def speed_of_sound(self, p=None, T=None):
"""NOT IMPLEMENTED"""
if p is None:
p = self.p
else:
p = Pressure(p)
if T is None:
T = self.T
else:
T = Temperature(T)
if self._is_in_region() == 1:
pi = self.p / Pressure(16.53).unit('MPa')
tau = Temperature(1386) / self.T
inside_frac = (((self._basic_equation1('gamma_pi') -
tau * self._basic_equation1('gamma_tau_pi'))**2) /
((tau**2) * self._basic_equation1('gamma_tau_tau')))
return sqrt(
((self._basic_equation1('gamma_pi')**2) /
(inside_frac - self._basic_equation1('gamma_pi_pi'))) *
self.R * self.T * 1000)
elif self._is_in_region() == 2:
pass
elif self._is_in_region() == 3:
pass
elif self._is_in_region() == 4:
pass
elif self._is_in_region() == 5:
pass
return -1
def heat_capacity_constant_v(self, p=None, T=None):
"""NOT IMPLEMENTED"""
if p is None:
p = self.p
else:
p = Pressure(p)
if T is None:
T = self.T
else:
T = Temperature(T)
if self._is_in_region() == 1:
pi = self.p / Pressure(16.53).unit('MPa')
tau = Temperature(1386) / self.T
return (-(tau**2) * self._basic_equation1('gamma_tau_tau') +
((self._basic_equation1('gamma_pi') -
tau * self._basic_equation1('gamma_pi_tau'))**2) /
self._basic_equation1('gamma_pi_pi')) * self.R
elif self._is_in_region() == 2:
pass
elif self._is_in_region() == 3:
pass
elif self._is_in_region() == 4:
pass
elif self._is_in_region() == 5:
pass
return -1
def entropy(self, p=None, T=None):
"""NOT IMPLEMENTED"""
if p is None:
p = self.p
else:
p = Pressure(p)
if T is None:
T = self.T
else:
T = Temperature(T)
if self._is_in_region() == 1:
pi = self.p / Pressure(16.53).unit('MPa')
tau = Temperature(1386) / self.T
return (tau * self._basic_equation1('gamma_tau') -
self._basic_equation1('gamma')) * self.R
elif self._is_in_region() == 2:
pi = self.p / Pressure(1).unit('MPa')
tau = 540 / self.T
return ((tau * (self._basic_equation2('gamma_0_tau') +
self._basic_equation2('gamma_r_tau')) -
(self._basic_equation2('gamma_0') +
self._basic_equation2('gamma_r'))) * self.R)
elif self._is_in_region() == 3:
pass
elif self._is_in_region() == 4:
pass
elif self._is_in_region() == 5:
pass
return -1
def test_units():
"""Test units."""
Tkel = Temperature(273.15).unit('K')
Tcel = Temperature(0).unit('C')
assert Tkel == Tcel
pressuremmhg = Pressure(760).unit('torr')
pressureatm = Pressure(1).unit('atm')
assert pressuremmhg == pressureatm
def temperature_saturation(self, p=None):
"""Yields Tsat given a pressure p."""
# module deals with pressure in MPa
if p is None:
p = self.p.MPa
else:
p = Pressure(p).MPa
if p < Pressure(611.213).unit('Pa').MPa or p > self.pc:
raise ValueError('Pressure out of range.')
# table 34
ni = array([
1167.0521452767, -724213.16703206, -17.073846940092,
12020.82470247, -3232555.0322333, 14.91510861353, -4823.2657361591,
405113.40542057, -0.23855557567849, 650.17534844798
],
dtype='d')
beta = p**0.25
E = 1 * beta**2 + ni[2] * beta + ni[5]
F = ni[0] * beta**2 + ni[3] * beta + ni[6]
G = ni[1] * beta**2 + ni[4] * beta + ni[7]
D = 2 * G / (-F - (F**2 - 4 * E * G)**0.5)
return Temperature((ni[9] + D - ((ni[9] + D)**2 - 4 *
(ni[8] + ni[9] * D))**0.5) * 0.5)
def heat_capacity(self, p=None, T=None):
"""Returns the isobaric heat capacity given p and T in kJ/(kg K)."""
