravity
#Density of Nitrogen at 100K as a liquid.
rho = CP.Props('D','T', T_operation, 'Q', 0,"Nitrogen")
dP_head = rho*g*cam_height/1000 # kPa, static pressure head from util room to camera
print "Pressure drop from height of cam", dP_head
# Flow characeristics of system
A_flow = np.pi*D**2/4
# Mean velocity of flow in the system
U_mean = m_dot/(A_flow*rho) # m/s
#Dynamic viscosity of saturated LN2 @ T_op
mu = CP.Props('V','T', T_operation, 'Q', 0,"Nitrogen") # Pa-s
Re = rho*U_mean*D/mu
#Friction factor solver for internal flows
# Solving for friction factor for next Darcy Weisbach
def friction(Re,epsilon,diam):
from scipy.optimize import fixed_point
def friction_funct(friction, Re, epsilon, diam):
LHS = - 2.*np.log10(epsilon/(3.7*diam)+ 2.51/(Re*np.sqrt(friction)))
return 1/LHS**2
return fixed_point(friction_funct, 0.2, args=(Re,epsilon,diam))
# Solver for friction factor for arbitrary Reynolds number
def DarcyWeisbach(Re,epsilon,diam):
if Re < 2100:
friction_laminar = 64/Re
return friction_laminar
else:
return friction(Re,epsilon,diam)
friction_pipe = DarcyWeisbach(Re,epsilon_pipe,D)
friction_hose = DarcyWeisbach(Re,epsilon_hose,D)
print friction_pipe
dP_flow_pipe = friction_pipe*L_pipe/D*rho*U_mean**2/2
dP_flow_hose = friction_hose*L_hose/D*rho*U_mean**2/2
print"Pressure drop from pipes is %.f" % dP_flow_pipe, " Pa"
print"Pressure drop from hoses is %.f" % dP_flow_hose, " Pa"
dP_pump = dP_flow_pipe+dP_flow_hose
print "Total flow pressure drop is %.f" % dP_pump, " Pa"
delta_height = 7.9 #meter, change in ht of camera
dP_head = rho*g*delta_height/1000 # kPa, static pressure head from util room to camera
p_top= CP.Props('P','T', T_operation, 'Q', 0,"Nitrogen") # Pa-s
print "Operating pressure", p_top
dT_movement = CP.Props('T','P', p_top, 'Q', 0,"Nitrogen")-CP.Props('T','P', (p_top-dP_head), 'Q', 0,"Nitrogen") # Pa-s
print "dP movement", dP_head
print "Temperature shift from movement, degrees K", dT_movement