#!/usr/bin/python
# -*- coding: utf-8 -*-
# pylint: disable=too-many-lines, too-many-statements, too-many-locals
# pylint: disable=too-many-instance-attributes, too-many-branches
# pylint: disable=invalid-name
"""IAPWS-IF97 standard implementation
.. image:: images/iapws97.png
:alt: iapws97
The module implement the fundamental equation for the five regions (rectangular
boxes) and the backward equation (marked in grey).
:class:`IAPWS97`: Global module class with all the functionality integrated
Fundamental equations:
* :func:`_Region1`
* :func:`_Region2`
* :func:`_Region3`
* :func:`_Region4`
* :func:`_TSat_P`
* :func:`_PSat_T`
* :func:`_Region5`
Backward equations:
* :func:`_Backward1_T_Ph`
* :func:`_Backward1_T_Ps`
* :func:`_Backward1_P_hs`
* :func:`_Backward2_T_Ph`
* :func:`_Backward2_T_Ps`
* :func:`_Backward2_P_hs`
* :func:`_Backward3_T_Ph`
* :func:`_Backward3_T_Ps`
* :func:`_Backward3_P_hs`
* :func:`_Backward3_v_Ph`
* :func:`_Backward3_v_Ps`
* :func:`_Backward3_v_PT`
* :func:`_Backward4_T_hs`
Boundary equations:
* :func:`_h13_s`
* :func:`_h3a_s`
* :func:`_h1_s`
* :func:`_t_hs`
* :func:`_PSat_h`
* :func:`_h2ab_s`
* :func:`_h_3ab`
* :func:`_h2c3b_s`
* :func:`_hab_s`
* :func:`_hbc_P`
References:
IAPWS, Revised Release on the IAPWS Industrial Formulation 1997 for the
Thermodynamic Properties of Water and Steam August 2007,
http://www.iapws.org/relguide/IF97-Rev.html
IAPWS, Revised Supplementary Release on Backward Equations for Pressure
as a Function of Enthalpy and Entropy p(h,s) for Regions 1 and 2 of the IAPWS
Industrial Formulation 1997 for the Thermodynamic Properties of Water and
Steam, http://www.iapws.org/relguide/Supp-PHS12-2014.pdf
IAPWS, Revised Supplementary Release on Backward Equations for the
Functions T(p,h), v(p,h) and T(p,s), v(p,s) for Region 3 of the IAPWS
Industrial Formulation 1997 for the Thermodynamic Properties of Water and
Steam, http://www.iapws.org/relguide/Supp-Tv%28ph,ps%293-2014.pdf
IAPWS, Revised Supplementary Release on Backward Equations p(h,s) for
Region 3, Equations as a Function of h and s for the Region Boundaries, and an
Equation Tsat(h,s) for Region 4 of the IAPWS Industrial Formulation 1997 for
the Thermodynamic Properties of Water and Steam,
http://www.iapws.org/relguide/Supp-phs3-2014.pdf
IAPWS, Revised Supplementary Release on Backward Equations for Specific
Volume as a Function of Pressure and Temperature v(p,T) for Region 3 of the
IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and
Steam, http://www.iapws.org/relguide/Supp-VPT3-2016.pdf
IAPWS, Revised Advisory Note No. 3: Thermodynamic Derivatives from IAPWS
Formulations, http://www.iapws.org/relguide/Advise3.pdf
Wagner, W; Kretzschmar, H-J: International Steam Tables: Properties of
Water and Steam Based on the Industrial Formulation IAPWS-IF97; Springer, 2008;
doi: 10.1007/978-3-540-74234-0
"""
from __future__ import division
from math import sqrt, log, exp
from scipy.optimize import fsolve, newton
import numpy as np
from . import _iapws97Constants as Const
from ._iapws import R, Tc, Pc, rhoc, Tt, Pt, Tb, Dipole, f_acent
from ._iapws import _Viscosity, _ThCond, _Tension, _Dielectric, _Refractive
from ._utils import getphase, deriv_G, _fase
# Critic properties
sc = 4.41202148223476
hc = 2087.5468451171537
# Pmin = _PSat_T(273.15) # Minimum pressure
Pmin = 0.000611212677444
# Ps_623 = _PSat_T(623.15) # P Saturation at 623.15 K, boundary region 1-3
Ps_623 = 16.5291642526
# Boundary Region1-Region3
[docs]
def _h13_s(s):
"""Define the boundary between Region 1 and 3, h=f(s)
Parameters
----------
s : float
Specific entropy, [kJ/kgK]
Returns
-------
h : float
Specific enthalpy, [kJ/kg]
Notes
-----
Raise :class:`NotImplementedError` if input isn't in limit:
* s(100MPa,623.15K) ≤ s ≤ s'(623.15K)
References
----------
IAPWS, Revised Supplementary Release on Backward Equations p(h,s) for
Region 3, Equations as a Function of h and s for the Region Boundaries, and
an Equation Tsat(h,s) for Region 4 of the IAPWS Industrial Formulation 1997
for the Thermodynamic Properties of Water and Steam,
http://www.iapws.org/relguide/Supp-phs3-2014.pdf. Eq 7
Examples
--------
>>> _h13_s(3.7)
1632.525047
>>> _h13_s(3.5)
1566.104611
"""
# Check input parameters
if s < 3.397782955 or s > 3.77828134:
raise NotImplementedError("Incoming out of bound")
sigma = s / 3.8
suma = np.sum(Const.h13_s_n * (sigma - 0.884) ** Const.h13_s_Li * (sigma - 0.864) ** Const.h13_s_Lj)
return 1700 * suma
# Boundary Region2-Region3
[docs]
def _P23_T(T):
"""Define the boundary between Region 2 and 3, P=f(T)
Parameters
----------
T : float
Temperature, [K]
Returns
-------
P : float
Pressure, [MPa]
References
----------
IAPWS, Revised Release on the IAPWS Industrial Formulation 1997 for the
Thermodynamic Properties of Water and Steam August 2007,
http://www.iapws.org/relguide/IF97-Rev.html, Eq 5
Examples
--------
>>> _P23_T(623.15)
16.52916425
"""
n = (0.34805185628969e3, -0.11671859879975e1, 0.10192970039326e-2)
return n[0] + n[1] * T + n[2] * T ** 2
[docs]
def _t_P(P):
"""Define the boundary between Region 2 and 3, T=f(P)
Parameters
----------
P : float
Pressure, [MPa]
Returns
-------
T : float
Temperature, [K]
References
----------
IAPWS, Revised Release on the IAPWS Industrial Formulation 1997 for the
Thermodynamic Properties of Water and Steam August 2007,
http://www.iapws.org/relguide/IF97-Rev.html, Eq 5
Examples
--------
>>> _t_P(16.52916425)
623.15
"""
n = (0.10192970039326e-2, 0.57254459862746e3, 0.1391883977870e2)
return n[1] + ((P - n[2]) / n[0]) ** 0.5
[docs]
def _t_hs(h, s):
"""Define the boundary between Region 2 and 3, T=f(h,s)
Parameters
----------
h : float
Specific enthalpy, [kJ/kg]
s : float
Specific entropy, [kJ/kgK]
Returns
-------
T : float
Temperature, [K]
Notes
-----
Raise :class:`NotImplementedError` if input isn't in limit:
* 5.048096828 ≤ s ≤ 5.260578707
* 2.563592004e3 ≤ h ≤ 2.812942061e3
References
----------
IAPWS, Revised Supplementary Release on Backward Equations p(h,s) for
Region 3, Equations as a Function of h and s for the Region Boundaries, and
an Equation Tsat(h,s) for Region 4 of the IAPWS Industrial Formulation 1997
for the Thermodynamic Properties of Water and Steam,
http://www.iapws.org/relguide/Supp-phs3-2014.pdf. Eq 8
Examples
--------
>>> _t_hs(2600, 5.1)
713.5259364
>>> _t_hs(2800, 5.2)
817.6202120
"""
# Check input parameters
if s < 5.048096828 or s > 5.260578707 or \
h < 2.563592004e3 or h > 2.812942061e3:
raise NotImplementedError("Incoming out of bound")
nu = h / 3000
sigma = s / 5.3
suma = np.sum(Const.t_hs_n * (nu - 0.727) ** Const.t_hs_Li * (sigma - 0.864) ** Const.t_hs_Lj)
return 900 * suma
# Saturated line
[docs]
def _PSat_T(T):
"""Define the saturated line, P=f(T)
Parameters
----------
T : float
Temperature, [K]
Returns
-------
P : float
Pressure, [MPa]
Notes
-----
Raise :class:`NotImplementedError` if input isn't in limit:
* 273.15 ≤ T ≤ 647.096
References
----------
IAPWS, Revised Release on the IAPWS Industrial Formulation 1997 for the
Thermodynamic Properties of Water and Steam August 2007,
http://www.iapws.org/relguide/IF97-Rev.html, Eq 30
Examples
--------
>>> _PSat_T(500)
2.63889776
"""
# Check input parameters
if T < 273.15 or T > Tc:
raise NotImplementedError("Incoming out of bound")
n = (0, 0.11670521452767E+04, -0.72421316703206E+06, -0.17073846940092E+02,
0.12020824702470E+05, -0.32325550322333E+07, 0.14915108613530E+02,
-0.48232657361591E+04, 0.40511340542057E+06, -0.23855557567849E+00,
0.65017534844798E+03)
tita = T + n[9] / (T - n[10])
A = tita ** 2 + n[1] * tita + n[2]
B = n[3] * tita ** 2 + n[4] * tita + n[5]
C = n[6] * tita ** 2 + n[7] * tita + n[8]
return (2 * C / (-B + (B ** 2 - 4 * A * C) ** 0.5)) ** 4
[docs]
def _TSat_P(P):
"""Define the saturated line, T=f(P)
Parameters
----------
P : float
Pressure, [MPa]
Returns
-------
T : float
Temperature, [K]
Notes
-----
Raise :class:`NotImplementedError` if input isn't in limit:
* 0.00061121 ≤ P ≤ 22.064
References
----------
IAPWS, Revised Release on the IAPWS Industrial Formulation 1997 for the
Thermodynamic Properties of Water and Steam August 2007,
http://www.iapws.org/relguide/IF97-Rev.html, Eq 31
Examples
--------
>>> _TSat_P(10)
584.149488
"""
# Check input parameters
if P < 611.212677 / 1e6 or P > 22.064:
raise NotImplementedError("Incoming out of bound")
n = (0, 0.11670521452767E+04, -0.72421316703206E+06, -0.17073846940092E+02,
0.12020824702470E+05, -0.32325550322333E+07, 0.14915108613530E+02,
-0.48232657361591E+04, 0.40511340542057E+06, -0.23855557567849E+00,
0.65017534844798E+03)
beta = P ** 0.25
E = beta ** 2 + n[3] * beta + n[6]
F = n[1] * beta ** 2 + n[4] * beta + n[7]
G = n[2] * beta ** 2 + n[5] * beta + n[8]
D = 2 * G / (-F - (F ** 2 - 4 * E * G) ** 0.5)
return (n[10] + D - ((n[10] + D) ** 2 - 4 * (n[9] + n[10] * D)) ** 0.5) / 2
[docs]
def _PSat_h(h):
"""Define the saturated line, P=f(h) for region 3
Parameters
----------
h : float
Specific enthalpy, [kJ/kg]
Returns
-------
P : float
Pressure, [MPa]
Notes
-----
Raise :class:`NotImplementedError` if input isn't in limit:
* h'(623.15K) ≤ h ≤ h''(623.15K)
References
----------
IAPWS, Revised Supplementary Release on Backward Equations for the
Functions T(p,h), v(p,h) and T(p,s), v(p,s) for Region 3 of the IAPWS
Industrial Formulation 1997 for the Thermodynamic Properties of Water and
Steam, http://www.iapws.org/relguide/Supp-Tv%28ph,ps%293-2014.pdf, Eq 10
Examples
--------
>>> _PSat_h(1700)
17.24175718
>>> _PSat_h(2400)
20.18090839
"""
# Check input parameters
hmin_Ps3 = _Region1(623.15, Ps_623)["h"]
hmax_Ps3 = _Region2(623.15, Ps_623)["h"]
if h < hmin_Ps3 or h > hmax_Ps3:
raise NotImplementedError("Incoming out of bound")
nu = h / 2600
suma = np.sum(Const.PSat_h_n * (nu - 1.02) ** Const.PSat_h_Li * (nu - 0.608) ** Const.PSat_h_Lj)
return 22 * suma
[docs]
def _PSat_s(s):
"""Define the saturated line, P=f(s) for region 3
Parameters
----------
s : float
Specific entropy, [kJ/kgK]
Returns
-------
P : float
Pressure, [MPa]
Notes
-----
Raise :class:`NotImplementedError` if input isn't in limit:
* s'(623.15K) ≤ s ≤ s''(623.15K)
References
----------
IAPWS, Revised Supplementary Release on Backward Equations for the
Functions T(p,h), v(p,h) and T(p,s), v(p,s) for Region 3 of the IAPWS
Industrial Formulation 1997 for the Thermodynamic Properties of Water and
Steam, http://www.iapws.org/relguide/Supp-Tv%28ph,ps%293-2014.pdf, Eq 11
Examples
--------
>>> _PSat_s(3.8)
16.87755057
>>> _PSat_s(5.2)
16.68968482
"""
# Check input parameters
smin_Ps3 = _Region1(623.15, Ps_623)["s"]
smax_Ps3 = _Region2(623.15, Ps_623)["s"]
if s < smin_Ps3 or s > smax_Ps3:
raise NotImplementedError("Incoming out of bound")
sigma = s / 5.2
suma = np.sum(Const.PSat_s_n * (sigma - 1.03) ** Const.PSat_s_Li * (sigma - 0.699) ** Const.PSat_s_Lj)
return 22 * suma
[docs]
def _h1_s(s):
"""Define the saturated line boundary between Region 1 and 4, h=f(s)
Parameters
----------
s : float
Specific entropy, [kJ/kgK]
Returns
-------
h : float
Specific enthalpy, [kJ/kg]
Notes
-----
Raise :class:`NotImplementedError` if input isn't in limit:
* s'(273.15K) ≤ s ≤ s'(623.15K)
References
----------
IAPWS, Revised Supplementary Release on Backward Equations p(h,s) for
Region 3, Equations as a Function of h and s for the Region Boundaries, and
an Equation Tsat(h,s) for Region 4 of the IAPWS Industrial Formulation 1997
for the Thermodynamic Properties of Water and Steam,
http://www.iapws.org/relguide/Supp-phs3-2014.pdf. Eq 3
Examples
--------
>>> _h1_s(1)
308.5509647
>>> _h1_s(3)
1198.359754
"""
# Check input parameters
if s < -1.545495919e-4 or s > 3.77828134:
raise NotImplementedError("Incoming out of bound")
sigma = s / 3.8
suma = np.sum(Const.h1_s_n * (sigma - 1.09) ** Const.h1_s_Li * (sigma + 0.366e-4) ** Const.h1_s_Lj)
return 1700 * suma
[docs]
def _h3a_s(s):
