Source code for iapws.iapws97

#!/usr/bin/python
# -*- coding: utf-8 -*-
"""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

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 Li = [0, 1, 1, 3, 5, 6] Lj = [0, -2, 2, -12, -4, -3] n = [0.913965547600543, -0.430944856041991e-4, 0.603235694765419e2, 0.117518273082168e-17, 0.220000904781292, -0.690815545851641e2] suma = 0 for i, j, ni in zip(Li, Lj, n): suma += ni * (sigma-0.884)**i * (sigma-0.864)**j 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 Li = [-12, -10, -8, -4, -3, -2, -2, -2, -2, 0, 1, 1, 1, 3, 3, 5, 6, 6, 8, 8, 8, 12, 12, 14, 14] Lj = [10, 8, 3, 4, 3, -6, 2, 3, 4, 0, -3, -2, 10, -2, -1, -5, -6, -3, -8, -2, -1, -12, -1, -12, 1] n = [0.629096260829810e-3, -0.823453502583165e-3, 0.515446951519474e-7, -0.117565945784945e1, 0.348519684726192e1, -0.507837382408313e-11, -0.284637670005479e1, -0.236092263939673e1, 0.601492324973779e1, 0.148039650824546e1, 0.360075182221907e-3, -0.126700045009952e-1, -0.122184332521413e7, 0.149276502463272, 0.698733471798484, -0.252207040114321e-1, 0.147151930985213e-1, -0.108618917681849e1, -0.936875039816322e-3, 0.819877897570217e2, -0.182041861521835e3, 0.261907376402688e-5, -0.291626417025961e5, 0.140660774926165e-4, 0.783237062349385e7] suma = 0 for i, j, ni in zip(Li, Lj, n): suma += ni * (nu-0.727)**i * (sigma-0.864)**j 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 Li = [0, 1, 1, 1, 1, 5, 7, 8, 14, 20, 22, 24, 28, 36] Lj = [0, 1, 3, 4, 36, 3, 0, 24, 16, 16, 3, 18, 8, 24] n = [0.600073641753024, -0.936203654849857e1, 0.246590798594147e2, -0.107014222858224e3, -0.915821315805768e14, -0.862332011700662e4, -0.235837344740032e2, 0.252304969384128e18, -0.389718771997719e19, -0.333775713645296e23, 0.356499469636328e11, -0.148547544720641e27, 0.330611514838798e19, 0.813641294467829e38] suma = 0 for i, j, ni in zip(Li, Lj, n): suma += ni * (nu-1.02)**i * (nu-0.608)**j 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 Li = [0, 1, 1, 4, 12, 12, 16, 24, 28, 32] Lj = [0, 1, 32, 7, 4, 14, 36, 10, 0, 18] n = [0.639767553612785, -0.129727445396014e2, -0.224595125848403e16, 0.177466741801846e7, 0.717079349571538e10, -0.378829107169011e18, -0.955586736431328e35, 0.187269814676188e24, 0.119254746466473e12, 0.110649277244882e37] suma = 0 for i, j, ni in zip(Li, Lj, n): suma += ni * (sigma-1.03)**i * (sigma-0.699)**j 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 Li = [0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 4, 5, 5, 7, 8, 12, 12, 14, 14, 16, 20, 20, 22, 24, 28, 32, 32] Lj = [14, 36, 3, 16, 0, 5, 4, 36, 4, 16, 24, 18, 24, 1, 4, 2, 4, 1, 22, 10, 12, 28, 8, 3, 0, 6, 8] n = [0.332171191705237, 0.611217706323496e-3, -0.882092478906822e1, -0.455628192543250, -0.263483840850452e-4, -0.223949661148062e2, -0.428398660164013e1, -0.616679338856916, -0.146823031104040e2, 0.284523138727299e3, -0.113398503195444e3, 0.115671380760859e4, 0.395551267359325e3, -0.154891257229285e1, 0.194486637751291e2, -0.357915139457043e1, -0.335369414148819e1, -0.664426796332460, 0.323321885383934e5, 0.331766744667084e4, -0.223501257931087e5, 0.573953875852936e7, 0.173226193407919e3, -0.363968822121321e-1, 0.834596332878346e-6, 0.503611916682674e1, 0.655444787064505e2] suma = 0 for i, j, ni in zip(Li, Lj, n): suma += ni * (sigma-1.09)**i * (sigma+0.366e-4)**j 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 Li = [0, 0, 0, 0, 2, 3, 4, 4, 5, 5, 6, 7, 7, 7, 10, 10, 10, 32, 32] Lj = [1, 4, 10, 16, 1, 36, 3, 16, 20, 36, 4, 2, 28, 32, 14, 32, 36, 0, 6] n = [0.822673364673336, 0.181977213534479, -0.112000260313624e-1, -0.746778287048033e-3, -0.179046263257381, 0.424220110836657e-1, -0.341355823438768, -0.209881740853565e1, -0.822477343323596e1, -0.499684082076008e1, 0.191413958471069, 0.581062241093136e-1, -0.165505498701029e4, 0.158870443421201e4, -0.850623535172818e2, -0.317714386511207e5, -0.945890406632871e5, -0.139273847088690e-5, 0.631052532240980] suma = 0 for i, j, ni in zip(Li, Lj, n): suma += ni * (sigma-1.09)**i * (sigma+0.366e-4)**j 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 Li = [1, 1, 2, 2, 4, 4, 7, 8, 8, 10, 12, 12, 18, 20, 24, 28, 28, 28, 28, 28, 32, 32, 32, 32, 32, 36, 36, 36, 36, 36] Lj = [8, 24, 4, 32, 1, 2, 7, 5, 12, 1, 0, 7, 10, 12, 32, 8, 12, 20, 22, 24, 2, 7, 12, 14, 24, 10, 12, 20, 22, 28] n = [-0.524581170928788e3, -0.926947218142218e7, -0.237385107491666e3, 0.210770155812776e11, -0.239494562010986e2, 0.221802480294197e3, -0.510472533393438e7, 0.124981396109147e7, 0.200008436996201e10, -0.815158509791035e3, -0.157612685637523e3, -0.114200422332791e11, 0.662364680776872e16, -0.227622818296144e19, -0.171048081348406e32, 0.660788766938091e16, 0.166320055886021e23, -0.218003784381501e30, -0.787276140295618e30, 0.151062329700346e32, 0.795732170300541e7, 0.131957647355347e16, -0.325097068299140e24, -0.418600611419248e26, 0.297478906557467e35, -0.953588761745473e20, 0.166957699620939e25, -0.175407764869978e33, 0.347581490626396e35, -0.710971318427851e39] suma = 0 for i, j, ni in zip(Li, Lj, n): suma += ni * (1/sigma1-0.513)**i * (sigma2-0.524)**j 