def x_iterate(t, xguess=X0, Tguess=400, eps=0.02):
"""Iterate to find x(t) and T(t)
Inputs:
t: time in s
xguess: where to start x at
Tguess: where to start T at (K)
eps: fractionally, how close to get
[Default: 0.02]
Outputs:
x: quality
T: Temperature (K)
"""
# Q_DOT is given as constant; the integral is trivial
Q_decay = Q_DOT * t
u_target = u0 + Q_decay / M0
Tmin = int(liquid0.T)
Tmax = Tmin + 200
for Tguess in range(Tmin, Tmax, 5):
#print("\n\n\nTguess:", Tguess)
xguess = 0.5
last_x = 10 * xguess
last_u = 0.0
c = 0
converged = True
overflooded = False
while abs(xguess - last_x) / xguess > eps or abs(
u_target - last_u) / u_target > eps:
last_x = xguess
liquid1 = steam(T=Tguess, x=0)
vapor1 = steam(T=Tguess, x=1)
u_fg = vapor1.u - liquid1.u
v_fg = vapor1.v - liquid1.v
v1 = liquid1.v + v_fg * xguess
# Revise the x guess based on specific volume
xguess = (v0 - liquid1.v) / v_fg
#print("xguess = {:.4e}".format(xguess))
last_u = liquid1.u + u_fg * xguess
c += 1
if c > 10:
converged = False
break
if converged or v1 > v0 or v1 == 0:
if converged:
print("Converged")
if v1 > v0:
overflooded = True
print("Overflooded at t = {:.3} hours!".format(t / 3600))
break
return v1, overflooded
def FW_main(A2, B, B2, Mi, Me):
if (A2):
Me.h = Mi.h + (B.m * (B.h - B2.h) + A2.m * (A2.h - B2.h)) / Mi.m
else:
Me.h = Mi.h + B.m * (B.h - B2.h) / Mi.m
Me.P = Mi.P
Me.T = steam(P=Me.P, h=Me.h).T
Me.s = steam(P=Me.P, h=Me.h).s
def Reheat(Mi, Me, temp):
Me.T = temp
Me.P = Mi.P
Me.m = Mi.m
Me.h = steam(T=Me.T, P=Me.P).h
Me.s = steam(T=Me.T, P=Me.P).s
Q = Me.m * (Me.h - Mi.h)
return Q
def Pump(Mi, Me, efficiency):
Me.m = Mi.m
ses = Mi.s
hes = steam(s=ses, P=Me.P).h
Me.h = (hes - Mi.h) / efficiency + Mi.h
Me.T = steam(P=Me.P, h=Me.h).T
Me.s = steam(P=Me.P, h=Me.h).s
Power = Me.m * (Me.h - Mi.h)
return Power
def Deaerator(A2, B, Mi, Me, deaerationCondensate):
if (A2):
Me.m = A2.m + B.m + Mi.m
Me.h = (Mi.h * Mi.m + A2.h * A2.m + B.h * B.m) / Me.m
else:
Me.m = B.m + Mi.m
Me.h = (Mi.h * Mi.m + B.h * B.m) / Me.m
Me.P = deaerationCondensate.condPressure
Me.T = deaerationCondensate.T = steam(P=Me.P, h=Me.h).T
Me.s = deaerationCondensate.s = steam(P=Me.P, h=Me.h).s
deaerationCondensate.h = steam(P=Me.P, h=Me.h).h
def Condenser(F2, Mi, Me):
if (F2):
mMF = Me.m = Mi.m + F2.m
hMF = (Mi.m * Mi.h + F2.m * F2.h) / mMF
else:
mMF = Me.m = Mi.m
hMF = Mi.h
Me.P = Mi.P
Me.h = steam(P=Me.P, x=0).h
Me.s = steam(P=Me.P, x=0).s
Me.T = steam(P=Me.P, x=0).T
Q = mMF * (hMF - Me.h)
return Q
def iterate(p_air2=0, tguess=1000.0, xguess=0.1, T2=liquid_in.T):
# Initialize some guesses before iterating
last_t = 1200
#v2 = V_WATER0/mguess
V_gas2 = V_VAPOR0
while abs(tguess - last_t) / last_t > EPS:
last_t = tguess
mflow = MDOT * last_t
mguess = M0 + mflow
if p_air2:
# Partial pressure of air at T2
p_air2 = T2 * M_AIR * R_AIR / V_gas2 * 1E-6 # MPa
psat = P_BURST - p_air2 # MPa
de_air = M_AIR * CV_AIR * (T2 - T_AIR0) * 1E-3 # kJ
else:
psat = P_BURST
de_air = 0
liquid2 = steam(P=psat, x=0)
vapor2 = steam(P=psat, x=1)
T2 = liquid2.T # K
vmix2 = lambda x: liquid2.v * (1 - x) + vapor2.v * x
umix2 = lambda x: liquid2.u * (1 - x) + vapor2.u * x
u_fg = vapor2.u - liquid2.u # kJ/kg
# Control volume
xguess = (V_TOTAL / mguess - liquid2.v) / (vapor2.v - liquid2.v)
# Conservation of energy
u2 = umix2(xguess)
mflow = (U0 - de_air - M0 * u2) / (u2 - liquid_in.u)
