def constantRangeIntegral(s, sLimit):
logArg = 1. - s / sLimit
retVal = clog(logArg)
retVal *= 2 * sLimit**2
retVal += s * (2 * sLimit + s)
retVal /= 2 * sLimit**2 * s**3
return retVal
def A(s, mPart, renScale2, allowSubThr=False):
sig = sigma(s, mPart, allowSubThr=allowSubThr)
retVal = log(
mPart**2 / renScale2) + 8 * mPart**2 / s - 5. / 3. + sig**3 * clog(
(sig + 1) /
(sig -
1.)) # +1.j pi to obtain the real part (at least above threshold)
return retVal
def DIPPR_EQ114_integral_by_T(T, Tc, a, b, c, d):
"""T-Integral of DPPR Equation #114."""
return (-a**2 * Tc * clog(T - Tc).real + d**2 * T**6 / (30 * Tc**5) -
T**5 * (c * d + 2 * d**2) / (10 * Tc**4) + T**4 *
(c**2 + 6 * c * d + 6 * d**2) / (12 * Tc**3) - T**3 *
(a * d + c**2 + 3 * c * d + 2 * d**2) / (3 * Tc**2) + T**2 *
(2 * a * c + 2 * a * d + c**2 + 2 * c * d + d**2) / (2 * Tc) + T *
(-2 * a * c - a * d + b - c**2 / 3 - c * d / 2 - d**2 / 5))
def constantRangeIntegral(s, sLimit):
logArg = 1. - s / sLimit
# retVal = log(abs(logArg))
# if logArg < 0.:
# retVal += 1.j*pi
retVal = clog(logArg)
retVal *= 2 * sLimit**2
retVal += s * (2 * sLimit + s)
retVal /= 2 * sLimit**2 * s**3
return retVal
def _set_coordonnees(self, x, y):
zA = self.__point1.z
zB = self.__point2.z
z = x + 1j * y
try:
if abs(zB - zA) > param.tolerance:
# TODO: cas où l'angle n'est pas en radian
self.__angle.val = clog((z - zA) / (zB - zA)).imag
except (OverflowError, ZeroDivisionError):
if param.debug:
print_error()
def _set_coordonnees(self, x, y):
zA = self.__point1.z
zB = self.__point2.z
z = x + 1j*y
try:
if abs(zB - zA) > param.tolerance:
# TODO: cas où l'angle n'est pas en radian
self.__angle.val = clog((z - zA)/(zB - zA)).imag
except (OverflowError, ZeroDivisionError):
if param.debug:
print_error()
def _set_coordonnees(self, x, y):
zA = self.__sommet_principal.z
zB = self.__point2.z
z = x + 1j*y
try:
if issympy(zA, zB):
self.__angle = sarg((z - zA)/(zB - zA))
else:
self.__angle = clog((z - zA)/(zB - zA)).imag
except (OverflowError, ZeroDivisionError):
if param.debug:
print_error()
def _set_coordonnees(self, x, y):
zA = self.__sommet_principal.z
zB = self.__point2.z
z = x + 1j * y
try:
if issympy(zA, zB):
self.__angle = sarg((z - zA) / (zB - zA))
else:
self.__angle = clog((z - zA) / (zB - zA)).imag
except (OverflowError, ZeroDivisionError):
if param.debug:
print_error()
def _set_coordonnees(self, x, y):
zA = self.__point1.z
zB = self.__point2.z
zI = (zA + zB)/2
z = x + 1j*y
try:
if issympy(zI):
self.__angle = sarg((z - zI)/(zB - zI))/2
else:
self.__angle = clog((z - zI)/(zB - zI)).imag/2
except (OverflowError, ZeroDivisionError):
if param.debug:
print_error()
def _set_coordonnees(self, x, y):
zA = self.__point1.z
zB = self.__point2.z
zI = (zA + zB) / 2
z = x + 1j * y
try:
if issympy(zI):
self.__angle = sarg((z - zI) / (zB - zI)) / 2
else:
self.__angle = clog((z - zI) / (zB - zI)).imag / 2
except (OverflowError, ZeroDivisionError):
if param.debug:
print_error()
def DIPPR_EQ114_integral_by_T_over_T(T, Tc, a, b, c, d):
"""T-Integral of DPPR Equation #114 divided by T."""
