def isentropic_at_fixed_quality(s, quality, T_initial=None):
"""
Returns None if solution cannot be found
Returns the T, P, rhoV, rhoL and enthalpy
"""
# Use IAPWS-84 for initial estimate
# Should be very good for IAPWS-95
if T_initial is None:
start_T_value = 100.0 + 273.15
else:
start_T_value = T_initial
def fcn(n, x, fvec, iflag):
T_sat = x[0]
sL_sat = 4.4514E-08*(T_sat**3) - 6.6115E-05*(T_sat**2) + 4.1971E-02*(T_sat) - 7.4527E+00
sV_sat = -1.1821E-07*(T_sat**3) + 1.7632E-04*(T_sat**2) - 9.4510E-02*(T_sat) + 2.4203E+01
#sL_sat = IAPWS84.specific_entropy_of_saturated_liquid(T)*1e-3
#sV_sat = IAPWS84.specific_entropy_of_saturated_vapor(T)*1e-3
fvec[0] = (s - (quality*sV_sat + (1.0 - quality)*sL_sat))
#print 'T_sat:', T_sat, 'fvec[0]:', fvec[0]
solution = dnsqe.dnsqe_nice(fcn, None, [start_T_value], bounds=((273.15, CRITICAL_TEMPERATURE),))
#print 'FROM IAPWS-84:', solution
solution_type = solution[3]
if int(solution_type) != 1:
return None
start_T_value = solution[0][0]
if start_T_value < 273.16 or start_T_value > CRITICAL_TEMPERATURE:
start_T_value = 373.15
def fcn2(n, x, fvec, iflag):
T_sat = x[0]
#print 'T_sat:', T_sat
fcn2.P_value = sat = saturation_pressure_at_fixed_temperature(T_sat)
rhoV, rhoL = sat[2], sat[3]
sV_sat = entropy(rhoV, T_sat)
sL_sat = entropy(rhoL, T_sat)
fvec[0] = (s - (quality*sV_sat + (1.0 - quality)*sL_sat))
fcn2.rhoV = rhoV
fcn2.rhoL = rhoL
fcn2.sV = sV_sat
fcn2.sL = sL_sat
solution = dnsqe.dnsqe_nice(fcn2, None, [start_T_value], bounds=((273.15, CRITICAL_TEMPERATURE),))
solution_type = solution[3]
if int(solution_type) != 1:
return None
T_value = solution[0][0]
return T_value, fcn2.P_value, fcn2.rhoV, fcn2.rhoL, fcn2.sV, fcn2.sL
def solve(self, x, f, bounds=None):
f_nle_string = self.generate_nle()
exec(f_nle_string)
x, f, fnorm, info_code, info_mesg = dnsqe_nice(f_nle, None, x, bounds=bounds)
i = 0
keys = self.Variables.keys()
for i in xrange(0, len(x)):
self.Variables[keys[i]] = x[i]
self.fnorm = fnorm;
#print 'Norm of function residual vector:', fnorm
self.info = info_code, info_mesg
#print 'Info:', info_code
#print 'Message:', info_mesg
ret = ''
if self.info[0] == 1:
ret = ret + "Most recent solution:\n"
ret = ret + "---------------------\n"
ret = ret + "Solution norm: " + str(self.fnorm) + "\n"
ret = ret + pretty_variables(self.Variables)
return '\n' + ret + '\n'
else:
ret = ret + self.info[1]
ret = ret + "---------------------\n"
ret = ret + "Solution norm: " + str(self.fnorm) + "\n"
ret = ret + pretty_variables(self.Variables)
return '\n' + ret + '\n'
def density_at_fixed_pressure_and_temperature(T, P, rho_initial=None):
"""
Returns None if solution cannot be found
Returns the T, P, rho
"""
T_value = T
P_value = P
if rho_initial is None:
if T_value >= CRITICAL_TEMPERATURE or P_value >= CRITICAL_PRESSURE:
rho_initial = IAPWS84.density_of_saturated_vapor(CRITICAL_TEMPERATURE - 10)
#rho_initial = CRITICAL_DENSITY + 1
else:
P_sat_value, rhoV_value, rhoL_value = saturation_pressure_at_fixed_temperature(T_value)[1:]
if P_value > P_sat_value:
rho_initial = rhoL_value
else:
rho_initial = rhoV_value
start_rho_value = rho_initial
def fcn(n, x, fvec, iflag):
rho_guess = x[0]