# This calculation is unstable. Underrelax it!
# (I'd like to thank Sterling for telling me to try this)
tguess = Y * mflow / MDOT + (1 - Y) * tguess
return mguess, xguess, tguess
def CycleHP(load,massFlow):
#--------------------------------------------------------------------------
# Initial Design Conditions
#--------------------------------------------------------------------------
#load = 1.0 # load as percentage of designed mass flow
#massFlow = 450 # mass flow rate at 100% load (kg/s)
mainTemp = 585 + 273 # temperature at inlet of HP turbine (K)
reheatTemp = 585 + 273 # temperature at inlet of IP turbine (K)
highPressure = 19 # pressure at inlet of HP turbine (MPa)
intPressure = 2 # pressure at inlet of IP turbine (MPa)
lowPressure = 0.8 # pressure at inlet of LP turbine (MPa)
condPressure = 0.01 # pressure at inlet of condensor (MPa)
pE_A = 10/100 # percent of mass flow extracted at A
pE_B = 10/100 # percent of mass flow extracted at B
pE_C = 5/100 # percent of mass flow extracted at C
#pE_D = 000 # percent of mass flow extracted at D
#pE_E = 000 # percent of mass flow extracted at E
#pE_F = 000 # percent of mass flow extracted at F
TTD = 5/1.8 # terminal temperature difference (K)
DCA = 10/1.8 # drain cooler approach (K)
deaeratorInletPressure = 0.2
#--------------------------------------------------------------------------
# Power Cycle
#--------------------------------------------------------------------------
# set inital state at the high pressure turbine inlet
M1 = state()
M1.T = mainTemp
M1.P = highPressure
M1.m = massFlow * load
M1.h = steam(T=M1.T, P=M1.P).h
M1.s = steam(T=M1.T, P=M1.P).s
# set deaeration conditions for determining extraction flows
deaerationConditions = components.preheatConditions()
deaerationConditions.condPressure = condPressure
deaerationConditions.P = deaeratorInletPressure
deaerationConditions.T = steam(P=deaerationConditions.P,x=0).T
deaerationConditions.h = steam(P=deaerationConditions.P,x=0).h
deaerationConditions.s = steam(P=deaerationConditions.P,x=0).s
deaerationConditions.TTD = TTD
deaerationConditions.DCA = DCA
deaeratorCondensate = components.preheatConditions()
deaeratorCondensate.condPressure = 0.02
deaeratorCondensate.P = M1.P
deaeratorCondensate.TTD = -5/1.8
deaeratorCondensate.DCA = 10/1.8
# high pressure turbine states and function
M2 = state()
A = state()
PR_HP = intPressure / M1.P # pressure ratio of the high pressure turbine
PowerHP = components.Turbine(M1,M2,A,None,None,pE_A,None,None,None,PR_HP,load)
deaeratorCondensate.T = steam(P=A.P,x=0).T
# reheat after high pressure turbine
M3 = state()
Qin_reheat = components.Reheat(M2, M3, reheatTemp)
# intermediate pressure turbine states and function
M4 = state()
B = state()
C = state()
PR_IP = lowPressure / M3.P # pressure ratio of the intermediate pressure turbine
PowerIP = components.Turbine(M3,M4,B,C,None,pE_B,pE_C,None,None,PR_IP,load)
# low pressure turbine states and function
M5 = state()
