/usr/lib/python2.7/dist-packages/iapws/iapws95.py is in python-iapws 1.1.3-1.
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#!/usr/bin/python
# -*- coding: utf-8 -*-
###############################################################################
# Implemented multiparameter equation of state
# o IAPWS-95 implementation
# o Heavy water formulation 2005
###############################################################################
from scipy import exp, log
from scipy.optimize import fsolve
from ._iapws import _fase, getphase
from ._iapws import _Viscosity, _ThCond, _Dielectric, _Refractive, _Tension
from .iapws97 import _TSat_P
class MEoS(_fase):
"""
General implementation of multiparameter equation of state
From this derived all child class specified per individual compounds
Incoming properties:
T - Temperature, K
P - Pressure, MPa
rho - Density, kg/m3
v - Specific volume, m3/kg
h - Specific enthalpy, kJ/kg
s - Specific entropy, kJ/kg·K
u - Specific internal energy, kJ/kg·K
x - Quality
l - Opcional parameter to light wavelength for Refractive index
It needs two incoming properties
Calculated properties:
P - Pressure, MPa
Pr - Reduce pressure
T - Temperature, K
Tr - Reduced temperature
x - Quality
v - Specific volume, m³/kg
rho - Density, kg/m³
h - Specific enthalpy, kJ/kg
s - Specific entropy, kJ/kg·K
u - Specific internal energy, kJ/kg
g - Specific Gibbs free energy, kJ/kg
a - Specific Helmholtz free energy, kJ/kg
cp - Specific isobaric heat capacity, kJ/kg·K
cv - Specific isochoric heat capacity, kJ/kg·K
cp_cv - Heat capacity ratio
w - Speed of sound, m/s
Z - Compression factor
fi - Fugacity coefficient
f - Fugacity, MPa
gamma - Isoentropic exponent
Hvap - Vaporization heat, kJ/kg
alfav - Thermal expansion coefficient (Volume expansivity), 1/K
kappa - Isothermal compressibility, 1/MPa
alfap - Relative pressure coefficient, 1/K
betap - Isothermal stress coefficient, kg/m³
betas - Isoentropic temperature-pressure coefficient
joule - Joule-Thomson coefficient, K/MPa
Gruneisen - Gruneisen parameter
virialB - Second virial coefficient, m³/kg
virialC - Third virial coefficient, m⁶/kg²
dpdT_rho - Derivatives, dp/dT at constant rho, MPa/K
dpdrho_T - Derivatives, dp/drho at constant T, MPa·m³/kg
drhodT_P - Derivatives, drho/dT at constant P, kg/m³·K
drhodP_T - Derivatives, drho/dP at constant T, kg/m³·MPa
dhdT_rho - Derivatives, dh/dT at constant rho, kJ/kg·K
dhdP_T - Isothermal throttling coefficient, kJ/kg·MPa
dhdT_P - Derivatives, dh/dT at constant P, kJ/kg·K
dhdrho_T - Derivatives, dh/drho at constant T, kJ·m³/kg²
dhdrho_P - Derivatives, dh/drho at constant P, kJ·m³/kg²
dhdP_rho - Derivatives, dh/dP at constant rho, kJ/kg·MPa
kt - Isothermal Expansion Coefficient
ks - Adiabatic Compressibility, 1/MPa
Ks - Adiabatic bulk modulus, MPa
Kt - Isothermal bulk modulus, MPa
Z_rho - (Z-1) over the density, m³/kg
IntP - Internal pressure
invT - Negative reciprocal temperature
hInput - Specific heat input, kJ/kg
mu - Dynamic viscosity, Pa·s
nu - Kinematic viscosity, m²/s
k - Thermal conductivity, W/m·K
sigma - Surface tension, N/m
alfa - Thermal diffusivity, m²/s
Pramdt - Prandtl number
epsilon - Dielectric constant
n - Refractive index
v0 - Ideal gas Specific volume, m³/kg
rho0 - Ideal gas Density, kg/m³
h0 - Ideal gas Specific enthalpy, kJ/kg
u0 - Ideal gas Specific internal energy, kJ/kg
s0 - Ideal gas Specific entropy, kJ/kg·K
a0 - Ideal gas Specific Helmholtz free energy, kJ/kg
g0 - Ideal gas Specific Gibbs free energy, kJ/kg
cp0 - Ideal gas Specific isobaric heat capacity, kJ/kg·K
cv0 - Ideal gas Specific isochoric heat capacity, kJ/kg·K
cp0_cv - Ideal gas Heat capacity ratio
gamma0 - Ideal gas Isoentropic exponent
"""
CP = None
_surface = None
_vapor_Pressure = None
_liquid_Density = None
_vapor_Density = None
kwargs = {"T": 0.0,
"P": 0.0,
"rho": 0.0,
"v": 0.0,
"h": None,
"s": None,
"u": None,
"x": None,
"l": 0.5893}
status = 0
msg = "Undefined"
def __init__(self, **kwargs):
"""Constructor, define common constant and initinialice kwargs"""
self.R = self._constants["R"]/self.M
self.Zc = self.Pc/self.rhoc/self.R/self.Tc
self.kwargs = MEoS.kwargs.copy()
self.__call__(**kwargs)
def __call__(self, **kwargs):
"""Make instance callable to can add input parameter one to one"""
if kwargs.get("v", 0):
kwargs["rho"] = 1./kwargs["v"]
del kwargs["v"]
self.kwargs.update(kwargs)
if self.calculable:
self.status = 1
self.calculo()
self.msg = ""
@property
def calculable(self):
"""Check if inputs are enough to define state"""
self._mode = ""
if self.kwargs["T"] and self.kwargs["P"]:
self._mode = "TP"
elif self.kwargs["T"] and self.kwargs["rho"]:
self._mode = "Trho"
elif self.kwargs["T"] and self.kwargs["h"] is not None:
self._mode = "Th"
elif self.kwargs["T"] and self.kwargs["s"] is not None:
self._mode = "Ts"
elif self.kwargs["T"] and self.kwargs["u"] is not None:
self._mode = "Tu"
elif self.kwargs["P"] and self.kwargs["rho"]:
self._mode = "Prho"
elif self.kwargs["P"] and self.kwargs["h"] is not None:
self._mode = "Ph"
elif self.kwargs["P"] and self.kwargs["s"] is not None:
self._mode = "Ps"
elif self.kwargs["P"] and self.kwargs["u"] is not None:
self._mode = "Pu"
elif self.kwargs["rho"] and self.kwargs["h"] is not None:
self._mode = "rhoh"
elif self.kwargs["rho"] and self.kwargs["s"] is not None:
self._mode = "rhos"
elif self.kwargs["rho"] and self.kwargs["u"] is not None:
self._mode = "rhou"
elif self.kwargs["h"] is not None and self.kwargs["s"] is not None:
self._mode = "hs"
elif self.kwargs["h"] is not None and self.kwargs["u"] is not None:
self._mode = "hu"
elif self.kwargs["s"] is not None and self.kwargs["u"] is not None:
self._mode = "su"
elif self.kwargs["T"] and self.kwargs["x"] is not None:
self._mode = "Tx"
elif self.kwargs["P"] and self.kwargs["x"] is not None:
self._mode = "Px"
return bool(self._mode)
def calculo(self):
"""Calculate procedure"""
T = self.kwargs["T"]
rho = self.kwargs["rho"]
P = self.kwargs["P"]
v = self.kwargs["v"]
s = self.kwargs["s"]
h = self.kwargs["h"]
u = self.kwargs["u"]
x = self.kwargs["x"]
self.R = self._constants["R"]/self.M
propiedades = None
if v and not rho:
rho = 1./v
if x is None:
# Method with iteration necessary to get x
if self._mode == "TP":
if T < self.Tc and P < self.Pc and \
self._Vapor_Pressure(T) < P:
rhoo = self._Liquid_Density(T)
elif T < self.Tc and P < self.Pc:
rhoo = self._Vapor_Density(T)
else:
rhoo = self.rhoc*3
rho = fsolve(
lambda rho: self._Helmholtz(rho, T)["P"]-P*1000, rhoo)
elif self._mode == "Th":
rhol = self._Liquid_Density(T)
rhov = self._Vapor_Density(T)
hv = self._Helmholtz(rhov, T)["h"]
if h > hv:
rhoo = rhov
else:
rhoo = 1000
rho = fsolve(lambda rho: self._Helmholtz(rho, T)["h"]-h, rhoo)
elif self._mode == "Ts":
rhol = self._Liquid_Density(T)
rhov = self._Vapor_Density(T)
sv = self._Helmholtz(rhov, T)["s"]
if s > sv:
rhoo = rhov
else:
rhoo = 1000
rho = fsolve(lambda rho: self._Helmholtz(rho, T)["s"]-s, rhoo)
elif self._mode == "Tu":
rhol = self._Liquid_Density(T)
rhov = self._Vapor_Density(T)
Ps = self._Vapor_Pressure(T)
vapor = self._Helmholtz(rhov, T)
uv = vapor["h"]-Ps*vapor["v"]
if u > uv:
rhoo = rhov
else:
rhoo = 1000
def funcion(rho):
par = self._Helmholtz(rho, T)
return par["h"]-par["P"]*par["v"]-u
rho = fsolve(funcion, rhoo)
elif self._mode == "Prho":
T = fsolve(lambda T: self._Helmholtz(rho, T)["P"]-P*1000, 600)
rhol = self._Liquid_Density(T)
rhov = self._Vapor_Density(T)
if T[0] == 600 or rhov <= rho <= rhol:
def funcion(T):
rhol, rhov, Ps = self._saturation(T)
return Ps-P*1000
T = fsolve(funcion, 600)
elif self._mode == "Ph":
def funcion(parr):
par = self._Helmholtz(parr[0], parr[1])
return par["P"]-P*1000, par["h"]-h
rho, T = fsolve(funcion, [1000, 300])
rhol = self._Liquid_Density(T)
rhov = self._Vapor_Density(T)
if rho == 1000 or rhov <= rho <= rhol:
def funcion(parr):
rho, T = parr
rhol, rhov, Ps = self._saturation(T)
vapor = self._Helmholtz(rhov, T)
liquido = self._Helmholtz(rhol, T)
x = (1./rho-1/rhol)/(1/rhov-1/rhol)
return Ps-P*1000, vapor["h"]*x+liquido["h"]*(1-x)-h
rho, T = fsolve(funcion, [2., 500.])