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 Li = [0, 0, 0, 1, 1, 5, 6, 7, 8, 8, 12, 16, 22, 22, 24, 36] Lj = [0, 3, 4, 0, 12, 36, 12, 16, 2, 20, 32, 36, 2, 32, 7, 20] n = [0.104351280732769e1, -0.227807912708513e1, 0.180535256723202e1, 0.420440834792042, -0.105721244834660e6, 0.436911607493884e25, -0.328032702839753e12, -0.678686760804270e16, 0.743957464645363e4, -0.356896445355761e20, 0.167590585186801e32, -0.355028625419105e38, 0.396611982166538e12, -0.414716268484468e41, 0.359080103867382e19, -0.116994334851995e41] suma = 0 for i, j, ni in zip(Li, Lj, n): suma += ni * (sigma-1.02)**i * (sigma-0.726)**j 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 Li = [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 8, 8, 21, 23, 29, 30, 31, 32] Lj = [-2, -1, 0, 1, 2, 3, 4, 5, -9, -7, -1, 0, 1, 3, -3, 0, 1, 3, 17, -4, 0, 6, -5, -2, 10, -8, -11, -6, -29, -31, -38, -39, -40, -41] n = [0.14632971213167, -0.84548187169114, -0.37563603672040e1, 0.33855169168385e1, -0.95791963387872, 0.15772038513228, -0.16616417199501e-1, 0.81214629983568e-3, 0.28319080123804e-3, -0.60706301565874e-3, -0.18990068218419e-1, -0.32529748770505e-1, -0.21841717175414e-1, -0.52838357969930e-4, -0.47184321073267e-3, -0.30001780793026e-3, 0.47661393906987e-4, -0.44141845330846e-5, -0.72694996297594e-15, -0.31679644845054e-4, -0.28270797985312e-5, -0.85205128120103e-9, -0.22425281908000e-5, -0.65171222895601e-6, -0.14341729937924e-12, -0.40516996860117e-6, -0.12734301741641e-8, -0.17424871230634e-9, -0.68762131295531e-18, 0.14478307828521e-19, 0.26335781662795e-22, -0.11947622640071e-22, 0.18228094581404e-23, -0.93537087292458e-25] Tr = 1386/T Pr = P/16.53 g = gp = gpp = gt = gtt = gpt = 0 for i, j, ni in zip(Li, Lj, n): g += ni * (7.1-Pr)**i * (Tr-1.222)**j gp -= ni*i * (7.1-Pr)**(i-1) * (Tr-1.222)**j gpp += ni*i*(i-1) * (7.1-Pr)**(i-2) * (Tr-1.222)**j gt += ni*j * (7.1-Pr)**i * (Tr-1.222)**(j-1) gtt += ni*j*(j-1) * (7.1-Pr)**i * (Tr-1.222)**(j-2) gpt -= ni*i*j * (7.1-Pr)**(i-1) * (Tr-1.222)**(j-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 """ Li = [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 4, 5, 6] Lj = [0, 1, 2, 6, 22, 32, 0, 1, 2, 3, 4, 10, 32, 10, 32, 10, 32, 32, 32, 32] n = [-0.23872489924521e3, 0.40421188637945e3, 0.11349746881718e3, -0.58457616048039e1, -0.15285482413140e-3, -0.10866707695377e-5, -0.13391744872602e2, 0.43211039183559e2, -0.54010067170506e2, 0.30535892203916e2, -0.65964749423638e1, 0.93965400878363e-2, 0.11573647505340e-6, -0.25858641282073e-4, -0.40644363084799e-8, 0.66456186191635e-7, 0.80670734103027e-10, -0.93477771213947e-12, 0.58265442020601e-14, -0.15020185953503e-16] Pr = P/1 nu = h/2500 T = 0 for i, j, ni in zip(Li, Lj, n): T += ni * Pr**i * (nu+1)**j 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 """ Li = [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 4] Lj = [0, 1, 2, 3, 11, 31, 0, 1, 2, 3, 12, 31, 0, 1, 2, 9, 31, 10, 32, 32] n = [0.17478268058307e3, 0.34806930892873e2, 0.65292584978455e1, 0.33039981775489, -0.19281382923196e-6, -0.24909197244573e-22, -0.26107636489332, 0.22592965981586, -0.64256463395226e-1, 0.78876289270526e-2, 0.35672110607366e-9, 0.17332496994895e-23, 0.56608900654837e-3, -0.32635483139717e-3, 0.44778286690632e-4, -0.51322156908507e-9, -0.42522657042207e-25, 0.26400441360689e-12, 0.78124600459723e-28, -0.30732199903668e-30] Pr = P/1 sigma = s/1 T = 0 for i, j, ni in zip(Li, Lj, n): T += ni * Pr**i * (sigma+2)**j 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 """ Li = [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 3, 4, 4, 5] Lj = [0, 1, 2, 4, 5, 6, 8, 14, 0, 1, 4, 6, 0, 1, 10, 4, 1, 4, 0] n = [-0.691997014660582, -0.183612548787560e2, -0.928332409297335e1, 0.659639569909906e2, -0.162060388912024e2, 0.450620017338667e3, 0.854680678224170e3, 0.607523214001162e4, 0.326487682621856e2, -0.269408844582931e2, -0.319947848334300e3, -0.928354307043320e3, 0.303634537455249e2, -0.650540422444146e2, -0.430991316516130e4, -0.747512324096068e3, 0.730000345529245e3, 0.114284032569021e4, -0.436407041874559e3] nu = h/3400 sigma = s/7.6 P = 0 for i, j, ni in zip(Li, Lj, n): P += ni * (nu+0.05)**i * (sigma+0.05)**j 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) Ir = [1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 5, 6, 6, 6, 7, 7, 7, 8, 8, 9, 10, 10, 10, 16, 16, 18, 20, 20, 20, 21, 22, 23, 24, 24, 24] Jr = [0, 1, 2, 3, 6, 1, 2, 4, 7, 36, 0, 1, 3, 6, 35, 1, 2, 3, 7, 3, 16, 35, 0, 11, 25, 8, 36, 13, 4, 10, 14, 29, 50, 57, 20, 35, 48, 21, 53, 39, 26, 40, 58] nr = [-0.0017731742473212999, -0.017834862292357999, -0.045996013696365003, -0.057581259083432, -0.050325278727930002, -3.3032641670203e-05, -0.00018948987516315, -0.0039392777243355001, -0.043797295650572998, -2.6674547914087001e-05, 2.0481737692308999e-08, 4.3870667284435001e-07, -3.2277677238570002e-05, -0.0015033924542148, -0.040668253562648998, -7.8847309559367001e-10, 1.2790717852285001e-08, 4.8225372718507002e-07, 2.2922076337661001e-06, -1.6714766451061001e-11, -0.0021171472321354998, -23.895741934103999, -5.9059564324270004e-18, -1.2621808899101e-06, -0.038946842435739003, 