def round_edge_grill(alpha, l=None, Dh=None, fd=None):
r'''Returns the loss coefficient for a rounded square grill or square bar
screen or perforated plate with rounded edges of thickness l, as shown in
[1]_.
for Dh < l < 50D
.. math::
K = lookup(alpha)
else:
.. math::
K = lookup(alpha) + \frac{fl}{\alpha^2D}
Parameters
----------
alpha : float
Fraction of grill open to flow [-]
l : float, optional
Thickness of the grill or plate [m]
Dh : float, optional
Hydraulic diameter of gap in grill, [m]
fd : float, optional
Darcy friction factor [-]
Returns
-------
K : float
Loss coefficient [-]
Notes
-----
If l, Dh, or fd is not provided, the first expression is used instead.
The alteration of the expression to include friction factor is there
if the grill is long enough to have considerable friction along the
surface of the grill.
alpha must be between 0.3 and 0.7.
The velocity the loss coefficient relates to is the approach velocity
before the grill.
Examples
--------
>>> round_edge_grill(.4)
1.0
>>> round_edge_grill(.4, l=.15, Dh=.002, fd=.0185)
2.3874999999999997
References
----------
.. [1] Blevins, Robert D. Applied Fluid Dynamics Handbook. New York, N.Y.:
Van Nostrand Reinhold Co., 1984.
'''
t1 = float(splev(alpha, grills_rounded_tck))
if Dh and l and fd and l > 50.0 * Dh:
return t1 + fd * l / Dh
else:
return t1
def round_edge_grill(alpha, l=None, Dh=None, fd=None):
r'''Returns the loss coefficient for a rounded square grill or square bar
screen or perforated plate with rounded edges of thickness l, as shown in
[1]_.
for Dh < l < 50D
.. math::
K = lookup(alpha)
else:
.. math::
K = lookup(alpha) + \frac{fl}{\alpha^2D}
Parameters
----------
alpha : float
Fraction of grill open to flow [-]
l : float, optional
Thickness of the grill or plate [m]
Dh : float, optional
Hydraulic diameter of gap in grill, [m]
fd : float, optional
Darcy friction factor [-]
Returns
-------
K : float
Loss coefficient [-]
Notes
-----
If l, Dh, or fd is not provided, the first expression is used instead.
The alteration of the expression to include friction factor is there
if the grill is long enough to have considerable friction along the
surface of the grill.
alpha must be between 0.3 and 0.7.
Examples
--------
>>> round_edge_grill(.4)
1.0
>>> round_edge_grill(.4, l=.15, Dh=.002, fd=.0185)
2.3874999999999997
References
----------
.. [1] Blevins, Robert D. Applied Fluid Dynamics Handbook. New York, N.Y.:
Van Nostrand Reinhold Co., 1984.
'''
t1 = float(splev(alpha, grills_rounded_tck))
if Dh and l and fd and l > 50*Dh:
return t1 + fd*l/Dh
else:
return t1
def K_separator_Watkins(x, rhol, rhog, horizontal=False, method='spline'):
r'''Calculates the Sounders-Brown `K` factor as used in determining maximum
allowable gas velocity in a two-phase separator in either a horizontal or
vertical orientation. This function approximates a graph published in [1]_
to determine `K` as used in the following equation:
.. math::
v_{max} = K_{SB}\sqrt{\frac{\rho_l-\rho_g}{\rho_g}}
The graph has `K_{SB}` on its y-axis, and the following as its x-axis:
.. math::
\frac{m_l}{m_g}\sqrt{\rho_g/\rho_l}
= \frac{(1-x)}{x}\sqrt{\rho_g/\rho_l}
Cubic spline interpolation is the default method of retrieving a value
from the graph, which was digitized with Engauge-Digitizer.