elif self._mode == "Ps":
def funcion(parr):
par = self._Helmholtz(parr[0], parr[1])
return par["P"]-P*1000, par["s"]-s
rho, T = fsolve(funcion, [2., 400])
rhol = self._Liquid_Density(T)
rhov = self._Vapor_Density(T)
if rho == 2. or rhov <= rho <= rhol:
def funcion(parr):
rho, T = parr
rhol, rhov, Ps = self._saturation(T)
vapor = self._Helmholtz(rhov, T)
liquido = self._Helmholtz(rhol, T)
x = (1./rho-1/rhol)/(1/rhov-1/rhol)
return Ps-P*1000, vapor["s"]*x+liquido["s"]*(1-x)-s
rho, T = fsolve(funcion, [2., 500.])
elif self._mode == "Pu":
def funcion(parr):
par = self._Helmholtz(parr[0], parr[1])
return par["h"]-par["P"]*par["v"]-u, par["P"]-P*1000
rho, T = fsolve(funcion, [1000, 600])
rhol = self._Liquid_Density(T)
rhov = self._Vapor_Density(T)
if rho == 1000 or rhov <= rho <= rhol:
def funcion(parr):
rho, T = parr
rhol, rhov, Ps = self._saturation(T)
vapor = self._Helmholtz(rhov, T)
liquido = self._Helmholtz(rhol, T)
vu = vapor["h"]-Ps/rhov
lu = liquido["h"]-Ps/rhol
x = (1./rho-1/rhol)/(1/rhov-1/rhol)
return Ps-P*1000, vu*x+lu*(1-x)-u
rho, T = fsolve(funcion, [2., 500.])
elif self._mode == "rhoh":
T = fsolve(lambda T: self._Helmholtz(rho, T)["h"]-h, 600)
rhol = self._Liquid_Density(T)
rhov = self._Vapor_Density(T)
if T[0] == 600 or rhov <= rho <= rhol:
def funcion(T):
rhol, rhov, Ps = self._saturation(T)
vapor = self._Helmholtz(rhov, T)
liquido = self._Helmholtz(rhol, T)
x = (1./rho-1/rhol)/(1/rhov-1/rhol)
return vapor["h"]*x+liquido["h"]*(1-x)-h
T = fsolve(funcion, 500.)
elif self._mode == "rhos":
T = fsolve(lambda T: self._Helmholtz(rho, T)["s"]-s, 600)
rhol = self._Liquid_Density(T)
rhov = self._Vapor_Density(T)
if T[0] == 600 or rhov <= rho <= rhol:
def funcion(T):
rhol, rhov, Ps = self._saturation(T)
vapor = self._Helmholtz(rhov, T)
liquido = self._Helmholtz(rhol, T)
x = (1./rho-1/rhol)/(1/rhov-1/rhol)
return vapor["s"]*x+liquido["s"]*(1-x)-s
T = fsolve(funcion, 500.)
elif self._mode == "rhou":
def funcion(T):
par = self._Helmholtz(rho, T)
return par["h"]-par["P"]/1000*par["v"]-u
T = fsolve(funcion, 600)
rhol = self._Liquid_Density(T)
rhov = self._Vapor_Density(T)
if T[0] == 600 or rhov <= rho <= rhol:
def funcion(T):
rhol, rhov, Ps = self._saturation(T)
vapor = self._Helmholtz(rhov, T)
liquido = self._Helmholtz(rhol, T)
vu = vapor["h"]-Ps/rhov
lu = liquido["h"]-Ps/rhol
x = (1./rho-1/rhol)/(1/rhov-1/rhol)
return vu*x+lu*(1-x)-u
T = fsolve(funcion, 500.)
elif self._mode == "hs":
def funcion(parr):
par = self._Helmholtz(parr[0], parr[1])
return par["h"]-h, par["s"]-s
rho, T = fsolve(funcion, [1000, 300])
rhol = self._Liquid_Density(T)
rhov = self._Vapor_Density(T)
if rhov <= rho <= rhol:
def funcion(parr):
rho, T = parr
rhol, rhov, Ps = self._saturation(T)
vapor = self._Helmholtz(rhov, T)
liquido = self._Helmholtz(rhol, T)
x = (1./rho-1/rhol)/(1/rhov-1/rhol)
return (vapor["h"]*x+liquido["h"]*(1-x)-h,
vapor["s"]*x+liquido["s"]*(1-x)-s)
rho, T = fsolve(funcion, [0.5, 400.])
elif self._mode == "hu":
def funcion(parr):
par = self._Helmholtz(parr[0], parr[1])
return par["h"]-par["P"]/1000*par["v"]-u, par["h"]-h
rho, T = fsolve(funcion, [1000, 600])
rhol = self._Liquid_Density(T)
rhov = self._Vapor_Density(T)
if T == 600 or rhov <= rho <= rhol:
def funcion(parr):
rho, T = parr
rhol, rhov, Ps = self._saturation(T)
vapor = self._Helmholtz(rhov, T)
liquido = self._Helmholtz(rhol, T)
vu = vapor["h"]-Ps/rhov
lu = liquido["h"]-Ps/rhol
x = (1./rho-1/rhol)/(1/rhov-1/rhol)
return (vapor["h"]*x+liquido["h"]*(1-x)-h,
vu*x+lu*(1-x)-u)
rho, T = fsolve(funcion, [2., 500.])
elif self._mode == "su":
def funcion(parr):
par = self._Helmholtz(parr[0], parr[1])
return par["h"]-par["P"]/1000*par["v"]-u, par["s"]-s
rho, T = fsolve(funcion, [1000, 600])
rhol = self._Liquid_Density(T)
rhov = self._Vapor_Density(T)
if T == 600 or rhov <= rho <= rhol:
def funcion(parr):
rho, T = parr
rhol, rhov, Ps = self._saturation(T)
vapor = self._Helmholtz(rhov, T)
liquido = self._Helmholtz(rhol, T)
vu = vapor["h"]-Ps/rhov
lu = liquido["h"]-Ps/rhol
x = (1./rho-1/rhol)/(1/rhov-1/rhol)
return (vapor["s"]*x+liquido["s"]*(1-x)-s,
vu*x+lu*(1-x)-u)
rho, T = fsolve(funcion, [2., 500.])