1.1256211360459e-11, -8.2311340897998004, 1.9809712802088e-08, 1.0406965210174e-19, -1.0234747095929e-13, -1.0018179379511e-09, -8.0882908646984998e-11, 0.10693031879409, -0.33662250574170999, 8.9185845355420999e-25, 3.0629316876231997e-13, -4.2002467698208001e-06, -5.9056029685639003e-26, 3.7826947613457002e-06, -1.2768608934681e-15, 7.3087610595061e-29, 5.5414715350778001e-17, -9.4369707241209998e-07] gr = grp = grpp = grt = grtt = grpt = 0 for i, j, ni in zip(Ir, Jr, nr): gr += ni * Pr**i * (Tr-0.5)**j grp += ni*i * Pr**(i-1) * (Tr-0.5)**j grpp += ni*i*(i-1) * Pr**(i-2) * (Tr-0.5)**j grt += ni*j * Pr**i * (Tr-0.5)**(j-1) grtt += ni*j*(j-1) * Pr**i * (Tr-0.5)**(j-2) grpt += ni*i*j * Pr**(i-1) * (Tr-0.5)**(j-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 """ Jo = [0, 1, -5, -4, -3, -2, -1, 2, 3] no = [-0.96927686500217E+01, 0.10086655968018E+02, -0.56087911283020E-02, 0.71452738081455E-01, -0.40710498223928E+00, 0.14240819171444E+01, -0.43839511319450E+01, -0.28408632460772E+00, 0.21268463753307E-01] go = log(Pr) gop = Pr**-1 gopp = -Pr**-2 got = gott = gopt = 0 for j, ni in zip(Jo, no): go += ni * Tr**j got += ni*j * Tr**(j-1) gott += ni*j*(j-1) * Tr**(j-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 """ Li = [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 7] Lj = [0, 1, 2, 3, 7, 20, 0, 1, 2, 3, 7, 9, 11, 18, 44, 0, 2, 7, 36, 38, 40, 42, 44, 24, 44, 12, 32, 44, 32, 36, 42, 34, 44, 28] n = [0.10898952318288e4, 0.84951654495535e3, -0.10781748091826e3, 0.33153654801263e2, -0.74232016790248e1, 0.11765048724356e2, 0.18445749355790e1, -0.41792700549624e1, 0.62478196935812e1, -0.17344563108114e2, -0.20058176862096e3, 0.27196065473796e3, -0.45511318285818e3, 0.30919688604755e4, 0.25226640357872e6, -0.61707422868339e-2, -0.31078046629583, 0.11670873077107e2, 0.12812798404046e9, -0.98554909623276e9, 0.28224546973002e10, -0.35948971410703e10, 0.17227349913197e10, -0.13551334240775e5, 0.12848734664650e8, 0.13865724283226e1, 0.23598832556514e6, -0.13105236545054e8, 0.73999835474766e4, -0.55196697030060e6, 0.37154085996233e7, 0.19127729239660e5, -0.41535164835634e6, -0.62459855192507e2] Pr = P/1 nu = h/2000 T = 0 for i, j, ni in zip(Li, Lj, n): T += ni * Pr**i * (nu-2.1)**j 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 """ Li = [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 6, 7, 7, 9, 9] Lj = [0, 1, 2, 12, 18, 24, 28, 40, 0, 2, 6, 12, 18, 24, 28, 40, 2, 8, 18, 40, 1, 2, 12, 24, 2, 12, 18, 24, 28, 40, 18, 24, 40, 28, 2, 28, 1, 40] n = [0.14895041079516e4, 0.74307798314034e3, -0.97708318797837e2, 0.24742464705674e1, -0.63281320016026, 0.11385952129658e1, -0.47811863648625, 0.85208123431544e-2, 0.93747147377932, 0.33593118604916e1, 0.33809355601454e1, 0.16844539671904, 0.73875745236695, -0.47128737436186, 0.15020273139707, -0.21764114219750e-2, -0.21810755324761e-1, -0.10829784403677, -0.46333324635812e-1, 0.71280351959551e-4, 0.11032831789999e-3, 0.18955248387902e-3, 0.30891541160537e-2, 0.13555504554949e-2, 0.28640237477456e-6, -0.10779857357512e-4, -0.76462712454814e-4, 0.14052392818316e-4, -0.31083814331434e-4, -0.10302738212103e-5, 0.28217281635040e-6, 0.12704902271945e-5, 0.73803353468292e-7, -0.11030139238909e-7, -0.81456365207833e-13, -0.25180545682962e-10, -0.17565233969407e-17, 0.86934156344163e-14] Pr = P/1 nu = h/2000 T = 0 for i, j, ni in zip(Li, Lj, n): T += ni * (Pr-2)**i * (nu-2.6)**j 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 """ Li = [-7, -7, -6, -6, -5, -5, -2, -2, -1, -1, 0, 0, 1, 1, 2, 6, 6, 6, 6, 6, 6, 6, 6] Lj = [0, 4, 0, 2, 0, 2, 0, 1, 0, 2, 0, 1, 4, 8, 4, 0, 1, 4, 10, 12, 16, 20, 22] n = [-0.32368398555242e13, 0.73263350902181e13, 0.35825089945447e12, -0.58340131851590e12, -0.10783068217470e11, 0.20825544563171e11, 0.61074783564516e6, 0.85977722535580e6, -0.25745723604170e5, 0.31081088422714e5, 0.12082315865936e4, 0.48219755109255e3, 0.37966001272486e1, -0.10842984880077e2, -0.45364172676660e-1, 0.14559115658698e-12, 0.11261597407230e-11, -0.17804982240686e-10, 0.12324579690832e-6, -0.11606921130984e-5, 0.27846367088554e-4, -0.59270038474176e-3, 0.12918582991878e-2] Pr = P/1 nu = h/2000 T = 0 for i, j, ni in zip(Li, Lj, n): T += ni * (Pr+25)**i * (nu-1.8)**j 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 """ Li = [-1.5, -1.5, -1.5, -1.5, -1.5, -1.5, -1.25, -1.25, -1.25, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -0.75, -0.75, -0.5, -0.5, -0.5, -0.5, -0.25, -0.25, -0.25, -0.25, 0.25, 0.25, 0.25, 0.25, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.75, 0.75, 0.75, 0.75, 1.0, 1.0, 1.25, 1.25, 1.5, 1.5] Lj = [-24, -23, -19, -13, -11, -10, -19, -15, -6, -26, -21, -17, -16, -9, -8, -15, -14, -26, -13, -9, -7, -27, -25, -11, -6, 1, 4, 8, 11, 0, 1, 5, 6, 10, 14, 16, 0, 4, 9, 17, 7, 18, 3, 15, 5, 18] n = [-0.39235983861984e6, 0.51526573827270e6, 0.40482443161048e5, -0.32193790923902e3, 0.96961424218694e2, -0.22867846371773e2, -0.44942914124357e6, -0.50118336020166e4, 0.35684463560015, 0.44235335848190e5, -0.13673388811708e5, 0.42163260207864e6, 0.22516925837475e5, 