if p is None:
p = self.p
else:
p = Pressure(p)
if T is None:
T = self.T
else:
T = Temperature(T)
if self._is_in_region() == 1:
tau = 1386 / T
return (-1 * tau * tau * self.R *
self._basic_equation1('gamma_tau_tau'))
elif self._is_in_region() == 2:
pass
elif self._is_in_region() == 3:
delta = rho / self.rhoc
tau = self.Tc / self.T
return (
-tau**2 / self._basic_equation3('PHI_tau_tau') +
(delta * self._basic_equation3('PHI_delta') -
delta * tau * self._basic_equation3('PHI_tau_delta'))**2 /
(2 * delta * self._basic_equation3('PHI_delta') +
delta**2 * self._basic_equation3('PHI_delta_delta'))) * self.R
elif self._is_in_region() == 4:
pass
elif self._is_in_region() == 5:
pass
return -1
def specific_volume(self, p=None, T=None):
"""Returns the specific volume in m³/kg"""
if p is None:
p = self.p
else:
p = Pressure(p)
if T is None:
T = self.T
else:
T = Temperature(T)
if self._is_in_region() == 1:
pi = self.p / Pressure(16.53).unit('MPa')
return (self._basic_equation1('gamma_pi') * self.R * self.T * pi /
self.p * 1e3) # because of kJ in R
elif self._is_in_region() == 2:
pi = self.p / Pressure(1).unit('MPa')
return (pi * (self._basic_equation2('gamma_0_pi') +
self._basic_equation2('gamma_r_pi')) * self.R *
self.T / self.p * 1e3)
elif self._is_in_region() == 3:
return None
elif self._is_in_region() == 4:
pass
elif self._is_in_region() == 5:
pass
return -1
def __init__(self, p, T, massic_basis=False):
u"""Initializes a Water object."""
self.p = Pressure(p)
self.T = Temperature(T)
# check if water is specified by IAPWS-IF97 for these values
if self.T < Temperature(273.15) or self.T > Temperature(2273.15):
raise ValueError('Temperature ' + str(T) +
' out of range (273.15 - 2273.15K)')
if self.p > Pressure(100).unit('MPa') or self.p < 0:
raise ValueError('Pressure ' + str(p) +
' out of range (0 - 100 MPa)')
if self.T > 1073.15 and self.p > Pressure(50).unit('MPa'):
raise ValueError('p or T value out of range')
# adjust R to mass or molar basis
if massic_basis is True:
self.R = ideal_gas_constant_massic_basis[0] # kJ/(kg K);
elif massic_basis is False:
self.R = ideal_gas_constant[0]
def _is_in_region(self):
"""Finds a region for the (T, p) point (see IAPWS-IF97 for details).
The usefulness of these regions are to divide the physical properties
of water into different sets of coefficients and equations."""
# for the 2 - 3 boundary line
ni = array([
348.05185628969, -1.1671859879975, 0.0010192970039326,
572.54459862746, 13.91883977887
],
dtype='d')
theta = self.T
pressure23 = Pressure(ni[0] + ni[1] * theta +
ni[2] * theta**2).unit('MPa')
# exceptional cases
if self.T == self.Tt and self.p == self.pt:
return 1
# regular cases
if self.T >= Temperature(273.15) and self.T <= Temperature(623.15):
if self.T < self.temperature_saturation(self.p):
return 1
else:
return 2
elif self.T > Temperature(623.15) and self.T <= Temperature(1073.15):
if self.p > pressure23:
return 3
else:
return 2
elif self.T >= Temperature(1073.15) and self.T <= Temperature(2273.15):
return 5
else:
raise Exception('Cannot assign region to the parameters p = ' +
str(self.p) + 'T = ' + str(self.T) + 'given.')
def _basic_equation1(self, value='gamma'):
"""Returns basic equation 1 and its derivatives, ex: 'gamma',
'gamma_tau', 'gamma_tau_pi', etc."""