rho = float(rho)
T = float(T)
propiedades = self._Helmholtz(rho, T)
if T <= self.Tc:
rhol = self._Liquid_Density(T)
rhov = self._Vapor_Density(T)
if rhol > rho > rhov:
rhol, rhov, Ps = self._saturation(T)
x = (1/rho-1/rhol)/(1/rhov-1/rhol)
if x < 0:
x = 0
elif x > 1:
x = 1
P = Ps/1000
elif rho <= rhov:
x = 1
elif rho >= rhol:
x = 0
vapor = self._Helmholtz(rhov, T)
liquido = self._Helmholtz(rhol, T)
elif T > self.Tc:
x = 1
else:
raise NotImplementedError("Incoming out of bound")
if not P:
P = propiedades["P"]/1000.
elif self._mode == "Tx":
# Check input T in saturation range
if self.Tt > T or self.Tc < T:
raise ValueError("Wrong input values")
rhol, rhov, Ps = self._saturation(T)
vapor = self._Helmholtz(rhov, T)
liquido = self._Helmholtz(rhol, T)
if x == 0:
propiedades = liquido
elif x == 1:
propiedades = vapor
P = Ps/1000.
elif self._mode == "Px":
# Iterate over saturation routine to get T
def funcion(T):
rhol = self._Liquid_Density(T)
rhog = self._Vapor_Density(T)
deltaL = rhol/self.rhoc
deltaG = rhog/self.rhoc
liquido = self._Helmholtz(rhol, T)
vapor = self._Helmholtz(rhog, T)
Ps = self.R*T*rhol*rhog/(rhol-rhog)*(
liquido["fir"]-vapor["fir"]+log(deltaL/deltaG))
return Ps/1000-P
To = _TSat_P(P)
T = fsolve(funcion, To)[0]
rhol, rhov, Ps = self._saturation(T)
vapor = self._Helmholtz(rhov, T)
liquido = self._Helmholtz(rhol, T)
if x == 0:
propiedades = liquido
elif x == 1:
propiedades = vapor
self.T = T
self.Tr = T/self.Tc
self.P = P
self.Pr = self.P/self.Pc
self.x = x
if self._mode in ["Tx", "Px"] or 0 < x < 1:
region = 4
else:
region = 0
self.phase = getphase(self.Tc, self.Pc, self.T, self.P, self.x, region)
self.Liquid = _fase()
self.Gas = _fase()
if x == 0:
# liquid phase
self.fill(self.Liquid, propiedades)
self.fill(self, propiedades)
elif x == 1:
# vapor phase
self.fill(self.Gas, propiedades)
self.fill(self, propiedades)
else:
self.fill(self.Liquid, liquido)
self.fill(self.Gas, vapor)
self.v = x*self.Gas.v+(1-x)*self.Liquid.v
self.rho = 1./self.v
self.h = x*self.Gas.h+(1-x)*self.Liquid.h
self.s = x*self.Gas.s+(1-x)*self.Liquid.s
self.u = x*self.Gas.u+(1-x)*self.Liquid.u
self.a = x*self.Gas.a+(1-x)*self.Liquid.a
self.g = x*self.Gas.g+(1-x)*self.Liquid.g
self.Z = x*self.Gas.Z+(1-x)*self.Liquid.Z
self.f = x*self.Gas.f+(1-x)*self.Liquid.f
self.Z_rho = x*self.Gas.Z_rho+(1-x)*self.Liquid.Z_rho
self.IntP = x*self.Gas.IntP+(1-x)*self.Liquid.IntP
# Calculate special properties useful only for one phase
if self._mode in ("Px", "Tx") or (x < 1 and self.Tt <= T <= self.Tc):
if self.name == "water":
self.sigma = _Tension(T)
else:
self.sigma = self._Tension(T)
else:
self.sigma = None
if 0 < x < 1:
self.virialB = vapor["B"]/self.rhoc
self.virialC = vapor["C"]/self.rhoc**2
else:
self.virialB = propiedades["B"]/self.rhoc
self.virialC = propiedades["C"]/self.rhoc**2
if self.Tt <= T <= self.Tc:
self.Hvap = vapor["h"]-liquido["h"]
else:
self.Hvap = None
self.invT = -1/self.T
# Ideal properties
cp0 = self._prop0(self.rho, self.T)
self.v0 = cp0.v
self.rho0 = 1./self.v0
self.h0 = cp0.h
self.u0 = self.h0-self.P*self.v0
self.s0 = cp0.s
self.a0 = self.u0-self.T*self.s0
self.g0 = self.h0-self.T*self.s0
self.cp0 = cp0.cp
self.cv0 = cp0.cv
self.cp0_cv = self.cp0/self.cv0
self.gamma0 = -self.v0/self.P/1000*self.derivative("P", "v", "s", cp0)
def fill(self, fase, estado):
"""Fill phase properties"""
fase.v = estado["v"]
fase.rho = 1/fase.v
fase.h = estado["h"]
fase.s = estado["s"]
fase.u = fase.h-self.P*1000*fase.v
fase.a = fase.u-self.T*fase.s
fase.g = fase.h-self.T*fase.s
fase.Z = self.P*fase.v/self.T/self.R*1e3
fase.fi = estado["fugacity"]
fase.f = fase.fi*self.P
fase.cp = estado["cp"]
fase.cv = estado["cv"]
fase.cp_cv = fase.cp/fase.cv
fase.w = estado["w"]
fase.alfap = estado["alfap"]
fase.betap = estado["betap"]
fase.joule = self.derivative("T", "P", "h", fase)*1e3
fase.Gruneisen = fase.v/fase.cv*self.derivative("P", "T", "v", fase)
fase.alfav = self.derivative("v", "T", "P", fase)/fase.v
fase.kappa = -self.derivative("v", "P", "T", fase)/fase.v*1e3
fase.betas = self.derivative("T", "P", "s", fase)
fase.gamma = -fase.v/self.P*self.derivative("P", "v", "s", fase)*1e-3
fase.kt = -fase.v/self.P*self.derivative("P", "v", "T", fase)*1e-3
fase.ks = -self.derivative("v", "P", "s", fase)/fase.v*1e3
fase.Kt = -fase.v*self.derivative("P", "v", "s", fase)*1e-3
fase.Ks = -fase.v*self.derivative("P", "v", "T", fase)*1e-3
fase.dhdT_rho = self.derivative("h", "T", "rho", fase)
fase.dhdT_P = self.derivative("h", "T", "P", fase)
fase.dhdP_T = self.derivative("h", "P", "T", fase)*1e3
fase.dhdP_rho = self.derivative("h", "P", "rho", fase)*1e3
fase.dhdrho_T = estado["dhdrho"]
fase.dhdrho_P = estado["dhdrho"]+fase.dhdT_rho/estado["drhodt"]
fase.dpdT_rho = self.derivative("P", "T", "rho", fase)*1e-3
fase.dpdrho_T = estado["dpdrho"]*1e-3
fase.drhodP_T = 1/estado["dpdrho"]*1e3
fase.drhodT_P = estado["drhodt"]
fase.Z_rho = (fase.Z-1)/fase.rho
fase.IntP = self.T*self.derivative("P", "T", "rho", fase)*1e-3-self.P
fase.hInput = fase.v*self.derivative("h", "v", "P", fase)
fase.mu = self._visco(fase.rho, self.T, fase)
fase.k = self._thermo(fase.rho, self.T, fase)
fase.nu = fase.mu/fase.rho
fase.alfa = fase.k/1000/fase.rho/fase.cp
fase.Prandt = fase.mu*fase.cp*1000/fase.k
if self.name == "water":
fase.epsilon = _Dielectric(fase.rho, self.T)
fase.n = _Refractive(fase.rho, self.T, self.kwargs["l"])
else:
fase.epsilon = None
fase.n = None
def _saturation(self, T=None):
"""Saturation calculation for two phase search"""
if not T:
T = self.T
rhoLo = self._Liquid_Density(T)
rhoGo = self._Vapor_Density(T)
def f(parr):
rhol, rhog = parr
deltaL = rhol/self.rhoc
deltaG = rhog/self.rhoc
liquido = self._Helmholtz(rhol, T)
vapor = self._Helmholtz(rhog, T)
Jl = deltaL*(1+deltaL*liquido["fird"])
Jv = deltaG*(1+deltaG*vapor["fird"])
Kl = deltaL*liquido["fird"]+liquido["fir"]+log(deltaL)
Kv = deltaG*vapor["fird"]+vapor["fir"]+log(deltaG)
return Kv-Kl, Jv-Jl
rhoL, rhoG = fsolve(f, [rhoLo, rhoGo])
if rhoL == rhoG:
Ps = self.Pc
else:
liquido = self._Helmholtz(rhoL, T)
vapor = self._Helmholtz(rhoG, T)
deltaL = rhoL/self.rhoc
deltaG = rhoG/self.rhoc
Ps = self.R*T*rhoL*rhoG/(rhoL-rhoG)*(
liquido["fir"]-vapor["fir"]+log(deltaL/deltaG))
