#!/usr/bin/python3
# -*- coding: utf-8 -*-
'''Pychemqt, Chemical Engineering Process simulator
Copyright (C) 2009-2023, Juan José Gómez Romera <jjgomera@gmail.com>
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see <http://www.gnu.org/licenses/>.
Module for drag coefficient correlations, for now only implemented the sphere
drag correlation
:func:`dragSphere`: Function to implement the drag coeficient for smooth
spheres including all available methods:
* :func:`Barati`
* :func:`Clift`
* :func:`Ceylan`
* :func:`Almedeij`
* :func:`Morrison`
* :func:`Morsi`
* :func:`Khan`
* :func:`Flemmer`
* :func:`Haider`
* :func:`Turton`
* :func:`Concha`
* :func:`Swamee`
* :func:`Cheng`
* :func:`Terfous`
* :func:`Mikhailov`
.. include:: drag.rst
'''
from math import exp, log, log10, tanh
import sys
from lib.utilities import refDoc
__doi__ = {
1:
{"autor": "Barati, R., Neyshabouri, S.A.A.S, Ahmadi, G.",
"title": "Development of Empirical Models with High Accuracy for "
"Estimation of Drag Coefficient of Flow around a Smooth "
"Sphere: An Evolutionary Approach",
"ref": "Powder Technology 257 (2014) 11-19",
"doi": "10.1016/j.powtec.2014.02.045"},
2:
{"autor": "Clift, R., Grace, J.R., Weber, M.E.",
"title": "Bubbles, Drops, and Particles",
"ref": "Academic Press, 1978.",
"doi": ""},
3:
{"autor": "Ceylan, K., Altunbaş, A., Kelbaliyev, G.",
"title": "A New Model for Estimation of Drag Force in the Flow of "
"Newtonian Fluids around Rigid or Deformable Particles",
"ref": "Powder Technology 119 (2001) 250-56",
"doi": "10.1016/s0032-5910(01)00261-3"},
4:
{"autor": "Almedeij, J.",
"title": "Drag Coefficient of Flow around a Sphere: Matching "
"Asymptotically the Wide Trend",
"ref": "Powder Technology 186(3) (2008) 218-223",
"doi": "10.1016/j.powtec.2007.12.006"},
5:
{"autor": "Morrison, F.A.",
"title": "An Introduction to Fluid Mechanics.",
"ref": "Cambridge University Press, 2013.",
"doi": ""},
6:
{"autor": "Morsi, S.A., Alexander, A.J.",
"title": "An Investigation of Particle Trajectories in Two-Phase "
"Flow Systems",
"ref": "J. Fluid Mechanics 55(2) (1972) 193-208",
"doi": "10.1017/S0022112072001806"},
7:
{"autor": "Brown, P.P., Lawler, D.F.",
"title": "Sphere Drag and Settling Velocity Revisited",
"ref": "J. Env. Eng. 129(3) (2003) 222-231",
"doi": "10.1061/(ASCE)0733-9372(2003)129:3(222)"},
8:
{"autor": "Khan, A.R., Richardson, J.F.",
"title": "The Resistance to Motion of a Solid Sphere in a Fluid.",
"ref": "Chem. Eng. Comm. 62 (1987) 135-150",
"doi": "10.1080/00986448708912056"},
9:
{"autor": "Flemmer, R.L.C., Banks, C.L.",
"title": "On the Drag Coefficient of a Sphere",
"ref": "Powder Technology 48(3) (1986) 217-221.",
"doi": "10.1016/0032-5910(86)80044-4"},
10:
{"autor": "Haider, A., Levenspiel, O.",
"title": "Drag Coefficient and Terminal Velocity of Spherical and "
"Nonspherical Particles",
"ref": "Powder Technology 58(1) (1989) 63-70",
"doi": "10.1016/0032-5910(89)80008-7"},
11:
{"autor": "Turton, R., Levenspiel, O.",
"title": "A Short Note on the Drag Correlation for Spheres",
"ref": "Powder Technology 47(1) (1986) 83-86",
"doi": "10.1016/0032-5910(86)80012-2"},
12:
{"autor": "Concha, F., Barrientos, A.",
"title": "Settling Velocities of Particulate Systems, 3. Power Series"
" Expansion for the Drag Coefficient of A Sphere and "
"Prediction of the Settling Velocity",
"ref": "Int. J. Miner. Process. 9 (1982) 167-172",
"doi": "10.1016/0301-7516(82)90025-4"},
13:
{"autor": "Swamee, P.K., Ojha, C.S.P.",
"title": "Drag Coefficient and Fall Velocity of Nonspherical "
"Particles",
"ref": "J. Hydraul. Eng. 117(5) (1991) 660-667",
"doi": "10.1061/(ASCE)0733-9429(1991)117:5(660)"},
14:
{"autor": "Cheng, N.-S.",
"title": "Comparison of Formulas for Drag Coefficient and Settling "
"Velocity of Spherical Particles",
"ref": "Powder Technology 189(3) (2009) 395-398",
"doi": "10.1016/j.powtec.2008.07.006"},
15:
{"autor": "Terfous, A., Hazzab, A., Ghenaim, A.",
"title": "Predicting the Drag Coefficient and Settling Velocity of "
"Spherical Particles",
"ref": "Powder Technology 239 (2013) 12-20",
"doi": "10.1016/j.powtec.2013.01.052"},
16:
{"autor": "Mikhailov, M.D., Silva Freire, A.P.",
"title": "The Drag Coefficient of a Sphere: An Approximation Using "
"Shanks Transform",
"ref": "Powder Technology 237 (2013) 432-435",
"doi": "10.1016/j.powtec.2012.12.033"},
}
[docs]
@refDoc(__doi__, [1])
def Barati(Re, extended=False):
r'''Calculates drag coefficient of a smooth sphere using the method in
[1]_.