# region1
Ii = array([
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
],
dtype='int')
Ji = array([
-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
],
dtype='int')
ni = array([
0.14632971213167, -0.84548187169114, -3.756360367204,
3.3855169168385, -0.95791963387872, 0.15772038513228,
-0.016616417199501, 0.00081214629983568, 0.00028319080123804,
-0.00060706301565874, -0.018990068218419, -0.032529748770505,
-0.021841717175414, -5.283835796993e-05, -0.00047184321073267,
-0.00030001780793026, 4.7661393906987e-05, -4.4141845330846e-06,
-7.2694996297594e-16, -3.1679644845054e-05, -2.8270797985312e-06,
-8.5205128120103e-10, -2.2425281908e-06, -6.5171222895601e-07,
-1.4341729937924e-13, -4.0516996860117e-07, -1.2734301741641e-09,
-1.7424871230634e-10, -6.8762131295531e-19, 1.4478307828521e-20,
2.6335781662795e-23, -1.1947622640071e-23, 1.8228094581404e-24,
-9.3537087292458e-26
],
dtype='d')
pi = self.p / Pressure(16.53).unit('MPa')
tau = Temperature(1386) / self.T
if value == 'gamma':
return sum(ni * ((7.1 - pi)**Ii) * ((tau - 1.222)**Ji))
elif value == 'gamma_tau':
return sum(ni * ((7.1 - pi)**Ii) * Ji * ((tau - 1.222)**(Ji - 1)))
elif value == 'gamma_tau_tau':
return sum(ni * ((7.1 - pi)**Ii) * Ji * (Ji - 1) *
((tau - 1.222)**(Ji - 2)))
elif value == 'gamma_pi':
return -1 * sum(ni * Ii * ((7.1 - pi)**(Ii - 1)) *
(tau - 1.222)**Ji)
elif value == 'gamma_pi_pi':
return sum(ni * Ii * (Ii - 1) * (7.1 - pi)**(Ii - 2) *
(tau - 1.222)**Ji)
elif value == 'gamma_pi_tau' or value == 'gamma_tau_pi':
return -1 * sum(ni * Ii * (7.1 - pi)**(Ii - 1) * Ji *
(tau - 1.222)**(Ji - 1))
else:
raise Exception('Function not assigned in _basic_equation1()')
def enthalpy(self, p=None, T=None):
"""Returns the enthalpy given p and T in kJ/kg."""
if p is None:
p = self.p
else:
p = Pressure(p)
if T is None:
T = self.T
else:
T = Temperature(T)
if self._is_in_region() == 1:
return Enthalpy(self._basic_equation1('gamma_tau') * 1386 * self.R)
elif self._is_in_region() == 2:
return Enthalpy(540 * self.R *
(self._basic_equation2('gamma_0_tau') +
self._basic_equation2('gamma_r_tau')))
elif self._is_in_region() == 3:
# for region 3 rho needs to be solved numerically
reg3_solved = self._basic_equation3('PHI_delta')
delta = reg3_solved[1] / self.rhoc
tau = self.Tc / self.T
return Enthalpy((tau * self._basic_equation3('PHI_tau')[0] +
delta * reg3_solved[0]) * self.R * self.T)
elif self._is_in_region() == 4:
return None
elif self._is_in_region() == 5:
pi = self.p / Pressure(1).unit('MPa')
tau = Temperature(1000) / self.T
return (tau * (self._basic_equation5('gamma_0_tau') +
self._basic_equation5('gamma_r_tau')) * self.R *
self.T)
def _basic_equation5(self, value='gamma'):
"""Returns equation 1 and its derivatives, ex: 'gamma',
'gamma_tau', 'gamma_tau_pi', etc."""