return rhoL, rhoG, Ps
# def _saturation2(self, T):
# """Akasaka (2008) "A Reliable and Useful Method to Determine the
# Saturation State from Helmholtz Energy Equations of State", Journal of
# Thermal Science and Technology, 3, 442-451
# http://dx.doi.org/10.1299/jtst.3.442"""
#
# rhoL = self._Liquid_Density(T)
# rhoG = self._Vapor_Density(T)
# g = 500.
# erroro = 1e6
# rholo = rhoL
# rhogo = rhoG
# contador = 0
# while True:
# contador += 1
# deltaL = rhoL/self.rhoc
# deltaG = rhoG/self.rhoc
# liquido = self._Helmholtz(rhoL, T)
# vapor = self._Helmholtz(rhoG, T)
# Jl = deltaL*(1+deltaL*liquido["fird"])
# Jv = deltaG*(1+deltaG*vapor["fird"])
# Kl = deltaL*liquido["fird"]+liquido["fir"]+log(deltaL)
# Kv = deltaG*vapor["fird"]+vapor["fir"]+log(deltaG)
# Jdl = 1+2*deltaL*liquido["fird"]+deltaL**2*liquido["firdd"]
# Jdv = 1+2*deltaG*vapor["fird"]+deltaG**2*vapor["firdd"]
# Kdl = 2*liquido["fird"]+deltaL*liquido["firdd"]+1/deltaL
# Kdv = 2*vapor["fird"]+deltaG*vapor["firdd"]+1/deltaG
# Delta = Jdv*Kdl-Jdl*Kdv
# error = abs(Kv-Kl)+abs(Jv-Jl)
# if error < 1e-12 or contador > 100:
# break
# elif error > erroro:
# rhoL = rholo
# rhoG = rhogo
# g = g*0.5
# else:
# erroro = error
# rholo = rhoL
# rhogo = rhoG
# rhoL = rhoL+g/Delta*((Kv-Kl)*Jdv-(Jv-Jl)*Kdv)
# rhoG = rhoG+g/Delta*((Kv-Kl)*Jdl-(Jv-Jl)*Kdl)
# if error > 1e-3:
# print("Iteration don´t converge, residual error %g" % error)
#
# Ps = self.R*T*rhoL*rhoG/(rhoL-rhoG)*(
# liquido["fir"]-vapor["fir"]+log(deltaL/deltaG))
# return rhoL, rhoG, Ps
def _Helmholtz(self, rho, T):
"""Calculated properties, table 3 pag 10"""
rhoc = self._constants.get("rhoref", self.rhoc)
Tc = self._constants.get("Tref", self.Tc)
delta = rho/rhoc
tau = Tc/T
fio, fiot, fiott, fiod, fiodd, fiodt = self._phi0(tau, delta)
fir, firt, firtt, fird, firdd, firdt, firdtt, B, C = self._phir(
tau, delta)
propiedades = {}
propiedades["fir"] = fir
propiedades["fird"] = fird
propiedades["firdd"] = firdd
propiedades["T"] = T
propiedades["P"] = (1+delta*fird)*self.R*T*rho
propiedades["v"] = 1./rho
propiedades["h"] = self.R*T*(1+tau*(fiot+firt)+delta*fird)
propiedades["s"] = self.R*(tau*(fiot+firt)-fio-fir)
propiedades["cv"] = -self.R*tau**2*(fiott+firtt)
propiedades["cp"] = self.R*(
-tau**2*(fiott+firtt) + (1+delta*fird-delta*tau*firdt)**2/(
1+2*delta*fird+delta**2*firdd))
propiedades["w"] = (
self.R*1000*T*(1+2*delta*fird+delta**2*firdd - (
1+delta*fird-delta*tau*firdt)**2/tau**2/(fiott+firtt)))**0.5
propiedades["alfap"] = (1-delta*tau*firdt/(1+delta*fird))/T
propiedades["betap"] = rho*(
1+(delta*fird+delta**2*firdd)/(1+delta*fird))
propiedades["fugacity"] = exp(fir+delta*fird-log(1+delta*fird))
propiedades["B"] = B
propiedades["C"] = C
propiedades["dpdrho"] = self.R*T*(1+2*delta*fird+delta**2*firdd)
propiedades["drhodt"] = -rho*(1+delta*fird-delta*tau*firdt) / \
(T*(1+2*delta*fird+delta**2*firdd))
propiedades["dhdrho"] = self.R*T/rho * \
(tau*delta*(fiodt+firdt)+delta*fird+delta**2*firdd)
# dbt=-phi11/rho/t
# propiedades["cps"] = propiedades["cv"] Add cps from Argon pag.27
return propiedades
def _prop0(self, rho, T):
"""Ideal gas properties"""
rhoc = self._constants.get("rhoref", self.rhoc)
Tc = self._constants.get("Tref", self.Tc)
delta = rho/rhoc
tau = Tc/T
fio, fiot, fiott, fiod, fiodd, fiodt = self._phi0(tau, delta)
propiedades = _fase()
propiedades.v = self.R*T/self.P/1000
propiedades.h = self.R*T*(1+tau*fiot)
propiedades.s = self.R*(tau*fiot-fio)
propiedades.cv = -self.R*tau**2*fiott
propiedades.cp = self.R*(-tau**2*fiott+1)
propiedades.alfap = 1/T
propiedades.betap = rho
return propiedades
def _phi0(self, tau, delta):
Fi0 = self.Fi0
fio = Fi0["ao_log"][0]*log(delta)+Fi0["ao_log"][1]*log(tau)
fiot = +Fi0["ao_log"][1]/tau
fiott = -Fi0["ao_log"][1]/tau**2
fiod = 1/delta
fiodd = -1/delta**2
fiodt = 0
for n, t in zip(Fi0["ao_pow"], Fi0["pow"]):
fio += n*tau**t
if t != 0:
fiot += t*n*tau**(t-1)
if t not in [0, 1]:
fiott += n*t*(t-1)*tau**(t-2)
for n, t in zip(Fi0["ao_exp"], Fi0["titao"]):
fio += n*log(1-exp(-tau*t))
fiot += n*t*((1-exp(-t*tau))**-1-1)
fiott -= n*t**2*exp(-t*tau)*(1-exp(-t*tau))**-2
return fio, fiot, fiott, fiod, fiodd, fiodt
def _phir(self, tau, delta):
delta_0 = 1e-200
fir = fird = firdd = firt = firtt = firdt = firdtt = B = C = 0
# Polinomial terms
nr1 = self._constants.get("nr1", [])
d1 = self._constants.get("d1", [])
t1 = self._constants.get("t1", [])
for n, d, t in zip(nr1, d1, t1):
fir += n*delta**d*tau**t
fird += n*d*delta**(d-1)*tau**t
firdd += n*d*(d-1)*delta**(d-2)*tau**t
firt += n*t*delta**d*tau**(t-1)
firtt += n*t*(t-1)*delta**d*tau**(t-2)
firdt += n*t*d*delta**(d-1)*tau**(t-1)
firdtt += n*t*d*(t-1)*delta**(d-1)*tau**(t-2)