"""Define the saturated line boundary between Region 4 and 3a, h=f(s)
Parameters
----------
s : float
Specific entropy, [kJ/kgK]
Returns
-------
h : float
Specific enthalpy, [kJ/kg]
Notes
-----
Raise :class:`NotImplementedError` if input isn't in limit:
* s'(623.15K) ≤ s ≤ sc
References
----------
IAPWS, Revised Supplementary Release on Backward Equations p(h,s) for
Region 3, Equations as a Function of h and s for the Region Boundaries, and
an Equation Tsat(h,s) for Region 4 of the IAPWS Industrial Formulation 1997
for the Thermodynamic Properties of Water and Steam,
http://www.iapws.org/relguide/Supp-phs3-2014.pdf. Eq 4
Examples
--------
>>> _h3a_s(3.8)
1685.025565
>>> _h3a_s(4.2)
1949.352563
"""
# Check input parameters
if s < 3.77828134 or s > 4.41202148223476:
raise NotImplementedError("Incoming out of bound")
sigma = s / 3.8
suma = np.sum(Const.h3a_s_n * (sigma - 1.09) ** Const.h3a_s_Li * (sigma + 0.366e-4) ** Const.h3a_s_Lj)
return 1700 * suma
[docs]
def _h2ab_s(s):
"""Define the saturated line boundary between Region 4 and 2a-2b, h=f(s)
Parameters
----------
s : float
Specific entropy, [kJ/kgK]
Returns
-------
h : float
Specific enthalpy, [kJ/kg]
Notes
-----
Raise :class:`NotImplementedError` if input isn't in limit:
* 5.85 ≤ s ≤ s"(273.15K)
References
----------
IAPWS, Revised Supplementary Release on Backward Equations p(h,s) for
Region 3, Equations as a Function of h and s for the Region Boundaries, and
an Equation Tsat(h,s) for Region 4 of the IAPWS Industrial Formulation 1997
for the Thermodynamic Properties of Water and Steam,
http://www.iapws.org/relguide/Supp-phs3-2014.pdf. Eq 5
Examples
--------
>>> _h2ab_s(7)
2723.729985
>>> _h2ab_s(9)
2511.861477
"""
# Check input parameters
if s < 5.85 or s > 9.155759395:
raise NotImplementedError("Incoming out of bound")
sigma1 = s / 5.21
sigma2 = s / 9.2
suma = np.sum(Const.h2ab_s_n * (1 / sigma1 - 0.513) ** Const.h2ab_s_Li * (sigma2 - 0.524) ** Const.h2ab_s_Lj)
return 2800 * exp(suma)
[docs]
def _h2c3b_s(s):
"""Define the saturated line boundary between Region 4 and 2c-3b, h=f(s)
Parameters
----------
s : float
Specific entropy, [kJ/kgK]
Returns
-------
h : float
Specific enthalpy, [kJ/kg]
Notes
-----
Raise :class:`NotImplementedError` if input isn't in limit:
* sc ≤ s ≤ 5.85
References
----------
IAPWS, Revised Supplementary Release on Backward Equations p(h,s) for
Region 3, Equations as a Function of h and s for the Region Boundaries, and
an Equation Tsat(h,s) for Region 4 of the IAPWS Industrial Formulation 1997
for the Thermodynamic Properties of Water and Steam,
http://www.iapws.org/relguide/Supp-phs3-2014.pdf. Eq 6
Examples
--------
>>> _h2c3b_s(5.5)
2687.693850
>>> _h2c3b_s(4.5)
2144.360448
"""
# Check input parameters
if s < 4.41202148223476 or s > 5.85:
raise NotImplementedError("Incoming out of bound")
sigma = s / 5.9
suma = np.sum(Const.h2c3b_s_n * (sigma - 1.02) ** Const.h2c3b_s_Li * (sigma - 0.726) ** Const.h2c3b_s_Lj)
return 2800 * suma ** 4
# Region 1
[docs]
def _Region1(T, P):
"""Basic equation for region 1
Parameters
----------
T : float
Temperature, [K]
P : float
Pressure, [MPa]
Returns
-------
prop : dict
Dict with calculated properties. The available properties are:
* v: Specific volume, [m³/kg]
* h: Specific enthalpy, [kJ/kg]
* s: Specific entropy, [kJ/kgK]
* cp: Specific isobaric heat capacity, [kJ/kgK]
* cv: Specific isocoric heat capacity, [kJ/kgK]
* w: Speed of sound, [m/s]
* alfav: Cubic expansion coefficient, [1/K]
* kt: Isothermal compressibility, [1/MPa]
References
----------
IAPWS, Revised Release on the IAPWS Industrial Formulation 1997 for the
Thermodynamic Properties of Water and Steam August 2007,
http://www.iapws.org/relguide/IF97-Rev.html, Eq 7
Examples
--------
>>> _Region1(300,3)["v"]
0.00100215168
>>> _Region1(300,3)["h"]
115.331273
>>> _Region1(300,3)["h"]-3000*_Region1(300,3)["v"]
112.324818
>>> _Region1(300,80)["s"]
0.368563852
>>> _Region1(300,80)["cp"]
4.01008987
>>> _Region1(300,80)["cv"]
3.91736606
>>> _Region1(500,3)["w"]
1240.71337
>>> _Region1(500,3)["alfav"]
0.00164118128
>>> _Region1(500,3)["kt"]
0.00112892188
"""
if P < 0:
P = Pmin
Tr = 1386 / T
Pr = P / 16.53
g = np.sum(Const.Region1_n * (7.1 - Pr) ** Const.Region1_Li * (Tr - 1.222) ** Const.Region1_Lj)
gp = -np.sum(
Const.Region1_n_Li_product * (7.1 - Pr) ** Const.Region1_Li_less_1 * (Tr - 1.222) ** Const.Region1_Lj)
gpp = np.sum(
Const.Region1_n_Li_product * Const.Region1_Li_less_1 * (7.1 - Pr) ** Const.Region1_Li_less_2 * (
Tr - 1.222) ** Const.Region1_Lj)
gt = np.sum(
Const.Region1_n_Lj_product * (7.1 - Pr) ** Const.Region1_Li * (Tr - 1.222) ** Const.Region1_Lj_less_1)
gtt = np.sum(
Const.Region1_n_Lj_product * Const.Region1_Lj_less_1 * (7.1 - Pr) ** Const.Region1_Li * (Tr - 1.222) ** (
Const.Region1_Lj_less_2))
gpt = -np.sum(Const.Region1_n_Li_Lj_product * (7.1 - Pr) ** Const.Region1_Li_less_1 * (Tr - 1.222) ** (
Const.Region1_Lj_less_1))
propiedades = {}
propiedades["T"] = T
propiedades["P"] = P
propiedades["v"] = Pr * gp * R * T / P / 1000
propiedades["h"] = Tr * gt * R * T
propiedades["s"] = R * (Tr * gt - g)
propiedades["cp"] = -R * Tr ** 2 * gtt
propiedades["cv"] = R * (-Tr ** 2 * gtt + (gp - Tr * gpt) ** 2 / gpp)
propiedades["w"] = sqrt(R * T * 1000 * gp ** 2 / ((gp - Tr * gpt) ** 2 / (Tr ** 2 * gtt) - gpp))
propiedades["alfav"] = (1 - Tr * gpt / gp) / T
propiedades["kt"] = -Pr * gpp / gp / P
propiedades["region"] = 1
propiedades["x"] = 0
return propiedades
[docs]
def _Backward1_T_Ph(P, h):
"""
Backward equation for region 1, T=f(P,h)
Parameters
----------
P : float
Pressure, [MPa]
h : float
Specific enthalpy, [kJ/kg]
Returns
-------
T : float
Temperature, [K]
References
----------
IAPWS, Revised Release on the IAPWS Industrial Formulation 1997 for the
Thermodynamic Properties of Water and Steam August 2007,
http://www.iapws.org/relguide/IF97-Rev.html, Eq 11
Examples
--------
>>> _Backward1_T_Ph(3,500)
391.798509
>>> _Backward1_T_Ph(80,1500)
611.041229
"""
Pr = P / 1
nu = h / 2500
T = np.sum(Const.Backward1_T_Ph_n * Pr ** Const.Backward1_T_Ph_Li * (nu + 1) ** Const.Backward1_T_Ph_Lj)
return T
[docs]
def _Backward1_T_Ps(P, s):
"""Backward equation for region 1, T=f(P,s)
Parameters
----------
P : float
Pressure, [MPa]
s : float
Specific entropy, [kJ/kgK]
Returns
-------
T : float
Temperature, [K]
References
----------
IAPWS, Revised Release on the IAPWS Industrial Formulation 1997 for the
Thermodynamic Properties of Water and Steam August 2007,
http://www.iapws.org/relguide/IF97-Rev.html, Eq 13
Examples
--------
>>> _Backward1_T_Ps(3,0.5)
307.842258
>>> _Backward1_T_Ps(80,3)
565.899909
"""
Pr = P / 1
sigma = s / 1
T = np.sum(Const.Backward1_T_Ps_n * Pr ** Const.Backward1_T_Ps_Li * (sigma + 2) ** Const.Backward1_T_Ps_Lj)
return T
[docs]
def _Backward1_P_hs(h, s):
"""Backward equation for region 1, P=f(h,s)
Parameters
----------
h : float
Specific enthalpy, [kJ/kg]
s : float
Specific entropy, [kJ/kgK]
Returns
-------
P : float
Pressure, [MPa]
References
----------
IAPWS, Revised Supplementary Release on Backward Equations for Pressure
as a Function of Enthalpy and Entropy p(h,s) for Regions 1 and 2 of the
IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of
Water and Steam, http://www.iapws.org/relguide/Supp-PHS12-2014.pdf, Eq 1
Examples
--------
>>> _Backward1_P_hs(0.001,0)
0.0009800980612
>>> _Backward1_P_hs(90,0)
91.92954727
>>> _Backward1_P_hs(1500,3.4)
58.68294423
"""
nu = h / 3400
sigma = s / 7.6
P = np.sum(
Const.Backward1_P_hs_n * (nu + 0.05) ** Const.Backward1_P_hs_Li * (sigma + 0.05) ** Const.Backward1_P_hs_Lj)
return 100 * P
# Region 2
[docs]
def _Region2(T, P):
"""Basic equation for region 2
Parameters
----------
T : float
Temperature, [K]
P : float
Pressure, [MPa]
Returns
-------
prop : dict
Dict with calculated properties. The available properties are:
* v: Specific volume, [m³/kg]
* h: Specific enthalpy, [kJ/kg]
* s: Specific entropy, [kJ/kgK]
* cp: Specific isobaric heat capacity, [kJ/kgK]
* cv: Specific isocoric heat capacity, [kJ/kgK]
* w: Speed of sound, [m/s]
* alfav: Cubic expansion coefficient, [1/K]
* kt: Isothermal compressibility, [1/MPa]
References
----------
IAPWS, Revised Release on the IAPWS Industrial Formulation 1997 for the
Thermodynamic Properties of Water and Steam August 2007,
http://www.iapws.org/relguide/IF97-Rev.html, Eq 15-17
Examples
--------
>>> _Region2(700,30)["v"]
0.00542946619
>>> _Region2(700,30)["h"]
2631.49474
>>> _Region2(700,30)["h"]-30000*_Region2(700,30)["v"]
2468.61076
>>> _Region2(700,0.0035)["s"]
10.1749996
>>> _Region2(700,0.0035)["cp"]
2.08141274
>>> _Region2(700,0.0035)["cv"]
1.61978333
>>> _Region2(300,0.0035)["w"]
427.920172
>>> _Region2(300,0.0035)["alfav"]
0.00337578289
>>> _Region2(300,0.0035)["kt"]
286.239651
"""
if P < 0:
P = Pmin
Tr = 540 / T
Pr = P / 1
go, gop, gopp, got, gott, gopt = Region2_cp0(Tr, Pr)
gr = np.sum(Const.Region2_nr * Pr ** Const.Region2_Ir * (Tr - 0.5) ** Const.Region2_Jr)
grp = np.sum(Const.Region2_nr_Ir_product * Pr ** Const.Region2_Ir_less_1 * (Tr - 0.5) ** Const.Region2_Jr)
grpp = np.sum(
Const.Region2_nr_Ir_product * Const.Region2_Ir_less_1 * Pr ** Const.Region2_Ir_less_2 * (
Tr - 0.5) ** Const.Region2_Jr)
grt = np.sum(Const.Region2_nr_Jr_product * Pr ** Const.Region2_Ir * (Tr - 0.5) ** Const.Region2_Jr_less_1)
grtt = np.sum(
Const.Region2_nr_Jr_product * Const.Region2_Jr_less_1 * Pr ** Const.Region2_Ir *
(Tr - 0.5) ** Const.Region2_Jr_less_2)
grpt = np.sum(
Const.Region2_nr_Ir_Jr_product * Pr ** Const.Region2_Ir_less_1 * (Tr - 0.5) ** Const.Region2_Jr_less_1)
propiedades = {}
propiedades["T"] = T
propiedades["P"] = P
propiedades["v"] = Pr * (gop + grp) * R * T / P / 1000
propiedades["h"] = Tr * (got + grt) * R * T
propiedades["s"] = R * (Tr * (got + grt) - (go + gr))
propiedades["cp"] = -R * Tr ** 2 * (gott + grtt)
propiedades["cv"] = R * (-Tr ** 2 * (gott + grtt) - (1 + Pr * grp - Tr * Pr * grpt) ** 2
/ (1 - Pr ** 2 * grpp))
propiedades["w"] = (R * T * 1000 * (1 + 2 * Pr * grp + Pr ** 2 * grp ** 2) / (1 - Pr ** 2 * grpp + (
1 + Pr * grp - Tr * Pr * grpt) ** 2 / Tr ** 2 / (gott + grtt))) ** 0.5
propiedades["alfav"] = (1 + Pr * grp - Tr * Pr * grpt) / (1 + Pr * grp) / T
propiedades["kt"] = (1 - Pr ** 2 * grpp) / (1 + Pr * grp) / P
propiedades["region"] = 2
propiedades["x"] = 1
return propiedades
[docs]
def Region2_cp0(Tr, Pr):
"""Ideal properties for Region 2
Parameters
----------
Tr : float
Reduced temperature, [-]
Pr : float
Reduced pressure, [-]
Returns
-------
prop : array
Array with ideal Gibbs energy partial derivatives:
* g: Ideal Specific Gibbs energy [kJ/kg]
* gp: ∂g/∂P|T
* gpp: ∂²g/∂P²|T
* gt: ∂g/∂T|P
* gtt: ∂²g/∂T²|P
* gpt: ∂²g/∂T∂P
References
----------
IAPWS, Revised Release on the IAPWS Industrial Formulation 1997 for the
Thermodynamic Properties of Water and Steam August 2007,
http://www.iapws.org/relguide/IF97-Rev.html, Eq 16
"""
go = log(Pr)
gop = Pr ** -1
gopp = -Pr ** -2
gopt = 0
go += np.sum(Const.Region2_cp0_no * Tr ** Const.Region2_cp0_Jo)
got = np.sum(Const.Region2_cp0_no * Const.Region2_cp0_Jo * Tr ** (Const.Region2_cp0_Jo - 1))
gott = np.sum(
Const.Region2_cp0_no * Const.Region2_cp0_Jo * (Const.Region2_cp0_Jo - 1) * Tr ** (Const.Region2_cp0_Jo - 2))
return go, gop, gopp, got, gott, gopt
[docs]
def _P_2bc(h):
"""Define the boundary between Region 2b and 2c, P=f(h)
Parameters
----------
h : float
Specific enthalpy, [kJ/kg]
Returns
-------
P : float
Pressure, [MPa]
References
----------
IAPWS, Revised Release on the IAPWS Industrial Formulation 1997 for the
Thermodynamic Properties of Water and Steam August 2007,
http://www.iapws.org/relguide/IF97-Rev.html, Eq 20
Examples
--------
>>> _P_2bc(3516.004323)
100.0
"""
return 905.84278514723 - 0.67955786399241 * h + 1.2809002730136e-4 * h ** 2
[docs]
def _hbc_P(P):
"""Define the boundary between Region 2b and 2c, h=f(P)
Parameters
----------
P : float