return (
-a**2 *
clog(T +
(-60 * a**2 * Tc + 60 * a * c * Tc + 30 * a * d * Tc -
30 * b * Tc + 10 * c**2 * Tc + 15 * c * d * Tc + 6 * d**2 * Tc) /
(60 * a**2 - 60 * a * c - 30 * a * d + 30 * b - 10 * c**2 -
15 * c * d - 6 * d**2)).real + d**2 * T**5 / (25 * Tc**5) -
T**4 * (c * d + 2 * d**2) / (8 * Tc**4) + T**3 *
(c**2 + 6 * c * d + 6 * d**2) / (9 * Tc**3) - T**2 *
(a * d + c**2 + 3 * c * d + 2 * d**2) / (2 * Tc**2) + T *
(2 * a * c + 2 * a * d + c**2 + 2 * c * d + d**2) / Tc +
(30 * a**2 - 60 * a * c - 30 * a * d + 30 * b - 10 * c**2 -
15 * c * d - 6 * d**2) *
clog(T +
(-30 * a**2 * Tc + 60 * a * c * Tc + 30 * a * d * Tc - 30 * b *
Tc + 10 * c**2 * Tc + 15 * c * d * Tc + 6 * d**2 * Tc + Tc *
(30 * a**2 - 60 * a * c - 30 * a * d + 30 * b - 10 * c**2 -
15 * c * d - 6 * d**2)) /
(60 * a**2 - 60 * a * c - 30 * a * d + 30 * b - 10 * c**2 -
15 * c * d - 6 * d**2)).real / 30)
def Lastovka_Shaw_Indefinite_Integral_Over_T(T, MW, similarity_variable, term):
a = similarity_variable
a2 = a * a
B11 = 0.73917383
B12 = 8.88308889
C11 = 1188.28051
C12 = 1813.04613
B21 = 0.0483019
B22 = 4.35656721
C21 = 2897.01927
C22 = 5987.80407
S = (term * clog(T) +
(-B11 - B12 * a) * clog(cexp((-C11 - C12 * a) / T) - 1.) +
(-B11 * C11 - B11 * C12 * a - B12 * C11 * a - B12 * C12 * a2) /
(T * cexp((-C11 - C12 * a) / T) - T) -
(B11 * C11 + B11 * C12 * a + B12 * C11 * a + B12 * C12 * a2) / T)
S += ((-B21 - B22 * a) * clog(cexp((-C21 - C22 * a) / T) - 1.) +
(-B21 * C21 - B21 * C22 * a - B22 * C21 * a - B22 * C22 * a2) /
(T * cexp((-C21 - C22 * a) / T) - T) -
(B21 * C21 + B21 * C22 * a + B22 * C21 * a + B22 * C22 * a**2) / T)
# There is a non-real component, but it is only a function of similariy
# variable and so will always cancel out.
return MW * S.real
def ghiggs(t):
if t<=1:
return csqrt(1-1/t)/2. * ( clog((1 + csqrt(1-1/t))/(1 - csqrt(1-1/t)))-pi*1j)
else:
return csqrt(1/t-1)*casin(csqrt(t))
def EQ114(T, Tc, A, B, C, D, order=0):
r'''DIPPR Equation #114. Rarely used, normally as an alternate liquid
heat capacity expression. All 4 parameters are required, as well as
critical temperature.