For Re < 2e5
.. math::
\begin{align*}
C_d = 5.4856·10^9\tanh(4.3774\times10^{-9}/Re)
+ 0.0709\tanh(700.6574/Re) \\
{} + 0.3894\tanh(74.1539/Re) - 0.1198\tanh(7429.0843/Re) \\
{} + 1.7174\tanh[9.9851/(Re+2.3384)] + 0.4744
\end{align*}
For 2e5 <= Re < 1e6
.. math::
\begin{align*}
C_d = 8·10^{-6}\left[(Re/6530)^2+\tanh(Re) - 8\ln(Re)/\ln(10)\right] \\
{} - 0.4119\exp(-2.08x10^{43}/[Re + Re^2]^4) \\
{} - 2.1344\exp(-{\left[\ln(Re^2 + 10.7563)/\ln(10)\right]^2
+ 9.9867}/Re) \\
{} + 0.1357\exp(-[(Re/1620)^2 + 10370]/Re) \\
{} - 8.5\times 10^{-3}\{2\ln[\tanh(\tanh(Re))]/\ln(10) - 2825.7162\}/Re
\end{align*}
Parameters
----------
Re : float
Reynolds number of the sphere, [-]
extended : boolean
Use the extended version on all Re range of equation
Returns
-------
Cd : float
Drag coefficient [-]
Notes
-----
Raise :class:`NotImplementedError` if Re isn't in range Re ≤ 1e6
Examples
--------
Selected values from Table 6 in [1]_.
>>> print("%0.2f" % Barati(0.002))
12008.86
>>> print("%0.2f" % Barati(0.002, extended=True))
12034.71
>>> print("%0.2f" % Barati(1000))
0.47
'''
if not extended and Re < 2e5:
# Eq 22
Cd = 5.4856e9*tanh(4.3774e-9/Re) + 0.0709*tanh(700.6574/Re) \
+ 0.3894*tanh(74.1539/Re) - 0.1198*tanh(7429.0843/Re) \
+ 1.7174*tanh(9.9851/(Re+2.3384)) + 0.4744
elif Re <= 1e6:
# Eq 23
Cd = 8e-6*((Re/6530)**2 + tanh(Re) - 8*log(Re)/log(10)) \
- 0.4119*exp(-2.08e43/(Re+Re**2)**4) \
- 2.1344*exp(-((log(Re**2 + 10.7563)/log(10))**2 + 9.9867)/Re) \
+ 0.1357*exp(-((Re/1620)**2 + 10370)/Re) \
- 8.5e-3*(2*log(tanh(tanh(Re)))/log(10) - 2825.7162)/Re + 2.4795
else:
raise NotImplementedError("Input out of range 0 < Re ≤ 1e6")
return Cd
[docs]
@refDoc(__doi__, [2])
def Clift(Re):
r'''Calculates drag coefficient of a smooth sphere using the method in
[2]_.