Pressure, [MPa]
Returns
-------
h : float
Specific enthalpy, [kJ/kg]
References
----------
IAPWS, Revised Release on the IAPWS Industrial Formulation 1997 for the
Thermodynamic Properties of Water and Steam August 2007,
http://www.iapws.org/relguide/IF97-Rev.html, Eq 21
Examples
--------
>>> _hbc_P(100)
3516.004323
"""
return 0.26526571908428e4 + ((P - 0.45257578905948e1) / 1.2809002730136e-4) ** 0.5
[docs]
def _hab_s(s):
"""Define the boundary between Region 2a and 2b, h=f(s)
Parameters
----------
s : float
Specific entropy, [kJ/kgK]
Returns
-------
h : float
Specific enthalpy, [kJ/kg]
References
----------
IAPWS, Revised Supplementary Release on Backward Equations for Pressure
as a Function of Enthalpy and Entropy p(h,s) for Regions 1 and 2 of the
IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of
Water and Steam, http://www.iapws.org/relguide/Supp-PHS12-2014.pdf, Eq 2
Examples
--------
>>> _hab_s(7)
3376.437884
"""
smin = _Region2(_TSat_P(4), 4)["s"]
smax = _Region2(1073.15, 4)["s"]
if s < smin:
h = 0
elif s > smax:
h = 5000
else:
h = -0.349898083432139e4 + 0.257560716905876e4 * s - \
0.421073558227969e3 * s ** 2 + 0.276349063799944e2 * s ** 3
return h
[docs]
def _Backward2a_T_Ph(P, h):
"""Backward equation for region 2a, T=f(P,h)
Parameters
----------
P : float
Pressure, [MPa]
h : float
Specific enthalpy, [kJ/kg]
Returns
-------
T : float
Temperature, [K]
References
----------
IAPWS, Revised Release on the IAPWS Industrial Formulation 1997 for the
Thermodynamic Properties of Water and Steam August 2007,
http://www.iapws.org/relguide/IF97-Rev.html, Eq 22
Examples
--------
>>> _Backward2a_T_Ph(0.001,3000)
534.433241
>>> _Backward2a_T_Ph(3,4000)
1010.77577
"""
Pr = P / 1
nu = h / 2000
T = np.sum(Const.Backward2a_T_Ph_n * Pr ** Const.Backward2a_T_Ph_Li * (nu - 2.1) ** Const.Backward2a_T_Ph_Lj)
return T
[docs]
def _Backward2b_T_Ph(P, h):
"""Backward equation for region 2b, T=f(P,h)
Parameters
----------
P : float
Pressure, [MPa]
h : float
Specific enthalpy, [kJ/kg]
Returns
-------
T : float
Temperature, [K]
References
----------
IAPWS, Revised Release on the IAPWS Industrial Formulation 1997 for the
Thermodynamic Properties of Water and Steam August 2007,
http://www.iapws.org/relguide/IF97-Rev.html, Eq 23
Examples
--------
>>> _Backward2b_T_Ph(5,4000)
1015.31583
>>> _Backward2b_T_Ph(25,3500)
875.279054
"""
Pr = P / 1
nu = h / 2000
T = np.sum(
Const.Backward2b_T_Ph_n * (Pr - 2) ** Const.Backward2b_T_Ph_Li * (nu - 2.6) ** Const.Backward2b_T_Ph_Lj)
return T
[docs]
def _Backward2c_T_Ph(P, h):
"""Backward equation for region 2c, T=f(P,h)
Parameters
----------
P : float
Pressure, [MPa]
h : float
Specific enthalpy, [kJ/kg]
Returns
-------
T : float
Temperature, [K]
References
----------
IAPWS, Revised Release on the IAPWS Industrial Formulation 1997 for the
Thermodynamic Properties of Water and Steam August 2007,
http://www.iapws.org/relguide/IF97-Rev.html, Eq 24
Examples
--------
>>> _Backward2c_T_Ph(40,2700)
743.056411
>>> _Backward2c_T_Ph(60,3200)
882.756860
"""
Pr = P / 1
nu = h / 2000
T = np.sum(
Const.Backward2c_T_Ph_n * (Pr + 25) ** Const.Backward2c_T_Ph_Li * (nu - 1.8) ** Const.Backward2c_T_Ph_Lj)
return T
[docs]
def _Backward2_T_Ph(P, h):
"""Backward equation for region 2, T=f(P,h)
Parameters
----------
P : float
Pressure, [MPa]
h : float
Specific enthalpy, [kJ/kg]
Returns
-------
T : float
Temperature, [K]
"""
if P <= 4:
T = _Backward2a_T_Ph(P, h)
elif 4 < P <= 6.546699678:
T = _Backward2b_T_Ph(P, h)
else:
hf = _hbc_P(P)
if h >= hf:
T = _Backward2b_T_Ph(P, h)
else:
T = _Backward2c_T_Ph(P, h)
if P <= 22.064:
Tsat = _TSat_P(P)
T = max(Tsat, T)
return T
[docs]
def _Backward2a_T_Ps(P, s):
"""Backward equation for region 2a, T=f(P,s)
Parameters
----------
P : float
Pressure, [MPa]
s : float
Specific entropy, [kJ/kgK]
Returns
-------
T : float
Temperature, [K]
References
----------
IAPWS, Revised Release on the IAPWS Industrial Formulation 1997 for the
Thermodynamic Properties of Water and Steam August 2007,
http://www.iapws.org/relguide/IF97-Rev.html, Eq 25
Examples
--------
>>> _Backward2a_T_Ps(0.1,7.5)
399.517097
>>> _Backward2a_T_Ps(2.5,8)
1039.84917
"""
Pr = P / 1
sigma = s / 2
T = np.sum(Const.Backward2a_T_Ps_n * Pr ** Const.Backward2a_T_Ps_Li * (sigma - 2) ** Const.Backward2a_T_Ps_Lj)
return T
[docs]
def _Backward2b_T_Ps(P, s):
"""Backward equation for region 2b, T=f(P,s)
Parameters
----------
P : float
Pressure, [MPa]
s : float
Specific entropy, [kJ/kgK]
Returns
-------
T : float
Temperature, [K]
References
----------
IAPWS, Revised Release on the IAPWS Industrial Formulation 1997 for the
Thermodynamic Properties of Water and Steam August 2007,
http://www.iapws.org/relguide/IF97-Rev.html, Eq 26
Examples
--------
>>> _Backward2b_T_Ps(8,6)
600.484040
>>> _Backward2b_T_Ps(90,6)
1038.01126
"""
Pr = P / 1
sigma = s / 0.7853
T = np.sum(Const.Backward2b_T_Ps_n * Pr ** Const.Backward2b_T_Ps_Li * (10 - sigma) ** Const.Backward2b_T_Ps_Lj)
return T
[docs]
def _Backward2c_T_Ps(P, s):
"""Backward equation for region 2c, T=f(P,s)
Parameters
----------
P : float
Pressure, [MPa]
s : float
Specific entropy, [kJ/kgK]
Returns
-------
T : float
Temperature, [K]
References
----------
IAPWS, Revised Release on the IAPWS Industrial Formulation 1997 for the
Thermodynamic Properties of Water and Steam August 2007,
http://www.iapws.org/relguide/IF97-Rev.html, Eq 27
Examples
--------
>>> _Backward2c_T_Ps(20,5.75)
697.992849
>>> _Backward2c_T_Ps(80,5.75)
949.017998
"""
Pr = P / 1
sigma = s / 2.9251
T = np.sum(Const.Backward2c_T_Ps_n * Pr ** Const.Backward2c_T_Ps_Li * (2 - sigma) ** Const.Backward2c_T_Ps_Lj)
return T
[docs]
def _Backward2_T_Ps(P, s):
"""Backward equation for region 2, T=f(P,s)
Parameters
----------
P : float
Pressure, [MPa]
s : float
Specific entropy, [kJ/kgK]
Returns
-------
T : float
Temperature, [K]
"""
if P <= 4:
T = _Backward2a_T_Ps(P, s)
elif s >= 5.85:
T = _Backward2b_T_Ps(P, s)
else:
T = _Backward2c_T_Ps(P, s)
if P <= 22.064:
Tsat = _TSat_P(P)
T = max(Tsat, T)
return T
[docs]
def _Backward2a_P_hs(h, s):
"""Backward equation for region 2a, P=f(h,s)
Parameters
----------
h : float
Specific enthalpy, [kJ/kg]
s : float
Specific entropy, [kJ/kgK]
Returns
-------
P : float
Pressure, [MPa]
References
----------
IAPWS, Revised Supplementary Release on Backward Equations for Pressure
as a Function of Enthalpy and Entropy p(h,s) for Regions 1 and 2 of the
IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of
Water and Steam, http://www.iapws.org/relguide/Supp-PHS12-2014.pdf, Eq 3
Examples
--------
>>> _Backward2a_P_hs(2800,6.5)
1.371012767
>>> _Backward2a_P_hs(2800,9.5)
0.001879743844
>>> _Backward2a_P_hs(4100,9.5)
0.1024788997
"""
nu = h / 4200
sigma = s / 12
suma = np.sum(
Const.Backward2a_P_hs_n * (nu - 0.5) ** Const.Backward2a_P_hs_Li * (sigma - 1.2) ** Const.Backward2a_P_hs_Lj)
return 4 * suma ** 4
[docs]
def _Backward2b_P_hs(h, s):
"""Backward equation for region 2b, P=f(h,s)
Parameters
----------
h : float
Specific enthalpy, [kJ/kg]
s : float
Specific entropy, [kJ/kgK]
Returns
-------
P : float
Pressure, [MPa]
References
----------
IAPWS, Revised Supplementary Release on Backward Equations for Pressure
as a Function of Enthalpy and Entropy p(h,s) for Regions 1 and 2 of the
IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of
Water and Steam, http://www.iapws.org/relguide/Supp-PHS12-2014.pdf, Eq 4
Examples
--------
>>> _Backward2b_P_hs(2800,6)
4.793911442
>>> _Backward2b_P_hs(3600,6)
83.95519209
>>> _Backward2b_P_hs(3600,7)
7.527161441
"""
nu = h / 4100
sigma = s / 7.9
suma = np.sum(Const.Backward2b_P_hs_n * (nu - 0.6) ** Const.Backward2b_P_hs_Li * (
sigma - 1.01) ** Const.Backward2b_P_hs_Lj)
return 100 * suma ** 4
[docs]
def _Backward2c_P_hs(h, s):
"""Backward equation for region 2c, P=f(h,s)
Parameters
----------
h : float
Specific enthalpy, [kJ/kg]
s : float
Specific entropy, [kJ/kgK]
Returns
-------
P : float
Pressure, [MPa]
References
----------
IAPWS, Revised Supplementary Release on Backward Equations for Pressure
as a Function of Enthalpy and Entropy p(h,s) for Regions 1 and 2 of the
IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of
Water and Steam, http://www.iapws.org/relguide/Supp-PHS12-2014.pdf, Eq 5
Examples
--------
>>> _Backward2c_P_hs(2800,5.1)
94.39202060
>>> _Backward2c_P_hs(2800,5.8)
8.414574124
>>> _Backward2c_P_hs(3400,5.8)
83.76903879
"""
nu = h / 3500
sigma = s / 5.9
suma = np.sum(
Const.Backward2c_P_hs_n * (nu - 0.7) ** Const.Backward2c_P_hs_Li * (sigma - 1.1) ** Const.Backward2c_P_hs_Lj)
return 100 * suma ** 4
[docs]
def _Backward2_P_hs(h, s):
"""Backward equation for region 2, P=f(h,s)
Parameters
----------
h : float
Specific enthalpy, [kJ/kg]
s : float
Specific entropy, [kJ/kgK]
Returns
-------
P : float
Pressure, [MPa]
"""
sfbc = 5.85
hamin = _hab_s(s)
if h <= hamin:
P = _Backward2a_P_hs(h, s)
elif s >= sfbc:
P = _Backward2b_P_hs(h, s)
else:
P = _Backward2c_P_hs(h, s)
return P
# Region 3
[docs]
def _Region3(rho, T):
"""Basic equation for region 3
Parameters
----------
rho : float
Density, [kg/m³]
T : float
Temperature, [K]
Returns
-------
prop : dict
Dict with calculated properties. The available properties are:
* v: Specific volume, [m³/kg]
* h: Specific enthalpy, [kJ/kg]
* s: Specific entropy, [kJ/kgK]
* cp: Specific isobaric heat capacity, [kJ/kgK]
* cv: Specific isocoric heat capacity, [kJ/kgK]
* w: Speed of sound, [m/s]
* alfav: Cubic expansion coefficient, [1/K]
* kt: Isothermal compressibility, [1/MPa]
References
----------
IAPWS, Revised Release on the IAPWS Industrial Formulation 1997 for the
Thermodynamic Properties of Water and Steam August 2007,
http://www.iapws.org/relguide/IF97-Rev.html, Eq 28
Examples
--------
>>> _Region3(500,650)["P"]
25.5837018
>>> _Region3(500,650)["h"]
1863.43019
>>> p = _Region3(500, 650)
>>> p["h"]-p["P"]*1000*p["v"]
1812.26279
>>> _Region3(200,650)["s"]
4.85438792
>>> _Region3(200,650)["cp"]
44.6579342
>>> _Region3(200,650)["cv"]
4.04118076
>>> _Region3(200,650)["w"]
383.444594
>>> _Region3(500,750)["alfav"]
0.00441515098
>>> _Region3(500,750)["kt"]
0.00806710817
"""
d = rho / rhoc
Tr = Tc / T
g = (1.0658070028513 * log(d)) + np.sum(Const.Region3_n * d ** Const.Region3_Li * Tr ** Const.Region3_Lj)
gd = (1.0658070028513 / d) + np.sum(
Const.Region3_n_Li_product * d ** Const.Region3_Li_less_1 * Tr ** Const.Region3_Lj)
gdd = (-1.0658070028513 / d ** 2) + np.sum(
Const.Region3_n_Li_product * Const.Region3_Li_less_1 * d ** (
Const.Region3_Li_less_2) * Tr ** Const.Region3_Lj)
gt = np.sum(Const.Region3_n_Lj_product * d ** Const.Region3_Li * Tr ** Const.Region3_Lj_less_1)
gtt = np.sum(Const.Region3_n_Lj_product * Const.Region3_Lj_less_1 * d ** Const.Region3_Li * Tr ** (
Const.Region3_Lj_less_2))
gdt = np.sum(Const.Region3_n_Li_Lj_product * d ** Const.Region3_Li_less_1 * Tr ** Const.Region3_Lj_less_1)
propiedades = {}
propiedades["T"] = T
propiedades["P"] = d * gd * R * T * rho / 1000
propiedades["v"] = 1 / rho
propiedades["h"] = R * T * (Tr * gt + d * gd)
propiedades["s"] = R * (Tr * gt - g)
propiedades["cp"] = R * (-Tr ** 2 * gtt + (d * gd - d * Tr * gdt) ** 2 / (2 * d * gd + d ** 2 * gdd))
propiedades["cv"] = -R * Tr ** 2 * gtt
propiedades["w"] = sqrt(R * T * 1000 * (2 * d * gd + d ** 2 * gdd - (d * gd - d * Tr * gdt) ** 2
/ Tr ** 2 / gtt))
propiedades["alfav"] = (gd - Tr * gdt) / (2 * gd + d * gdd) / T
propiedades["kt"] = 1 / (2 * d * gd + d ** 2 * gdd) / rho / R / T * 1000
propiedades["region"] = 3
propiedades["x"] = 1
return propiedades
[docs]
def _h_3ab(P):
"""Define the boundary between Region 3a-3b, h=f(P)
Parameters
----------
P : float
Pressure, [MPa]
Returns
-------
h : float
Specific enthalpy, [kJ/kg]
Examples
--------
>>> _h_3ab(25)
2095.936454
"""
return 0.201464004206875e4 + 3.74696550136983 * P - 0.0219921901054187 * P ** 2 + 0.875131686009950e-4 * P ** 3
[docs]