.. math::
Y = \frac{A^2}{\tau} + B - 2AC\tau - AD\tau^2 - \frac{1}{3}C^2\tau^3
- \frac{1}{2}CD\tau^4 - \frac{1}{5}D^2\tau^5
\tau = 1 - \frac{T}{Tc}
Parameters
----------
T : float
Temperature, [K]
Tc : float
Critical temperature, [K]
A-D : float
Parameter for the equation; chemical and property specific [-]
order : int, optional
Order of the calculation. 0 for the calculation of the result itself;
for 1, the first derivative of the property is returned, for
-1, the indefinite integral of the property with respect to temperature
is returned; and for -1j, the indefinite integral of the property
divided by temperature with respect to temperature is returned. No
other integrals or derivatives are implemented, and an exception will
be raised if any other order is given.
Returns
-------
Y : float
Property [constant-specific; if order == 1, property/K; if order == -1,
property*K; if order == -1j, unchanged from default]
Notes
-----
The derivative with respect to T, integral with respect to T, and integral
over T with respect to T are computed as follows. All expressions can be
obtained with SymPy readily.
.. math::
\frac{d Y}{dT} = \frac{A^{2}}{T_{c} \left(- \frac{T}{T_{c}}
+ 1\right)^{2}} + \frac{2 A}{T_{c}} C + \frac{2 A}{T_{c}} D \left(
- \frac{T}{T_{c}} + 1\right) + \frac{C^{2}}{T_{c}} \left(
- \frac{T}{T_{c}} + 1\right)^{2} + \frac{2 C}{T_{c}} D \left(
- \frac{T}{T_{c}} + 1\right)^{3} + \frac{D^{2}}{T_{c}} \left(
- \frac{T}{T_{c}} + 1\right)^{4}
.. math::
\int Y dT = - A^{2} T_{c} \log{\left (T - T_{c} \right )} + \frac{D^{2}
T^{6}}{30 T_{c}^{5}} - \frac{T^{5}}{10 T_{c}^{4}} \left(C D + 2 D^{2}
\right) + \frac{T^{4}}{12 T_{c}^{3}} \left(C^{2} + 6 C D + 6 D^{2}
\right) - \frac{T^{3}}{3 T_{c}^{2}} \left(A D + C^{2} + 3 C D
+ 2 D^{2}\right) + \frac{T^{2}}{2 T_{c}} \left(2 A C + 2 A D + C^{2}
+ 2 C D + D^{2}\right) + T \left(- 2 A C - A D + B - \frac{C^{2}}{3}
- \frac{C D}{2} - \frac{D^{2}}{5}\right)
.. math::
\int \frac{Y}{T} dT = - A^{2} \log{\left (T + \frac{- 60 A^{2} T_{c}
+ 60 A C T_{c} + 30 A D T_{c} - 30 B T_{c} + 10 C^{2} T_{c}
+ 15 C D T_{c} + 6 D^{2} T_{c}}{60 A^{2} - 60 A C - 30 A D + 30 B
- 10 C^{2} - 15 C D - 6 D^{2}} \right )} + \frac{D^{2} T^{5}}
{25 T_{c}^{5}} - \frac{T^{4}}{8 T_{c}^{4}} \left(C D + 2 D^{2}
\right) + \frac{T^{3}}{9 T_{c}^{3}} \left(C^{2} + 6 C D + 6 D^{2}
\right) - \frac{T^{2}}{2 T_{c}^{2}} \left(A D + C^{2} + 3 C D
+ 2 D^{2}\right) + \frac{T}{T_{c}} \left(2 A C + 2 A D + C^{2}
+ 2 C D + D^{2}\right) + \frac{1}{30} \left(30 A^{2} - 60 A C
- 30 A D + 30 B - 10 C^{2} - 15 C D - 6 D^{2}\right) \log{\left
(T + \frac{1}{60 A^{2} - 60 A C - 30 A D + 30 B - 10 C^{2} - 15 C D
- 6 D^{2}} \left(- 30 A^{2} T_{c} + 60 A C T_{c} + 30 A D T_{c}
- 30 B T_{c} + 10 C^{2} T_{c} + 15 C D T_{c} + 6 D^{2} T_{c}
+ T_{c} \left(30 A^{2} - 60 A C - 30 A D + 30 B - 10 C^{2} - 15 C D
- 6 D^{2}\right)\right) \right )}
Strictly speaking, the integral over T has an imaginary component, but
only the real component is relevant and the complex part discarded.