fvec[0] = ((pressure(rho_guess, T_value) - P_value))#/P_value)
#print 'fvec[0]:', fvec[0], 'fvec[1]:', fvec[1]
solution = dnsqe.dnsqe_nice(fcn, None, [start_rho_value], bounds=((0, 1e10),))
#print solution
solution_type = solution[3]
if int(solution_type) != 1:
return None
rho_value = solution[0][0]
return T_value, pressure(rho_value, T_value), rho_value
def isentropic_at_fixed_pressure(P, s, T_initial=None):
"""
Returns None if solution cannot be found
Returns the T, P, rho and entropy
"""
if T_initial is None:
if P * 1e-3 > IAPWS84.IAPWS84_CRITICAL_PRESSURE - 10:
start_T_value = CRITICAL_TEMPERATURE - 1.0
else:
start_T_value = IAPWS84.saturation_temperature(P*1e-3)
else:
start_T_value = T_initial
def fcn(n, x, fvec, iflag):
T_guess = x[0]
if hasattr(fcn, 'last_solution'):
last_rho = fcn.last_solution[2]
else:
last_rho = None
solution = isentropic_at_fixed_temperature(T_guess, s, rho_initial=last_rho)
#print solution
fvec[0] = (P - solution[1])
fcn.T_value = solution[0]
fcn.P_value = solution[1]
fcn.rho_value = solution[2]
fcn.s_value = solution[3]
solution = dnsqe.dnsqe_nice(fcn, None, [start_T_value], bounds=((1e-10, 1e100),))
solution_type = solution[3]
if int(solution_type) != 1:
return None
return fcn.T_value, fcn.P_value, fcn.rho_value, fcn.s_value
def temperature_at_fixed_pressure_and_density(P, rho, T_initial=None):
"""
Returns None if solution cannot be found
Returns the T, P and rho
"""
if T_initial is None:
if P * 1e-3 > IAPWS84.IAPWS84_CRITICAL_PRESSURE - 1.0:
start_T_value = IAPWS84.IAPWS84.CRITICAL_TEMPERATURE - 1.0
start_rho_value = IAPWS84.density_of_saturated_liquid(start_T_value)
else:
start_T_value = IAPWS84.saturation_temperature(P*1e-3)
else:
start_T_value = T_initial
def fcn(n, x, fvec, iflag):
T_guess = x[0]
fvec[0] = ((pressure(rho, T_guess) - P))#/P_value)
#print 'fvec[0]:', fvec[0], 'fvec[1]:', fvec[1]
solution = dnsqe.dnsqe_nice(fcn, None, [start_T_value])
#print solution
solution_type = solution[3]
if int(solution_type) != 1:
return None
T_value = solution[0][0]
rho_value = rho
return T_value, pressure(rho_value, T_value), rho_value
def saturation_temperature_at_fixed_pressure(P):
"""
Returns None if solution cannot be found
Returns the T, P, rho_Vapor, rho_Liquid
"""
#This is actually a very good guess of the saturation temperature
#If we get a None, that means there's no solution
T_value = IAPWS84.saturation_temperature(P*1e-3)
if T_value is None:
return None
rhoV_value = IAPWS84.density_of_saturated_vapor(T_value)
rhoL_value = IAPWS84.density_of_saturated_liquid(T_value)
P_value = P
def fcn (n, x, fvec, iflag):
x0 = x[0]
x1 = x[1]
x2 = x[2]
res = phase_equilibrium(x0, x1, x2, P_value)
fvec[0] = res[0]
fvec[1] = res[1]
fvec[2] = res[2]
solution = dnsqe.dnsqe_nice(fcn, None, [rhoV_value, rhoL_value, T_value], bounds=((1e-10, 1e10),(1e-10, 1e10), (1e-10, 1e10)))
solution_type = solution[3]
if int(solution_type) != 1:
return None
rhoV_value, rhoL_value, T_value = solution[0]
return T_value, P_value, rhoV_value, rhoL_value
def saturation_pressure_at_fixed_temperature(T):
"""
Returns None if solution cannot be found
Returns the T, P, rho_Vapor and rho_Liquid.