0.47442144865646e3, -0.14931130797647e3, -0.19781126320452e6, -0.23554399470760e5, -0.19070616302076e5, 0.55375669883164e5, 0.38293691437363e4, -0.60391860580567e3, 0.19363102620331e4, 0.42660643698610e4, -0.59780638872718e4, -0.70401463926862e3, 0.33836784107553e3, 0.20862786635187e2, 0.33834172656196e-1, -0.43124428414893e-4, 0.16653791356412e3, -0.13986292055898e3, -0.78849547999872, 0.72132411753872e-1, -0.59754839398283e-2, -0.12141358953904e-4, 0.23227096733871e-6, -0.10538463566194e2, 0.20718925496502e1, -0.72193155260427e-1, 0.20749887081120e-6, -0.18340657911379e-1, 0.29036272348696e-6, 0.21037527893619, 0.25681239729999e-3, -0.12799002933781e-1, -0.82198102652018e-5] Pr = P/1 sigma = s/2 T = 0 for i, j, ni in zip(Li, Lj, n): T += ni * Pr**i * (sigma-2)**j 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 """ Li = [-6, -6, -5, -5, -4, -4, -4, -3, -3, -3, -3, -2, -2, -2, -2, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5] Lj = [0, 11, 0, 11, 0, 1, 11, 0, 1, 11, 12, 0, 1, 6, 10, 0, 1, 5, 8, 9, 0, 1, 2, 4, 5, 6, 9, 0, 1, 2, 3, 7, 8, 0, 1, 5, 0, 1, 3, 0, 1, 0, 1, 2] n = [0.31687665083497e6, 0.20864175881858e2, -0.39859399803599e6, -0.21816058518877e2, 0.22369785194242e6, -0.27841703445817e4, 0.99207436071480e1, -0.75197512299157e5, 0.29708605951158e4, -0.34406878548526e1, 0.38815564249115, 0.17511295085750e5, -0.14237112854449e4, 0.10943803364167e1, 0.89971619308495, -0.33759740098958e4, 0.47162885818355e3, -0.19188241993679e1, 0.41078580492196, -0.33465378172097, 0.13870034777505e4, -0.40663326195838e3, 0.41727347159610e2, 0.21932549434532e1, -0.10320050009077e1, 0.35882943516703, 0.52511453726066e-2, 0.12838916450705e2, -0.28642437219381e1, 0.56912683664855, -0.99962954584931e-1, -0.32632037778459e-2, 0.23320922576723e-3, -0.15334809857450, 0.29072288239902e-1, 0.37534702741167e-3, 0.17296691702411e-2, -0.38556050844504e-3, -0.35017712292608e-4, -0.14566393631492e-4, 0.56420857267269e-5, 0.41286150074605e-7, -0.20684671118824e-7, 0.16409393674725e-8] Pr = P/1 sigma = s/0.7853 T = 0 for i, j, ni in zip(Li, Lj, n): T += ni * Pr**i * (10-sigma)**j 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 """ Li = [-2, -2, -1, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 7, 7, 7, 7, 7] Lj = [0, 1, 0, 0, 1, 2, 3, 0, 1, 3, 4, 0, 1, 2, 0, 1, 5, 0, 1, 4, 0, 1, 2, 0, 1, 0, 1, 3, 4, 5] n = [0.90968501005365e3, 0.24045667088420e4, -0.59162326387130e3, 0.54145404128074e3, -0.27098308411192e3, 0.97976525097926e3, -0.46966772959435e3, 0.14399274604723e2, -0.19104204230429e2, 0.53299167111971e1, -0.21252975375934e2, -0.31147334413760, 0.60334840894623, -0.42764839702509e-1, 0.58185597255259e-2, -0.14597008284753e-1, 0.56631175631027e-2, -0.76155864584577e-4, 0.22440342919332e-3, -0.12561095013413e-4, 0.63323132660934e-6, -0.20541989675375e-5, 0.36405370390082e-7, -0.29759897789215e-8, 0.10136618529763e-7, 0.59925719692351e-11, -0.20677870105164e-10, -0.20874278181886e-10, 0.10162166825089e-9, -0.16429828281347e-9] Pr = P/1 sigma = s/2.9251 T = 0 for i, j, ni in zip(Li, Lj, n): T += ni * Pr**i * (2-sigma)**j 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 """ Li = [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 3, 3, 4, 5, 5, 6, 7] Lj = [1, 3, 6, 16, 20, 22, 0, 1, 2, 3, 5, 6, 10, 16, 20, 22, 3, 16, 20, 0, 2, 3, 6, 16, 16, 3, 16, 3, 1] n = [-0.182575361923032e-1, -0.125229548799536, 0.592290437320145, 0.604769706185122e1, 0.238624965444474e3, -0.298639090222922e3, 0.512250813040750e-1, -0.437266515606486, 0.413336902999504, -0.516468254574773e1, -0.557014838445711e1, 0.128555037824478e2, 0.114144108953290e2, -0.119504225652714e3, -0.284777985961560e4, 0.431757846408006e4, 0.112894040802650e1, 0.197409186206319e4, 0.151612444706087e4, 0.141324451421235e-1, 0.585501282219601, -0.297258075863012e1, 0.594567314847319e1, -0.623656565798905e4, 0.965986235133332e4, 0.681500934948134e1, -0.633207286824489e4, -0.558919224465760e1, 0.400645798472063e-1] nu = h/4200 sigma = s/12 suma = 0 for i, j, ni in zip(Li, Lj, n): suma += ni * (nu-0.5)**i * (sigma-1.2)**j 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 """ Li = [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 5, 5, 6, 6, 6, 7, 7, 8, 8, 8, 8, 12, 14] Lj = [0, 1, 2, 4, 8, 0, 1, 2, 3, 5, 12, 1, 6, 18, 0, 1, 7, 12, 1, 16, 1, 12, 1, 8, 18, 1, 16, 1, 3, 14, 18, 10, 16] n = [0.801496989929495e-1, -0.543862807146111, 0.337455597421283, 0.890555451157450e1, 0.313840736431485e3, 0.797367065977789, -0.121616973556240e1, 0.872803386937477e1, -0.169769781757602e2, -0.186552827328416e3, 0.951159274344237e5, -0.189168510120494e2, -0.433407037194840e4, 0.543212633012715e9, 0.144793408386013, 0.128024559637516e3, -0.672309534071268e5, 0.336972380095287e8, -0.586634196762720e3, -0.221403224769889e11, 0.171606668708389e4, -0.570817595806302e9, -0.312109693178482e4, -0.207841384633010e7, 0.305605946157786e13, 0.322157004314333e4, 0.326810259797295e12, -0.144104158934487e4, 0.410694867802691e3, 0.109077066873024e12, -0.247964654258893e14, 0.188801906865134e10, -0.123651009018773e15] nu = h/4100 sigma = s/7.9 suma = 0 for i, j, ni in