B += n*d*delta_0**(d-1)*tau**t
C += n*d*(d-1)*delta_0**(d-2)*tau**t
# Exponential terms
nr2 = self._constants.get("nr2", [])
d2 = self._constants.get("d2", [])
g2 = self._constants.get("gamma2", [])
t2 = self._constants.get("t2", [])
c2 = self._constants.get("c2", [])
for n, d, g, t, c in zip(nr2, d2, g2, t2, c2):
fir += n*delta**d*tau**t*exp(-g*delta**c)
fird += n*exp(-g*delta**c)*delta**(d-1)*tau**t*(d-g*c*delta**c)
firdd += n*exp(-g*delta**c)*delta**(d-2)*tau**t * \
((d-g*c*delta**c)*(d-1-g*c*delta**c)-g**2*c**2*delta**c)
firt += n*t*delta**d*tau**(t-1)*exp(-g*delta**c)
firtt += n*t*(t-1)*delta**d*tau**(t-2)*exp(-g*delta**c)
firdt += n*t*delta**(d-1)*tau**(t-1)*(d-g*c*delta**c)*exp(
-g*delta**c)
firdtt += n*t*(t-1)*delta**(d-1)*tau**(t-2)*(d-g*c*delta**c) * \
exp(-g*delta**c)
B += n*exp(-g*delta_0**c)*delta_0**(d-1)*tau**t*(d-g*c*delta_0**c)
C += n*exp(-g*delta_0**c)*(delta_0**(d-2)*tau**t*(
(d-g*c*delta_0**c)*(d-1-g*c*delta_0**c)-g**2*c**2*delta_0**c))
# Gaussian terms
nr3 = self._constants.get("nr3", [])
d3 = self._constants.get("d3", [])
t3 = self._constants.get("t3", [])
a3 = self._constants.get("alfa3", [])
e3 = self._constants.get("epsilon3", [])
b3 = self._constants.get("beta3", [])
g3 = self._constants.get("gamma3", [])
for i in range(len(nr3)):
exp1 = self._constants.get("exp1", [2]*len(nr3))
exp2 = self._constants.get("exp2", [2]*len(nr3))
fir += nr3[i]*delta**d3[i]*tau**t3[i]*exp(-a3[i]*(
delta-e3[i])**exp1[i]-b3[i]*(tau-g3[i])**exp2[i])
fird += nr3[i]*delta**d3[i]*tau**t3[i]*exp(
-a3[i]*(delta-e3[i])**exp1[i]-b3[i]*(tau-g3[i])**exp2[i])*(
d3[i]/delta-2*a3[i]*(delta-e3[i]))
firdd += nr3[i]*tau**t3[i]*exp(
-a3[i]*(delta-e3[i])**exp1[i]-b3[i]*(tau-g3[i])**exp2[i])*(
-2*a3[i]*delta**d3[i]+4*a3[i]**2*delta**d3[i]*(
delta-e3[i])**exp1[i]-4*d3[i]*a3[i]*delta**2*(
delta-e3[i])+d3[i]*2*delta)
firt += nr3[i]*delta**d3[i]*tau**t3[i]*exp(-a3[i]*(
delta-e3[i])**exp1[i]-b3[i]*(tau-g3[i])**exp2[i])*(
t3[i]/tau-2*b3[i]*(tau-g3[i]))
firtt += nr3[i]*delta**d3[i]*tau**t3[i]*exp(-a3[i]*(
delta-e3[i])**exp1[i]-b3[i]*(tau-g3[i])**exp2[i])*(
(t3[i]/tau-2*b3[i]*(tau-g3[i]))**exp2[i]-t3[i]/tau**2 -
2*b3[i])
firdt += nr3[i]*delta**d3[i]*tau**t3[i]*exp(-a3[i]*(
delta-e3[i])**exp1[i]-b3[i]*(tau-g3[i])**exp2[i])*(
t3[i]/tau-2*b3[i]*(tau-g3[i]))*(d3[i]/delta-2*a3[i]*(
delta-e3[i]))
firdtt += nr3[i]*delta**d3[i]*tau**t3[i]*exp(-a3[i]*(
delta-e3[i])**exp1[i]-b3[i]*(tau-g3[i])**exp2[i])*((
t3[i]/tau-2*b3[i]*(tau-g3[i]))**exp2[i]-t3[i]/tau**2-2 *
b3[i])*(d3[i]/delta-2*a3[i]*(delta-e3[i]))
B += nr3[i]*delta_0**d3[i]*tau**t3[i]*exp(-a3[i]*(
delta_0-e3[i])**exp1[i]-b3[i]*(tau-g3[i])**exp2[i])*(
d3[i]/delta_0-2*a3[i]*(delta_0-e3[i]))
C += nr3[i]*tau**t3[i]*exp(-a3[i]*(delta_0-e3[i])**exp1[i]-b3[i]*(
tau-g3[i])**exp2[i])*(
-2*a3[i]*delta_0**d3[i]+4*a3[i]**2*delta_0**d3[i]*(
delta_0-e3[i])**exp1[i]-4*d3[i]*a3[i]*delta_0**2*(
delta_0-e3[i])+d3[i]*2*delta_0)
# Non analitic terms
nr4 = self._constants.get("nr4", [])
a4 = self._constants.get("a4", [])
b = self._constants.get("b4", [])
A = self._constants.get("A", [])
Bi = self._constants.get("B", [])
Ci = self._constants.get("C", [])
D = self._constants.get("D", [])
bt = self._constants.get("beta4", [])
for i in range(len(nr4)):
Tita = (1-tau)+A[i]*((delta-1)**2)**(0.5/bt[i])
F = exp(-Ci[i]*(delta-1)**2-D[i]*(tau-1)**2)
Fd = -2*Ci[i]*F*(delta-1)
Fdd = 2*Ci[i]*F*(2*Ci[i]*(delta-1)**2-1)
Ft = -2*D[i]*F*(tau-1)
Ftt = 2*D[i]*F*(2*D[i]*(tau-1)**2-1)
Fdt = 4*Ci[i]*D[i]*F*(delta-1)*(tau-1)
Fdtt = 4*Ci[i]*D[i]*F*(delta-1)*(2*D[i]*(tau-1)**2-1)
Delta = Tita**2+Bi[i]*((delta-1)**2)**a4[i]
Deltad = (delta-1)*(A[i]*Tita*2/bt[i]*((delta-1)**2)**(
0.5/bt[i]-1)+2*Bi[i]*a4[i]*((delta-1)**2)**(a4[i]-1))
if delta == 1:
Deltadd = 0
else:
Deltadd = Deltad/(delta-1)+(delta-1)**2*(4*Bi[i]*a4[i]*(
a4[i]-1)*((delta-1)**2)**(a4[i]-2)+2*A[i]**2/bt[i]**2*(((
delta-1)**2)**(0.5/bt[i]-1))**2+A[i]*Tita*4/bt[i]*(
0.5/bt[i]-1)*((delta-1)**2)**(0.5/bt[i]-2))
DeltaBd = b[i]*Delta**(b[i]-1)*Deltad
DeltaBdd = b[i]*(Delta**(b[i]-1)*Deltadd+(b[i]-1)*Delta**(
b[i]-2)*Deltad**2)
DeltaBt = -2*Tita*b[i]*Delta**(b[i]-1)
DeltaBtt = 2*b[i]*Delta**(b[i]-1)+4*Tita**2*b[i]*(
b[i]-1)*Delta**(b[i]-2)
DeltaBdt = -A[i]*b[i]*2/bt[i]*Delta**(b[i]-1)*(delta-1)*((
delta-1)**2)**(0.5/bt[i]-1)-2*Tita*b[i]*(b[i]-1)*Delta**(
b[i]-2)*Deltad
DeltaBdtt = 2*b[i]*(b[i]-1)*Delta**(b[i]-2)*(Deltad*(
1+2*Tita**2*(b[i]-2)/Delta)+4*Tita*A[i]*(delta-1)/bt[i]*((
delta-1)**2)**(0.5/bt[i]-1))
fir += nr4[i]*Delta**b[i]*delta*F
fird += nr4[i]*(Delta**b[i]*(F+delta*Fd)+DeltaBd*delta*F)
firdd += nr4[i]*(Delta**b[i]*(2*Fd+delta*Fdd)+2*DeltaBd*(
F+delta*Fd)+DeltaBdd*delta*F)
firt += nr4[i]*delta*(DeltaBt*F+Delta**b[i]*Ft)