def _tab_P(P):
"""Define the boundary between Region 3a-3b, T=f(P)
Parameters
----------
P : float
Pressure, [MPa]
Returns
-------
T : float
Temperature, [K]
References
----------
IAPWS, Revised Supplementary Release on Backward Equations for Specific
Volume as a Function of Pressure and Temperature v(p,T) for Region 3 of the
IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water
and Steam, http://www.iapws.org/relguide/Supp-VPT3-2016.pdf, Eq. 2
Examples
--------
>>> _tab_P(40)
693.0341408
"""
Pr = P / 1
T = np.sum(Const.tab_P_n * log(Pr) ** Const.tab_P_Li)
return T
[docs]
def _top_P(P):
"""Define the boundary between Region 3o-3p, T=f(P)
Parameters
----------
P : float
Pressure, [MPa]
Returns
-------
T : float
Temperature, [K]
References
----------
IAPWS, Revised Supplementary Release on Backward Equations for Specific
Volume as a Function of Pressure and Temperature v(p,T) for Region 3 of the
IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water
and Steam, http://www.iapws.org/relguide/Supp-VPT3-2016.pdf, Eq. 2
Examples
--------
>>> _top_P(22.8)
650.0106943
"""
Pr = P / 1
T = np.sum(Const.top_P_n * log(Pr) ** Const.top_P_Li)
return T
[docs]
def _twx_P(P):
"""Define the boundary between Region 3w-3x, T=f(P)
Parameters
----------
P : float
Pressure, [MPa]
Returns
-------
T : float
Temperature, [K]
References
----------
IAPWS, Revised Supplementary Release on Backward Equations for Specific
Volume as a Function of Pressure and Temperature v(p,T) for Region 3 of the
IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water
and Steam, http://www.iapws.org/relguide/Supp-VPT3-2016.pdf, Eq. 2
Examples
--------
>>> _twx_P(22.3)
648.2049480
"""
Pr = P / 1
T = np.sum(Const.twx_P_n * log(Pr) ** Const.twx_P_Li)
return T
[docs]
def _tef_P(P):
"""Define the boundary between Region 3e-3f, T=f(P)
Parameters
----------
P : float
Pressure, [MPa]
Returns
-------
T : float
Temperature, [K]
References
----------
IAPWS, Revised Supplementary Release on Backward Equations for Specific
Volume as a Function of Pressure and Temperature v(p,T) for Region 3 of the
IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water
and Steam, http://www.iapws.org/relguide/Supp-VPT3-2016.pdf, Eq. 3
Examples
--------
>>> _tef_P(40)
713.9593992
"""
return 3.727888004 * (P - 22.064) + 647.096
[docs]
def _txx_P(P, xy):
"""Define the boundary between 3x-3y, T=f(P)
Parameters
----------
P : float
Pressure, [MPa]
xy: string
Subregions options: cd, gh, ij, jk, mn, qu, rx, uv
Returns
-------
T : float
Temperature, [K]
References
----------
IAPWS, Revised Supplementary Release on Backward Equations for Specific
Volume as a Function of Pressure and Temperature v(p,T) for Region 3 of the
IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water
and Steam, http://www.iapws.org/relguide/Supp-VPT3-2016.pdf, Eq. 1
Examples
--------
>>> _txx_P(25,"cd")
649.3659208
>>> _txx_P(23,"gh")
649.8873759
>>> _txx_P(23,"ij")
651.5778091
>>> _txx_P(23,"jk")
655.8338344
>>> _txx_P(22.8,"mn")
649.6054133
>>> _txx_P(22,"qu")
645.6355027
>>> _txx_P(22,"rx")
648.2622754
>>> _txx_P(22.3,"uv")
647.7996121
"""
ng = {
"cd": [0.585276966696349e3, 0.278233532206915e1, -0.127283549295878e-1,
0.159090746562729e-3],
"gh": [-0.249284240900418e5, 0.428143584791546e4, -0.269029173140130e3,
0.751608051114157e1, -0.787105249910383e-1],
"ij": [0.584814781649163e3, -0.616179320924617, 0.260763050899562,
-0.587071076864459e-2, 0.515308185433082e-4],
"jk": [0.617229772068439e3, -0.770600270141675e1, 0.697072596851896,
-0.157391839848015e-1, 0.137897492684194e-3],
"mn": [0.535339483742384e3, 0.761978122720128e1, -0.158365725441648,
0.192871054508108e-2],
"qu": [0.565603648239126e3, 0.529062258221222e1, -0.102020639611016,
0.122240301070145e-2],
"rx": [0.584561202520006e3, -0.102961025163669e1, 0.243293362700452,
-0.294905044740799e-2],
"uv": [0.528199646263062e3, 0.890579602135307e1, -0.222814134903755,
0.286791682263697e-2]}
n = ng[xy]
Pr = P / 1
T = 0
for i, ni in enumerate(n):
T += ni * Pr ** i
return T
[docs]
def _Backward3a_v_Ph(P, h):
"""Backward equation for region 3a, v=f(P,h)
Parameters
----------
P : float
Pressure, [MPa]
h : float
Specific enthalpy, [kJ/kg]
References
----------
IAPWS, Revised Supplementary Release on Backward Equations for the
Functions T(p,h), v(p,h) and T(p,s), v(p,s) for Region 3 of the IAPWS
Industrial Formulation 1997 for the Thermodynamic Properties of Water and
Steam, http://www.iapws.org/relguide/Supp-Tv%28ph,ps%293-2014.pdf, Eq 4
Returns
-------
v : float
Specific volume, [m³/kg]
Examples
--------
>>> _Backward3a_v_Ph(20,1700)
0.001749903962
>>> _Backward3a_v_Ph(100,2100)
0.001676229776
"""
Pr = P / 100
nu = h / 2100
suma = np.sum(
Const.Backward3a_v_Ph_n * (Pr + 0.128) ** Const.Backward3a_v_Ph_Li * (nu - 0.727) ** Const.Backward3a_v_Ph_Lj)
return 0.0028 * suma
[docs]
def _Backward3b_v_Ph(P, h):
"""Backward equation for region 3b, v=f(P,h)
Parameters
----------
P : float
Pressure, [MPa]
h : float
Specific enthalpy, [kJ/kg]
Returns
-------
v : float
Specific volume, [m³/kg]
References
----------
IAPWS, Revised Supplementary Release on Backward Equations for the
Functions T(p,h), v(p,h) and T(p,s), v(p,s) for Region 3 of the IAPWS
Industrial Formulation 1997 for the Thermodynamic Properties of Water and
Steam, http://www.iapws.org/relguide/Supp-Tv%28ph,ps%293-2014.pdf, Eq 5
Examples
--------
>>> _Backward3b_v_Ph(20,2500)
0.006670547043
>>> _Backward3b_v_Ph(100,2700)
0.002404234998
"""
Pr = P / 100
nu = h / 2800
suma = np.sum(Const.Backward3b_v_Ph_n * (Pr + 0.0661) ** Const.Backward3b_v_Ph_Li * (
nu - 0.72) ** Const.Backward3b_v_Ph_Lj)
return 0.0088 * suma
[docs]
def _Backward3_v_Ph(P, h):
"""Backward equation for region 3, v=f(P,h)
Parameters
----------
P : float
Pressure, [MPa]
h : float
Specific enthalpy, [kJ/kg]
Returns
-------
v : float
Specific volume, [m³/kg]
"""
hf = _h_3ab(P)
if h <= hf:
return _Backward3a_v_Ph(P, h)
return _Backward3b_v_Ph(P, h)
[docs]
def _Backward3a_T_Ph(P, h):
"""Backward equation for region 3a, T=f(P,h)
Parameters
----------
P : float
Pressure, [MPa]
h : float
Specific enthalpy, [kJ/kg]
Returns
-------
T : float
Temperature, [K]
References
----------
IAPWS, Revised Supplementary Release on Backward Equations for the
Functions T(p,h), v(p,h) and T(p,s), v(p,s) for Region 3 of the IAPWS
Industrial Formulation 1997 for the Thermodynamic Properties of Water and
Steam, http://www.iapws.org/relguide/Supp-Tv%28ph,ps%293-2014.pdf, Eq 2
Examples
--------
>>> _Backward3a_T_Ph(20,1700)
629.3083892
>>> _Backward3a_T_Ph(100,2100)
733.6163014
"""
Pr = P / 100.
nu = h / 2300.
suma = np.sum(Const.Backward3a_T_Ph_n * (Pr + 0.240) ** Const.Backward3a_T_Ph_Li * (
nu - 0.615) ** Const.Backward3a_T_Ph_Lj)
return 760 * suma
[docs]
def _Backward3b_T_Ph(P, h):
"""Backward equation for region 3b, T=f(P,h)
Parameters
----------
P : float
Pressure, [MPa]
h : float
Specific enthalpy, [kJ/kg]
Returns
-------
T : float
Temperature, [K]
References
----------
IAPWS, Revised Supplementary Release on Backward Equations for the
Functions T(p,h), v(p,h) and T(p,s), v(p,s) for Region 3 of the IAPWS
Industrial Formulation 1997 for the Thermodynamic Properties of Water and
Steam, http://www.iapws.org/relguide/Supp-Tv%28ph,ps%293-2014.pdf, Eq 3
Examples
--------
>>> _Backward3b_T_Ph(20,2500)
641.8418053
>>> _Backward3b_T_Ph(100,2700)
842.0460876
"""
Pr = P / 100.
nu = h / 2800.
suma = np.sum(
Const.Backward3b_T_Ph_n * (Pr + 0.298) ** Const.Backward3b_T_Ph_Li * (nu - 0.72) ** Const.Backward3b_T_Ph_Lj)
return 860 * suma
[docs]
def _Backward3_T_Ph(P, h):
"""Backward equation for region 3, T=f(P,h)
Parameters
----------
P : float
Pressure, [MPa]
h : float
Specific enthalpy, [kJ/kg]
Returns
-------
T : float
Temperature, [K]
"""
hf = _h_3ab(P)
if h <= hf:
T = _Backward3a_T_Ph(P, h)
else:
T = _Backward3b_T_Ph(P, h)
return T
[docs]
def _Backward3a_v_Ps(P, s):
"""Backward equation for region 3a, v=f(P,s)
Parameters
----------
P : float
Pressure, [MPa]
s : float
Specific entropy, [kJ/kgK]
Returns
-------
v : float
Specific volume, [m³/kg]
References
----------
IAPWS, Revised Supplementary Release on Backward Equations for the
Functions T(p,h), v(p,h) and T(p,s), v(p,s) for Region 3 of the IAPWS
Industrial Formulation 1997 for the Thermodynamic Properties of Water and
Steam, http://www.iapws.org/relguide/Supp-Tv%28ph,ps%293-2014.pdf, Eq 8
Examples
--------
>>> _Backward3a_v_Ps(20,3.8)
0.001733791463
>>> _Backward3a_v_Ps(100,4)
0.001555893131
"""
Pr = P / 100
sigma = s / 4.4
suma = np.sum(Const.Backward3a_v_Ps_n * (Pr + 0.187) ** Const.Backward3a_v_Ps_Li * (
sigma - 0.755) ** Const.Backward3a_v_Ps_Lj)
return 0.0028 * suma
[docs]
def _Backward3b_v_Ps(P, s):
"""Backward equation for region 3b, v=f(P,s)
Parameters
----------
P : float
Pressure, [MPa]
s : float
Specific entropy, [kJ/kgK]
Returns
-------
v : float
Specific volume, [m³/kg]
References
----------
IAPWS, Revised Supplementary Release on Backward Equations for the
Functions T(p,h), v(p,h) and T(p,s), v(p,s) for Region 3 of the IAPWS
Industrial Formulation 1997 for the Thermodynamic Properties of Water and
Steam, http://www.iapws.org/relguide/Supp-Tv%28ph,ps%293-2014.pdf, Eq 9
Examples
--------
>>> _Backward3b_v_Ps(20,5)
0.006262101987
>>> _Backward3b_v_Ps(100,5)
0.002449610757
"""
Pr = P / 100
sigma = s / 5.3
suma = np.sum(Const.Backward3b_v_Ps_n * (Pr + 0.298) ** Const.Backward3b_v_Ps_Li * (
sigma - 0.816) ** Const.Backward3b_v_Ps_Lj)
return 0.0088 * suma
[docs]
def _Backward3_v_Ps(P, s):
"""Backward equation for region 3, v=f(P,s)
Parameters
----------
P : float
Pressure, [MPa]
s : float
Specific entropy, [kJ/kgK]
Returns
-------
v : float
Specific volume, [m³/kg]
"""
if s <= sc:
return _Backward3a_v_Ps(P, s)
return _Backward3b_v_Ps(P, s)
[docs]
def _Backward3a_T_Ps(P, s):
"""Backward equation for region 3a, T=f(P,s)
Parameters
----------
P : float
Pressure, [MPa]
s : float
Specific entropy, [kJ/kgK]
Returns
-------
T : float
Temperature, [K]
References
----------
IAPWS, Revised Supplementary Release on Backward Equations for the
Functions T(p,h), v(p,h) and T(p,s), v(p,s) for Region 3 of the IAPWS
Industrial Formulation 1997 for the Thermodynamic Properties of Water and
Steam, http://www.iapws.org/relguide/Supp-Tv%28ph,ps%293-2014.pdf, Eq 6
Examples
--------
>>> _Backward3a_T_Ps(20,3.8)
628.2959869
>>> _Backward3a_T_Ps(100,4)
705.6880237
"""
Pr = P / 100
sigma = s / 4.4
suma = np.sum(Const.Backward3a_T_Ps_n * (Pr + 0.240) ** Const.Backward3a_T_Ps_Li * (
sigma - 0.703) ** Const.Backward3a_T_Ps_Lj)
return 760 * suma
[docs]
def _Backward3b_T_Ps(P, s):
"""Backward equation for region 3b, T=f(P,s)
Parameters
----------
P : float
Pressure, [MPa]
s : float
Specific entropy, [kJ/kgK]
Returns
-------
T : float
Temperature, [K]
References
----------
IAPWS, Revised Supplementary Release on Backward Equations for the
Functions T(p,h), v(p,h) and T(p,s), v(p,s) for Region 3 of the IAPWS
Industrial Formulation 1997 for the Thermodynamic Properties of Water and
Steam, http://www.iapws.org/relguide/Supp-Tv%28ph,ps%293-2014.pdf, Eq 7
Examples
--------
>>> _Backward3b_T_Ps(20,5)
640.1176443
>>> _Backward3b_T_Ps(100,5)
847.4332825
"""
Pr = P / 100
sigma = s / 5.3
suma = np.sum(Const.Backward3b_T_Ps_n * (Pr + 0.760) ** Const.Backward3b_T_Ps_Li * (
sigma - 0.818) ** Const.Backward3b_T_Ps_Lj)
return 860 * suma
[docs]
def _Backward3_T_Ps(P, s):
"""Backward equation for region 3, T=f(P,s)
Parameters
----------
P : float
Pressure, [MPa]
s : float
Specific entropy, [kJ/kgK]
Returns
-------
T : float
Temperature, [K]
"""
if s <= sc:
return _Backward3a_T_Ps(P, s)
return _Backward3b_T_Ps(P, s)
[docs]
def _Backward3a_P_hs(h, s):
"""Backward equation for region 3a, P=f(h,s)
Parameters
----------
h : float
Specific enthalpy, [kJ/kg]
s : float
Specific entropy, [kJ/kgK]
Returns