D = state()
E = state()
F = state()
PR_LP = condPressure / M4.P # pressure ratio of the low pressure turbine
PowerLP = components.Turbine(M4,M5,D,E,F,None,None,None,deaerationConditions,PR_LP,load)
# extracted steam through closed feedwater heaters
A2 = state()
B2 = state()
D2 = state()
E2 = state()
F2 = state()
components.FW_extracted(A,A2,B,B2,None,None,deaeratorCondensate)
components.FW_extracted(D,D2,E,E2,F,F2,deaerationConditions)
# [main + extracted steam from LP] though condenser
M6 = state()
Qout = components.Condenser(F2, M5, M6)
M7 = state()
M7.P = deaerationConditions.P
PowerPump1 = components.Pump(M6, M7, 0.85)
# feedwater heaters for LP section
M8 = state()
M9 = state()
M10 = state()
M10.m = M9.m = M8.m = M7.m
components.FW_main(E2,F,F2,M7,M8)
components.FW_main(D2,E,E2,M8,M9)
components.FW_main(None,D,D2,M9,M10)
# deaerator combining extracted steam at C,
# combined feedwater from HP & IP, and main steam
M11 = state()
components.Deaerator(B2,C,M10,M11,deaeratorCondensate)
# pump 2 to reach high pressure for the HP turbine
M12 = state()
M12.P = M1.P
PowerPump2 = components.Pump(M11, M12, 0.85)
# feedwater heating from HP and IP turbines
M14 = state()
M13 = state()
M13.m=M14.m = M12.m
components.FW_main(A2,B,B2,M12,M13)
components.FW_main(None,A,A2,M13,M14)
# heat in from the steam generator
Qin_main = components.SteamGenerator(M14, M1, 0.95)
# efficiency calculations
Power = PowerHP+PowerIP+PowerLP-PowerPump1-PowerPump2
Qin = Qin_reheat + Qin_main
nth = Power/Qin
nc = 1 - M6.T / M1.T
return PowerHP/1000
def Turbine(Mi, Me, A, B, C, pE_A, pE_B, pE_C, preheatConditions, PR, load):
efficiency = (0.86 - 0.72) / (1.0 - 0.6) * load + 0.51
# find exit properties
ses = Mi.s # isentropic exit entropy (kJ/kg/K)
Me.P = Mi.P * PR
# set rest of state with steam tables
hes = steam(P=Me.P, s=ses).h
Me.h = Mi.h - efficiency * (Mi.h - hes)
Me.T = steam(h=Me.h, P=Me.P).T
Me.s = steam(h=Me.h, P=Me.P).s
numExtract = 0
if (A):
numExtract += 1
if (B):
numExtract += 1
if (C):
numExtract += 1
if (preheatConditions):
if (numExtract == 3):
P0 = preheatConditions.condPressure
h0 = steam(P=P0, x=0).h
s0 = steam(P=P0, x=0).s
m2 = m3 = Mi.m
P1 = P2 = P3 = preheatConditions.P
s1s = s0
h1s = steam(s=s1s, P=P1).h
h1 = (h1s - h0) / preheatConditions.pumpEfficiency + h0
T1 = steam(P=P1, h=h1).T
T4 = preheatConditions.T
h4 = preheatConditions.h
T2 = 1 * (T4 - T1) / 3 + T1
T3 = 2 * (T4 - T1) / 3 + T1
h2 = steam(T=T2, P=P2).h
h3 = steam(T=T3, P=P3).h
A.P = PA2 = steam(T=(T4 + preheatConditions.TTD), x=0).P
TA2 = T3 + preheatConditions.DCA
hA2 = steam(T=TA2, P=PA2).h
hAs = steam(P=A.P, s=ses).h
A.h = Mi.h - efficiency * (Mi.h - hAs)
A.T = steam(P=A.P, h=A.h).T
A.s = steam(P=A.P, h=A.h).s
A.m = mA2 = m3 * (h4 - h3) / (A.h - hA2)
B.P = PB2 = steam(T=(T3 + preheatConditions.TTD), x=0).P
TB2 = T2 + preheatConditions.DCA
hB2 = steam(T=TB2, P=PB2).h
hBs = steam(P=B.P, s=ses).h
B.h = Mi.h - efficiency * (Mi.h - hBs)