J0 = array([0, 1, -3, -2, -1, 2], dtype='d')
n0 = array([
-13.179983674201, 6.8540841634434, -0.024805148933466,
0.36901534980333, -3.1161318213925, -0.32961626538917
],
dtype='d')
Ii = array([1, 1, 1, 2, 2, 3], dtype='d')
Ji = array([1, 2, 3, 3, 9, 7], dtype='d')
ni = array([
0.0015736404855259, 0.00090153761673944, -0.0050270077677648,
2.2440037409485e-06, -4.1163275453471e-06, 3.7919454822955e-08
],
dtype='d')
pi = self.p / Pressure(1).unit('MPa')
tau = Temperature(1000) / self.T
if value == 'gamma':
return (self._basic_equation5('gamma_0') +
self._basic_equation5('gamma_r'))
elif value == 'gamma_0':
return log(pi) + sum(n0 * (tau**J0))
elif value == 'gamma_r':
return sum(ni * (pi**Ii) * (tau**Ji))
elif value == 'gamma_0_pi':
return 1 / pi
elif value == 'gamma_0_pi_pi':
return -1 / (pi**2)
elif value == 'gamma_0_tau':
return sum(n0 * J0 * (tau**(J0 - 1)))
elif value == 'gamma_0_tau_tau':
sum(n0 * J0 * (J0 - 1) * (tau**(J0 - 2)))
elif value == 'gamma_0_tau_pi' or value == 'gamma_0_pi_tau':
return 0 + 0
elif value == 'gamma_r_pi':
return sum(ni * Ii * (pi**(Ii - 1)) * (tau**Ji))
elif value == 'gamma_r_tau':
return sum(ni * (pi**Ii) * Ji * (tau**(Ji - 1)))
elif value == 'gamma_r_pi_pi':
return sum(ni * Ii * (Ii - 1) * (pi**(Ii - 2)) * (tau**Ji))
elif value == 'gamma_r_tau_tau':
return sum(ni * (pi**Ii) * Ji * (Ji - 1) * (tau**(Ji - 2)))
elif value == 'gamma_r_tau_pi' or 'gamma_r_pi_tau':
return sum(ni * Ii * (pi**(Ii - 1)) * Ji * (tau**(Ji - 1)))
def gibbs_energy(self, p=None, T=None):
"""Returns the Gibbs Energy given p and T in kJ/kg."""
if p is None:
p = self.p
else:
p = Pressure(p)
if T is None:
T = self.T
else:
T = Temperature(T)
if self._is_in_region() == 1:
return self._basic_equation1('gamma') * self.R * T
elif self._is_in_region() == 2:
return self._basic_equation2('gamma') * self.R * T
elif self._is_in_region() == 3:
pass
elif self._is_in_region() == 4:
pass
elif self._is_in_region() == 5:
pass
def pressure_saturation(self, T=None):
"""Yields Psat given a temperature T"""
if T is None:
T = self.T
else:
T = Temperature(T)
if T < 273.15 or T > self.Tc:
raise ValueError('Temperature out of range.')
# table 34
ni = array([
1167.0521452767, -724213.16703206, -17.073846940092,
12020.82470247, -3232555.0322333, 14.91510861353, -4823.2657361591,
405113.40542057, -0.23855557567849, 650.17534844798
],
dtype='d')
v = T + ni[8] / (T - ni[9])
A = 1 * v**2 + ni[0] * v + ni[1]
B = ni[2] * v**2 + ni[3] * v + ni[4]
C = ni[5] * v**2 + ni[6] * v + ni[7]
return Pressure(
(2 * C / (-B + (B**2 - 4 * A * C)**0.5))**4).unit('MPa')
def test_iapws():
"""
Tests are given inside the IAPWS document. See references for more details.