-------
P : float
Pressure, [MPa]
References
----------
IAPWS, Revised Supplementary Release on Backward Equations p(h,s) for
Region 3, Equations as a Function of h and s for the Region Boundaries, and
an Equation Tsat(h,s) for Region 4 of the IAPWS Industrial Formulation 1997
for the Thermodynamic Properties of Water and Steam,
http://www.iapws.org/relguide/Supp-phs3-2014.pdf. Eq 1
Examples
--------
>>> _Backward3a_P_hs(1700,3.8)
25.55703246
>>> _Backward3a_P_hs(2000,4.2)
45.40873468
>>> _Backward3a_P_hs(2100,4.3)
60.78123340
"""
nu = h / 2300
sigma = s / 4.4
suma = np.sum(Const.Backward3a_P_hs_n * (nu - 1.01) ** Const.Backward3a_P_hs_Li * (
sigma - 0.75) ** Const.Backward3a_P_hs_Lj)
return 99 * suma
[docs]
def _Backward3b_P_hs(h, s):
"""Backward equation for region 3b, P=f(h,s)
Parameters
----------
h : float
Specific enthalpy, [kJ/kg]
s : float
Specific entropy, [kJ/kgK]
Returns
-------
P : float
Pressure, [MPa]
References
----------
IAPWS, Revised Supplementary Release on Backward Equations p(h,s) for
Region 3, Equations as a Function of h and s for the Region Boundaries, and
an Equation Tsat(h,s) for Region 4 of the IAPWS Industrial Formulation 1997
for the Thermodynamic Properties of Water and Steam,
http://www.iapws.org/relguide/Supp-phs3-2014.pdf. Eq 1
Examples
--------
>>> _Backward3b_P_hs(2400,4.7)
63.63924887
>>> _Backward3b_P_hs(2600,5.1)
34.34999263
>>> _Backward3b_P_hs(2700,5.0)
88.39043281
"""
nu = h / 2800
sigma = s / 5.3
suma = np.sum(Const.Backward3b_P_hs_n * (nu - 0.681) ** Const.Backward3b_P_hs_Li * (
sigma - 0.792) ** Const.Backward3b_P_hs_Lj)
return 16.6 / suma
[docs]
def _Backward3_P_hs(h, s):
"""Backward equation for region 3, P=f(h,s)
Parameters
----------
h : float
Specific enthalpy, [kJ/kg]
s : float
Specific entropy, [kJ/kgK]
Returns
-------
P : float
Pressure, [MPa]
"""
if s <= sc:
return _Backward3a_P_hs(h, s)
return _Backward3b_P_hs(h, s)
[docs]
def _Backward3_sat_v_P(P, T, x):
"""Backward equation for region 3 for saturated state, vs=f(P,x)
Parameters
----------
T : float
Temperature, [K]
P : float
Pressure, [MPa]
x : integer
Vapor quality, [-]
Returns
-------
v : float
Specific volume, [m³/kg]
Notes
-----
The vapor quality (x) can be 0 (saturated liquid) or 1 (saturated vapour)
"""
if x == 0:
if P < 19.00881189:
region = "c"
elif P < 21.0434:
region = "s"
elif P < 21.9316:
region = "u"
else:
region = "y"
else:
if P < 20.5:
region = "t"
elif P < 21.0434:
region = "r"
elif P < 21.9009:
region = "x"
else:
region = "z"
return _Backward3x_v_PT(T, P, region)
[docs]
def _Backward3_v_PT(P, T):
"""Backward equation for region 3, v=f(P,T)
Parameters
----------
T : float
Temperature, [K]
P : float
Pressure, [MPa]
Returns
-------
v : float
Specific volume, [m³/kg]
References
----------
IAPWS, Revised Supplementary Release on Backward Equations for Specific
Volume as a Function of Pressure and Temperature v(p,T) for Region 3 of the
IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water
and Steam, http://www.iapws.org/relguide/Supp-VPT3-2016.pdf, Table 2 and 10
"""
if P > 40:
if T <= _tab_P(P):
region = "a"
else:
region = "b"
elif 25 < P <= 40:
tcd = _txx_P(P, "cd")
tab = _tab_P(P)
tef = _tef_P(P)
if T <= tcd:
region = "c"
elif tcd < T <= tab:
region = "d"
elif tab < T <= tef:
region = "e"
else:
region = "f"
elif 23.5 < P <= 25:
tcd = _txx_P(P, "cd")
tgh = _txx_P(P, "gh")
tef = _tef_P(P)
tij = _txx_P(P, "ij")
tjk = _txx_P(P, "jk")
if T <= tcd:
region = "c"
elif tcd < T <= tgh:
region = "g"
elif tgh < T <= tef:
region = "h"
elif tef < T <= tij:
region = "i"
elif tij < T <= tjk:
region = "j"
else:
region = "k"
elif 23 < P <= 23.5:
tcd = _txx_P(P, "cd")
tgh = _txx_P(P, "gh")
tef = _tef_P(P)
tij = _txx_P(P, "ij")
tjk = _txx_P(P, "jk")
if T <= tcd:
region = "c"
elif tcd < T <= tgh:
region = "l"
elif tgh < T <= tef:
region = "h"
elif tef < T <= tij:
region = "i"
elif tij < T <= tjk:
region = "j"
else:
region = "k"
elif 22.5 < P <= 23:
tcd = _txx_P(P, "cd")
tgh = _txx_P(P, "gh")
tmn = _txx_P(P, "mn")
tef = _tef_P(P)
top = _top_P(P)
tij = _txx_P(P, "ij")
tjk = _txx_P(P, "jk")
if T <= tcd:
region = "c"
elif tcd < T <= tgh:
region = "l"
elif tgh < T <= tmn:
region = "m"
elif tmn < T <= tef:
region = "n"
elif tef < T <= top:
region = "o"
elif top < T <= tij:
region = "p"
elif tij < T <= tjk:
region = "j"
else:
region = "k"
elif _PSat_T(643.15) < P <= 22.5:
tcd = _txx_P(P, "cd")
tqu = _txx_P(P, "qu")
trx = _txx_P(P, "rx")
tjk = _txx_P(P, "jk")
if T <= tcd:
region = "c"
elif tcd < T <= tqu:
region = "q"
elif tqu < T <= trx:
# Table 10
tef = _tef_P(P)
twx = _twx_P(P)
tuv = _txx_P(P, "uv")
if 22.11 < P <= 22.5:
if T <= tuv:
region = "u"
elif tuv <= T <= tef:
region = "v"
elif tef <= T <= twx:
region = "w"
else:
region = "x"
elif 22.064 < P <= 22.11:
if T <= tuv:
region = "u"
elif tuv <= T <= tef:
region = "y"
elif tef <= T <= twx:
region = "z"
else:
region = "x"
elif T > _TSat_P(P):
if _PSat_T(643.15) < P <= 21.90096265:
region = "x"
elif 21.90096265 < P <= 22.064:
if T <= twx:
region = "z"
else:
region = "x"
elif T <= _TSat_P(P):
if _PSat_T(643.15) < P <= 21.93161551:
region = "u"
elif 21.93161551 < P <= 22.064:
if T <= tuv:
region = "u"
else:
region = "y"
elif trx < T <= tjk:
region = "r"
else:
region = "k"
elif 20.5 < P <= _PSat_T(643.15):
tcd = _txx_P(P, "cd")
Ts = _TSat_P(P)
tjk = _txx_P(P, "jk")
if T <= tcd:
region = "c"
elif tcd < T <= Ts:
region = "s"
elif Ts < T <= tjk:
region = "r"
else:
region = "k"
elif 19.00881189173929 < P <= 20.5:
tcd = _txx_P(P, "cd")
Ts = _TSat_P(P)
if T <= tcd:
region = "c"
elif tcd < T <= Ts:
region = "s"
else:
region = "t"
elif Ps_623 < P <= 19.00881189173929:
Ts = _TSat_P(P)
if T <= Ts:
region = "c"
else:
region = "t"
return _Backward3x_v_PT(T, P, region)
[docs]
def _Backward3x_v_PT(T, P, x):
"""Backward equation for region 3x, v=f(P,T)
Parameters
----------
T : float
Temperature, [K]
P : float
Pressure, [MPa]
x : char
Region 3 subregion code
Returns
-------
v : float
Specific volume, [m³/kg]
References
----------
IAPWS, Revised Supplementary Release on Backward Equations for Specific
Volume as a Function of Pressure and Temperature v(p,T) for Region 3 of the
IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water
and Steam, http://www.iapws.org/relguide/Supp-VPT3-2016.pdf, Eq. 4-5
Examples
--------
>>> _Backward3x_v_PT(630,50,"a")
0.001470853100
>>> _Backward3x_v_PT(670,80,"a")
0.001503831359
>>> _Backward3x_v_PT(710,50,"b")
0.002204728587
>>> _Backward3x_v_PT(750,80,"b")
0.001973692940
>>> _Backward3x_v_PT(630,20,"c")
0.001761696406
>>> _Backward3x_v_PT(650,30,"c")
0.001819560617
>>> _Backward3x_v_PT(656,26,"d")
0.002245587720
>>> _Backward3x_v_PT(670,30,"d")
0.002506897702
>>> _Backward3x_v_PT(661,26,"e")
0.002970225962
>>> _Backward3x_v_PT(675,30,"e")
0.003004627086
>>> _Backward3x_v_PT(671,26,"f")
0.005019029401
>>> _Backward3x_v_PT(690,30,"f")
0.004656470142
>>> _Backward3x_v_PT(649,23.6,"g")
0.002163198378
>>> _Backward3x_v_PT(650,24,"g")
0.002166044161
>>> _Backward3x_v_PT(652,23.6,"h")
0.002651081407
>>> _Backward3x_v_PT(654,24,"h")
0.002967802335
>>> _Backward3x_v_PT(653,23.6,"i")
0.003273916816
>>> _Backward3x_v_PT(655,24,"i")
0.003550329864
>>> _Backward3x_v_PT(655,23.5,"j")
0.004545001142
>>> _Backward3x_v_PT(660,24,"j")
0.005100267704
>>> _Backward3x_v_PT(660,23,"k")
0.006109525997
>>> _Backward3x_v_PT(670,24,"k")
0.006427325645
>>> _Backward3x_v_PT(646,22.6,"l")
0.002117860851
>>> _Backward3x_v_PT(646,23,"l")
0.002062374674
>>> _Backward3x_v_PT(648.6,22.6,"m")
0.002533063780
>>> _Backward3x_v_PT(649.3,22.8,"m")
0.002572971781
>>> _Backward3x_v_PT(649,22.6,"n")
0.002923432711
>>> _Backward3x_v_PT(649.7,22.8,"n")
0.002913311494
>>> _Backward3x_v_PT(649.1,22.6,"o")
0.003131208996
>>> _Backward3x_v_PT(649.9,22.8,"o")
0.003221160278
>>> _Backward3x_v_PT(649.4,22.6,"p")
0.003715596186
>>> _Backward3x_v_PT(650.2,22.8,"p")
0.003664754790
>>> _Backward3x_v_PT(640,21.1,"q")
0.001970999272
>>> _Backward3x_v_PT(643,21.8,"q")
0.002043919161
>>> _Backward3x_v_PT(644,21.1,"r")
0.005251009921
>>> _Backward3x_v_PT(648,21.8,"r")
0.005256844741
>>> _Backward3x_v_PT(635,19.1,"s")
0.001932829079
>>> _Backward3x_v_PT(638,20,"s")
0.001985387227
>>> _Backward3x_v_PT(626,17,"t")
0.008483262001
>>> _Backward3x_v_PT(640,20,"t")
0.006227528101
>>> _Backward3x_v_PT(644.6,21.5,"u")
0.002268366647
>>> _Backward3x_v_PT(646.1,22,"u")
0.002296350553
>>> _Backward3x_v_PT(648.6,22.5,"v")
0.002832373260
>>> _Backward3x_v_PT(647.9,22.3,"v")
0.002811424405
>>> _Backward3x_v_PT(647.5,22.15,"w")
0.003694032281
>>> _Backward3x_v_PT(648.1,22.3,"w")
0.003622226305
>>> _Backward3x_v_PT(648,22.11,"x")
0.004528072649
>>> _Backward3x_v_PT(649,22.3,"x")
0.004556905799
>>> _Backward3x_v_PT(646.84,22,"y")
0.002698354719
>>> _Backward3x_v_PT(647.05,22.064,"y")
0.002717655648
>>> _Backward3x_v_PT(646.89,22,"z")
0.003798732962
>>> _Backward3x_v_PT(647.15,22.064,"z")
0.003701940009
"""
par = {
"a": [0.0024, 100, 760, 0.085, 0.817, 1, 1, 1],
"b": [0.0041, 100, 860, 0.280, 0.779, 1, 1, 1],
"c": [0.0022, 40, 690, 0.259, 0.903, 1, 1, 1],
"d": [0.0029, 40, 690, 0.559, 0.939, 1, 1, 4],
"e": [0.0032, 40, 710, 0.587, 0.918, 1, 1, 1],
"f": [0.0064, 40, 730, 0.587, 0.891, 0.5, 1, 4],
"g": [0.0027, 25, 660, 0.872, 0.971, 1, 1, 4],
"h": [0.0032, 25, 660, 0.898, 0.983, 1, 1, 4],
"i": [0.0041, 25, 660, 0.910, 0.984, 0.5, 1, 4],
"j": [0.0054, 25, 670, 0.875, 0.964, 0.5, 1, 4],
"k": [0.0077, 25, 680, 0.802, 0.935, 1, 1, 1],
"l": [0.0026, 24, 650, 0.908, 0.989, 1, 1, 4],
"m": [0.0028, 23, 650, 1.000, 0.997, 1, 0.25, 1],
"n": [0.0031, 23, 650, 0.976, 0.997, None, None, None],
"o": [0.0034, 23, 650, 0.974, 0.996, 0.5, 1, 1],
"p": [0.0041, 23, 650, 0.972, 0.997, 0.5, 1, 1],
"q": [0.0022, 23, 650, 0.848, 0.983, 1, 1, 4],
"r": [0.0054, 23, 650, 0.874, 0.982, 1, 1, 1],
"s": [0.0022, 21, 640, 0.886, 0.990, 1, 1, 4],
"t": [0.0088, 20, 650, 0.803, 1.020, 1, 1, 1],
"u": [0.0026, 23, 650, 0.902, 0.988, 1, 1, 1],
"v": [0.0031, 23, 650, 0.960, 0.995, 1, 1, 1],
"w": [0.0039, 23, 650, 0.959, 0.995, 1, 1, 4],
"x": [0.0049, 23, 650, 0.910, 0.988, 1, 1, 1],
"y": [0.0031, 22, 650, 0.996, 0.994, 1, 1, 4],
"z": [0.0038, 22, 650, 0.993, 0.994, 1, 1, 4],
}
Li = {
"a": [-12, -12, -12, -10, -10, -10, -8, -8, -8, -6, -5, -5, -5, -4, -3,
-3, -3, -3, -2, -2, -2, -1, -1, -1, 0, 0, 1, 1, 2, 2],
"b": [-12, -12, -10, -10, -8, -6, -6, -6, -5, -5, -5, -4, -4, -4, -3,
-3, -3, -3, -3, -2, -2, -2, -1, -1, 0, 0, 1, 1, 2, 3, 4, 4],
"c": [-12, -12, -12, -10, -10, -10, -8, -8, -8, -6, -5, -5, -5, -4, -4,
-3, -3, -2, -2, -2, -1, -1, -1, 0, 0, 0, 1, 1, 2, 2, 2, 2, 3, 3,
8],
"d": [-12, -12, -12, -12, -12, -12, -10, -10, -10, -10, -10, -10, -10,
-8, -8, -8, -8, -6, -6, -5, -5, -5, -5, -4, -4, -4, -3, -3, -2,
-2, -1, -1, -1, 0, 0, 1, 1, 3],
"e": [-12, -12, -10, -10, -10, -10, -10, -8, -8, -8, -6, -5, -4, -4,
-3, -3, -3, -2, -2, -2, -2, -1, 0, 0, 1, 1, 1, 2, 2],
"f": [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 3, 3, 3, 4, 5, 5, 6, 7, 7,
10, 12, 12, 12, 14, 14, 14, 14, 14, 16, 16, 18, 18, 20, 20, 20,
22, 24, 24, 28, 32],
"g": [-12, -12, -12, -12, -12, -12, -10, -10, -10, -8, -8, -8, -8, -6,
-6, -5, -5, -4, -3, -2, -2, -2, -2, -1, -1, -1, 0, 0, 0, 1, 1, 1,
3, 5, 6, 8, 10, 10],
"h": [-12, -12, -10, -10, -10, -10, -10, -10, -8, -8, -8, -8, -8, -6,
-6, -6, -5, -5, -5, -4, -4, -3, -3, -2, -1, -1, 0, 1, 1],
"i": [0, 0, 0, 1, 1, 1, 1, 2, 3, 3, 4, 4, 4, 5, 5, 5, 7, 7, 8, 8, 10,
12, 12, 12, 14, 14, 14, 14, 18, 18, 18, 18, 18, 20, 20, 22, 24,
24, 32, 32, 36, 36],
"j": [0, 0, 0, 1, 1, 1, 2, 2, 3, 4, 4, 5, 5, 5, 6, 10, 12, 12, 14, 14,
14, 16, 18, 20, 20, 24, 24, 28, 28],
"k": [-2, -2, -1, -1, 0, -0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2,
2, 2, 2, 2, 5, 5, 5, 6, 6, 6, 6, 8, 10, 12],
"l": [-12, -12, -12, -12, -12, -10, -10, -8, -8, -8, -8, -8, -8, -8,
-6, -5, -5, -4, -4, -3, -3, -3, -3, -2, -2, -2, -1, -1, -1, 0, 0,