B.T = steam(P=B.P, h=B.h).T
B.s = steam(P=B.P, h=B.h).s
B.m = (m2 * (h3 - h2) - mA2 * (hA2 - hB2)) / (B.h - hB2)
mB2 = B.m + mA2
C.P = PC2 = steam(T=(T2 + preheatConditions.TTD), x=0).P
TC2 = T1 + preheatConditions.DCA
hC2 = steam(T=TC2, P=PC2).h
hCs = steam(P=C.P, s=ses).h
C.h = Mi.h - efficiency * (Mi.h - hCs)
C.T = steam(P=C.P, h=C.h).T
C.s = steam(P=C.P, h=C.h).s
C.m = (m2 * (h2 - h1) - mB2 * (hB2 - hC2)) / (C.h - hC2)
Me.m = Mi.m - A.m - B.m - C.m
Power = Mi.m * (Mi.h - A.h) + (Mi.m - A.m) * (A.h - B.h) + (
Mi.m - A.m - B.m) * (B.h - Me.h)
else:
print("ERROR: Turbine()")
else:
if (numExtract == 1):
A.P = Me.P
A.h = Me.h
A.T = Me.T
A.s = Me.s
A.m = Mi.m * pE_A
Me.m = Mi.m - A.m
Power = Mi.m * (Mi.h - Me.h)
elif (numExtract == 2):
TH = steam(P=Mi.P, x=1).T
TL = steam(P=Me.P, x=1).T
TA = (TH - TL) / (numExtract) + TL
A.P = steam(T=TA, x=1).P
hAs = steam(P=A.P, s=ses).h
A.h = Mi.h - efficiency * (Mi.h - hAs)
A.T = steam(P=A.P, h=A.h).T
A.s = steam(P=A.P, h=A.h).s
A.m = Mi.m * pE_A
B.P = Me.P
B.h = Me.h
B.T = Me.T
B.s = Me.s
B.m = Mi.m * pE_B
Me.m = Mi.m - A.m - B.m
Power = Mi.m * (Mi.h - A.h) + (Mi.m - A.m) * (A.h - Me.h)
elif (numExtract == 3):
TH = steam(P=Mi.P, x=1).T
TL = steam(P=Me.P, x=1).T
TA = 2 * (TH - TL) / (numExtract) + TL
A.P = steam(T=TA, x=1).P
hAs = steam(P=A.P, s=ses).h
A.h = Mi.h - efficiency * (Mi.h - hAs)
A.T = steam(P=A.P, h=A.h).T
A.s = steam(P=A.P, h=A.h).s
A.m = Mi.m * pE_A
TB = (TH - TL) / (numExtract) + TL
B.P = steam(T=TB, x=1).P
hBs = steam(P=B.P, s=ses).h
B.h = Mi.h - efficiency * (Mi.h - hBs)
B.T = steam(P=B.P, h=B.h).T
B.s = steam(P=B.P, h=B.h).s
B.m = Mi.m * pE_B
C.P = Me.P
C.h = Me.h
C.T = Me.T
C.s = Me.s
C.m = Mi.m * pE_C
Me.m = Mi.m - A.m - B.m - C.m
Power = Mi.m * (Mi.h - A.h) + (Mi.m - A.m) * (A.h - B.h) + (
Mi.m - A.m - B.m) * (B.h - Me.h)
else:
Me.m = Mi.m
Power = Mi.m * (Mi.h - Me.h)
return Power
def x(temp):
vf = steam(T=temp, x=0).v
vg = steam(T=temp, x=1).v
return (VOL - vf) / (vg - vf)
V_TOT = 2500 # m^3
M_TOT = 2.12E6 # kg
VOL = V_TOT / M_TOT # specific volume
T0 = 373 # K
def x(temp):
vf = steam(T=temp, x=0).v
vg = steam(T=temp, x=1).v
return (VOL - vf) / (vg - vf)
temperatures = linspace(T0, T0 + 110)
qualities = array([x(ti) for ti in temperatures])
for i, q in enumerate(qualities):
if q == max(qualities):
break
txmax = temperatures[i]
plot(temperatures, qualities, label="X")
plot([temperatures.min(), temperatures.max()], [q, q], 'gray')
plot([txmax, txmax], [qualities.min(), qualities.max()], 'gray')
text(txmax,
1.05 * q,
"$X_{max} = $" + "{:.3e}".format(q) + " @ {:.4} K".format(txmax),
ha="center")
vmin = steam(T=txmax, x=0).v * M_TOT * (1 - q)
print("Minimum water volume: {:.5} m^3".format(vmin))
grid()
legend()
show()