zip(Li, Lj, n): suma += ni * (nu-0.6)**i * (sigma-1.01)**j 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 """ Li = [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 5, 5, 5, 5, 6, 6, 10, 12, 16] Lj = [0, 1, 2, 3, 4, 8, 0, 2, 5, 8, 14, 2, 3, 7, 10, 18, 0, 5, 8, 16, 18, 18, 1, 4, 6, 14, 8, 18, 7, 7, 10] n = [0.112225607199012, -0.339005953606712e1, -0.320503911730094e2, -0.197597305104900e3, -0.407693861553446e3, 0.132943775222331e5, 0.170846839774007e1, 0.373694198142245e2, 0.358144365815434e4, 0.423014446424664e6, -0.751071025760063e9, 0.523446127607898e2, -0.228351290812417e3, -0.960652417056937e6, -0.807059292526074e8, 0.162698017225669e13, 0.772465073604171, 0.463929973837746e5, -0.137317885134128e8, 0.170470392630512e13, -0.251104628187308e14, 0.317748830835520e14, 0.538685623675312e2, -0.553089094625169e5, -0.102861522421405e7, 0.204249418756234e13, 0.273918446626977e9, -0.263963146312685e16, -0.107890854108088e10, -0.296492620980124e11, -0.111754907323424e16] nu = h/3500 sigma = s/5.9 suma = 0 for i, j, ni in zip(Li, Lj, n): suma += ni * (nu-0.7)**i * (sigma-1.1)**j 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 """ Li = [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 8, 9, 9, 10, 10, 11] Lj = [0, 1, 2, 7, 10, 12, 23, 2, 6, 15, 17, 0, 2, 6, 7, 22, 26, 0, 2, 4, 16, 26, 0, 2, 4, 26, 1, 3, 26, 0, 2, 26, 2, 26, 2, 26, 0, 1, 26] n = [-0.15732845290239e2, 0.20944396974307e2, -0.76867707878716e1, 0.26185947787954e1, -0.28080781148620e1, 0.12053369696517e1, -0.84566812812502e-2, -0.12654315477714e1, -0.11524407806681e1, 0.88521043984318, -0.64207765181607, 0.38493460186671, -0.85214708824206, 0.48972281541877e1, -0.30502617256965e1, 0.39420536879154e-1, 0.12558408424308, -0.27999329698710, 0.13899799569460e1, -0.20189915023570e1, -0.82147637173963e-2, -0.47596035734923, 0.43984074473500e-1, -0.44476435428739, 0.90572070719733, .70522450087967, .10770512626332, -0.32913623258954, -0.50871062041158, -0.22175400873096e-1, 0.94260751665092e-1, 0.16436278447961, -0.13503372241348e-1, -0.14834345352472e-1, 0.57922953628084e-3, 0.32308904703711e-2, 0.80964802996215e-4, -0.16557679795037e-3, -0.44923899061815e-4] d = rho/rhoc Tr = Tc/T g = 1.0658070028513*log(d) gd = 1.0658070028513/d gdd = -1.0658070028513/d**2 gt = gtt = gdt = 0 for i, j, ni in zip(Li, Lj, n): g += ni * d**i * Tr**j gd += ni*i * d**(i-1) * Tr**j gdd += ni*i*(i-1) * d**(i-2) * Tr**j gt += ni*j * d**i * Tr**(j-1) gtt += ni*j*(j-1) * d**i * Tr**(j-2) gdt += ni*i*j * d**(i-1) * Tr**(j-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 """ Li = [0, 1, 2, -1, -2] n = [0.154793642129415e4, -0.187661219490113e3, 0.213144632222113e2, -0.191887498864292e4, 0.918419702359447e3] Pr = P/1 T = 0 for i, ni in zip(Li, n): T += ni * log(Pr)**i 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 """ Li = [0, 1, 2, -1, -2] n = [0.969461372400213e3, -0.332500170441278e3, 0.642859598466067e2, 0.773845935768222e3, -0.152313732937084e4] Pr = P/1 T = 0 for i, ni in zip(Li, n): T += ni * log(Pr)**i 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 """ Li = [0, 1, 2, -1, -2] n = [0.728052609145380e1, 0.973505869861952e2, 0.147370491183191e2, 0.329196213998375e3, 0.873371668682417e3] Pr = P/1 T = 0 for i, ni in zip(Li, n): T += ni * log(Pr)**i 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 """ Li = [-12, -12, -12, -12, -10, -10, -10, -8, -8, -6, -6, -6, -4, -4, -3, -2, -2, -1, -1, -1, -1, 0, 0, 1, 1, 1, 2, 2, 3, 4, 5, 8] Lj = [6, 8, 12, 18, 4, 7, 10, 5, 12, 3, 4, 22, 2, 3, 7, 3, 16, 0, 1, 2, 3, 0, 1, 0, 1, 2, 0, 2, 0, 2, 2, 2] n = [0.529944062966028e-2, -0.170099690234461, 0.111323814312927e2, -0.217898123145125e4, -0.506061827980875e-3, 0.556495239685324, -0.943672726094016e1, -0.297856807561527, 0.939353943717186e2, 0.192944939465981e-1, 0.421740664704763, -0.368914126282330e7, -0.737566847600639e-2, -0.354753242424366, -0.199768169338727e1, 0.115456297059049e1, 0.568366875815960e4, 0.808169540124668e-2, 0.172416341519307, 0.104270175292927e1, -0.297691372792847, 0.560394465163593, 0.275234661176914, -0.148347894866012, -0.651142513478515e-1, -0.292468715386302e1, 0.664876096952665e-1, 0.352335014263844e1, -0.146340792313332e-1, -0.224503486668184e1, 0.110533464706142e1, -0.408757344495612e-1] Pr = P/100 nu = h/2100 suma = 0 for i, j, ni in zip(Li, Lj, n): suma += ni * (Pr+0.128)**i * (nu-0.727)**j 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 """ Li = [-12, -12, -8, -8, -8, -8, -8, -8, -6, -6, -6, -6, -6, -6, -4, -4, -4, -3, -3, -2, -2, -1, -1, -1, -1, 0, 1, 1, 2, 2] Lj = [0, 1, 0, 1, 3, 6, 7, 8, 0, 1, 2, 5, 6, 10, 3, 6, 10, 0, 2, 1, 2, 0, 1, 4, 5, 0, 0, 1, 2, 6] n = [-0.225196934336318e-8, 0.140674363313486e-7, 0.233784085280560e-5, -0.331833715229001e-4, 0.107956778514318e-2, -0.271382067378863, 0.107202262490333e1, -0.853821329075382, -0.215214194340526e-4, 0.769656088222730e-3, -0.431136580433864e-2, 0.453342167309331, -0.507749535873652, -0.100475154528389e3, -0.219201924648793, -0.321087965668917e1, 0.607567815637771e3, 0.557686450685932e-3, 0.187499040029550, 0.905368030448107e-2, 0.285417173048685, 