firtt += nr4[i]*delta*(DeltaBtt*F+2*DeltaBt*Ft+Delta**b[i]*Ftt)
firdt += nr4[i]*(Delta**b[i]*(Ft+delta*Fdt)+delta*DeltaBd*Ft +
DeltaBt*(F+delta*Fd)+DeltaBdt*delta*F)
firdtt += nr4[i]*((DeltaBtt*F+2*DeltaBt*Ft+Delta**b[i]*Ftt)+delta*(
DeltaBdtt*F+DeltaBtt*Fd+2*DeltaBdt*Ft+2*DeltaBt*Fdt+DeltaBt *
Ftt+Delta**b[i]*Fdtt))
Tita_ = (1-tau)+A[i]*((delta_0-1)**2)**(0.5/bt[i])
Delta_ = Tita_**2+Bi[i]*((delta_0-1)**2)**a4[i]
Deltad_ = (delta_0-1)*(A[i]*Tita_*2/bt[i]*((delta_0-1)**2)**(
0.5/bt[i]-1)+2*Bi[i]*a4[i]*((delta_0-1)**2)**(a4[i]-1))
Deltadd_ = Deltad_/(delta_0-1)+(delta_0-1)**2*(
4*Bi[i]*a4[i]*(a4[i]-1)*((delta_0-1)**2)**(
a4[i]-2)+2*A[i]**2/bt[i]**2*(((delta_0-1)**2)**(
0.5/bt[i]-1))**2+A[i]*Tita_*4/bt[i]*(0.5/bt[i]-1)*((
delta_0-1)**2)**(0.5/bt[i]-2))
DeltaBd_ = b[i]*Delta_**(b[i]-1)*Deltad_
DeltaBdd_ = b[i]*(Delta_**(b[i]-1)*Deltadd_+(b[i]-1)*Delta_**(
b[i]-2)*Deltad_**2)
F_ = exp(-Ci[i]*(delta_0-1)**2-D[i]*(tau-1)**2)
Fd_ = -2*Ci[i]*F_*(delta_0-1)
Fdd_ = 2*Ci[i]*F_*(2*Ci[i]*(delta_0-1)**2-1)
B += nr4[i]*(Delta_**b[i]*(F_+delta_0*Fd_)+DeltaBd_*delta_0*F_)
C += nr4[i]*(Delta_**b[i]*(2*Fd_+delta_0*Fdd_)+2*DeltaBd_*(
F_+delta_0*Fd_)+DeltaBdd_*delta_0*F_)
return fir, firt, firtt, fird, firdd, firdt, firdtt, B, C
def derivative(self, z, x, y, fase):
"""Calculate generic partial derivative: (δz/δx)y
where x, y, z can be: P, T, v, u, h, s, g, a"""
dT = {"P": self.P*1000*fase.alfap,
"T": 1,
"v": 0,
"rho": 0,
"u": fase.cv,
"h": fase.cv+self.P*1000*fase.v*fase.alfap,
"s": fase.cv/self.T,
"g": self.P*1000*fase.v*fase.alfap-fase.s,
"a": -fase.s}
dv = {"P": -self.P*1000*fase.betap,
"T": 0,
"v": 1,
"rho": -1,
"u": self.P*1000*(self.T*fase.alfap-1),
"h": self.P*1000*(self.T*fase.alfap-fase.v*fase.betap),
"s": self.P*1000*fase.alfap,
"g": -self.P*1000*fase.v*fase.betap,
"a": -self.P*1000}
return (dv[z]*dT[y]-dT[z]*dv[y])/(dv[x]*dT[y]-dT[x]*dv[y])
def _Vapor_Pressure(self, T):
eq = self._vapor_Pressure["eq"]
Tita = 1-T/self.Tc
if eq in [2, 4, 6]:
Tita = Tita**0.5
suma = sum([n*Tita**x for n, x in zip(
self._vapor_Pressure["ao"], self._vapor_Pressure["exp"])])
if eq in [1, 2]:
Pr = suma+1
elif eq in [3, 4]:
Pr = exp(suma)
else:
Pr = exp(self.Tc/T*suma)
Pv = Pr*self.Pc
return Pv
def _Liquid_Density(self, T=None):
if not T:
T = self.T
eq = self._liquid_Density["eq"]
Tita = 1-T/self.Tc
if eq in [2, 4, 6]:
Tita = Tita**(1./3)
suma = sum([n*Tita**x for n, x in zip(
self._liquid_Density["ao"], self._liquid_Density["exp"])])
if eq in [1, 2]:
Pr = suma+1
elif eq in [3, 4]:
Pr = exp(suma)
else:
Pr = exp(self.Tc/T*suma)
rho = Pr*self.rhoc
return rho
def _Vapor_Density(self, T=None):
eq = self._vapor_Density["eq"]
Tita = 1-T/self.Tc
if eq in [2, 4, 6]:
Tita = Tita**(1./3)
suma = sum([n*Tita**x for n, x in zip(
self._vapor_Density["ao"], self._vapor_Density["exp"])])
if eq in [1, 2]:
Pr = suma+1
elif eq in [3, 4]:
Pr = exp(suma)
else:
Pr = exp(self.Tc/T*suma)
rho = Pr*self.rhoc
return rho
def _Tension(self, T):
"""Equation for the surface tension"""
tau = 1-T/self.Tc
tension = 0
for sigma, n in zip(self._surface["sigma"],
self._surface["exp"]):
tension += sigma*tau**n
return tension
class IAPWS95(MEoS):
"""Multiparameter equation of state for water (including IAPWS95)
>>> water=IAPWS95(T=300, rho=996.5560)
>>> print("%0.10f %0.8f %0.5f %0.9f" % ( \
water.P, water.cv, water.w, water.s))
0.0992418350 4.13018112 1501.51914 0.393062643
>>> water=IAPWS95(T=500, rho=0.435)
>>> print("%0.10f %0.8f %0.5f %0.9f" % ( \
water.P, water.cv, water.w, water.s))
0.0999679423 1.50817541 548.31425 7.944882714
>>> water=IAPWS95(T=900., P=700)
>>> print("%0.4f %0.8f %0.5f %0.8f" % ( \
water.rho, water.cv, water.w, water.s))
870.7690 2.66422350 2019.33608 4.17223802
>>> water=IAPWS95(T=300., P=0.1)
>>> print("%0.2f %0.5f %0.2f %0.2f %0.5f %0.4f %0.1f %0.6f" % ( \
water.T, water.P, water.rho, water.h, water.s, water.cp, water.w, \
water.virialB))
300.00 0.10000 996.56 112.65 0.39306 4.1806 1501.5 -0.066682
>>> water=IAPWS95(T=500., P=0.1)
>>> print("%0.2f %0.5f %0.5f %0.1f %0.4f %0.4f %0.2f %0.7f" % ( \
water.T, water.P, water.rho, water.h, water.s, water.cp, water.w, \
water.virialB))
500.00 0.10000 0.43514 2928.6 7.9447 1.9813 548.31 -0.0094137
>>> water=IAPWS95(T=450., x=0.5)
>>> print("%0.2f %0.5f %0.4f %0.1f %0.4f %0.6f" % ( \
water.T, water.P, water.rho, water.h, water.s, water.virialB))
450.00 0.93220 9.5723 1761.8 4.3589 -0.013028
>>> water=IAPWS95(P=1.5, rho=1000.)
>>> print("%0.2f %0.4f %0.1f %0.3f %0.5f %0.4f %0.1f %0.6f" % ( \
water.T, water.P, water.rho, water.h, water.s, water.cp, water.w, \
water.virialB))
286.44 1.5000 1000.0 57.253 0.19931 4.1855 1462.1 -0.085566
>>> water=IAPWS95(h=3000, s=8.)