R_VESSEL = 6.5 # m AXS_VESSEL = math.pi * R_VESSEL**2 # m^2; cross-sectional area of vessel ZCORE = 2.0 # m ZCYL = 14.5 # m ZSTEAM0 = 2.17 # m Z_ABOVE = ZCYL - ZSTEAM0 - ZCORE # m V_STEAM0 = AXS_VESSEL * ZSTEAM0 # m^3; volume of the initial steam V_BELOW = math.pi * 2 / 3 * R_VESSEL**3 # m^3; volume below core V_ZCORE = AXS_VESSEL * ZCORE # m^3; volume around core V_ABOVE = AXS_VESSEL * Z_ABOVE # m^3; volume above core V_LIQUID0 = V_BELOW + V_ZCORE + V_ABOVE # m^3; volume if the initial liquid water V_VESSEL = V_LIQUID0 + V_STEAM0 # m^3; entire pressure vessel volume # Thermal hydraulic parameters P0 = 0.10135 # MPa liquid0 = steam(P=P0, x=0) vapor0 = steam(P=P0, x=1) M_LIQUID0 = V_LIQUID0 / liquid0.v M_VAPOR0 = V_STEAM0 / vapor0.v M0 = M_LIQUID0 + M_VAPOR0 X0 = M_VAPOR0 / M0 U0 = M_LIQUID0 + liquid0.u + M_VAPOR0 * vapor0.u u0 = liquid0.u * (1 - X0) + vapor0.u * X0 v0 = V_VESSEL / M0 """ Unknowns: 1. T2 or P2 at one week 2. X2 at one week 3. U, V at one week Equations:
#pE_F = 000 # percent of mass flow extracted at F TTD = 5 / 1.8 # terminal temperature difference (K) DCA = 10 / 1.8 # drain cooler approach (K) deaeratorInletPressure = 0.2 # ----------------------------------------------------------------------------- # Power Cycle # ----------------------------------------------------------------------------- # set inital state at the high pressure turbine inlet M1 = state() M1.T = mainTemp M1.P = highPressure M1.m = massFlow * load M1.h = steam(T=M1.T, P=M1.P).h M1.s = steam(T=M1.T, P=M1.P).s # set deaeration conditions for determining extraction flows deaerationConditions = components.preheatConditions() deaerationConditions.condPressure = condPressure deaerationConditions.P = deaeratorInletPressure deaerationConditions.T = steam(P=deaerationConditions.P, x=0).T deaerationConditions.h = steam(P=deaerationConditions.P, x=0).h deaerationConditions.s = steam(P=deaerationConditions.P, x=0).s deaerationConditions.TTD = TTD deaerationConditions.DCA = DCA deaeratorCondensate = components.preheatConditions() deaeratorCondensate.condPressure = 0.02 deaeratorCondensate.P = M1.P
# Constants
V_C = 50970 # m^3
R_AIR = 286 # J/kg-K
M_AIR = 5.9E4 # kg
CV_AIR = 719 # J/kg-K
EPS = 0.02
# Starting conditions from Example 7.1
P0 = 0.523 # MPa
Pa0 = 0.137 # MPa
T0 = 415.6 # Kelvins
X0 = 0.505
m_pw = 2.1E5 # kg
m_pg = 2.11E5 # kg
mp = m_pw + m_pg
sat_liquid0 = steam(T=T0, x=0)
sat_vapor0 = steam(T=T0, x=1)
st0 = steam(T=T0, x=X0)
V_vapor0 = m_pg * sat_vapor0.v
e_p0 = m_pw * sat_liquid0.u + m_pg * sat_vapor0.u
#print("Partial pressure of st0 =", st0.P)
# Saturated liquid released from the secondary system
PS = 6.89 # MPa
VS = 89 # m^3
sts = steam(P=PS, x=0)
print("Temperature of the secondary coolant at break: {:.4} K".format(sts.T))
ms = VS / sts.v
e_s0 = ms * sts.u
#print("Mass of secondary coolant released at {:.4} K: {:.4} kg".format(sts.T, ms))
m_w = ms + mp # Total mass of coolant (primary + secondary)