This method use different correlation for several ranges of Re, as describe
in Table 5.2, pag 112
.. math::
C_d = \left\{ \begin{array}{ll}
\frac{24}{Re} + \frac{3}{16} & \mbox{if $Re < 0.01$}\\
\frac{24}{Re}(1 + 0.1315Re^{0.82-0.05w}) & \mbox{if $0.01 < Re < 20$}\\
\frac{24}{Re}(1 + 0.1935Re^{0.6305}) & \mbox{if $20 < Re < 260$}\\
10^{[1.6435 - 1.1242w + 0.1558w^2} & \mbox{if $260 < Re < 1500$}\\
10^{[-2.4571 + 2.5558w - 0.9295w^2 + 0.1049w^3} &
\mbox{if $1500 < Re < 1.2x10^4$}\\
10^{[-1.9181 + 0.6370w - 0.0636w^2} &
\mbox{if $1.2x10^4 < Re < 4.4x10^4$}\\
10^{[-4.3390 + 1.5809w - 0.1546w^2} &
\mbox{if $4.4x10^4 < Re < 3.38x10^5$}\\
29.78 - 5.3w & \mbox{if $3.38x10^5 < Re < 4x10^5$}\\
0.1w - 0.49 & \mbox{if $4x10^5 < Re < 10^6$}\\
0.19w - \frac{8x10^4}{Re} & \mbox{if $10^6 < Re$}\end{array}\right.
where :math:`w = \log_{10}{Re}`
Parameters
----------
Re : float
Reynolds number of the sphere, [-]
Returns
-------
Cd : float
Drag coefficient [-]
Notes
-----
Raise :class:`NotImplementedError` if Re isn't in range Re ≤ 6e6
The last equation is based in Achenbach data and this reach 6e6 as maximum
Reynolds number
Examples
--------
There isn´t testing values but checking a value similar to Barati
correlation would be enough
>>> print("%0.0f" % Clift(0.002))
12000
>>> print("%0.2f" % Clift(1000))
0.47
'''
w = log10(Re)
if Re < 0.01:
Cd = 3/16 + 24/Re
elif Re < 20:
Cd = 24/Re*(1 + 0.1315*Re**(0.82 - 0.05*w))
elif Re < 260:
Cd = 24/Re*(1 + 0.1935*Re**(0.6305))
elif Re < 1500:
Cd = 10**(1.6435 - 1.1242*w + 0.1558*w**2)
elif Re < 1.2e4:
Cd = 10**(-2.4571 + 2.5558*w - 0.9295*w**2 + 0.1049*w**3)
elif Re < 4.4e4:
Cd = 10**(-1.9181 + 0.6370*w - 0.0636*w**2)
elif Re < 3.38e5:
Cd = 10**(-4.3390 + 1.5809*w - 0.1546*w**2)
elif Re < 4e5:
Cd = 29.78 - 5.3*w
elif Re < 1e6:
Cd = 0.1*w - 0.49
elif Re < 6e6:
Cd = 0.19 - 8e4/Re
else:
raise NotImplementedError("Input out of range 0 < Re ≤ 6e6")
return Cd
[docs]
@refDoc(__doi__, [3])
def Ceylan(Re):
r'''Calculates drag coefficient of a smooth sphere using the method in
[3]_.
.. math::
\begin{align*}
C_d = 1 - 0.5e^{0.182} + 10.11Re^{-2/3}e^{0.952Re^{-1/4}}
- 0.03859Re^{-4/3}e^{1.30Re^{-1/2}} \\
{} + 0.037\times10^{-4}Re e^{-0.125\times10^{-4}Re}
-0.116\times10^{-10}Re^2 e^{-0.444\times10^{-5}Re}
\end{align*}
Parameters
----------
Re : float
Reynolds number of the sphere, [-]
Returns
-------
Cd : float
Drag coefficient [-]
Notes
-----
Raise :class:`NotImplementedError` if Re isn't in range Re ≤ 1e6
Examples
--------
Selected values from Table 2, pag 253
# >>> print("%0.0f" % Ceylan(0.1))
# 238
# >>> print("%0.2f" % Ceylan(0.5))
# 49.50
# >>> print("%0.2f" % Ceylan(1e3))
# 0.46
>>> print("%0.2f" % Ceylan(1e6))
0.26
This correlation dont return the expected vaues in paper for low Reynolds
numbers, possible a typo in paper
'''
if Re <= 0 or Re > 1e6:
raise NotImplementedError("Input out of range 0 < Re ≤ 1e6")
# Eq 15
K1 = 1 - 0.5*exp(0.182) + 10.11*Re**(-2/3)*exp(0.952*Re**-0.25) \
- 0.03859*Re**(-4/3)*exp(1.3*Re**(-0.5))
K2 = 0.037e-4*Re*exp(-0.125e-4*Re) - 0.116e-10*Re**2*exp(-0.444e-5*Re)
# Eq 14
Cd = K1 + K2
return Cd
[docs]
@refDoc(__doi__, [4])
def Almedeij(Re):
r'''Calculates drag coefficient of a smooth sphere using the method in
[4]_.