Examples
--------
Hydrogen liquid heat capacity; DIPPR coefficients normally in J/kmol/K.
>>> EQ114(20, 33.19, 66.653, 6765.9, -123.63, 478.27)
19423.948911676463
References
----------
.. [1] Design Institute for Physical Properties, 1996. DIPPR Project 801
DIPPR/AIChE
'''
if order == 0:
t = 1. - T / Tc
return (A**2. / t + B - 2. * A * C * t - A * D * t**2. -
C**2. * t**3. / 3. - C * D * t**4. / 2. - D**2 * t**5. / 5.)
elif order == 1:
return (A**2 / (Tc * (-T / Tc + 1)**2) + 2 * A * C / Tc + 2 * A * D *
(-T / Tc + 1) / Tc + C**2 * (-T / Tc + 1)**2 / Tc + 2 * C * D *
(-T / Tc + 1)**3 / Tc + D**2 * (-T / Tc + 1)**4 / Tc)
elif order == -1:
return (-A**2 * Tc * clog(T - Tc).real + D**2 * T**6 / (30 * Tc**5) -
T**5 * (C * D + 2 * D**2) / (10 * Tc**4) + T**4 *
(C**2 + 6 * C * D + 6 * D**2) / (12 * Tc**3) - T**3 *
(A * D + C**2 + 3 * C * D + 2 * D**2) / (3 * Tc**2) + T**2 *
(2 * A * C + 2 * A * D + C**2 + 2 * C * D + D**2) / (2 * Tc) +
T * (-2 * A * C - A * D + B - C**2 / 3 - C * D / 2 - D**2 / 5))
elif order == -1j:
return (
-A**2 *
clog(T +
(-60 * A**2 * Tc + 60 * A * C * Tc + 30 * A * D * Tc - 30 *
B * Tc + 10 * C**2 * Tc + 15 * C * D * Tc + 6 * D**2 * Tc) /
(60 * A**2 - 60 * A * C - 30 * A * D + 30 * B - 10 * C**2 -
15 * C * D - 6 * D**2)).real + D**2 * T**5 / (25 * Tc**5) -
T**4 * (C * D + 2 * D**2) / (8 * Tc**4) + T**3 *
(C**2 + 6 * C * D + 6 * D**2) / (9 * Tc**3) - T**2 *
(A * D + C**2 + 3 * C * D + 2 * D**2) / (2 * Tc**2) + T *
(2 * A * C + 2 * A * D + C**2 + 2 * C * D + D**2) / Tc +
(30 * A**2 - 60 * A * C - 30 * A * D + 30 * B - 10 * C**2 -
15 * C * D - 6 * D**2) *
clog(T + (-30 * A**2 * Tc + 60 * A * C * Tc + 30 * A * D * Tc -
30 * B * Tc + 10 * C**2 * Tc + 15 * C * D * Tc +
6 * D**2 * Tc + Tc *
(30 * A**2 - 60 * A * C - 30 * A * D + 30 * B -
10 * C**2 - 15 * C * D - 6 * D**2)) /
(60 * A**2 - 60 * A * C - 30 * A * D + 30 * B - 10 * C**2 -
15 * C * D - 6 * D**2)).real / 30)
else:
raise Exception(order_not_found_msg)
def py_catan(x):
# Implemented only because micropython is missing this function
return 0.5j * (clog(1.0 - 1.0j * x) - clog(1.0 + 1.0j * x))
def ghiggs(t):
if t <= 1:
return csqrt(1 - 1 / t) / 2. * (clog(
(1 + csqrt(1 - 1 / t)) / (1 - csqrt(1 - 1 / t))) - pi * 1j)
else:
return csqrt(1 / t - 1) * casin(csqrt(t))
def EQ114(T, Tc, A, B, C, D, order=0):
r'''DIPPR Equation #114. Rarely used, normally as an alternate liquid
heat capacity expression. All 4 parameters are required, as well as
critical temperature.