0, 0, 1, 1, 2, 4, 5, 5, 6, 10, 10, 14],
"m": [0, 3, 8, 20, 1, 3, 4, 5, 1, 6, 2, 4, 14, 2, 5, 3, 0, 1, 1, 1, 28,
2, 16, 0, 5, 0, 3, 4, 12, 16, 1, 8, 14, 0, 2, 3, 4, 8, 14, 24],
"n": [0, 3, 4, 6, 7, 10, 12, 14, 18, 0, 3, 5, 6, 8, 12, 0, 3, 7, 12,
2, 3, 4, 2, 4, 7, 4, 3, 5, 6, 0, 0, 3, 1, 0, 1, 0, 1, 0, 1],
"o": [0, 0, 0, 2, 3, 4, 4, 4, 4, 4, 5, 5, 6, 7, 8, 8, 8, 10, 10, 14,
14, 20, 20, 24],
"p": [0, 0, 0, 0, 1, 2, 3, 3, 4, 6, 7, 7, 8, 10, 12, 12, 12, 14, 14,
14, 16, 18, 20, 22, 24, 24, 36],
"q": [-12, -12, -10, -10, -10, -10, -8, -6, -5, -5, -4, -4, -3, -2,
-2, -2, -2, -1, -1, -1, 0, 1, 1, 1],
"r": [-8, -8, -3, -3, -3, -3, -3, 0, 0, 0, 0, 3, 3, 8, 8, 8, 8, 10,
10, 10, 10, 10, 10, 10, 10, 12, 14],
"s": [-12, -12, -10, -8, -6, -5, -5, -4, -4, -3, -3, -2, -1, -1, -1, 0,
0, 0, 0, 1, 1, 3, 3, 3, 4, 4, 4, 5, 14],
"t": [0, 0, 0, 0, 1, 1, 2, 2, 2, 3, 3, 4, 4, 7, 7, 7, 7, 7, 10, 10, 10,
10, 10, 18, 20, 22, 22, 24, 28, 32, 32, 32, 36],
"u": [-12, -10, -10, -10, -8, -8, -8, -6, -6, -5, -5, -5, -3, -1, -1,
-1, -1, 0, 0, 1, 2, 2, 3, 5, 5, 5, 6, 6, 8, 8, 10, 12, 12, 12,
14, 14, 14, 14],
"v": [-10, -8, -6, -6, -6, -6, -6, -6, -5, -5, -5, -5, -5, -5, -4, -4,
-4, -4, -3, -3, -3, -2, -2, -1, -1, 0, 0, 0, 1, 1, 3, 4, 4, 4, 5,
8, 10, 12, 14],
"w": [-12, -12, -10, -10, -8, -8, -8, -6, -6, -6, -6, -5, -4, -4, -3,
-3, -2, -2, -1, -1, -1, 0, 0, 1, 2, 2, 3, 3, 5, 5, 5, 8, 8, 10,
10],
"x": [-8, -6, -5, -4, -4, -4, -3, -3, -1, 0, 0, 0, 1, 1, 2, 3, 3, 3, 4,
5, 5, 5, 6, 8, 8, 8, 8, 10, 12, 12, 12, 12, 14, 14, 14, 14],
"y": [0, 0, 0, 0, 1, 2, 2, 2, 2, 3, 3, 3, 4, 4, 5, 5, 8, 8, 10, 12],
"z": [-8, -6, -5, -5, -4, -4, -4, -3, -3, -3, -2, -1, 0, 1, 2, 3, 3, 6,
6, 6, 6, 8, 8]}
Lj = {
"a": [5, 10, 12, 5, 10, 12, 5, 8, 10, 1, 1, 5, 10, 8, 0, 1, 3, 6, 0,
2, 3, 0, 1, 2, 0, 1, 0, 2, 0, 2],
"b": [10, 12, 8, 14, 8, 5, 6, 8, 5, 8, 10, 2, 4, 5, 0, 1, 2, 3, 5, 0,
2, 5, 0, 2, 0, 1, 0, 2, 0, 2, 0, 1],
"c": [6, 8, 10, 6, 8, 10, 5, 6, 7, 8, 1, 4, 7, 2, 8, 0, 3, 0, 4, 5, 0,
1, 2, 0, 1, 2, 0, 2, 0, 1, 3, 7, 0, 7, 1],
"d": [4, 6, 7, 10, 12, 16, 0, 2, 4, 6, 8, 10, 14, 3, 7, 8, 10, 6, 8, 1,
2, 5, 7, 0, 1, 7, 2, 4, 0, 1, 0, 1, 5, 0, 2, 0, 6, 0],
"e": [14, 16, 3, 6, 10, 14, 16, 7, 8, 10, 6, 6, 2, 4, 2, 6, 7, 0, 1,
3, 4, 0, 0, 1, 0, 4, 6, 0, 2],
"f": [-3, -2, -1, 0, 1, 2, -1, 1, 2, 3, 0, 1, -5, -2, 0, -3, -8, 1, -6,
-4, 1, -6, -10, -8, -4, -12, -10, -8, -6, -4, -10, -8, -12, -10,
-12, -10, -6, -12, -12, -4, -12, -12],
"g": [7, 12, 14, 18, 22, 24, 14, 20, 24, 7, 8, 10, 12, 8, 22, 7, 20,
22, 7, 3, 5, 14, 24, 2, 8, 18, 0, 1, 2, 0, 1, 3, 24, 22, 12, 3,
0, 6],
"h": [8, 12, 4, 6, 8, 10, 14, 16, 0, 1, 6, 7, 8, 4, 6, 8, 2, 3, 4, 2,
4, 1, 2, 0, 0, 2, 0, 0, 2],
"i": [0, 1, 10, -4, -2, -1, 0, 0, -5, 0, -3, -2, -1, -6, -1, 12, -4,
-3, -6, 10, -8, -12, -6, -4, -10, -8, -4, 5, -12, -10, -8, -6,
2, -12, -10, -12, -12, -8, -10, -5, -10, -8],
"j": [-1, 0, 1, -2, -1, 1, -1, 1, -2, -2, 2, -3, -2, 0, 3, -6, -8, -3,
-10, -8, -5, -10, -12, -12, -10, -12, -6, -12, -5],
"k": [10, 12, -5, 6, -12, -6, -2, -1, 0, 1, 2, 3, 14, -3, -2, 0, 1, 2,
-8, -6, -3, -2, 0, 4, -12, -6, -3, -12, -10, -8, -5, -12, -12,
-10],
"l": [14, 16, 18, 20, 22, 14, 24, 6, 10, 12, 14, 18, 24, 36, 8, 4, 5,
7, 16, 1, 3, 18, 20, 2, 3, 10, 0, 1, 3, 0, 1, 2, 12, 0, 16, 1, 0,
0, 1, 14, 4, 12, 10],
"m": [0, 0, 0, 2, 5, 5, 5, 5, 6, 6, 7, 8, 8, 10, 10, 12, 14, 14, 18,
20, 20, 22, 22, 24, 24, 28, 28, 28, 28, 28, 32, 32, 32, 36, 36,
36, 36, 36, 36, 36],
"n": [-12, -12, -12, -12, -12, -12, -12, -12, -12, -10, -10, -10, -10,
-10, -10, -8, -8, -8, -8, -6, -6, -6, -5, -5, -5, -4, -3, -3,
-3, -2, -1, -1, 0, 1, 1, 2, 4, 5, 6],
"o": [-12, -4, -1, -1, -10, -12, -8, -5, -4, -1, -4, -3, -8, -12, -10,
-8, -4, -12, -8, -12, -8, -12, -10, -12],
"p": [-1, 0, 1, 2, 1, -1, -3, 0, -2, -2, -5, -4, -2, -3, -12, -6, -5,
-10, -8, -3, -8, -8, -10, -10, -12, -8, -12],
"q": [10, 12, 6, 7, 8, 10, 8, 6, 2, 5, 3, 4, 3, 0, 1, 2, 4, 0, 1, 2,
0, 0, 1, 3],
"r": [6, 14, -3, 3, 4, 5, 8, -1, 0, 1, 5, -6, -2, -12, -10, -8, -5,
-12, -10, -8, -6, -5, -4, -3, -2, -12, -12],
"s": [20, 24, 22, 14, 36, 8, 16, 6, 32, 3, 8, 4, 1, 2, 3, 0, 1, 4, 28,
0, 32, 0, 1, 2, 3, 18, 24, 4, 24],
"t": [0, 1, 4, 12, 0, 10, 0, 6, 14, 3, 8, 0, 10, 3, 4, 7, 20, 36, 10,
12, 14, 16, 22, 18, 32, 22, 36, 24, 28, 22, 32, 36, 36],
"u": [14, 10, 12, 14, 10, 12, 14, 8, 12, 4, 8, 12, 2, -1, 1, 12, 14,
-3, 1, -2, 5, 10, -5, -4, 2, 3, -5, 2, -8, 8, -4, -12, -4, 4,
-12, -10, -6, 6],
"v": [-8, -12, -12, -3, 5, 6, 8, 10, 1, 2, 6, 8, 10, 14, -12, -10, -6,
10, -3, 10, 12, 2, 4, -2, 0, -2, 6, 10, -12, -10, 3, -6, 3, 10,
2, -12, -2, -3, 1],
"w": [8, 14, -1, 8, 6, 8, 14, -4, -3, 2, 8, -10, -1, 3, -10, 3, 1, 2,
-8, -4, 1, -12, 1, -1, -1, 2, -12, -5, -10, -8, -6, -12, -10,
-12, -8],
"x": [14, 10, 10, 1, 2, 14, -2, 12, 5, 0, 4, 10, -10, -1, 6, -12, 0,
8, 3, -6, -2, 1, 1, -6, -3, 1, 8, -8, -10, -8, -5, -4, -12, -10,
-8, -6],
"y": [-3, 1, 5, 8, 8, -4, -1, 4, 5, -8, 4, 8, -6, 6, -2, 1, -8, -2,
-5, -8],
"z": [3, 6, 6, 8, 5, 6, 8, -2, 5, 6, 2, -6, 3, 1, 6, -6, -2, -6, -5,
-4, -1, -8, -4]}
n = {
"a": [0.110879558823853e-2, 0.572616740810616e3, -0.767051948380852e5,
-0.253321069529674e-1, 0.628008049345689e4, 0.234105654131876e6,
0.216867826045856, -0.156237904341963e3, -0.269893956176613e5,
-0.180407100085505e-3, 0.116732227668261e-2, 0.266987040856040e2,
0.282776617243286e5, -0.242431520029523e4, 0.435217323022733e-3,
-0.122494831387441e-1, 0.179357604019989e1, 0.442729521058314e2,
-0.593223489018342e-2, 0.453186261685774, 0.135825703129140e1,
0.408748415856745e-1, 0.474686397863312, 0.118646814997915e1,
0.546987265727549, 0.195266770452643, -0.502268790869663e-1,
-0.369645308193377, 0.633828037528420e-2, 0.797441793901017e-1],
"b": [-0.827670470003621e-1, 0.416887126010565e2, 0.483651982197059e-1,
-0.291032084950276e5, -0.111422582236948e3, -.202300083904014e-1,
0.294002509338515e3, 0.140244997609658e3, -0.344384158811459e3,
0.361182452612149e3, -0.140699677420738e4, -0.202023902676481e-2,
0.171346792457471e3, -0.425597804058632e1, 0.691346085000334e-5,
0.151140509678925e-2, -0.416375290166236e-1, -.413754957011042e2,
-0.506673295721637e2, -0.572212965569023e-3, 0.608817368401785e1,
0.239600660256161e2, 0.122261479925384e-1, 0.216356057692938e1,
0.398198903368642, -0.116892827834085, -0.102845919373532,
-0.492676637589284, 0.655540456406790e-1, -0.240462535078530,
-0.269798180310075e-1, 0.128369435967012],
"c": [0.311967788763030e1, 0.276713458847564e5, 0.322583103403269e8,
-0.342416065095363e3, -0.899732529907377e6, -0.793892049821251e8,
0.953193003217388e2, 0.229784742345072e4, 0.175336675322499e6,
0.791214365222792e7, 0.319933345844209e-4, -0.659508863555767e2,
-0.833426563212851e6, 0.645734680583292e-1, -0.382031020570813e7,
0.406398848470079e-4, 0.310327498492008e2, -0.892996718483724e-3,
0.234604891591616e3, 0.377515668966951e4, 0.158646812591361e-1,
0.707906336241843, 0.126016225146570e2, 0.736143655772152,
0.676544268999101, -0.178100588189137e2, -0.156531975531713,
0.117707430048158e2, 0.840143653860447e-1, -0.186442467471949,
-0.440170203949645e2, 0.123290423502494e7, -0.240650039730845e-1,
-0.107077716660869e7, 0.438319858566475e-1],
"d": [-0.452484847171645e-9, .315210389538801e-4, -.214991352047545e-2,
0.508058874808345e3, -0.127123036845932e8, 0.115371133120497e13,
-.197805728776273e-15, .241554806033972e-10,
-.156481703640525e-5, 0.277211346836625e-2, -0.203578994462286e2,
0.144369489909053e7, -0.411254217946539e11, 0.623449786243773e-5,
-.221774281146038e2, -0.689315087933158e5, -0.195419525060713e8,
0.316373510564015e4, 0.224040754426988e7, -0.436701347922356e-5,
-.404213852833996e-3, -0.348153203414663e3, -0.385294213555289e6,
0.135203700099403e-6, 0.134648383271089e-3, 0.125031835351736e6,
0.968123678455841e-1, 0.225660517512438e3, -0.190102435341872e-3,
-.299628410819229e-1, 0.500833915372121e-2, 0.387842482998411,
-0.138535367777182e4, 0.870745245971773, 0.171946252068742e1,
-.326650121426383e-1, 0.498044171727877e4, 0.551478022765087e-2],
"e": [0.715815808404721e9, -0.114328360753449e12, .376531002015720e-11,
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-0.432355225319745e11, -.59287424559861e12, 0.133061647281106e1,
0.157338197797544e7, 0.258189614270853e14, 0.262413209706358e25,
-.920011937431142e-1, 0.220213765905426e-2, -0.110433759109547e2,
0.847004870612087e7, -0.592910695762536e9, -0.183027173269660e-4,
0.181339603516302, -0.119228759669889e4, 0.430867658061468e7],
"y": [-0.525597995024633e-9, 0.583441305228407e4, -.134778968457925e17,
.118973500934212e26, -0.159096490904708e27, -.315839902302021e-6,
0.496212197158239e3, 0.327777227273171e19, -0.527114657850696e22,
.210017506281863e-16, 0.705106224399834e21, -.266713136106469e31,
-0.145370512554562e-7, 0.149333917053130e28, -.149795620287641e8,
-.3818819062711e16, 0.724660165585797e-4, -0.937808169550193e14,
0.514411468376383e10, -0.828198594040141e5],
"z": [0.24400789229065e-10, -0.463057430331242e7, 0.728803274777712e10,
.327776302858856e16, -.110598170118409e10, -0.323899915729957e13,
.923814007023245e16, 0.842250080413712e-12, 0.663221436245506e12,
-.167170186672139e15, .253749358701391e4, -0.819731559610523e-20,
0.328380587890663e12, -0.625004791171543e8, 0.803197957462023e21,
-.204397011338353e-10, -.378391047055938e4, 0.97287654593862e-2,
0.154355721681459e2, -0.373962862928643e4, -0.682859011374572e11,
-0.248488015614543e-3, 0.394536049497068e7]}
v_, P_, T_, a, b, c, d, e = par[x]
Pr = P / P_
Tr = T / T_
suma = 0
if x == "n":
for i, j, ni in zip(Li[x], Lj[x], n[x]):
suma += ni * (Pr - a) ** i * (Tr - b) ** j
return v_ * exp(suma)
for i, j, ni in zip(Li[x], Lj[x], n[x]):
suma += ni * (Pr - a) ** (c * i) * (Tr - b) ** (j * d)
return v_ * suma ** e
# Region 4
[docs]
def _Region4(P, x):
"""Basic equation for region 4
Parameters
----------
P : float
Pressure, [MPa]
x : float
Vapor quality, [-]
Returns
-------
prop : dict
Dict with calculated properties. The available properties are:
* T: Saturated temperature, [K]
* P: Saturated pressure, [MPa]
* x: Vapor quality, [-]
* v: Specific volume, [m³/kg]
* h: Specific enthalpy, [kJ/kg]
* s: Specific entropy, [kJ/kgK]
"""
T = _TSat_P(P)
if T > 623.15:
rhol = 1. / _Backward3_sat_v_P(P, T, 0)
P1 = _Region3(rhol, T)
rhov = 1. / _Backward3_sat_v_P(P, T, 1)
P2 = _Region3(rhov, T)
else:
P1 = _Region1(T, P)
P2 = _Region2(T, P)
propiedades = {}
propiedades["T"] = T
propiedades["P"] = P
propiedades["v"] = P1["v"] + x * (P2["v"] - P1["v"])
propiedades["h"] = P1["h"] + x * (P2["h"] - P1["h"])
propiedades["s"] = P1["s"] + x * (P2["s"] - P1["s"])
propiedades["cp"] = None
propiedades["cv"] = None
propiedades["w"] = None
propiedades["alfav"] = None
propiedades["kt"] = None
propiedades["region"] = 4
propiedades["x"] = x
return propiedades
[docs]
def _Backward4_T_hs(h, s):
"""Backward equation for region 4, T=f(h,s)
Parameters
----------
h : float
Specific enthalpy, [kJ/kg]
s : float
Specific entropy, [kJ/kgK]
Returns
-------
T : float
Temperature, [K]
References
----------
IAPWS, Revised Supplementary Release on Backward Equations p(h,s) for
Region 3, Equations as a Function of h and s for the Region Boundaries, and
an Equation Tsat(h,s) for Region 4 of the IAPWS Industrial Formulation 1997
for the Thermodynamic Properties of Water and Steam,
http://www.iapws.org/relguide/Supp-phs3-2014.pdf. Eq 9
Examples
--------
>>> _Backward4_T_hs(1800,5.3)
346.8475498
>>> _Backward4_T_hs(2400,6.0)
425.1373305
>>> _Backward4_T_hs(2500,5.5)
522.5579013
"""
nu = h / 2800
sigma = s / 9.2
suma = np.sum(
Const.Backward4_T_hs_n * (nu - 0.119) ** Const.Backward4_T_hs_Li * (sigma - 1.07) ** Const.Backward4_T_hs_Lj)
return 550 * suma
# Region 5
[docs]
def _Region5(T, P):
"""Basic equation for region 5
Parameters
----------
T : float
Temperature, [K]
P : float
Pressure, [MPa]
Returns
-------
prop : dict
Dict with calculated properties. The available properties are:
* v: Specific volume, [m³/kg]
* h: Specific enthalpy, [kJ/kg]
* s: Specific entropy, [kJ/kgK]
* cp: Specific isobaric heat capacity, [kJ/kgK]
* cv: Specific isocoric heat capacity, [kJ/kgK]
* w: Speed of sound, [m/s]
* alfav: Cubic expansion coefficient, [1/K]
* kt: Isothermal compressibility, [1/MPa]
References
----------
IAPWS, Revised Release on the IAPWS Industrial Formulation 1997 for the
Thermodynamic Properties of Water and Steam August 2007,
http://www.iapws.org/relguide/IF97-Rev.html, Eq 32-34
Examples
--------
>>> _Region5(1500,0.5)["v"]
1.38455090
>>> _Region5(1500,0.5)["h"]
5219.76855
>>> _Region5(1500,0.5)["h"]-500*_Region5(1500,0.5)["v"]
4527.49310
>>> _Region5(1500,30)["s"]
7.72970133
>>> _Region5(1500,30)["cp"]
2.72724317
>>> _Region5(1500,30)["cv"]
2.19274829
>>> _Region5(2000,30)["w"]
1067.36948
>>> _Region5(2000,30)["alfav"]
0.000508830641
>>> _Region5(2000,30)["kt"]
0.0329193892
"""
if P < 0:
P = Pmin
Tr = 1000 / T
Pr = P / 1
go, gop, gopp, got, gott, gopt = Region5_cp0(Tr, Pr)
gr = np.sum(Const.Region5_nr * Pr ** Const.Region5_Ir * Tr ** Const.Region5_Jr)
grp = np.sum(Const.Region5_nr_Ir_product * Pr ** Const.Region5_Ir_less_1 * Tr ** Const.Region5_Jr)
grpp = np.sum(Const.Region5_nr_Ir_product * Const.Region5_Ir_less_1 * Pr ** (
Const.Region5_Ir_less_2) * Tr ** Const.Region5_Jr)
grt = np.sum(Const.Region5_nr_Jr_product * Pr ** Const.Region5_Ir * Tr ** Const.Region5_Jr_less_1)
grtt = np.sum(Const.Region5_nr_Jr_product * Const.Region5_Jr_less_1 * Pr ** Const.Region5_Ir * Tr ** (
Const.Region5_Jr_less_2))
grpt = np.sum(Const.Region5_nr_Ir_Jr_product * Pr ** Const.Region5_Ir_less_1 * Tr ** Const.Region5_Jr_less_1)
propiedades = {}
propiedades["T"] = T
propiedades["P"] = P
propiedades["v"] = Pr * (gop + grp) * R * T / P / 1000
propiedades["h"] = Tr * (got + grt) * R * T
propiedades["s"] = R * (Tr * (got + grt) - (go + gr))
propiedades["cp"] = -R * Tr ** 2 * (gott + grtt)
propiedades["cv"] = R * (-Tr ** 2 * (gott + grtt) + ((gop + grp) - Tr * (gopt + grpt)) ** 2
/ (gopp + grpp))
propiedades["w"] = (R * T * 1000 * (1 + 2 * Pr * grp + Pr ** 2 * grp ** 2) / (1 - Pr ** 2 * grpp + (
1 + Pr * grp - Tr * Pr * grpt) ** 2 / Tr ** 2 / (gott + grtt))) ** 0.5
propiedades["alfav"] = (1 + Pr * grp - Tr * Pr * grpt) / (1 + Pr * grp) / T
propiedades["kt"] = (1 - Pr ** 2 * grpp) / (1 + Pr * grp) / P
propiedades["region"] = 5
propiedades["x"] = 1
return propiedades
[docs]
def Region5_cp0(Tr, Pr):
"""Ideal properties for Region 5
Parameters
----------
Tr : float
Reduced temperature, [-]
Pr : float
Reduced pressure, [-]
Returns
-------
prop : array
Array with ideal Gibbs energy partial derivatives:
* g: Ideal Specific Gibbs energy, [kJ/kg]
* gp: [∂g/∂P]T
* gpp: [∂²g/∂P²]T
* gt: [∂g/∂T]P
* gtt: [∂²g/∂T²]P
* gpt: [∂²g/∂T∂P]
References
----------
IAPWS, Revised Release on the IAPWS Industrial Formulation 1997 for the
Thermodynamic Properties of Water and Steam August 2007,
http://www.iapws.org/relguide/IF97-Rev.html, Eq 33
"""
gop = Pr ** -1
gopp = -Pr ** -2
gopt = 0
go = log(Pr) + np.sum(Const.Region5_cp0_no * Tr ** Const.Region5_cp0_Jo)
got = np.sum(Const.Region5_cp0_no_Jo_product * Tr ** Const.Region5_cp0_Jo_less_1)
gott = np.sum(Const.Region5_cp0_no_Jo_Jo_less_1_product * Tr ** Const.Region5_cp0_Jo_less_2)
return go, gop, gopp, got, gott, gopt
# Region definitions
[docs]
def _Bound_TP(T, P):
"""Region definition for input T and P
Parameters
----------
T : float
Temperature, [K]
P : float
Pressure, [MPa]
Returns
-------
region : float
IAPWS-97 region code
References
----------
Wagner, W; Kretzschmar, H-J: International Steam Tables: Properties of
Water and Steam Based on the Industrial Formulation IAPWS-IF97; Springer,
2008; doi: 10.1007/978-3-540-74234-0. Fig. 2.3
"""
region = None
if 1073.15 < T <= 2273.15 and Pmin <= P <= 50:
region = 5
elif Pmin <= P <= Ps_623:
Tsat = _TSat_P(P)
if 273.15 <= T <= Tsat:
region = 1
elif Tsat < T <= 1073.15:
region = 2
elif Ps_623 < P <= 100:
T_b23 = _t_P(P)
if 273.15 <= T <= 623.15:
region = 1
elif 623.15 < T < T_b23:
region = 3
elif T_b23 <= T <= 1073.15:
region = 2
return region
[docs]
def _Bound_Ph(P, h):
"""Region definition for input P y h
Parameters
----------
P : float
Pressure, [MPa]
h : float
Specific enthalpy, [kJ/kg]
Returns
-------
region : float
IAPWS-97 region code
References
----------
Wagner, W; Kretzschmar, H-J: International Steam Tables: Properties of
Water and Steam Based on the Industrial Formulation IAPWS-IF97; Springer,
2008; doi: 10.1007/978-3-540-74234-0. Fig. 2.5
"""
region = None
if Pmin <= P <= Ps_623:
h14 = _Region1(_TSat_P(P), P)["h"]
h24 = _Region2(_TSat_P(P), P)["h"]
h25 = _Region2(1073.15, P)["h"]
hmin = _Region1(273.15, P)["h"]
hmax = _Region5(2273.15, P)["h"]
if hmin <= h <= h14:
region = 1
elif h14 < h < h24:
region = 4
elif h24 <= h <= h25:
region = 2
elif h25 < h <= hmax:
region = 5
elif Ps_623 < P < Pc:
hmin = _Region1(273.15, P)["h"]
h13 = _Region1(623.15, P)["h"]
h32 = _Region2(_t_P(P), P)["h"]
h25 = _Region2(1073.15, P)["h"]
hmax = _Region5(2273.15, P)["h"]
if hmin <= h <= h13:
region = 1
elif h13 < h < h32:
try:
p34 = _PSat_h(h)
except NotImplementedError:
hmin_Ps3 = _Region1(623.15, Ps_623)["h"]
if h < hmin_Ps3:
p34 = Ps_623
else:
p34 = Pc
if P < p34:
region = 4
else:
region = 3
elif h32 <= h <= h25:
region = 2
elif h25 < h <= hmax:
region = 5
elif Pc <= P <= 100:
hmin = _Region1(273.15, P)["h"]
h13 = _Region1(623.15, P)["h"]
h32 = _Region2(_t_P(P), P)["h"]
h25 = _Region2(1073.15, P)["h"]
hmax = _Region5(2273.15, P)["h"]
if hmin <= h <= h13:
region = 1
elif h13 < h < h32:
region = 3
elif h32 <= h <= h25:
region = 2
elif P <= 50 and h25 <= h <= hmax:
region = 5
return region
[docs]
def _Bound_Ps(P, s):
"""Region definition for input P and s
Parameters
----------
P : float
Pressure, [MPa]
s : float
Specific entropy, [kJ/kgK]
Returns
-------
region : float
IAPWS-97 region code
References
----------
Wagner, W; Kretzschmar, H-J: International Steam Tables: Properties of
Water and Steam Based on the Industrial Formulation IAPWS-IF97; Springer,
2008; doi: 10.1007/978-3-540-74234-0. Fig. 2.9
"""
region = None
if Pmin <= P <= Ps_623:
smin = _Region1(273.15, P)["s"]
s14 = _Region1(_TSat_P(P), P)["s"]
s24 = _Region2(_TSat_P(P), P)["s"]
s25 = _Region2(1073.15, P)["s"]
smax = _Region5(2273.15, P)["s"]
if smin <= s <= s14:
region = 1
elif s14 < s < s24:
region = 4
elif s24 <= s <= s25:
region = 2
elif s25 < s <= smax:
region = 5
elif Ps_623 < P < Pc:
smin = _Region1(273.15, P)["s"]
s13 = _Region1(623.15, P)["s"]
s32 = _Region2(_t_P(P), P)["s"]
s25 = _Region2(1073.15, P)["s"]
smax = _Region5(2273.15, P)["s"]
if smin <= s <= s13:
region = 1
elif s13 < s < s32:
try:
p34 = _PSat_s(s)
except NotImplementedError:
smin_Ps3 = _Region1(623.15, Ps_623)["s"]
if s < smin_Ps3:
p34 = Ps_623
else:
p34 = Pc
if P < p34:
region = 4
else:
region = 3
elif s32 <= s <= s25:
region = 2
elif s25 < s <= smax:
region = 5
elif Pc <= P <= 100:
smin = _Region1(273.15, P)["s"]
s13 = _Region1(623.15, P)["s"]
s32 = _Region2(_t_P(P), P)["s"]
s25 = _Region2(1073.15, P)["s"]
smax = _Region5(2273.15, P)["s"]
if smin <= s <= s13:
region = 1
elif s13 < s < s32:
region = 3
elif s32 <= s <= s25:
region = 2
elif P <= 50 and s25 <= s <= smax:
region = 5
return region
[docs]
def _Bound_hs(h, s):
"""Region definition for input h and s
Parameters
----------
h : float
Specific enthalpy, [kJ/kg]
s : float
Specific entropy, [kJ/kgK]
Returns
-------
region : float
IAPWS-97 region code
References
----------
Wagner, W; Kretzschmar, H-J: International Steam Tables: Properties of
Water and Steam Based on the Industrial Formulation IAPWS-IF97; Springer,
2008; doi: 10.1007/978-3-540-74234-0. Fig. 2.14
"""
region = None
s13 = _Region1(623.15, 100)["s"]
s13s = _Region1(623.15, Ps_623)["s"]
sTPmax = _Region2(1073.15, 100)["s"]
s2ab = _Region2(1073.15, 4)["s"]
# Left point in h-s plot
smin = _Region1(273.15, 100)["s"]
hmin = _Region1(273.15, Pmin)["h"]
# Right point in h-s plot
_Pmax = _Region2(1073.15, Pmin)
hmax = _Pmax["h"]
smax = _Pmax["s"]
# Region 4 left and right point
_sL = _Region1(273.15, Pmin)
h4l = _sL["h"]
s4l = _sL["s"]
_sV = _Region2(273.15, Pmin)
h4v = _sV["h"]
s4v = _sV["s"]
if smin <= s <= s13:
hmin = h4l + (s - s4l) / (s4v - s4l) * (h4v - h4l)
hs = _h1_s(s)
T = _Backward1_T_Ps(100, s) - 0.0218
hmax = _Region1(T, 100)["h"]
if hmin <= h < hs:
region = 4
elif hs <= h <= hmax:
region = 1
elif s13 < s <= s13s:
hmin = h4l + (s - s4l) / (s4v - s4l) * (h4v - h4l)
hs = _h1_s(s)
h13 = _h13_s(s)
v = _Backward3_v_Ps(100, s) * (1 + 9.6e-5)
T = _Backward3_T_Ps(100, s) - 0.0248
hmax = _Region3(1 / v, T)["h"]
if hmin <= h < hs:
region = 4
elif hs <= h < h13:
region = 1
elif h13 <= h <= hmax:
region = 3
elif s13s < s <= sc:
hmin = h4l + (s - s4l) / (s4v - s4l) * (h4v - h4l)
hs = _h3a_s(s)
v = _Backward3_v_Ps(100, s) * (1 + 9.6e-5)
T = _Backward3_T_Ps(100, s) - 0.0248
hmax = _Region3(1 / v, T)["h"]
if hmin <= h < hs:
region = 4
elif hs <= h <= hmax:
region = 3
elif sc < s < 5.049096828:
hmin = h4l + (s - s4l) / (s4v - s4l) * (h4v - h4l)
hs = _h2c3b_s(s)
v = _Backward3_v_Ps(100, s) * (1 + 9.6e-5)
T = _Backward3_T_Ps(100, s) - 0.0248
hmax = _Region3(1 / v, T)["h"]
if hmin <= h < hs:
region = 4
elif hs <= h <= hmax:
region = 3
elif 5.049096828 <= s < 5.260578707:
# Specific zone with 2-3 boundary in s shape
hmin = h4l + (s - s4l) / (s4v - s4l) * (h4v - h4l)
hs = _h2c3b_s(s)
h23max = _Region2(863.15, 100)["h"]
h23min = _Region2(623.15, Ps_623)["h"]
T = _Backward2_T_Ps(100, s) - 0.019
hmax = _Region2(T, 100)["h"]
if hmin <= h < hs:
region = 4
elif hs <= h < h23min:
region = 3
elif h23min <= h < h23max:
if _Backward2c_P_hs(h, s) <= _P23_T(_t_hs(h, s)):
region = 2
else:
region = 3
elif h23max <= h <= hmax:
region = 2
elif 5.260578707 <= s < 5.85:
hmin = h4l + (s - s4l) / (s4v - s4l) * (h4v - h4l)
hs = _h2c3b_s(s)
T = _Backward2_T_Ps(100, s) - 0.019
hmax = _Region2(T, 100)["h"]
if hmin <= h < hs:
region = 4
elif hs <= h <= hmax:
region = 2
elif 5.85 <= s < sTPmax:
hmin = h4l + (s - s4l) / (s4v - s4l) * (h4v - h4l)
hs = _h2ab_s(s)
T = _Backward2_T_Ps(100, s) - 0.019
hmax = _Region2(T, 100)["h"]
if hmin <= h < hs:
region = 4
elif hs <= h <= hmax:
region = 2
elif sTPmax <= s < s2ab:
hmin = h4l + (s - s4l) / (s4v - s4l) * (h4v - h4l)
hs = _h2ab_s(s)
P = _Backward2_P_hs(h, s)
hmax = _Region2(1073.15, P)["h"]
if hmin <= h < hs:
region = 4
elif hs <= h <= hmax:
region = 2
elif s2ab <= s < s4v:
hmin = h4l + (s - s4l) / (s4v - s4l) * (h4v - h4l)
hs = _h2ab_s(s)
P = _Backward2_P_hs(h, s)
hmax = _Region2(1073.15, P)["h"]
if hmin <= h < hs:
region = 4
elif hs <= h <= hmax:
region = 2
elif s4v <= s <= smax:
hmin = _Region2(273.15, Pmin)["h"]
P = _Backward2a_P_hs(h, s)
hmax = _Region2(1073.15, P)["h"]
if Pmin <= P <= 100 and hmin <= h <= hmax:
region = 2
# Check region 5
if not region and \
_Region5(1073.15, 50)["s"] < s <= _Region5(2273.15, Pmin)["s"] \
and _Region5(1073.15, 50)["h"] < h <= _Region5(2273.15, Pmin)["h"]:
def funcion(par):
return (_Region5(par[0], par[1])["h"] - h,
_Region5(par[0], par[1])["s"] - s)
T, P = fsolve(funcion, [1400, 1])
if 1073.15 < T <= 2273.15 and Pmin <= P <= 50:
region = 5
return region
[docs]
def prop0(T, P):
"""Ideal gas properties
Parameters
----------
T : float
Temperature, [K]
P : float
Pressure, [MPa]
Returns
-------
prop : dict
Dict with calculated properties. The available properties are:
* v: Specific volume, [m³/kg]
* h: Specific enthalpy, [kJ/kg]
* s: Specific entropy, [kJ/kgK]
* cp: Specific isobaric heat capacity, [kJ/kgK]
* cv: Specific isocoric heat capacity, [kJ/kgK]
* w: Speed of sound, [m/s]
* alfav: Cubic expansion coefficient, [1/K]
* kt: Isothermal compressibility, [1/MPa]
"""
if T <= 1073.15:
Tr = 540 / T
Pr = P / 1.
go, gop, gopp, got, gott, gopt = Region2_cp0(Tr, Pr)
else:
Tr = 1000 / T
Pr = P / 1.