"""
if T > CRITICAL_TEMPERATURE:
return None
rhoV_value = IAPWS84.density_of_saturated_vapor(T)
rhoL_value = IAPWS84.density_of_saturated_liquid(T)
P_value_temp = IAPWS84.vapor_pressure(T)
T_value = T
def fcn (n, x, fvec, iflag):
x0 = x[0]
x1 = x[1]
x2 = x[2]
res = phase_equilibrium(x0, x1, T_value, x2)
fvec[0] = res[0]
fvec[1] = res[1]
fvec[2] = res[2]
solution = dnsqe.dnsqe_nice(fcn, None, [rhoV_value, rhoL_value, P_value_temp], bounds=((1e-10, 1e10),(1e-10, 1e10), (1e-10, 1e100)))
solution_type = solution[3]
if int(solution_type) != 1:
return None
rhoV_value, rhoL_value, P_value_sat = solution[0]
return T, P_value_sat, rhoV_value, rhoL_value
def isentropic_at_fixed_temperature(T, s, rho_initial=None):
"""
Returns None if solution cannot be found
Returns the T, P, rho and enthalpy
"""
s_value = s
if rho_initial is None:
if T < CRITICAL_TEMPERATURE:
T_sat = T
sL_sat = IAPWS84.specific_entropy_of_saturated_liquid(T_sat)*1e-3
sV_sat = IAPWS84.specific_entropy_of_saturated_vapor(T_sat)*1e-3
rhoV_sat = IAPWS84.density_of_saturated_vapor(T_sat)
rhoL_sat = IAPWS84.density_of_saturated_liquid(T_sat)
#print 'T_sat:', T_sat
#print 'hL_sat:', sL_sat, 'hV_sat:', sV_sat
#print 'rhoV_sat:', rhoV_sat, 'rhoL_sat:', rhoL_sat
#print '(sL_sat - s):', (sL_sat - s)
#print '(sV_sat - s):', (sV_sat - s)
if abs(sL_sat - s) <= abs(sV_sat - s):
start_rho_value = rhoL_sat
else:
start_rho_value = rhoV_sat
#start_rho_value = rhoV_sat
else:
T_sat = CRITICAL_TEMPERATURE
start_rho_value = sL_sat = IAPWS84.specific_entropy_of_saturated_liquid(T_sat)
else:
start_rho_value = rho_initial
def jac(n, x, fvec, fjac, ldfjac, iflag):
delta = x[0]
tau = CRITICAL_TEMPERATURE/T
fjac[0][0] = tau*(RES_phi_delta_tau(delta, tau)) - RES_phi_delta(delta, tau) # Derivative of first eqn wrt to first var
def fcn(n, x, fvec, iflag):
#print 'x:', x
delta = x[0]
tau = CRITICAL_TEMPERATURE/T
fvec[0] = ((entropy_raw(delta, tau) - s_value/SPECIFIC_GAS_CONSTANT))#/h_value)
T_value = T
solution = dnsqe.dnsqe_nice(fcn, jac, [start_rho_value/CRITICAL_DENSITY], bounds=((1e-10, 1e10),))
solution_type = solution[3]
if int(solution_type) != 1:
return None
#print solution
delta_value = solution[0][0]
rho_value = delta_value*CRITICAL_DENSITY
return T_value, pressure(rho_value, T_value), rho_value, entropy(rho_value, T_value)
def isenthalpic_at_fixed_pressure(P, h):
"""
Returns None if solution cannot be found
Returns the T, P, rho and enthalpy
"""
h_value = h
P_value = P
if P_value * 1e-3 > IAPWS84.IAPWS84_CRITICAL_PRESSURE - 10.0:
start_T_value = 373.15
start_rho_value = IAPWS84.density_of_saturated_liquid(start_T_value)
elif P_value < 1:
start_T_value = 273.16
start_rho_value = IAPWS84.density_of_saturated_vapor(start_T_value)
else:
T_sat = IAPWS84.saturation_temperature(P*1e-3)
hL_sat = IAPWS84.specific_enthalpy_of_saturated_liquid(T_sat)*1e-3
hV_sat = IAPWS84.specific_enthalpy_of_saturated_vapor(T_sat)*1e-3
rhoV_sat = IAPWS84.density_of_saturated_vapor(T_sat)
rhoL_sat = IAPWS84.density_of_saturated_liquid(T_sat)
#print 'T_sat:', T_sat
#print 'hL_sat:', hL_sat, 'hV_sat:', hV_sat
#print 'rhoV_sat:', rhoV_sat, 'rhoL_sat:', rhoL_sat
#print '(hL_sat - h):', (hL_sat - h)
