def residualsLiBr(T,P,x,deltaT=1e-4,deltaP=1e-4):
TT = [T, T, T + deltaT]
PP = [P, P + deltaP, P]
hh = [0,0,0]
vv = [0,0,0]
for i in range(3):
# TODO: make this a function
h_liquid = libr_props.massSpecificEnthalpy(T,x)
v_liquid = 1. / libr_props.massDensity(T,x) # m3/kg
x_liquid = libr_props.massFraction(T,P)
cp_liquid = libr_props.massSpecificHeat(T,x)
# Now let's figure out the other thing
Qu = 1. - x / x_liquid
Q_vapor = 1
h_vap = CP.PropsSI('H','T',T,'Q',Q_vapor,'Water')
v_vap = CP.PropsSI('D','T',T,'Q',Q_vapor,'Water')
cp_vap = CP.PropsSI('C','T',T,'Q',Q_vapor,'Water')
h = (1.0 - Qu) * h_liquid + Qu * h_vap
v = (1.0 - Qu) * v_liquid + Qu * v_vap
hh[i] = h
vv[i] = v
dhdp_T = (hh[1] - hh[0]) / deltaP
dvdT_p = (vv[2] - vv[0]) / deltaT
a = dhdp_T - (vv[0] - T * dvdT_p)
dhdT_p = (state3.h - state1.h) / deltaT
b = dhdT_p - cp
print(state1)
print(state2)
print(state3)
print("a = {}. b = {}".format(a,b))
return a,b
def updateSHX_hot_side(self):
DeltaT_max = self.T_gen_outlet - self.T_abs_outlet_max
DeltaT_SHX_concentrate = self.Eff_SHX * DeltaT_max
self.T_SHX_concentrate_outlet = self.T_gen_outlet \
- DeltaT_SHX_concentrate
self.h_SHX_concentrate_outlet = libr_props.massSpecificEnthalpy(
C2K(self.T_SHX_concentrate_outlet), self.x2)
self.Q_SHX = self.m_concentrate \
* (self.h_gen_outlet - self.h_SHX_concentrate_outlet)
def update(self, P, m_in, T_in, x_in, x_out):
self.P = P
self.m_in = m_in
self.T_in = T_in
self.x_in = x_in
self.x_out = x_out
# Find inlet enthalpy.
# Find saturation point at inlet concentration.
# Find ...
self.T_sat = K2C(libr_props.temperature(self.P * 1e-5, self.x_in))
self.T_out = K2C(libr_props.temperature(self.P * 1e-5, self.x_out))
self.h_sat = libr_props.massSpecificEnthalpy(C2K(self.T_sat), self.x_in)
self.h_out = libr_props.massSpecificEnthalpy(C2K(self.T_out),self.x_out)
self.cp_in = libr_props.massSpecificHeat(C2K(self.T_in),self.x_in)
# If h_in is an input:
if False:
preheat = (self.h_sat - self.h_in)/self.cp_in
self.T_in = self.T_sat - preheat
else:
preheat = self.T_sat - self.T_in
self.h_in = self.h_sat - preheat * self.cp_in
pwater.update(CP.PT_INPUTS, self.P, C2K(self.T_sat))
self.h_vapor_out = pwater.hmass() - h_w_ref
# Mass balance on LiBr
self.m_out = self.m_in * self.x_in / self.x_out
# Mass balance on Water
self.m_vapor_out = self.m_in - self.m_out
self.m_total = self.m_out
self.Q_preheat = self.m_in * (self.h_sat - self.h_in)
self.Q_desorb = self.m_out * self.h_out \
+ self.m_vapor_out * self.h_vapor_out \
- self.m_in * self.h_sat
# Determine a reasonable limit for extending the domain.
self.Tmax = K2C(libr_props.temperature(self.P*1e-5,libr_props.xmax))
def _qx(self,x_local):
T = K2C(libr_props.temperature(self.P*1e-5,x_local))
dx = self.x_in - x_local
# TODO
h_local = libr_props.massSpecificEnthalpy(C2K(T),x_local)
# And calculate
m_vapor = self.m_in * dx / x_local
m_out = self.m_in + m_vapor
# Heat is inbound.
result = -self.m_in * self.h_in - m_vapor * self.h_vapor_inlet \
+ m_out * h_local
return T,result
def _q_helper(self,T):
x_local = libr_props.massFraction(C2K(T),self.P * 1e-5)
# Could parametrize this by x, but libr_props.temperature also has an
# implicit solve. Only P(T,x) is explicit.
pwater.update(CP.PT_INPUTS, self.P, C2K(T))
h_vapor_local = pwater.hmass() - h_w_ref
h_solution_local = libr_props.massSpecificEnthalpy(C2K(T), x_local)
# Mass balance on LiBr
m_solution_local = self.m_in * self.x_in / x_local
hlv1 = h_vapor_local - h_solution_local
q1 = self.m_total * h_vapor_local - m_solution_local * hlv1
return q1
def _q(self,T):
"""Provide process heat canonical curve for generator in various forms.