0.329924030996098e-1, 0.239897419685483, 0.482754995951394e1, -0.118035753702231e2, 0.169490044091791, -0.179967222507787e-1, 0.371810116332674e-1, -0.536288335065096e-1, 0.160697101092520e1] Pr = P/100 nu = h/2800 suma = 0 for i, j, ni in zip(Li, Lj, n): suma += ni * (Pr+0.0661)**i * (nu-0.72)**j 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) else: 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 """ Li = [-12, -12, -12, -12, -12, -12, -12, -12, -10, -10, -10, -8, -8, -8, -8, -5, -3, -2, -2, -2, -1, -1, 0, 0, 1, 3, 3, 4, 4, 10, 12] Lj = [0, 1, 2, 6, 14, 16, 20, 22, 1, 5, 12, 0, 2, 4, 10, 2, 0, 1, 3, 4, 0, 2, 0, 1, 1, 0, 1, 0, 3, 4, 5] n = [-0.133645667811215e-6, 0.455912656802978e-5, -0.146294640700979e-4, 0.639341312970080e-2, 0.372783927268847e3, -0.718654377460447e4, 0.573494752103400e6, -0.267569329111439e7, -0.334066283302614e-4, -0.245479214069597e-1, 0.478087847764996e2, 0.764664131818904e-5, 0.128350627676972e-2, 0.171219081377331e-1, -0.851007304583213e1, -0.136513461629781e-1, -0.384460997596657e-5, 0.337423807911655e-2, -0.551624873066791, 0.729202277107470, -0.992522757376041e-2, -.119308831407288, .793929190615421, .454270731799386, .20999859125991, -0.642109823904738e-2, -0.235155868604540e-1, 0.252233108341612e-2, -0.764885133368119e-2, 0.136176427574291e-1, -0.133027883575669e-1] Pr = P/100. nu = h/2300. suma = 0 for i, j, n in zip(Li, Lj, n): suma += n*(Pr+0.240)**i*(nu-0.615)**j 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 """ Li = [-12, -12, -10, -10, -10, -10, -10, -8, -8, -8, -8, -8, -6, -6, -6, -4, -4, -3, -2, -2, -1, -1, -1, -1, -1, -1, 0, 0, 1, 3, 5, 6, 8] Lj = [0, 1, 0, 1, 5, 10, 12, 0, 1, 2, 4, 10, 0, 1, 2, 0, 1, 5, 0, 4, 2, 4, 6, 10, 14, 16, 0, 2, 1, 1, 1, 1, 1] n = [0.323254573644920e-4, -0.127575556587181e-3, -0.475851877356068e-3, 0.156183014181602e-2, 0.105724860113781, -0.858514221132534e2, 0.724140095480911e3, 0.296475810273257e-2, -0.592721983365988e-2, -0.126305422818666e-1, -0.115716196364853, 0.849000969739595e2, -0.108602260086615e-1, 0.154304475328851e-1, 0.750455441524466e-1, 0.252520973612982e-1, -0.602507901232996e-1, -0.307622221350501e1, -0.574011959864879e-1, 0.503471360939849e1, -0.925081888584834, 0.391733882917546e1, -0.773146007130190e2, 0.949308762098587e4, -0.141043719679409e7, 0.849166230819026e7, 0.861095729446704, 0.323346442811720, 0.873281936020439, -0.436653048526683, 0.286596714529479, -0.131778331276228, 0.676682064330275e-2] Pr = P/100. nu = h/2800. suma = 0 for i, j, n in zip(Li, Lj, n): suma += n*(Pr+0.298)**i*(nu-0.72)**j 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 """ Li = [-12, -12, -12, -10, -10, -10, -10, -8, -8, -8, -8, -6, -5, -4, -3, -3, -2, -2, -1, -1, 0, 0, 0, 1, 2, 4, 5, 6] Lj = [10, 12, 14, 4, 8, 10, 20, 5, 6, 14, 16, 28, 1, 5, 2, 4, 3, 8, 1, 2, 0, 1, 3, 0, 0, 2, 2, 0] n = [0.795544074093975e2, -0.238261242984590e4, 0.176813100617787e5, -0.110524727080379e-2, -0.153213833655326e2, 0.297544599376982e3, -0.350315206871242e8, 0.277513761062119, -0.523964271036888, -0.148011182995403e6, 0.160014899374266e7, 0.170802322663427e13, 0.246866996006494e-3, 0.165326084797980e1, -0.118008384666987, 0.253798642355900e1, 0.965127704669424, -0.282172420532826e2, 0.203224612353823, 0.110648186063513e1, 0.526127948451280, 0.277000018736321, 0.108153340501132e1, -0.744127885357893e-1, 0.164094443541384e-1, -0.680468275301065e-1, 0.257988576101640e-1, -0.145749861944416e-3] Pr = P/100 sigma = s/4.4 suma = 0 for i, j, ni in zip(Li, Lj, n): suma += ni * (Pr+0.187)**i * (sigma-0.755)**j 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 """ Li = [-12, -12, -12, -12, -12, -12, -10, -10, -10, -10, -8, -5, -5, -5, -4, -4, -4, -4, -3, -2, -2, -2, -2, -2, -2, 0, 0, 0, 1, 1, 2] Lj = [0, 1, 2, 3, 5, 6, 0, 1, 2, 4, 0, 1, 2, 3, 0, 1, 2, 3, 1, 0, 1, 2, 3, 4, 12, 0, 1, 2, 0, 2, 2] n = [0.591599780322238e-4, -0.185465997137856e-2, 0.104190510480013e-1, 0.598647302038590e-2, -0.771391189901699, 0.172549765557036e1, -0.467076079846526e-3, 0.134533823384439e-1, -0.808094336805495e-1, 0.508139374365767, 0.128584643361683e-2, -0.163899353915435e1, 0.586938199318063e1, -0.292466667918613e1, -0.614076301499537e-2, 0.576199014049172e1, -0.121613320606788e2, 0.167637540957944e1, -0.744135838773463e1, 0.378168091437659e-1, 0.401432203027688e1, 0.160279837479185e2, 0.317848779347728e1, -0.358362310304853e1, -0.115995260446827e7, 0.199256573577909, -0.122270624794624, -0.191449143716586e2, -0.150448002905284e-1, 0.146407900162154e2, -0.327477787188230e1] Pr = P/100 sigma = s/5.3 suma = 0 for i, j, ni in zip(Li, Lj, n): suma += ni * (Pr+0.298)**i * (sigma-0.816)**j 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) else: 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 """ Li = [-12, -12, -10, -10, -10, -10, -8, -8, -8, -8, -6, -6, -6, -5, -5, -5, -4, -4, -4, -2, -2, -1, -1, 0, 0, 0, 1, 2, 2, 3, 8, 8, 10] Lj = [28, 32, 4, 10, 12, 14, 5, 7, 8, 28, 2, 6, 32, 0, 14, 32, 6, 10, 36, 1, 4, 1, 6, 0, 1, 4, 0, 0, 3, 2, 0, 1, 2] n = [0.150042008263875e10, -0.159397258480424e12, 0.502181140217975e-3, -0.672057767855466e2, 