"""
#test Tsat given P
assert round(Water(1e5, 373.15).temperature_saturation(0.1e6),
6) == 372.755919
assert round(Water(1e5, 373.15).temperature_saturation(1e6),
6) == 453.035632
assert round(Water(1e5, 373.15).temperature_saturation(10e6),
6) == 584.149488
#test Psat given T
assert round(Water(1e5, 373.15).pressure_saturation(300).MPa,
11) == 0.00353658941
assert round(Water(1e5, 373.15).pressure_saturation(500).MPa,
8) == 2.63889776
assert round(Water(1e5, 373.15).pressure_saturation(600).MPa,
7) == 12.3443146
#test regions
# arbitrary points
point_in_region1 = (Pressure(20e6), Temperature(300))
point_in_region2 = (Pressure(1e5), Temperature(373.15))
point_in_region3 = (Pressure(40e6), Temperature(700))
point_in_region4 = (Pressure(1).unit('atm'), Temperature(373.1243))
point_in_region5 = (Pressure(20e6), Temperature(1500))
assert Water(*point_in_region1)._is_in_region() == 1
assert Water(*point_in_region2)._is_in_region() == 2
assert Water(*point_in_region3)._is_in_region() == 3
# region 4 does not exist as a region; it is rather the saturation line
assert Water(*point_in_region5)._is_in_region() == 5
#region 1
#assert specific volume
assert round(Water(3e6, 300, massic_basis=True).specific_volume(),
11) == 0.00100215168
assert round(Water(80e6, 300, massic_basis=True).specific_volume(),
12) == 0.000971180894
assert round(Water(3e6, 500, massic_basis=True).specific_volume(),
11) == 0.00120241800
#
# #assert internal energy
assert round(Water(3e6, 300, massic_basis=True).internal_energy(),
6) == 112.324818
assert round(Water(80e6, 300, massic_basis=True).internal_energy(),
6) == 106.448356
assert round(Water(3e6, 500, massic_basis=True).internal_energy(),
6) == 971.934985
#
# #assert enthropy
assert round(Water(3e6, 300, massic_basis=True).entropy(),
9) == 0.392294792
assert round(Water(80e6, 300, massic_basis=True).entropy(),
9) == 0.368563852
assert round(Water(3e6, 500, massic_basis=True).entropy(), 8) == 2.58041912
#assert enthalpy
assert round(Water(3e6, 300, massic_basis=True).enthalpy(),
6) == 115.331273
assert round(Water(80e6, 300, massic_basis=True).enthalpy(),
6) == 184.142828
assert round(Water(3e6, 500, massic_basis=True).enthalpy(),
6) == 975.542239
#assert cp
assert round(Water(3e6, 300, massic_basis=True).heat_capacity(),
8) == 4.17301218
assert round(Water(80e6, 300, massic_basis=True).heat_capacity(),
8) == 4.01008987
assert round(Water(3e6, 500, massic_basis=True).heat_capacity(),
8) == 4.65580682
# #assert cv
# assert round(Water(3e6, 300).enthalpy(),6) == 115.331273
# assert round(Water(80e6, 300).enthalpy(),6) == 184.142828
# assert round(Water(3e6, 500).enthalpy(),6) == 975.542239
#
#assert speed of sound
assert round(Water(3e6, 300, massic_basis=True).speed_of_sound(),
5) == 1507.73921
assert round(Water(80e6, 300, massic_basis=True).speed_of_sound(),
5) == 1634.69054
assert round(Water(3e6, 500, massic_basis=True).speed_of_sound(),
5) == 1240.71337
#region 2
#assert specific volume
assert round(Water(3500, 300, massic_basis=True).specific_volume(),
7) == 39.4913866
assert round(Water(3500, 700, massic_basis=True).specific_volume(),
7) == 92.3015898
assert round(Water(30e6, 700, massic_basis=True).specific_volume(),
11) == 0.00542946619
#
# #assert internal energy
assert round(Water(3500, 300, massic_basis=True).internal_energy(),
5) == 2411.69160
assert round(Water(3500, 700, massic_basis=True).internal_energy(),
5) == 3012.62819
assert round(Water(30e6, 700, massic_basis=True).internal_energy(),
5) == 2468.61076
#
# #assert enthropy
assert round(Water(3500, 300, massic_basis=True).entropy(),