>>> print("%0.2f %0.5f %0.5f %0.1f %0.4f %0.4f %0.2f %0.7f" % ( \
water.T, water.P, water.rho, water.h, water.s, water.cp, water.w, \
water.virialB))
536.24 0.11970 0.48547 3000.0 8.0000 1.9984 567.04 -0.0076606
>>> water=IAPWS95(h=150, s=0.4)
>>> print("%0.2f %0.5f %0.2f %0.2f %0.5f %0.4f %0.1f %0.6f" % ( \
water.T, water.P, water.rho, water.h, water.s, water.cp, water.w, \
water.virialB))
301.27 35.50549 1011.48 150.00 0.40000 4.0932 1564.1 -0.065238
>>> water=IAPWS95(T=450., rho=300)
>>> print("%0.2f %0.5f %0.2f %0.2f %0.4f %0.6f %0.6f" % ( \
water.T, water.P, water.rho, water.h, water.s, water.x, water.virialB))
450.00 0.93220 300.00 770.82 2.1568 0.010693 -0.013028
>>> water=IAPWS95(rho=300., P=0.1)
>>> print("%0.2f %0.5f %0.2f %0.2f %0.4f %0.7f %0.6f" % ( \
water.T, water.P, water.rho, water.h, water.s, water.x, water.virialB))
372.76 0.10000 300.00 420.56 1.3110 0.0013528 -0.025144
>>> water=IAPWS95(h=1500., P=0.1)
>>> print("%0.2f %0.5f %0.4f %0.1f %0.4f %0.5f %0.6f" % ( \
water.T, water.P, water.rho, water.h, water.s, water.x, water.virialB))
372.76 0.10000 1.2303 1500.0 4.2068 0.47952 -0.025144
>>> water=IAPWS95(s=5., P=3.5)
>>> print("%0.2f %0.4f %0.3f %0.1f %0.4f %0.5f %0.7f" % ( \
water.T, water.P, water.rho, water.h, water.s, water.x, water.virialB))
515.71 3.5000 25.912 2222.8 5.0000 0.66921 -0.0085877
>>> water=IAPWS95(T=500., u=900)
>>> print("%0.2f %0.2f %0.2f %0.2f %0.1f %0.4f %0.4f %0.1f %0.7f" % ( \
water.T, water.P, water.rho, water.u, water.h, water.s, water.cp, \
water.w, water.virialB))
500.00 108.21 903.62 900.00 1019.8 2.4271 4.1751 1576.0 -0.0094137
>>> water=IAPWS95(P=0.3, u=1550.)
>>> print("%0.2f %0.5f %0.4f %0.1f %0.1f %0.4f %0.5f %0.6f" % ( \
water.T, water.P, water.rho, water.u, water.h, water.s, water.x, \
water.virialB))
406.67 0.30000 3.3029 1550.0 1640.8 4.3260 0.49893 -0.018263
>>> water=IAPWS95(rho=300, h=1000.)
>>> print("%0.2f %0.4f %0.2f %0.2f %0.1f %0.4f %0.6f %0.7f" % ( \
water.T, water.P, water.rho, water.u, water.h, water.s, water.x, \
water.virialB))
494.92 2.3991 300.00 992.00 1000.0 2.6315 0.026071 -0.0097064
>>> water=IAPWS95(rho=30, s=8.)
>>> print("%0.2f %0.3f %0.3f %0.1f %0.1f %0.4f %0.4f %0.2f %0.9f" % ( \
water.T, water.P, water.rho, water.u, water.h, water.s, water.cp, \
water.w, water.virialB))
1562.42 21.671 30.000 4628.5 5350.9 8.0000 2.7190 943.53 0.000047165
>>> water=IAPWS95(rho=30, s=4.)
>>> print("%0.2f %0.4f %0.3f %0.1f %0.1f %0.4f %0.5f %0.7f" % ( \
water.T, water.P, water.rho, water.u, water.h, water.s, water.x, \
water.virialB))
495.00 2.4029 30.000 1597.3 1677.4 4.0000 0.39218 -0.0097015
>>> water=IAPWS95(rho=300, u=1000.)
>>> print("%0.2f %0.4f %0.3f %0.1f %0.1f %0.4f %0.5f %0.7f" % ( \
water.T, water.P, water.rho, water.u, water.h, water.s, water.x, \
water.virialB))
496.44 2.4691 300.000 1000.0 1008.2 2.6476 0.02680 -0.0096173
>>> water=IAPWS95(s=3., h=1000.)
>>> print("%0.2f %0.6f %0.5f %0.2f %0.1f %0.4f %0.5f %0.6f" % ( \
water.T, water.P, water.rho, water.u, water.h, water.s, water.x, \
water.virialB))
345.73 0.034850 0.73526 952.60 1000.0 3.0000 0.29920 -0.034124
>>> water=IAPWS95(u=995., h=1000.)
>>> print("%0.2f %0.4f %0.2f %0.2f %0.1f %0.4f %0.5f %0.6f" % ( \
water.T, water.P, water.rho, water.u, water.h, water.s, water.x, \
water.virialB))
501.89 2.7329 546.58 995.00 1000.0 2.6298 0.00866 -0.009308
>>> water=IAPWS95(u=1000., s=3.)
>>> print("%0.2f %0.6f %0.5f %0.2f %0.1f %0.4f %0.5f %0.6f" % ( \
water.T, water.P, water.rho, water.u, water.h, water.s, water.x, \
water.virialB))
371.24 0.094712 1.99072 1000.00 1047.6 3.0000 0.28144 -0.025543
"""
name = "water"
CASNumber = "7732-18-5"
formula = "H2O"
synonym = "R-718"
Tc = 647.096
rhoc = 322.
Pc = 22.064
M = 18.015268 # g/mol
Tt = 273.16
Tb = 373.1243
f_acent = 0.3443
momentoDipolar = 1.855
Fi0 = {"ao_log": [1, 3.00632],
"pow": [0, 1],
"ao_pow": [-8.3204464837497, 6.6832105275932],
"ao_exp": [0.012436, 0.97315, 1.2795, 0.96956, 0.24873],
"titao": [1.28728967, 3.53734222, 7.74073708, 9.24437796,
27.5075105]}
_constants = {
"R": 8.314371357587,
"nr1": [0.12533547935523e-1, 0.78957634722828e1, -0.87803203303561e1,
0.31802509345418, -0.26145533859358, -0.78199751687981e-2,
0.88089493102134e-2],
"d1": [1, 1, 1, 2, 2, 3, 4],
"t1": [-0.5, 0.875, 1, 0.5, 0.75, 0.375, 1],
"nr2": [-0.66856572307965, 0.20433810950965, -0.66212605039687e-4,
-0.19232721156002, -0.25709043003438, 0.16074868486251,
-0.4009282892587e-1, 0.39343422603254e-6, -0.75941377088144e-5,
0.56250979351888e-3, -0.15608652257135e-4, 0.11537996422951e-8,
.36582165144204e-6, -.13251180074668e-11, -.62639586912454e-9,
-0.10793600908932, 0.17611491008752e-1, 0.22132295167546,
-0.40247669763528, 0.58083399985759, 0.49969146990806e-2,
-0.31358700712549e-1, -0.74315929710341, 0.47807329915480,
0.20527940895948e-1, -0.13636435110343, 0.14180634400617e-1,
0.83326504880713e-2, -0.29052336009585e-1, 0.38615085574206e-1,
-0.20393486513704e-1, -0.16554050063734e-2, .19955571979541e-2,
0.15870308324157e-3, -0.16388568342530e-4, 0.43613615723811e-1,
0.34994005463765e-1, -0.76788197844621e-1, 0.22446277332006e-1,
-0.62689710414685e-4, -0.55711118565645e-9, -0.19905718354408,
0.31777497330738, -0.11841182425981],
"c2": [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2,
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 6, 6,
6, 6],
"d2": [1, 1, 1, 2, 2, 3, 4, 4, 5, 7, 9, 10, 11, 13, 15, 1, 2, 2, 2, 3,
4, 4, 4, 5, 6, 6, 7, 9, 9, 9, 9, 9, 10, 10, 12, 3, 4, 4, 5, 14,
3, 6, 6, 6],
"t2": [4, 6, 12, 1, 5, 4, 2, 13, 9, 3, 4, 11, 4, 13, 1, 7, 1, 9, 10,
10, 3, 7, 10, 10, 6, 10, 10, 1, 2, 3, 4, 8, 6, 9, 8, 16, 22, 23,
23, 10, 50, 44, 46, 50],
"gamma2": [1]*44,
"nr3": [-0.31306260323435e2, 0.31546140237781e2, -0.25213154341695e4],
"d3": [3]*3,
"t3": [0, 1, 4],