.. math::
Y = \frac{A^2}{\tau} + B - 2AC\tau - AD\tau^2 - \frac{1}{3}C^2\tau^3
- \frac{1}{2}CD\tau^4 - \frac{1}{5}D^2\tau^5
\tau = 1 - \frac{T}{Tc}
Parameters
----------
T : float
Temperature, [K]
Tc : float
Critical temperature, [K]
A-D : float
Parameter for the equation; chemical and property specific [-]
order : int, optional
Order of the calculation. 0 for the calculation of the result itself;
for 1, the first derivative of the property is returned, for
-1, the indefinite integral of the property with respect to temperature
is returned; and for -1j, the indefinite integral of the property
divided by temperature with respect to temperature is returned. No
other integrals or derivatives are implemented, and an exception will
be raised if any other order is given.
Returns
-------
Y : float
Property [constant-specific; if order == 1, property/K; if order == -1,
property*K; if order == -1j, unchanged from default]
Notes
-----
The derivative with respect to T, integral with respect to T, and integral
over T with respect to T are computed as follows. All expressions can be
obtained with SymPy readily.
.. math::
\frac{d Y}{dT} = \frac{A^{2}}{T_{c} \left(- \frac{T}{T_{c}}
+ 1\right)^{2}} + \frac{2 A}{T_{c}} C + \frac{2 A}{T_{c}} D \left(
- \frac{T}{T_{c}} + 1\right) + \frac{C^{2}}{T_{c}} \left(
- \frac{T}{T_{c}} + 1\right)^{2} + \frac{2 C}{T_{c}} D \left(
- \frac{T}{T_{c}} + 1\right)^{3} + \frac{D^{2}}{T_{c}} \left(
- \frac{T}{T_{c}} + 1\right)^{4}
.. math::
\int Y dT = - A^{2} T_{c} \log{\left (T - T_{c} \right )} + \frac{D^{2}
T^{6}}{30 T_{c}^{5}} - \frac{T^{5}}{10 T_{c}^{4}} \left(C D + 2 D^{2}
\right) + \frac{T^{4}}{12 T_{c}^{3}} \left(C^{2} + 6 C D + 6 D^{2}
\right) - \frac{T^{3}}{3 T_{c}^{2}} \left(A D + C^{2} + 3 C D
+ 2 D^{2}\right) + \frac{T^{2}}{2 T_{c}} \left(2 A C + 2 A D + C^{2}
+ 2 C D + D^{2}\right) + T \left(- 2 A C - A D + B - \frac{C^{2}}{3}
- \frac{C D}{2} - \frac{D^{2}}{5}\right)
.. math::
\int \frac{Y}{T} dT = - A^{2} \log{\left (T + \frac{- 60 A^{2} T_{c}
+ 60 A C T_{c} + 30 A D T_{c} - 30 B T_{c} + 10 C^{2} T_{c}
+ 15 C D T_{c} + 6 D^{2} T_{c}}{60 A^{2} - 60 A C - 30 A D + 30 B
- 10 C^{2} - 15 C D - 6 D^{2}} \right )} + \frac{D^{2} T^{5}}
{25 T_{c}^{5}} - \frac{T^{4}}{8 T_{c}^{4}} \left(C D + 2 D^{2}
\right) + \frac{T^{3}}{9 T_{c}^{3}} \left(C^{2} + 6 C D + 6 D^{2}
\right) - \frac{T^{2}}{2 T_{c}^{2}} \left(A D + C^{2} + 3 C D
+ 2 D^{2}\right) + \frac{T}{T_{c}} \left(2 A C + 2 A D + C^{2}
+ 2 C D + D^{2}\right) + \frac{1}{30} \left(30 A^{2} - 60 A C
- 30 A D + 30 B - 10 C^{2} - 15 C D - 6 D^{2}\right) \log{\left
(T + \frac{1}{60 A^{2} - 60 A C - 30 A D + 30 B - 10 C^{2} - 15 C D
- 6 D^{2}} \left(- 30 A^{2} T_{c} + 60 A C T_{c} + 30 A D T_{c}
- 30 B T_{c} + 10 C^{2} T_{c} + 15 C D T_{c} + 6 D^{2} T_{c}
+ T_{c} \left(30 A^{2} - 60 A C - 30 A D + 30 B - 10 C^{2} - 15 C D
- 6 D^{2}\right)\right) \right )}
Strictly speaking, the integral over T has an imaginary component, but
only the real component is relevant and the complex part discarded.