8) == 8.52238967
assert round(Water(3500, 700, massic_basis=True).entropy(),
7) == 10.1749996
assert round(Water(30e6, 700, massic_basis=True).entropy(),
8) == 5.17540298
#assert enthalpy
assert round(Water(3500, 300, massic_basis=True).enthalpy(),
5) == 2549.91145
assert round(Water(3500, 700, massic_basis=True).enthalpy(),
5) == 3335.68375
assert round(Water(30e6, 700, massic_basis=True).enthalpy(),
5) == 2631.49474
#assert cp
# assert round(Water(3e6, 300).heat_capacity(),8) == 4.17301218
# assert round(Water(80e6, 300).heat_capacity(),8) == 4.01008987
# assert round(Water(3e6, 500).heat_capacity(),8) == 4.65580682
# #assert enthalpy
# assert round(Water(3e6, 300).enthalpy(),6) == 115.331273
# assert round(Water(80e6, 300).enthalpy(),6) == 184.142828
# assert round(Water(3e6, 500).enthalpy(),6) == 975.542239
#
# #assert enthalpy
# assert round(Water(3e6, 300).enthalpy(),6) == 115.331273
# assert round(Water(80e6, 300).enthalpy(),6) == 184.142828
# assert round(Water(3e6, 500).enthalpy(),6) == 975.542239
#region 3
#assert specific volume
# assert round(Water(3500, 300).specific_volume(),7) == 39.4913866
# assert round(Water(3500, 700).specific_volume(),7) == 92.3015898
# assert round(Water(30e6, 700).specific_volume(),11) == 0.00542946619
#
# #assert internal energy
# assert round(Water(3e6, 300).enthalpy(),6) == 115.331273
# assert round(Water(80e6, 300).enthalpy(),6) == 184.142828
# assert round(Water(3e6, 500).enthalpy(),6) == 975.542239
#
# #assert enthropy
# assert round(Water(3e6, 300).enthalpy(),6) == 115.331273
# assert round(Water(80e6, 300).enthalpy(),6) == 184.142828
# assert round(Water(3e6, 500).enthalpy(),6) == 975.542239
#assert enthalpy
assert round(Water(25.5837018e6, 650, massic_basis=True).enthalpy(),
5) == 1863.43019
assert round(Water(22.2930643e6, 650, massic_basis=True).enthalpy(),
5) == round(2375.12401, 3)
assert round(Water(78.3095639e6, 750, massic_basis=True).enthalpy(),
5) == 2258.68845
#assert cp
# assert round(Water(3e6, 300).heat_capacity(),8) == 4.17301218
# assert round(Water(80e6, 300).heat_capacity(),8) == 4.01008987
# assert round(Water(3e6, 500).heat_capacity(),8) == 4.65580682
# #assert enthalpy
# assert round(Water(3e6, 300).enthalpy(),6) == 115.331273
# assert round(Water(80e6, 300).enthalpy(),6) == 184.142828
# assert round(Water(3e6, 500).enthalpy(),6) == 975.542239
#
# #assert enthalpy
# assert round(Water(3e6, 300).enthalpy(),6) == 115.331273
# assert round(Water(80e6, 300).enthalpy(),6) == 184.142828
# assert round(Water(3e6, 500).enthalpy(),6) == 975.542239
# region 4
# There is no region 4; instead region 4 is the saturation line
# region 5
#assert specific volume
# assert round(Water(3500, 300).specific_volume(),7) == 39.4913866
# assert round(Water(3500, 700).specific_volume(),7) == 92.3015898
# assert round(Water(30e6, 700).specific_volume(),11) == 0.00542946619
#
# #assert internal energy
# assert round(Water(3e6, 300).enthalpy(),6) == 115.331273
# assert round(Water(80e6, 300).enthalpy(),6) == 184.142828
# assert round(Water(3e6, 500).enthalpy(),6) == 975.542239
#
# #assert enthropy
# assert round(Water(3e6, 300).enthalpy(),6) == 115.331273
# assert round(Water(80e6, 300).enthalpy(),6) == 184.142828
# assert round(Water(3e6, 500).enthalpy(),6) == 975.542239
#assert enthalpy
assert round(Water(0.5e6, 1500, massic_basis=True).enthalpy(),
5) == 5219.76855
assert round(Water(30e6, 1500, massic_basis=True).enthalpy(),
5) == 5167.23514
assert round(Water(30e6, 2000, massic_basis=True).enthalpy(),
5) == 6571.22604