go, gop, gopp, got, gott, gopt = Region5_cp0(Tr, Pr)
p0 = {}
p0["v"] = Pr * gop * R * T / P / 1000
p0["h"] = Tr * got * R * T
p0["s"] = R * (Tr * got - go)
p0["cp"] = -R * Tr ** 2 * gott
p0["cv"] = R * (-Tr ** 2 * gott - 1)
p0["w"] = (R * T * 1000 / (1 + 1 / Tr ** 2 / gott)) ** 0.5
p0["alfav"] = 1 / T
p0["xkappa"] = 1 / P
return p0
[docs]
class IAPWS97(_fase):
"""Class to model a state of liquid water or steam with the IAPWS-IF97
Parameters
----------
T : float
Temperature, [K]
P : float
Pressure, [MPa]
h : float
Specific enthalpy, [kJ/kg]
s : float
Specific entropy, [kJ/kgK]
x : float
Vapor quality, [-]
l : float, optional
Wavelength of light, for refractive index, [μm]
Notes
-----
Definitions options:
* T, P: Not valid for two-phases region
* P, h
* P, s
* h, s
* T, x: Only for two-phases region
* P, x: Only for two-phases region
Returns
-------
prop : dict
The calculated instance has the following properties:
* P: Pressure, [MPa]
* T: Temperature, [K]
* g: Specific Gibbs free energy, [kJ/kg]
* a: Specific Helmholtz free energy, [kJ/kg]
* v: Specific volume, [m³/kg]
* rho: Density, [kg/m³]
* h: Specific enthalpy, [kJ/kg]
* u: Specific internal energy, [kJ/kg]
* s: Specific entropy, [kJ/kg·K]
* cp: Specific isobaric heat capacity, [kJ/kg·K]
* cv: Specific isochoric heat capacity, [kJ/kg·K]
* Z: Compression factor, [-]
* fi: Fugacity coefficient, [-]
* f: Fugacity, [MPa]
* gamma: Isoentropic exponent, [-]
* alfav: Isobaric cubic expansion coefficient, [1/K]
* xkappa: Isothermal compressibility, [1/MPa]
* kappas: Adiabatic compresibility, [1/MPa]
* alfap: Relative pressure coefficient, [1/K]
* betap: Isothermal stress coefficient, [kg/m³]
* joule: Joule-Thomson coefficient, [K/MPa]
* deltat: Isothermal throttling coefficient, [kJ/kg·MPa]
* region: Region
* v0: Ideal specific volume, [m³/kg]
* u0: Ideal specific internal energy, [kJ/kg]
* h0: Ideal specific enthalpy, [kJ/kg]
* s0: Ideal specific entropy, [kJ/kg·K]
* a0: Ideal specific Helmholtz free energy, [kJ/kg]
* g0: Ideal specific Gibbs free energy, [kJ/kg]
* cp0: Ideal specific isobaric heat capacity, [kJ/kg·K]
* cv0: Ideal specific isochoric heat capacity [kJ/kg·K]
* w0: Ideal speed of sound, [m/s]
* gamma0: Ideal isoentropic exponent, [-]
* w: Speed of sound, [m/s]
* mu: Dynamic viscosity, [Pa·s]
* nu: Kinematic viscosity, [m²/s]
* k: Thermal conductivity, [W/m·K]
* alfa: Thermal diffusivity, [m²/s]
* sigma: Surface tension, [N/m]
* epsilon: Dielectric constant, [-]
* n: Refractive index, [-]
* Prandt: Prandtl number, [-]
* Pr: Reduced Pressure, [-]
* Tr: Reduced Temperature, [-]
* Hvap: Vaporization heat, [kJ/kg]
* Svap: Vaporization entropy, [kJ/kg·K]
Examples
--------
>>> water=IAPWS97(T=170+273.15, x=0.5)
>>> water.Liquid.cp, water.Vapor.cp, water.Liquid.w, water.Vapor.w
4.3695 2.5985 1418.3 498.78
>>> water=IAPWS97(T=325+273.15, x=0.5)
>>> water.P, water.Liquid.v, water.Vapor.v, water.Liquid.h, water.Vapor.h
12.0505 0.00152830 0.0141887 1493.37 2684.48
>>> water=IAPWS97(T=50+273.15, P=0.0006112127)
>>> water.cp0, water.cv0, water.h0, water.s0, water.w0
1.8714 1.4098 2594.66 9.471 444.93
"""
M = 18.015257 # kg/kmol
Pc = Pc
Tc = Tc
rhoc = rhoc
Tt = Tt
Tb = Tb
f_accent = f_acent
dipole = Dipole
kwargs = {"T": 0.0,
"P": 0.0,
"x": None,
"h": None,
"s": None,
"v": 0.0,
"l": 0.5893}
status = 0
msg = "Unknown variables"
_thermo = ""
region = None
Liquid = None
Vapor = None
T = None
P = None
v = None
rho = None
phase = None
x = None
Tr = None
Pr = None
sigma = None
v0 = None
h0 = None
u0 = None
s0 = None
a0 = None
g0 = None
cp0 = None
cv0 = None
cp0_cv = None
w0 = None
gamma0 = None
h = None
u = None
s = None
a = None
g = None
Hvap = None
Svap = None
def __init__(self, **kwargs):
self.kwargs = IAPWS97.kwargs.copy()
self.__call__(**kwargs)
def __call__(self, **kwargs):
"""Invoke the solver."""
self.kwargs.update(kwargs)
if self.calculable:
self.status = 1
self.calculo()
self.msg = "Solved"
@property
def calculable(self):
"""Check if class is calculable by its kwargs"""
self._thermo = ""
if self.kwargs["T"] and self.kwargs["P"]:
self._thermo = "TP"
elif self.kwargs["P"] and self.kwargs["h"] is not None:
self._thermo = "Ph"
elif self.kwargs["P"] and self.kwargs["s"] is not None:
self._thermo = "Ps"
elif self.kwargs["h"] is not None and self.kwargs["s"] is not None:
self._thermo = "hs"
elif self.kwargs["T"] and self.kwargs["x"] is not None:
self._thermo = "Tx"
elif self.kwargs["P"] and self.kwargs["x"] is not None:
self._thermo = "Px"
# TODO: Add other pairs definitions options
# elif self.kwargs["P"] and self.kwargs["v"]:
# self._thermo = "Pv"
# elif self.kwargs["T"] and self.kwargs["s"] is not None:
# self._thermo = "Ts"
return self._thermo
[docs]
def calculo(self):
"""Calculate procedure"""
propiedades = None
args = (self.kwargs[self._thermo[0]], self.kwargs[self._thermo[1]])
if self._thermo == "TP":
T, P = args
region = _Bound_TP(T, P)
if region == 1:
propiedades = _Region1(T, P)
elif region == 2:
propiedades = _Region2(T, P)
elif region == 3:
if T == Tc and P == Pc:
rho = rhoc
else:
vo = _Backward3_v_PT(P, T)
def funcion(rho):
return _Region3(rho, self.kwargs["T"])["P"] - P
rho = newton(funcion, 1 / vo)
propiedades = _Region3(rho, T)
elif region == 5:
propiedades = _Region5(T, P)
else:
raise NotImplementedError("Incoming out of bound")
elif self._thermo == "Ph":
P, h = args
region = _Bound_Ph(P, h)
if region == 1:
To = _Backward1_T_Ph(P, h)
T = newton(lambda T: _Region1(T, P)["h"] - h, To)
propiedades = _Region1(T, P)
elif region == 2:
To = _Backward2_T_Ph(P, h)
T = newton(lambda T: _Region2(T, P)["h"] - h, To)
propiedades = _Region2(T, P)
elif region == 3:
vo = _Backward3_v_Ph(P, h)
To = _Backward3_T_Ph(P, h)
def funcion(par):
return (_Region3(par[0], par[1])["h"] - h,
_Region3(par[0], par[1])["P"] - P)
rho, T = fsolve(funcion, [1 / vo, To])
propiedades = _Region3(rho, T)
elif region == 4:
T = _TSat_P(P)
if T <= 623.15:
h1 = _Region1(T, P)["h"]
h2 = _Region2(T, P)["h"]
x = (h - h1) / (h2 - h1)
propiedades = _Region4(P, x)
else:
h1 = _Region4(P, 0)["h"]
h2 = _Region4(P, 1)["h"]
x = (h - h1) / (h2 - h1)
propiedades = _Region4(P, x)
elif region == 5:
T = newton(lambda T: _Region5(T, P)["h"] - h, 1500)
propiedades = _Region5(T, P)
else:
raise NotImplementedError("Incoming out of bound")
elif self._thermo == "Ps":
P, s = args
region = _Bound_Ps(P, s)
if region == 1:
To = _Backward1_T_Ps(P, s)
T = newton(lambda T: _Region1(T, P)["s"] - s, To)
propiedades = _Region1(T, P)
elif region == 2:
To = _Backward2_T_Ps(P, s)
T = newton(lambda T: _Region2(T, P)["s"] - s, To)
propiedades = _Region2(T, P)
elif region == 3:
vo = _Backward3_v_Ps(P, s)
To = _Backward3_T_Ps(P, s)
def funcion(par):
return (_Region3(par[0], par[1])["s"] - s,
_Region3(par[0], par[1])["P"] - P)
rho, T = fsolve(funcion, [1 / vo, To])
propiedades = _Region3(rho, T)
elif region == 4:
T = _TSat_P(P)
if T <= 623.15:
s1 = _Region1(T, P)["s"]
s2 = _Region2(T, P)["s"]
x = (s - s1) / (s2 - s1)
propiedades = _Region4(P, x)
else:
s1 = _Region4(P, 0)["s"]
s2 = _Region4(P, 1)["s"]
x = (s - s1) / (s2 - s1)
propiedades = _Region4(P, x)
elif region == 5:
T = newton(lambda T: _Region5(T, P)["s"] - s, 1500)
propiedades = _Region5(T, P)
else:
raise NotImplementedError("Incoming out of bound")
elif self._thermo == "hs":
h, s = args
region = _Bound_hs(h, s)
if region == 1:
Po = _Backward1_P_hs(h, s)
To = _Backward1_T_Ph(Po, h)
def funcion(par):
return (_Region1(par[0], par[1])["h"] - h,
_Region1(par[0], par[1])["s"] - s)
T, P = fsolve(funcion, [To, Po])
propiedades = _Region1(T, P)
elif region == 2:
Po = _Backward2_P_hs(h, s)
To = _Backward2_T_Ph(Po, h)
def funcion(par):
return (_Region2(par[0], par[1])["h"] - h,
_Region2(par[0], par[1])["s"] - s)
T, P = fsolve(funcion, [To, Po])
propiedades = _Region2(T, P)
elif region == 3:
P = _Backward3_P_hs(h, s)
vo = _Backward3_v_Ph(P, h)
To = _Backward3_T_Ph(P, h)
def funcion(par):
return (_Region3(par[0], par[1])["h"] - h,
_Region3(par[0], par[1])["s"] - s)
rho, T = fsolve(funcion, [1 / vo, To])
propiedades = _Region3(rho, T)
elif region == 4:
if round(s - sc, 6) == 0 and round(h - hc, 6) == 0:
propiedades = _Region3(rhoc, Tc)
else:
To = _Backward4_T_hs(h, s)
if To < 273.15 or To > Tc:
To = 300
def funcion(par):
if par[1] < 0:
par[1] = 0
elif par[1] > 1:
par[1] = 1
if par[0] < 273.15:
par[0] = 273.15
elif par[0] > Tc:
par[0] = Tc
Po = _PSat_T(par[0])
liquid = _Region1(par[0], Po)
vapor = _Region2(par[0], Po)
hl = liquid["h"]
sl = liquid["s"]
hv = vapor["h"]
sv = vapor["s"]
return (hv * par[1] + hl * (1 - par[1]) - h,
sv * par[1] + sl * (1 - par[1]) - s)
T, x = fsolve(funcion, [To, 0.5])
P = _PSat_T(T)
if Pt <= P < Pc and 0 < x < 1:
propiedades = _Region4(P, x)
elif Pt <= P <= Ps_623 and x == 0:
propiedades = _Region1(T, P)
elif region == 5:
def funcion(par):
return (_Region5(par[0], par[1])["h"] - h,
_Region5(par[0], par[1])["s"] - s)
T, P = fsolve(funcion, [1400, 1])
propiedades = _Region5(T, P)
else:
raise NotImplementedError("Incoming out of bound")
elif self._thermo == "Px":
P, x = args
T = _TSat_P(P)
if Pt <= P < Pc and 0 < x < 1:
propiedades = _Region4(P, x)
elif Pt <= P <= Ps_623 and x == 0:
propiedades = _Region1(T, P)
elif Pt <= P <= Ps_623 and x == 1:
propiedades = _Region2(T, P)
elif Ps_623 < P < Pc and x in (0, 1):
def funcion(rho):
return _Region3(rho, T)["P"] - P
rhoo = 1. / _Backward3_sat_v_P(P, T, x)
rho = fsolve(funcion, rhoo)[0]
propiedades = _Region3(rho, T)
elif P == Pc and 0 <= x <= 1:
propiedades = _Region3(rhoc, Tc)
else:
raise NotImplementedError("Incoming out of bound")
self.sigma = _Tension(T)
propiedades["x"] = x
elif self._thermo == "Tx":
T, x = args
P = _PSat_T(T)
if 273.15 <= T < Tc and 0 < x < 1:
propiedades = _Region4(P, x)
elif 273.15 <= T <= 623.15 and x == 0:
propiedades = _Region1(T, P)
elif 273.15 <= T <= 623.15 and x == 1:
propiedades = _Region2(T, P)
elif 623.15 < T < Tc and x in (0, 1):
rho = 1. / _Backward3_sat_v_P(P, T, x)
propiedades = _Region3(rho, T)
elif T == Tc and 0 <= x <= 1:
propiedades = _Region3(rhoc, Tc)
else:
raise NotImplementedError("Incoming out of bound")
self.sigma = _Tension(T)
propiedades["x"] = x
self.x = propiedades["x"]
self.region = propiedades["region"]
self.T = propiedades["T"]
self.P = propiedades["P"]
self.v = propiedades["v"]
self.rho = 1 / self.v
self.phase = getphase(self.Tc, self.Pc, self.T, self.P, self.x,
self.region)
self.Tr = self.T / self.Tc
self.Pr = self.P / self.Pc
# Ideal properties
cp0 = prop0(self.T, self.P)
self.v0 = cp0["v"]
self.h0 = cp0["h"]
self.u0 = self.h0 - self.P * 1000 * 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.w0 = cp0["w"]
self.gamma0 = self.cp0_cv
self.Liquid = _fase()
self.Vapor = _fase()
if self.x == 0:
# only liquid phase
self.fill(self, propiedades)
self.fill(self.Liquid, propiedades)
self.sigma = _Tension(self.T)
elif self.x == 1:
# only vapor phase
self.fill(self, propiedades)
self.fill(self.Vapor, propiedades)
else:
# two phases
liquido = _Region1(self.T, self.P)
self.fill(self.Liquid, liquido)
vapor = _Region2(self.T, self.P)
self.fill(self.Vapor, vapor)
self.h = propiedades["h"]
self.u = self.h - self.P * 1000 * self.v
self.s = propiedades["s"]
self.a = self.u - self.T * self.s
self.g = self.h - self.T * self.s
self.sigma = _Tension(self.T)
self.Hvap = vapor["h"] - liquido["h"]
self.Svap = vapor["s"] - liquido["s"]
[docs]
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.cv = estado["cv"]
fase.cp = estado["cp"]
fase.cp_cv = fase.cp / fase.cv
fase.w = estado["w"]
fase.Z = self.P * fase.v / R * 1000 / self.T
fase.alfav = estado["alfav"]
fase.xkappa = estado["kt"]
fase.kappas = -1 / fase.v * self.derivative("v", "P", "s", fase)
fase.joule = self.derivative("T", "P", "h", fase)
fase.deltat = self.derivative("h", "P", "T", fase)
fase.gamma = -fase.v/self.P \
* self.derivative("P", "v", "T", fase)*fase.cp_cv
fase.alfap = fase.alfav / self.P / fase.xkappa
fase.betap = -1 / self.P * self.derivative("P", "v", "T", fase)
fase.fi = exp((fase.g - self.g0) / R / self.T)
fase.f = self.P * fase.fi
fase.mu = _Viscosity(fase.rho, self.T)
# Use industrial formulation for critical enhancement in thermal
# conductivity calculation
fase.drhodP_T = self.derivative("rho", "P", "T", fase)
fase.k = _ThCond(fase.rho, self.T, fase)
fase.nu = fase.mu / fase.rho
fase.alfa = fase.k / 1000 / fase.rho / fase.cp
try:
fase.epsilon = _Dielectric(fase.rho, self.T)
except NotImplementedError:
fase.epsilon = None
fase.Prandt = fase.mu * fase.cp * 1000 / fase.k
try:
fase.n = _Refractive(fase.rho, self.T, self.kwargs["l"])
except NotImplementedError:
fase.n = None
[docs]
def derivative(self, z, x, y, fase):
"""
Wrapper derivative for custom derived properties
where x, y, z can be: P, T, v, u, h, s, g, a
"""
return deriv_G(self, z, x, y, fase)
[docs]
class IAPWS97_PT(IAPWS97):
"""Derivated class for direct P and T input"""
def __init__(self, P, T):
IAPWS97.__init__(self, T=T, P=P)
[docs]
class IAPWS97_Ph(IAPWS97):
"""Derivated class for direct P and h input"""
def __init__(self, P, h):
IAPWS97.__init__(self, P=P, h=h)
[docs]
class IAPWS97_Ps(IAPWS97):
"""Derivated class for direct P and s input"""
def __init__(self, P, s):
IAPWS97.__init__(self, P=P, s=s)
[docs]
class IAPWS97_Px(IAPWS97):
"""Derivated class for direct P and x input"""
def __init__(self, P, x):
IAPWS97.__init__(self, P=P, x=x)
[docs]
class IAPWS97_Tx(IAPWS97):
"""Derivated class for direct T and x input"""
def __init__(self, T, x):
IAPWS97.__init__(self, T=T, x=x)