from iapws import IAPWS97 as steam # Constants EPS = 0.02 # How close to converge Y = 0.2 # Underrelaxation factor # Given parameters: # Tank itself P_TANK0 = 3 # MPa P_BURST = 10 # MPa P_SAT0 = 15.4 # MPa V_TOTAL = 12 # m^3 V_WATER0 = 2 # m^3 V_VAPOR0 = V_TOTAL - V_WATER0 # m^3 # Water in tank water0 = steam(P=P_TANK0, x=0) vapor0 = steam(P=P_TANK0, x=1) M_l0 = V_WATER0 / water0.v # kg M_v0 = V_VAPOR0 / vapor0.v # kg M0 = M_v0 + M_l0 # kg X0 = M_v0 / (M_l0 + M_v0) U0 = M_l0 * water0.u + M_v0 * vapor0.u # kJ # Flow in MDOT = 3 # kg/s liquid_in = steam(P=P_SAT0, x=0) # Air in tank (for part C only) M_AIR = 11.93 # kg R_AIR = 268 # J/kg-K CV_AIR = 719 # J/kg-K V_AIR0 = V_VAPOR0 T_AIR0 = vapor0.T
def FW_extracted(A, A2, B, B2, C, C2, preheatConditions):
numExtract = 0
if (A):
numExtract += 1
if (B):
numExtract += 1
if (C):
numExtract += 1
if (preheatConditions):
P0 = preheatConditions.condPressure
h0 = steam(P=P0, x=0).h
s0 = steam(P=P0, x=0).s
P1 = preheatConditions.P
s1s = s0
h1s = steam(s=s1s, P=P1).h
h1 = (h1s - h0) / preheatConditions.pumpEfficiency + h0
T1 = steam(P=P1, h=h1).T
if (numExtract == 1):
T2 = preheatConditions.T
A2.P = steam(T=(T2 + preheatConditions.TTD), x=0).P
A2.T = T1 + preheatConditions.DCA
A2.h = steam(T=A2.T, P=A2.P).h
A2.s = steam(T=A2.T, P=A2.P).s
A2.m = A.m
elif (numExtract == 2):
T3 = preheatConditions.T
T2 = (T3 - T1) / 2 + T1
A2.P = steam(T=(T3 + preheatConditions.TTD), x=0).P
A2.T = T2 + preheatConditions.DCA
A2.h = steam(T=A2.T, P=A2.P).h
A2.s = steam(T=A2.T, P=A2.P).s
A2.m = A.m
B2.P = steam(T=(T2 + preheatConditions.TTD), x=0).P
B2.T = T1 + preheatConditions.DCA
B2.h = steam(T=B2.T, P=B2.P).h
B2.s = steam(T=B2.T, P=B2.P).s
B2.m = B.m + A2.m
elif (numExtract == 3):
T4 = preheatConditions.T
T2 = 1 * (T4 - T1) / 3 + T1
T3 = 2 * (T4 - T1) / 3 + T1
A2.P = steam(T=(T4 + preheatConditions.TTD), x=0).P
A2.T = T3 + preheatConditions.DCA
A2.h = steam(T=A2.T, P=A2.P).h
A2.s = steam(T=A2.T, P=A2.P).s
A2.m = A.m
B2.P = steam(T=(T3 + preheatConditions.TTD), x=0).P
B2.T = T2 + preheatConditions.DCA
B2.h = steam(T=B2.T, P=B2.P).h
B2.s = steam(T=B2.T, P=B2.P).s
B2.m = B.m + A2.m
C2.P = steam(T=(T2 + preheatConditions.TTD), x=0).P
C2.T = T1 + preheatConditions.DCA
C2.h = steam(T=C2.T, P=C2.P).h
C2.s = steam(T=C2.T, P=C2.P).s
C2.m = C.m + B2.m
else:
print("ERROR: no preheat conditions")
from iapws import IAPWS97 as steam from scipy.optimize import fsolve # Fixed parameters P_MAX = 0.4 # MPa V_C = 5.05E4 # m^3 (containment volume) C0 = 273.15 # 0 degrees Celcius EPS = 0.005 # Get within 0.5% of the answer MAX_ITER = 100 # Prevent infinite loops # Initial conditions P0 = 0.1013 # MPa (containment pressure) T_c0 = 300 # K (containment temperature) P_p0 = 15.5 # MPa (primary coolant pressure) V_p0 = 500 # m^3 (primary coolant volume) st0 = steam(P=P_p0, x=0) # primary coolant, sat liquid mp = V_p0 / st0.v # Ice T_ice0 = 263 # K lf_ice = 333 # kJ/kg c_ice = 4.230 # kJ/kg-K c_water = 4.18 # kJ/kg-K liquid_ice = steam(T=T_c0, x=0) # Air R_AIR = 268 # J/kg-K CV_AIR = 719 # J/kg-K # PV = mRT --> m = PV/RT M_AIR = (P0 * 1E6 * V_C) / (R_AIR * T_c0) # kg MRV_AIR = M_AIR * R_AIR / (V_C - V_p0) * 1E-6 # MPa