0.145058545404456e4, -0.823889534888890e4, -0.154852214233853, 0.112305046746695e2, -0.297000213482822e2, 0.438565132635495e11, 0.137837838635464e-2, -0.297478527157462e1, 0.971777947349413e13, -0.571527767052398e-4, 0.288307949778420e5, -0.744428289262703e14, 0.128017324848921e2, -0.368275545889071e3, 0.664768904779177e16, 0.449359251958880e-1, -0.422897836099655e1, -0.240614376434179, -0.474341365254924e1, 0.724093999126110, 0.923874349695897, 0.399043655281015e1, 0.384066651868009e-1, -0.359344365571848e-2, -0.735196448821653, 0.188367048396131, 0.141064266818704e-3, -0.257418501496337e-2, 0.123220024851555e-2] Pr = P/100 sigma = s/4.4 suma = 0 for i, j, ni in zip(Li, Lj, n): suma += ni * (Pr+0.240)**i * (sigma-0.703)**j 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 """ Li = [-12, -12, -12, -12, -8, -8, -8, -6, -6, -6, -5, -5, -5, -5, -5, -4, -3, -3, -2, 0, 2, 3, 4, 5, 6, 8, 12, 14] Lj = [1, 3, 4, 7, 0, 1, 3, 0, 2, 4, 0, 1, 2, 4, 6, 12, 1, 6, 2, 0, 1, 1, 0, 24, 0, 3, 1, 2] n = [0.527111701601660, -0.401317830052742e2, 0.153020073134484e3, -0.224799398218827e4, -0.193993484669048, -0.140467557893768e1, 0.426799878114024e2, 0.752810643416743, 0.226657238616417e2, -0.622873556909932e3, -0.660823667935396, 0.841267087271658, -0.253717501764397e2, 0.485708963532948e3, 0.880531517490555e3, 0.265015592794626e7, -0.359287150025783, -0.656991567673753e3, 0.241768149185367e1, 0.856873461222588, 0.655143675313458, -0.213535213206406, 0.562974957606348e-2, -0.316955725450471e15, -0.699997000152457e-3, 0.119845803210767e-1, 0.193848122022095e-4, -0.215095749182309e-4] Pr = P/100 sigma = s/5.3 suma = 0 for i, j, ni in zip(Li, Lj, n): suma += ni * (Pr+0.760)**i * (sigma-0.818)**j 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] """ sc = 4.41202148223476 if s <= sc: T = _Backward3a_T_Ps(P, s) else: T = _Backward3b_T_Ps(P, s) return T
[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 """ Li = [0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 6, 7, 8, 10, 10, 14, 18, 20, 22, 22, 24, 28, 28, 32, 32] Lj = [0, 1, 5, 0, 3, 4, 8, 14, 6, 16, 0, 2, 3, 0, 1, 4, 5, 28, 28, 24, 1, 32, 36, 22, 28, 36, 16, 28, 36, 16, 36, 10, 28] n = [0.770889828326934e1, -0.260835009128688e2, 0.267416218930389e3, 0.172221089496844e2, -0.293542332145970e3, 0.614135601882478e3, -0.610562757725674e5, -0.651272251118219e8, 0.735919313521937e5, -0.116646505914191e11, 0.355267086434461e2, -0.596144543825955e3, -0.475842430145708e3, 0.696781965359503e2, 0.335674250377312e3, 0.250526809130882e5, 0.146997380630766e6, 0.538069315091534e20, 0.143619827291346e22, 0.364985866165994e20, -0.254741561156775e4, 0.240120197096563e28, -0.393847464679496e30, 0.147073407024852e25, -0.426391250432059e32, 0.194509340621077e39, 0.666212132114896e24, 0.706777016552858e34, 0.175563621975576e42, 0.108408607429124e29, 0.730872705175151e44, 0.159145847398870e25, 0.377121605943324e41] nu = h/2300 sigma = s/4.4 suma = 0 for i, j, ni in zip(Li, Lj, n): suma += ni * (nu-1.01)**i * (sigma-0.75)**j 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 """ Li = [-12, -12, -12, -12, -12, -10, -10, -10, -10, -8, -8, -6, -6, -6, -6, -5, -4, -4, -4, -3, -3, -3, -3, -2, -2, -1, 0, 2, 2, 5, 6, 8, 10, 14, 14] Lj = [2, 10, 12, 14, 20, 2, 10, 14, 18, 2, 8, 2, 6, 7, 8, 10, 4, 5, 8, 1, 3, 5, 6, 0, 1, 0, 3, 0, 1, 0, 1, 1, 1, 3, 7] n = [0.125244360717979e-12, -0.126599322553713e-1, 0.506878030140626e1, 0.317847171154202e2, -0.391041161399932e6, -0.975733406392044e-10, -0.186312419488279e2, 0.510973543414101e3, 0.373847005822362e6, 0.299804024666572e-7, 0.200544393820342e2, -0.498030487662829e-5, -0.102301806360030e2, 0.552819126990325e2, -0.206211367510878e3, -0.794012232324823e4, 0.782248472028153e1, -0.586544326902468e2, 0.355073647696481e4, -0.115303107290162e-3, -0.175092403171802e1, 0.257981687748160e3, -0.727048374179467e3, 0.121644822609198e-3, 0.393137871762692e-1, 0.704181005909296e-2, -0.829108200698110e2, -0.265178818131250, 0.137531682453991e2, -0.522394090753046e2, 0.240556298941048e4, -0.227361631268929e5, 0.890746343932567e5, -0.239234565822486e8, 0.568795808129714e10] nu = h/2800 sigma = s/5.3 suma = 0 for i, j, ni in zip(Li, Lj, n): suma += ni * (nu-0.681)**i * (sigma-0.792)**j 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] """ sc = 4.41202148223476 if s <= sc: return _Backward3a_P_hs(h, s) else: 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, 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-.436677034051655e-41, .926990036530639e-29, .587793105620748e21, .280375725094731e-17, -0.192359972440634e23, .742705723302738e27, -0.517429682450605e2, 0.820612048645469e7, -0.188214882341448e-8, .184587261114837e-1, -0.135830407782663e-5, -.723681885626348e17, -.223449194054124e27, -.111526741826431e-34, .276032601145151e-28, 0.134856491567853e15, 0.652440293345860e-9, 0.510655119774360e17, -.468138358908732e32, -.760667491183279e16, -.417247986986821e-18, 0.312545677756104e14, -.100375333864186e15, .247761392329058e27], "w": [-.586219133817016e-7, -.894460355005526e11, .531168037519774e-30, 