Assumes that
* inlet solution state is obtained from self,
* generated vapor is flowing in reverse direction and
* it is everywhere in local equilibrium with solution.
Args
----
T : Temperature (deg C)
The local temperature
Returns
-------
q : Local progress index
Measured as cumulative heat flux (W).
Q : Total heat flux (W)
The total amount of heat transferred into the generator.
"""
hlv0 = self.h_vapor_out - self.h_sat
q0 = self.m_total * self.h_vapor_out - self.m_in * hlv0
if T < self.T_in:
raise "Generator outlet must be greater than pre-inlet temperature!"
elif T < self.T_sat:
# The state is either saturated or subcooled.
# Use linear interpolation.
q = self.m_in * self.cp_in * (T - self.T_in)
else:
x_local = libr_props.massFraction(C2K(T),self.P * 1e-5)
pwater.update(CP.PT_INPUTS, self.P, C2K(T))
h_vapor_local = pwater.hmass() - h_w_ref
h_solution_local = libr_props.massSpecificEnthalpy(C2K(T), x_local)
# Mass balance on LiBr
m_solution_local = self.m_in * self.x_in / x_local
hlv1 = h_vapor_local - h_solution_local
q1 = self.m_total * h_vapor_local - m_solution_local * hlv1
q = (q1 - q0) + self.Q_preheat
# TODO
# If q > Q (iff T > T_solution_outlet) then result is invalid.
return q
def generatorHeatCurveQ(self,T,x_out):
"""Provide process heat canonical curve for generator in various forms.
Assumes that
* inlet solution state is obtained from self,
* generated vapor is flowing in reverse direction and
* it is everywhere in local equilibrium with solution.
Args
----
T : Temperature (deg C)
The local temperature
x_out : Mass fraction (kg/kg)
The outlet solution LiBr mass fraction
Returns
-------
q : Local progress index
Measured as cumulative heat flux (W).
Q : Total heat flux (W)
The total amount of heat transferred into the generator.
"""
# We may need m_concentrate. It depends on Q -- solve from inlet.
h_solution_inlet = self.h_gen_inlet
h_vapor_outlet = self.h_gen_vapor_outlet
T_solution_outlet = K2C(libr_props.temperature(self.P_cond * 1e-5,
x_out))
h_solution_outlet = libr_props.massSpecificEnthalpy(
C2K(T_solution_outlet), x_out)
# Mass balance on LiBr
m_solution_outlet = self.m_pump * self.x1 / x_out
# Mass balance on Water
m_vapor_outlet = self.m_pump - m_solution_outlet
m_total = m_solution_outlet
hlv0 = h_vapor_outlet - h_solution_inlet
q0 = m_total * h_vapor_outlet - self.m_pump * hlv0
Q = m_solution_outlet * h_solution_outlet \
+ m_vapor_outlet * h_vapor_outlet \
- self.m_pump * h_solution_inlet
q = 0
T0,T1,T2=self.genpoints[0][1],self.genpoints[1][1],self.genpoints[2][1]
Q0,Q1,Q2=self.genpoints[0][0],self.genpoints[1][0],self.genpoints[2][0]
if T < T0:
raise "Generator outlet must be greater than pre-inlet temperature!"
elif T < T1:
# The state is either saturated or subcooled.
# Use linear interpolation.
q = (T - T0) / (T1 - T0) * (Q1 - Q0)
else:
x_local = libr_props.massFraction(C2K(T),self.P_cond * 1e-5)
pwater.update(CP.PT_INPUTS, self.P_cond, C2K(T))
h_vapor_local = pwater.hmass() - h_w_ref
h_solution_local = libr_props.massSpecificEnthalpy(C2K(T), x_local)
# Mass balance on LiBr
m_solution_local = self.m_pump * self.x1 / x_local
hlv1 = h_vapor_local - h_solution_local
q1 = m_total * h_vapor_local - m_solution_local * hlv1
q = (q1 - q0) + (Q1 - Q0)
# TODO
# If q > Q (iff T > T_solution_outlet) then result is invalid.
return q, Q
def iterate1(self):
"""Update the internal parameters."""