Also supported are two published curve fits to the graph. The first is that
of Blackwell (1984) [2]_, as follows:
.. math::
K_{SB} = \exp(-1.942936 -0.814894X -0.179390 X^2 -0.0123790 X^3
+ 0.000386235 X^4 + 0.000259550 X^5)
X = \ln\left[\frac{(1-x)}{x}\sqrt{\rho_g/\rho_l}\right]
The second is that of Branan (1999), as follows:
.. math::
K_{SB} = \exp(-1.877478097 -0.81145804597X -0.1870744085 X^2
-0.0145228667 X^3 -0.00101148518 X^4)
X = \ln\left[\frac{(1-x)}{x}\sqrt{\rho_g/\rho_l}\right]
Parameters
----------
x : float
Quality of fluid entering separator, [-]
rhol : float
Density of liquid phase [kg/m^3]
rhog : float
Density of gas phase [kg/m^3]
horizontal : bool, optional
Whether to use the vertical or horizontal value; horizontal is 1.25
higher
method : str
One of 'spline, 'blackwell', or 'branan'
Returns
-------
K : float
Sounders Brown horizontal or vertical `K` factor for two-phase
separator design only, [m/s]
Notes
-----
Both the 'branan' and 'blackwell' models are used frequently. However,
the spline is much more accurate.
No limits checking is enforced. However, the x-axis spans only 0.006 to
5.4, and the function should not be used outside those limits.
Examples
--------
>>> K_separator_Watkins(0.88, 985.4, 1.3, horizontal=True)
0.07951613600476297
References
----------
.. [1] Watkins (1967). Sizing Separators and Accumulators, Hydrocarbon
Processing, November 1967.
.. [2] Blackwell, W. Wayne. Chemical Process Design on a Programmable
Calculator. New York: Mcgraw-Hill, 1984.
.. [3] Branan, Carl R. Pocket Guide to Chemical Engineering. 1st edition.
Houston, Tex: Gulf Professional Publishing, 1999.
'''
factor = (1. - x) / x * sqrt(rhog / rhol)
if method == 'spline':
K = exp(float(splev(log(factor), tck_Watkins)))
elif method == 'blackwell':
X = log(factor)
A = -1.877478097
B = -0.81145804597
C = -0.1870744085
D = -0.0145228667
E = -0.00101148518
K = exp(A + X * (B + X * (C + X * (D + E * X))))
elif method == 'branan':
X = log(factor)
A = -1.942936
B = -0.814894
C = -0.179390
D = -0.0123790
E = 0.000386235
F = 0.000259550
K = exp(A + X * (B + X * (C + X * (D + X * (E + F * X)))))
else:
raise ValueError(
"Only methods 'spline', 'branan', and 'blackwell' are supported.")
K *= foot # Converts units of ft/s to m/s; the graph and all fits are in ft/s
if horizontal:
K *= 1.25 # Watkins recommends a factor of 1.25 for horizontal separators over vertical separators
return K
def Bhirud_normal(T, Tc, Pc, omega):
r'''Calculates saturation liquid density using the Bhirud [1]_ CSP method.
Uses Critical temperature and pressure and acentric factor.
The density of a liquid is given by:
.. math::
\ln \frac{P_c}{\rho RT} = \ln U^{(0)} + \omega\ln U^{(1)}
.. math::
\ln U^{(0)} = 1.396 44 - 24.076T_r+ 102.615T_r^2
-255.719T_r^3+355.805T_r^4-256.671T_r^5 + 75.1088T_r^6
.. math::
\ln U^{(1)} = 13.4412 - 135.7437 T_r + 533.380T_r^2-
1091.453T_r^3+1231.43T_r^4 - 728.227T_r^5 + 176.737T_r^6
Parameters
----------
T : float
Temperature of fluid [K]
Tc : float
Critical temperature of fluid [K]
Pc : float
Critical pressure of fluid [Pa]
omega : float
Acentric factor for fluid, [-]
Returns
-------
Vm : float
Saturated liquid molar volume, [mol/m^3]
Notes
-----
Claimed inadequate by others.
An interpolation table for ln U values are used from Tr = 0.98 - 1.000.
Has terrible behavior at low reduced temperatures.
Examples
--------
Pentane
>>> Bhirud_normal(280.0, 469.7, 33.7E5, 0.252)
0.00011249657842514176
References
----------
.. [1] Bhirud, Vasant L. "Saturated Liquid Densities of Normal Fluids."