"alfa3": [20]*3,
"beta3": [150, 150, 250],
"gamma3": [1.21, 1.21, 1.25],
"epsilon3": [1.]*3,
"nr4": [-0.14874640856724, 0.31806110878444],
"a4": [3.5, 3.5],
"b4": [0.85, 0.95],
"B": [0.2, 0.2],
"C": [28, 32],
"D": [700, 800],
"A": [0.32, .32],
"beta4": [0.3, 0.3]}
_vapor_Pressure = {
"eq": 6,
"ao": [-7.85951783, 1.84408259, -11.7866497, 22.6807411, -15.9618719,
1.80122502],
"exp": [2, 3, 6, 7, 8, 15]}
_liquid_Density = {
"eq": 2,
"ao": [1.99274064, 1.09965342, -0.510839303, -1.75493479, -45.5170352,
-6.74694450e5],
"exp": [1, 2, 5, 16, 43, 110]}
_vapor_Density = {
"eq": 4,
"ao": [-2.0315024, -2.6830294, -5.38626492, -17.2991605, -44.7586581,
-63.9201063],
"exp": [1, 2, 4, 9, 18.5, 35.5]}
def _visco(self, rho, T, fase):
ref = IAPWS95()
estado = ref._Helmholtz(rho, 1.5*647.096)
drho = 1/estado["dpdrho"]*1e3
return _Viscosity(rho, T, fase, drho)
def _thermo(self, rho, T, fase):
ref = IAPWS95()
estado = ref._Helmholtz(rho, 1.5*647.096)
drho = 1/estado["dpdrho"]*1e3
return _ThCond(rho, T, fase, drho)
class IAPWS95_PT(IAPWS95):
"""Derivated class for direct P and T input"""
def __init__(self, P, T):
IAPWS95.__init__(self, T=T, P=P)
class IAPWS95_Ph(IAPWS95):
"""Derivated class for direct P and h input"""
def __init__(self, P, h):
IAPWS95.__init__(self, P=P, h=h)
class IAPWS95_Ps(IAPWS95):
"""Derivated class for direct P and s input"""
def __init__(self, P, s):
IAPWS95.__init__(self, P=P, s=s)
class IAPWS95_Pv(IAPWS95):
"""Derivated class for direct P and v input"""
def __init__(self, P, v):
IAPWS95.__init__(self, P=P, v=v)
class IAPWS95_Tx(IAPWS95):
"""Derivated class for direct T and x input"""
def __init__(self, T, x):
IAPWS95.__init__(self, T=T, x=x)
class D2O(MEoS):
"""Multiparameter equation of state for heavy water
>>> water=D2O(T=300, rho=996.5560)
>>> print("%0.10f %0.8f %0.5f" % ( \
water.P, water.Liquid.cv, water.Liquid.w))
0.0030675947 4.21191157 5332.04871
"""
name = "heavy water"
CASNumber = "7789-20-0"
formula = "D2O"
synonym = "deuterium oxide"
Tc = 643.847
rhoc = 356.0
Pc = 21.671
M = 20.027508 # g/mol
Tt = 276.97
Tb = 374.563
f_acent = 0.364
momentoDipolar = 1.9
Fi0 = {'ao_log': [1, 2.9176485],
'ao_pow': [-5.60420745, 5.4495718, 0.100195196505025,
-0.2844660508898171, 0.06437609920676933,
-0.005436994367359454],
'pow': [0, 1, -1.0, -2.0, -3.0, -4.0],
'ao_exp': [], 'titao': []}
_constants = {
"R": 8.3143565,
"rhoref": 358.,
"nr1": [-0.384820628204e3, 0.108213047259e4, -0.110768260635e4,
0.164668954246e4, -0.137959852228e4, 0.598964185629e3,
-0.100451752702e3, 0.419192736351e3, -0.107279987867e4,
0.653852283544e3, -0.984305985655e3, 0.845444459339e3,
-0.376799930490e3, 0.644512590492e2, -0.214911115714e3,
0.531113962967e3, -0.135454224420e3, 0.202814416558e3,
-0.178293865031e3, 0.818739394970e2, -0.143312594493e2,
0.651202383207e2, -0.171227351208e3, 0.100859921516e2,
-0.144684680657e2, 0.128871134847e2, -0.610605957134e1,
0.109663804408e1, -0.115734899702e2, 0.374970075409e2,
0.897967147669, -0.527005883203e1, 0.438084681795e-1,
0.406772082680, -0.965258571044e-2, -0.119044600379e-1],
"d1": [1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3,
4, 4, 4, 4, 4, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8],
"t1": [0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6,
0, 1, 2, 3, 4, 5, 6, 0, 1, 0, 1, 0, 1, 0, 1],
"nr2": [0.382589102341e3, -0.106406466204e4, 0.105544952919e4,
-0.157579942855e4, 0.132703387531e4, -0.579348879870e3,
0.974163902526e2, 0.286799294226e3, -0.127543020847e4,
0.275802674911e4, -0.381284331492e4, 0.293755152012e4,
-0.117858249946e4, 0.186261198012e3],
"c2": [1]*14,
"d2": [1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2],
"t2": [0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6],
"gamma2": [1.5394]*14}
_surface = {"sigma": [0.238, -0.152082], "exp": [1.25, 2.25]}
_vapor_Pressure = {
"eq": 5,
"ao": [-0.80236e1, 0.23957e1, -0.42639e2, 0.99569e2, -0.62135e2],
"exp": [1.0, 1.5, 2.75, 3.0, 3.2]}
_liquid_Density = {
"eq": 1,
"ao": [0.26406e1, 0.97090e1, -0.18058e2, 0.87202e1, -0.74487e1],
"exp": [0.3678, 1.9, 2.2, 2.63, 7.3]}
_vapor_Density = {
"eq": 3,
"ao": [-0.37651e1, -0.38673e2, 0.73024e2, -0.13251e3, 0.75235e2,
-0.70412e2],
"exp": [0.409, 1.766, 2.24, 3.04, 3.42, 6.9]}
@classmethod
def _visco(cls, rho, T, fase=None):
Tr = T/643.847
rhor = rho/358.0
no = [1.0, 0.940695, 0.578377, -0.202044]
fi0 = Tr**0.5/sum([n/Tr**i for i, n in enumerate(no)])
Li = [0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 0, 1, 2, 5, 0, 1, 2, 3, 0, 1, 3,
5, 0, 1, 5, 3]
Lj = [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4,
4, 5, 5, 5, 6]
Lij = [0.4864192, -0.2448372, -0.8702035, 0.8716056, -1.051126,
0.3458395, 0.3509007, 1.315436, 1.297752, 1.353448, -0.2847572,
-1.037026, -1.287846, -0.02148229, 0.07013759, 0.4660127,
0.2292075, -0.4857462, 0.01641220, -0.02884911, 0.1607171,
-.009603846, -.01163815, -.008239587, 0.004559914, -0.003886659]
arr = [lij*(1./Tr-1)**i*(rhor-1)**j for i, j, lij in zip(Li, Lj, Lij)]
fi1 = exp(rhor*sum(arr))
return 55.2651e-6*fi0*fi1
@classmethod
def _thermo(cls, rho, T, fase=None):
rhor = rho/358
Tr = T/643.847
tau = Tr/(abs(Tr-1.1)+1.1)
no = [1.0, 37.3223, 22.5485, 13.0465, 0.0, -2.60735]
Lo = sum([Li*Tr**i for i, Li in enumerate(no)])
nr = [483.656, -191.039, 73.0358, -7.57467]
Lr = -167.31*(1-exp(-2.506*rhor))+sum(
[Li*rhor**(i+1) for i, Li in enumerate(nr)])
f1 = exp(0.144847*Tr-5.64493*Tr**2)
f2 = exp(-2.8*(rhor-1)**2)-0.080738543*exp(-17.943*(rhor-0.125698)**2)
f3 = 1+exp(60*(tau-1)+20)
f4 = 1+exp(100*(tau-1)+15)
Lc = 35429.6*f1*f2*(1+f2**2*(5e9*f1**4/f3+3.5*f2/f4))
Ll = -741.112*f1**1.2*(1-exp(-(rhor/2.5)**10))
return 0.742128e-3*(Lo+Lr+Lc+Ll)
if __name__ == "__main__":
import doctest
doctest.testmod()
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