#print '(hV_sat - h):', (hV_sat - h)
if abs(hL_sat - h) <= abs(hV_sat - h):
start_rho_value = rhoL_sat
else:
start_rho_value = rhoV_sat
start_T_value = T_sat
def fcn(n, x, fvec, iflag):
rho_guess = x[0]
T_guess = x[1]
fvec[0] = ((enthalpy(rho_guess, T_guess) - h_value))#/h_value)
fvec[1] = ((pressure(rho_guess, T_guess) - P_value))#/P_value)
#print 'fvec[0]:', fvec[0], 'fvec[1]:', fvec[1]
solution = dnsqe.dnsqe_nice(fcn, None, [start_rho_value, start_T_value], bounds=((1e-10, 1e10), (1e-10, 1e10)))
solution_type = solution[3]
if int(solution_type) != 1:
return None
#print solution
rho_value, T_value = solution[0]
return T_value, pressure(rho_value, T_value), rho_value, enthalpy(rho_value, T_value)
def isenthalpic_at_fixed_temperature(T, h):
"""
Returns None if solution cannot be found
Returns the T, P, rho and enthalpy
"""
h_value = h
last_solution = None
start_P_value = 101.325
def fcn(n, x, fvec, iflag):
P_guess = x[0]
last_solution = isenthalpic_at_fixed_pressure(P_guess, h)
fvec[0] = (T - last_solution[0])
fcn.last_solution = last_solution
#fvec[1] = ((pressure(rho_guess, T_guess) - P_value))#/P_value)
#print 'P_guess:', P_guess, 'fvec[0]:', fvec[0]
solution = dnsqe.dnsqe_nice(fcn, None, [start_P_value], bounds=((1e-10, 1e100),))
solution_type = solution[3]
if int(solution_type) != 1:
return None
return fcn.last_solution
def isenthalpic_at_fixed_quality(h, quality, T_initial=None):
"""
Returns None if solution cannot be found
Returns the T, P, rhoV, rhoL and enthalpy
"""
# Use IAPWS-84 for initial estimate
# Should be very good for IAPWS-95
if T_initial is None:
start_T_value = 100.0 + 273.15
else:
start_T_value = T_initial
def fcn(n, x, fvec, iflag):
T_sat = x[0]
#hL_sat = IAPWS84.specific_enthalpy_of_saturated_liquid(T_sat)*1e-3
#hV_sat = IAPWS84.specific_enthalpy_of_saturated_vapor(T_sat)*1e-3
hL_sat = 1.0554E-07*(T_sat**4) - 1.7366E-04*(T_sat**3) + 1.0645E-01*(T_sat**2) - 2.4465E+01*(T_sat) + 1.7031E+03
hV_sat = -1.7621E-07*(T_sat**4) + 2.8586E-04*(T_sat**3) - 1.7493E-01*(T_sat**2) + 4.9073E+01*(T_sat) - 2.7153E+03
fvec[0] = (h - (quality*hV_sat + (1.0 - quality)*hL_sat))
#print 'T_sat:', T_sat, 'fvec[0]:', fvec[0]
solution = dnsqe.dnsqe_nice(fcn, None, [start_T_value], bounds=((1e-10, CRITICAL_TEMPERATURE),))
#print 'FROM IAPWS-84:', solution
solution_type = solution[3]
if int(solution_type) != 1:
return None
start_T_value = solution[0][0]
if start_T_value < 273.16 or start_T_value > CRITICAL_TEMPERATURE:
start_T_value = 373.15
def fcn2(n, x, fvec, iflag):
T_sat = x[0]
fcn2.P_value = sat = saturation_pressure_at_fixed_temperature(T_sat)
rhoV, rhoL = sat[2], sat[3]
hV_sat = enthalpy(rhoV, T_sat)
hL_sat = enthalpy(rhoL, T_sat)
fcn2.rhoV = rhoV
fcn2.rhoL = rhoL
fcn2.hV_sat = hV_sat
fcn2.hL_sat = hL_sat
fvec[0] = (h - (quality*hV_sat + (1.0 - quality)*hL_sat))
solution = dnsqe.dnsqe_nice(fcn2, None, [start_T_value], bounds=((273.15, CRITICAL_TEMPERATURE),))
#print 'FROM IAPWS-95:', solution
solution_type = solution[3]
if int(solution_type) != 1:
return None
T_value = solution[0][0]
rhoV = fcn2.rhoV
rhoL = fcn2.rhoL
hV = fcn2.hV_sat
hL = fcn2.hL_sat
return T_value, fcn2.P_value, rhoV, rhoL, hV, hL