AIChE Journal 24, no. 6 (November 1, 1978): 1127-31.
doi:10.1002/aic.690240630
'''
Tr = T / Tc
if Tr <= 0.98:
lnU0 = Tr * (Tr *
(Tr * (Tr *
(Tr *
(75.1088 * Tr - 256.671) + 355.805) - 255.719) +
102.615) - 24.076) + 1.39644
lnU1 = Tr * (Tr *
(Tr * (Tr *
(Tr *
(176.737 * Tr - 728.227) + 1231.43) - 1091.453) +
533.38) - 135.7437) + 13.4412
elif Tr > 1.0:
raise ValueError('Critical phase, correlation does not apply')
else:
lnU0 = float(splev(Tr, Bhirud_normal_lnU0_tck))
lnU1 = float(splev(Tr, Bhirud_normal_lnU1_tck))
Unonpolar = exp(lnU0 + omega * lnU1)
Vm = Unonpolar * R * T / Pc
return Vm
def K_separator_Watkins(x, rhol, rhog, horizontal=False, method='spline'):
r'''Calculates the Sounders-Brown `K` factor as used in determining maximum
allowable gas velocity in a two-phase separator in either a horizontal or
vertical orientation. This function approximates a graph published in [1]_
to determine `K` as used in the following equation:
.. math::
v_{max} = K_{SB}\sqrt{\frac{\rho_l-\rho_g}{\rho_g}}
The graph has `K_{SB}` on its y-axis, and the following as its x-axis:
.. math::
\frac{m_l}{m_g}\sqrt{\rho_g/\rho_l}
= \frac{(1-x)}{x}\sqrt{\rho_g/\rho_l}
Cubic spline interpolation is the default method of retrieving a value
from the graph, which was digitized with Engauge-Digitizer.
Also supported are two published curve fits to the graph. The first is that
of Blackwell (1984) [2]_, as follows:
.. math::
K_{SB} = \exp(-1.942936 -0.814894X -0.179390 X^2 -0.0123790 X^3
+ 0.000386235 X^4 + 0.000259550 X^5)
X = \log\left[\frac{(1-x)}{x}\sqrt{\rho_g/\rho_l}\right]
The second is that of Branan (1999), as follows:
.. math::
K_{SB} = \exp(-1.877478097 -0.81145804597X -0.1870744085 X^2
-0.0145228667 X^3 -0.00101148518 X^4)
X = \log\left[\frac{(1-x)}{x}\sqrt{\rho_g/\rho_l}\right]
Parameters
----------
x : float
Quality of fluid entering separator, [-]
rhol : float
Density of liquid phase [kg/m^3]
rhog : float
Density of gas phase [kg/m^3]
horizontal : bool, optional
Whether to use the vertical or horizontal value; horizontal is 1.25
higher
method : str
One of 'spline, 'blackwell', or 'branan'
Returns
-------
K : float
Sounders Brown horizontal or vertical `K` factor for two-phase
separator design only, [m/s]
Notes
-----
Both the 'branan' and 'blackwell' models are used frequently. However,
the spline is much more accurate.
No limits checking is enforced. However, the x-axis spans only 0.006 to
5.4, and the function should not be used outside those limits.
Examples
--------
>>> K_separator_Watkins(0.88, 985.4, 1.3, horizontal=True)
0.07951613600476297
References
----------
.. [1] Watkins (1967). Sizing Separators and Accumulators, Hydrocarbon
Processing, November 1967.
.. [2] Blackwell, W. Wayne. Chemical Process Design on a Programmable
Calculator. New York: Mcgraw-Hill, 1984.
.. [3] Branan, Carl R. Pocket Guide to Chemical Engineering. 1st edition.
Houston, Tex: Gulf Professional Publishing, 1999.
'''
factor = (1. - x)/x*(rhog/rhol)**0.5
if method == 'spline':
K = exp(float(splev(log(factor), tck_Watkins)))
elif method == 'blackwell':
X = log(factor)
A = -1.877478097
B = -0.81145804597
C = -0.1870744085
D = -0.0145228667
E = -0.00101148518
K = exp(A + X*(B + X*(C + X*(D + E*X))))
elif method == 'branan':
X = log(factor)
A = -1.942936
B = -0.814894
C = -0.179390
D = -0.0123790
E = 0.000386235
F = 0.000259550
K = exp(A + X*(B + X*(C + X*(D + X*(E + F*X)))))
else:
raise Exception("Only methods 'spline', 'branan', and 'blackwell' are supported.")
K *= foot # Converts units of ft/s to m/s; the graph and all fits are in ft/s
if horizontal:
K *= 1.25 # Watkins recommends a factor of 1.25 for horizontal separators over vertical separators
return K