0.109892402329239, -0.575368389425212e-1, 0.228276853990249e5, -.158548609655002e19, .329865748576503e-27, -.634987981190669e-24, 0.615762068640611e-8, -.961109240985747e8, -.406274286652625e-44, -0.471103725498077e-12, 0.725937724828145, .187768525763682e-38, -.103308436323771e4, -0.662552816342168e-1, 0.579514041765710e3, .237416732616644e-26, .271700235739893e-14, -0.9078862134836e2, -0.171242509570207e-36, 0.156792067854621e3, 0.923261357901470, -0.597865988422577e1, 0.321988767636389e7, -.399441390042203e-29, .493429086046981e-7, .812036983370565e-19, -.207610284654137e-11, -.340821291419719e-6, .542000573372233e-17, -.856711586510214e-12, 0.266170454405981e-13, 0.858133791857099e-5], "x": [.377373741298151e19, -.507100883722913e13, -0.10336322559886e16, .184790814320773e-5, -.924729378390945e-3, -0.425999562292738e24, -.462307771873973e-12, .107319065855767e22, 0.648662492280682e11, 0.244200600688281e1, -0.851535733484258e10, 0.169894481433592e22, 0.215780222509020e-26, -0.320850551367334, -0.382642448458610e17, -.275386077674421e-28, -.563199253391666e6, -.326068646279314e21, 0.397949001553184e14, 0.100824008584757e-6, 0.162234569738433e5, -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) else: 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 """ Li = [0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 5, 5, 5, 5, 6, 6, 6, 8, 10, 10, 12, 14, 14, 16, 16, 18, 18, 18, 20, 28] Lj = [0, 3, 12, 0, 1, 2, 5, 0, 5, 8, 0, 2, 3, 4, 0, 1, 1, 2, 4, 16, 6, 8, 22, 1, 20, 36, 24, 1, 28, 12, 32, 14, 22, 36, 24, 36] n = [0.179882673606601, -0.267507455199603, 0.116276722612600e1, 0.147545428713616, -0.512871635973248, 0.421333567697984, 0.563749522189870, 0.429274443819153, -0.335704552142140e1, 0.108890916499278e2, -0.248483390456012, 0.304153221906390, -0.494819763939905, 0.107551674933261e1, 0.733888415457688e-1, 0.140170545411085e-1, -0.106110975998808, 0.168324361811875e-1, 0.125028363714877e1, 0.101316840309509e4, -0.151791558000712e1, 0.524277865990866e2, 0.230495545563912e5, 0.249459806365456e-1, 0.210796467412137e7, 0.366836848613065e9, -0.144814105365163e9, -0.179276373003590e-2, 0.489955602100459e10, 0.471262212070518e3, -0.829294390198652e11, -0.171545662263191e4, 0.355777682973575e7, 0.586062760258436e12, -0.129887635078195e8, 0.317247449371057e11] nu = h/2800 sigma = s/9.2 suma = 0 for i, j, ni in zip(Li, Lj, n): suma += ni * (nu-0.119)**i * (sigma-1.07)**j 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) Ir = [1, 1, 1, 2, 2, 3] Jr = [1, 2, 3, 3, 9, 7] nr = [0.15736404855259e-2, 0.90153761673944e-3, -0.50270077677648e-2, 0.22440037409485e-5, -0.41163275453471e-5, 0.37919454822955e-7] gr = grp = grpp = grt = grtt = grpt = 0 for i, j, ni in zip(Ir, Jr, nr): gr += ni * Pr**i * Tr**j grp += ni*i * Pr**(i-1) * Tr**j grpp += ni*i*(i-1) * Pr**(i-2) * Tr**j grt += ni*j * Pr**i * Tr**(j-1) grtt += ni*j*(j-1) * Pr**i * Tr**(j-2) grpt += ni*i*j * Pr**(i-1) * Tr**(j-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 """ Jo = [0, 1, -3, -2, -1, 2] no = [-0.13179983674201e2, 0.68540841634434e1, -0.24805148933466e-1, 0.36901534980333, -0.31161318213925e1, -0.32961626538917] go = log(Pr) gop = Pr**-1 gopp = -Pr**-2 got = gott = gopt = 0 for j, ni in zip(Jo, no): go += ni * Tr**j got += ni*j * Tr**(j-1) gott += ni*j*(j-1) * Tr**(j-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: 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: 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) prop0 = {} prop0["v"] = Pr*gop*R*T/P/1000 prop0["h"] = Tr*got*R*T prop0["s"] = R*(Tr*got-go) prop0["cp"] = -R*Tr**2*gott prop0["cv"] = R*(-Tr**2*gott-1) prop0["w"] = (R*T*1000/(1+1/Tr**2/gott))**0.5 prop0["alfav"] = 1/T prop0["xkappa"] = 1/P return prop0
[docs]class IAPWS97(object): """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 """ kwargs = {"T": 0.0, "P": 0.0, "x": None, "h": None, "s": None, "v": 0.0, "l": 0.5893} status = 0 msg = "Unknown variables" 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" # 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" 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" 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: 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 == 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: 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 == 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.M = 18.015257 # kg/kmol self.Pc = Pc self.Tc = Tc self.rhoc = rhoc self.Tt = Tt self.Tb = Tb self.f_accent = f_acent self.dipole = Dipole self.x = propiedades["x"] self.region = propiedades["region"] self.name = "water" self.synonim = "R-718" self.CAS = "7732-18-5" 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 if self.region in [2, 5]: 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 else: self.v0 = None self.h0 = None self.u0 = None self.s0 = None self.a0 = None self.g0 = 0 self.cp0 = None self.cv0 = None self.cp0_cv = None self.w0 = None self.gamma0 = None 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", "s", fase) 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)