self.T_gen_inlet = K2C(libr_props.temperature(self.P_cond*1e-5,
self.x1))
self.T_gen_outlet = K2C(libr_props.temperature(self.P_cond * 1e-5,
self.x2))
self.T_abs_inlet_max = K2C(libr_props.temperature(self.P_evap * 1e-5,
self.x2))
self.T_abs_outlet_max = K2C(libr_props.temperature(self.P_evap * 1e-5,
self.x1))
self.h_gen_inlet = libr_props.massSpecificEnthalpy(
C2K(self.T_gen_inlet), self.x1)
self.h_gen_outlet = libr_props.massSpecificEnthalpy(
C2K(self.T_gen_outlet), self.x2)
self.h_abs_inlet = libr_props.massSpecificEnthalpy(
C2K(self.T_abs_inlet_max), self.x2)
self.h_abs_outlet = libr_props.massSpecificEnthalpy(
C2K(self.T_abs_outlet_max), self.x1)
# Mass balance on LiBr
self.m_concentrate = self.m_pump * self.x1 / self.x2
# Mass balance on Water
self.m_refrig = self.m_pump - self.m_concentrate
self.f = self.m_pump / self.m_refrig
# Compute SHX outlets, assuming concentrate limits heat flow (C_min)
# Neglect pump work for the present.
DeltaT_max = self.T_gen_outlet - self.T_abs_outlet_max
DeltaT_SHX_concentrate = self.Eff_SHX * DeltaT_max
self.T_SHX_concentrate_outlet = self.T_gen_outlet \
- DeltaT_SHX_concentrate
self.h_SHX_concentrate_outlet = libr_props.massSpecificEnthalpy(
C2K(self.T_SHX_concentrate_outlet), self.x2)
self.Q_SHX = self.m_concentrate \
* (self.h_gen_outlet - self.h_SHX_concentrate_outlet)
# Expansion valve
self.h_abs_pre = self.h_SHX_concentrate_outlet
if self.h_abs_pre > self.h_abs_inlet:
# Pre-cooling is required to reach saturation temperature
self.Q_abs_pre_cool = self.m_concentrate \
* (self.h_abs_pre - self.h_abs_inlet)
q,t,xl = libr_props.twoPhaseProps(self.h_abs_pre,
self.P_evap*1e-5,
self.x2)
self.T_abs_pre = K2C(t)
self.x_abs_pre = xl
# ignore vapor quality, q
# Minimum vapor pressure for absorption to occur
self.P_abs_pre = np.inf
else:
self.Q_abs_pre_cool = 0
#self.T_abs_pre = K2C(CP.PropsSI('T',
# 'H', self.h_abs_pre,
# 'P', self.P_evap,
# librname(self.x2)))
self.T_abs_pre = np.nan
# Minimum vapor pressure for absorption to occur
# self.P_abs_pre = CP.PropsSI('P',
# 'T', C2K(self.T_abs_pre),
# 'Q', 0,
# librname(self.x2))
self.P_abs_pre = np.nan
# Heat rejection in absorber: energy balance
pwater.update(CP.PQ_INPUTS, self.P_evap, 1)
self.h_abs_vapor_inlet = pwater.hmass() - h_w_ref
self.Q_abs_main = self.m_refrig * self.h_abs_vapor_inlet \
+ self.m_concentrate * self.h_abs_inlet \
- self.m_pump * self.h_abs_outlet
self.Q_abs_total = self.Q_abs_main + self.Q_abs_pre_cool
# Energy balance in SHX, pump side
D_in = CP.PropsSI('D',
'T',C2K(self.T_abs_outlet_max),
'Q',0,
librname(self.x1))
DeltaH_pump = (self.P_cond - self.P_evap) / D_in
self.W_pump = self.m_pump * DeltaH_pump
self.h_pump_outlet = self.h_abs_outlet + DeltaH_pump
DeltaH_SHX_pumpside = self.Q_SHX / self.m_pump
self.h_gen_pre = self.h_pump_outlet + DeltaH_SHX_pumpside
if self.h_gen_pre > self.h_gen_inlet:
# Flash steam
self.T_gen_pre = np.nan
else:
# The state is either saturated or subcooled.
# We need to calculate the temperature from specific heat.
cp = libr_props.massSpecificHeat(C2K(self.T_gen_inlet),self.x1)
deltaHsub = self.h_gen_inlet - self.h_gen_pre
deltaT = deltaHsub / cp
self.T_gen_pre = self.T_gen_inlet - deltaT
self.Q_gen_pre_heat = self.m_pump * (self.h_gen_inlet - self.h_gen_pre)
# Heat input to generator: energy balance
pwater.update(CP.PT_INPUTS, self.P_cond, C2K(self.T_gen_inlet))
self.h_gen_vapor_outlet = pwater.hmass() - h_w_ref
self.vapor_superheat = self.T_gen_inlet - self.T_cond
self.Q_gen_main = self.m_refrig * self.h_gen_vapor_outlet \
+ self.m_concentrate * self.h_gen_outlet \
- self.m_pump * self.h_gen_inlet
self.Q_gen_total = self.Q_gen_main + self.Q_gen_pre_heat
# Condenser
pwater.update(CP.PQ_INPUTS, self.P_cond, 0)
self.h_condenser_outlet = pwater.hmass() - h_w_ref
self.Q_condenser_reject = self.m_refrig * (self.h_gen_vapor_outlet
- self.h_condenser_outlet)
# Expansion valve
self.h_evap_inlet = self.h_condenser_outlet
# Evaporator
self.h_evap_outlet = self.h_abs_vapor_inlet
self.Q_evap_heat = self.m_refrig * (self.h_evap_outlet
- self.h_evap_inlet)
self.COP = self.Q_evap_heat / self.Q_gen_total
def __init__(self,P,m_in,h_in,x_in,h_vapor_inlet,debug=False):
self.P=P
self.m_in=m_in
self.h_in=h_in
self.x_in=x_in
self.h_vapor_inlet = h_vapor_inlet
self.T_sat = K2C(libr_props.temperature(self.P * 1e-5,
self.x_in))
self.h_sat = libr_props.massSpecificEnthalpy(C2K(self.T_sat),self.x_in)
if self.h_in > self.h_sat:
q,t,xl = libr_props.twoPhaseProps(self.h_in,self.P*1e-5,self.x_in)
# Pre-cooling is required to reach saturation temperature
self.Q_pre_cool = self.m_in * (self.h_sat - self.h_in)
self.T_in = K2C(t)
prepoints_x = np.linspace(xl,self.x_in,20,endpoint=False)
prepoints_T = np.zeros_like(prepoints_x)
prepoints_q = np.zeros_like(prepoints_x)
for i,x in enumerate(prepoints_x):
#q,t,xl = libr_props.twoPhaseProps(h,self.P*1e-5,self.x_in)
t = libr_props.temperature(self.P * 1e-5, x)
h = libr_props.massSpecificEnthalpy(t,x)
prepoints_T[i] = K2C(t)
prepoints_q[i] = self.m_in * (h - self.h_in)
prepoints_x[i] = x
else:
self.Q_pre_cool = 0
self.T_in = K2C(libr_props.temperature(self.P * 1e-5, self.x_in))
prepoints_T = []
prepoints_q = []
prepoints_x = []
# Set up bounds and points for interpolation.
# Absorber limit is liquid water.
pwater.update(CP.PQ_INPUTS,P,0)
self.Tmin = pwater.T()
x_points = np.linspace(x_in,0.1,100)
T_points = np.zeros_like(x_points)
q_points = np.zeros_like(x_points)
#q_func = np.vectorize(self._q)
#q_points = q_func(T_points)
for i,x in enumerate(x_points):
T_points[i],q_points[i] = self._qx(x)
x_points = np.concatenate([prepoints_x,x_points])
T_points = np.concatenate([prepoints_T,T_points])
q_points = np.concatenate([prepoints_q,q_points])
# Forward function
T_points1 = np.resize(T_points,len(T_points)+1)
q_points1 = np.resize(q_points,len(T_points)+1)
T_points1[-1] = T_points[-1] - 5
q_points1[-1] = q_points[-1]
# Inverse function
T_points2 = np.resize(T_points,len(T_points)+1)
q_points2 = np.resize(q_points,len(T_points)+1)
T_points2[-1] = T_points[-1]
q_points2[-1] = q_points[-1] * 1.05
if debug:
import matplotlib.pyplot as plt
import tabulate
xmod = np.resize(x_points,len(x_points)+1)
print(tabulate.tabulate(zip(xmod,T_points1,q_points1,
T_points2,q_points2),
headers=['x','T1','q1','T2','q2']))
plt.figure(); plt.plot(T_points1,q_points1); plt.title("q(T)")
plt.figure(); plt.plot(q_points2,T_points2); plt.title("T(q)")
# Interpolate data must be in increasing order, so we reverse it
# compared to reaction direction.
self.q = PchipInterpolator(T_points1[::-1], q_points1[::-1])
self.T = PchipInterpolator(q_points2[::-1], T_points2[::-1])