Examples
--------
Hydrogen liquid heat capacity; DIPPR coefficients normally in J/kmol/K.
>>> EQ114(20, 33.19, 66.653, 6765.9, -123.63, 478.27)
19423.948911676463
References
----------
.. [1] Design Institute for Physical Properties, 1996. DIPPR Project 801
DIPPR/AIChE
'''
if order == 0:
t = 1.-T/Tc
return (A**2./t + B - 2.*A*C*t - A*D*t**2. - C**2.*t**3./3.
- C*D*t**4./2. - D**2*t**5./5.)
elif order == 1:
return (A**2/(Tc*(-T/Tc + 1)**2) + 2*A*C/Tc + 2*A*D*(-T/Tc + 1)/Tc
+ C**2*(-T/Tc + 1)**2/Tc + 2*C*D*(-T/Tc + 1)**3/Tc
+ D**2*(-T/Tc + 1)**4/Tc)
elif order == -1:
return (-A**2*Tc*clog(T - Tc).real + D**2*T**6/(30*Tc**5)
- T**5*(C*D + 2*D**2)/(10*Tc**4)
+ T**4*(C**2 + 6*C*D + 6*D**2)/(12*Tc**3) - T**3*(A*D + C**2
+ 3*C*D + 2*D**2)/(3*Tc**2) + T**2*(2*A*C + 2*A*D + C**2 + 2*C*D
+ D**2)/(2*Tc) + T*(-2*A*C - A*D + B - C**2/3 - C*D/2 - D**2/5))
elif order == -1j:
return (-A**2*clog(T + (-60*A**2*Tc + 60*A*C*Tc + 30*A*D*Tc - 30*B*Tc
+ 10*C**2*Tc + 15*C*D*Tc + 6*D**2*Tc)/(60*A**2 - 60*A*C
- 30*A*D + 30*B - 10*C**2 - 15*C*D - 6*D**2)).real
+ D**2*T**5/(25*Tc**5) - T**4*(C*D + 2*D**2)/(8*Tc**4)
+ T**3*(C**2 + 6*C*D + 6*D**2)/(9*Tc**3) - T**2*(A*D + C**2
+ 3*C*D + 2*D**2)/(2*Tc**2) + T*(2*A*C + 2*A*D + C**2 + 2*C*D
+ D**2)/Tc + (30*A**2 - 60*A*C - 30*A*D + 30*B - 10*C**2
- 15*C*D - 6*D**2)*clog(T + (-30*A**2*Tc + 60*A*C*Tc
+ 30*A*D*Tc - 30*B*Tc + 10*C**2*Tc + 15*C*D*Tc + 6*D**2*Tc
+ Tc*(30*A**2 - 60*A*C - 30*A*D + 30*B - 10*C**2 - 15*C*D
- 6*D**2))/(60*A**2 - 60*A*C - 30*A*D + 30*B - 10*C**2
- 15*C*D - 6*D**2)).real/30)
else:
raise Exception(order_not_found_msg)
def A(self, s, mPart, sheet): sig = self.sigma(s, mPart) retVal = log(mPart**2/self.mu**2) + 8*mPart**2/s - 5./3. + sig**3*clog((sig+1)/(sig-1.)) # +1.j pi to obtain the real part (at least above threshold) if sheet == 2: retVal += 2*pi* (4*mPart**2/s-1.+0.j)**1.5 return retVal