.. math::
\begin{align*}
C_d = \left(\frac{1}{(\phi_1 + \phi_2)^{-1} + (\phi_3)^{-1}} + \phi_4
\right)^{0.1} \\
{} \phi_1 = \left(\frac{24}{Re}\right)^{10} +
\left(\frac{21}{Re^{0.67}}\right)^{10} +
\left(\frac{4}{Re^{0.33}}\right)^{10} + 0.4^{10} \\
{} \phi_2 = \frac{1}{\left[(0.148 Re^{0.11})^{-10} +
(0.5)^{-10}\right]} \\
{} \phi_3 = \left(\frac{1.57x10^8} {Re^{1.625}}\right)^{10} \\
{} \phi_4 = \frac{1}{(6x10^{-17}Re^{2.63})^{-10} + (0.2)^{-10}}
\end{align*}
Parameters
----------
Re : float
Reynolds number of the sphere, [-]
Returns
-------
Cd : float
Drag coefficient [-]
Notes
-----
Raise :class:`NotImplementedError` if Re isn't in range Re ≤ 1e6
Examples
--------
There isn´t testing values but checking a value similar to Barati
correlation would be enough
>>> print("%0.0f" % Almedeij(0.002))
12000
>>> print("%0.2f" % Almedeij(1000))
0.44
'''
if Re <= 0 or Re > 1e6:
raise NotImplementedError("Input out of range 0 < Re ≤ 1e6")
f1 = (24/Re)**10 + (21/Re**0.67)**10 + (4/Re**0.33)**10 + 0.4**10
f2 = 1/((0.148*Re**0.11)**-10 + 0.5**-10)
f3 = (1.57e8*Re**-1.625)**10
f4 = 1/((6e-17*Re**2.63)**-10 + 0.2**-10)
Cd = (1/((f1 + f2)**-1 + f3**-1) + f4)**0.1
return Cd
[docs]
@refDoc(__doi__, [5])
def Morrison(Re):
r'''Calculates drag coefficient of a smooth sphere using the method in
[5]_.
.. math::
C_d = \frac{24}{Re}+\frac{2.6 Re/5}{1+\left(\frac{Re}{5}\right)^{1.52}}
+ \frac{0.411 \left(\frac{Re}{263.000}\right)^{-7.94}}
{1 + \left(\frac{Re}{263000}\right)^{-8}}
+ \frac{0.25 \left(\frac{Re}{10^6}\right)}
{1+\left(\frac{Re}{10^6}\right)}
Parameters
----------
Re : float
Reynolds number of the sphere, [-]
Returns
-------
Cd : float
Drag coefficient [-]
Notes
-----
Raise :class:`NotImplementedError` if Re isn't in range Re ≤ 1e6
Examples
--------
There isn´t testing values but checking a value similar to Barati
correlation would be enough
>>> print("%0.0f" % Morrison(0.002))
12000
>>> print("%0.2f" % Morrison(1000))
0.48
'''
if Re <= 0 or Re > 1e6:
raise NotImplementedError("Input out of range 0 < Re ≤ 1e6")
Cd = 24/Re + 2.6*Re/5/(1 + (Re/5)**1.52) \
+ 0.411*(Re/263000)**-7.94/(1 + (Re/263000)**-8) \
+ 0.25*Re/1e6/(1+Re/1e6)
return Cd
[docs]
@refDoc(__doi__, [6])
def Morsi(Re):
r'''Calculates drag coefficient of a smooth sphere using the method in
[6]_.
.. math::
C_d = \left\{ \begin{array}{ll}
\frac{24}{Re} & \mbox{if $Re<0.1$}\\
\frac{22.73}{Re}+\frac{0.0903}{Re^2}+3.69 & \mbox{if $0.1<Re<1$}\\
\frac{29.1667}{Re}-\frac{3.8889}{Re^2}+1.222 & \mbox{if $1<Re<10$}\\
\frac{46.5}{Re}-\frac{116.67}{Re^2}+0.6167 & \mbox{if $10<Re<100$}\\
\frac{98.33}{Re}-\frac{2778}{Re^2}+0.3644 & \mbox{if $100<Re<1000$}\\
\frac{148.62}{Re}-\frac{4.75x10^4}{Re^2}+0.3570 &
\mbox{if $1000<Re<5000$}\\
\frac{-490.546}{Re}+\frac{57.87x10^4}{Re^2}+0.46 &
\mbox{if $5000<Re<10000$}\\
\frac{-1662.5}{Re}+\frac{5.4167x10^6}{Re^2}+0.5191 &
\mbox{if $10000<Re<50000$}\end{array} \right.
Parameters
----------
Re : float
Reynolds number of the sphere, [-]
Returns
-------
Cd : float
Drag coefficient [-]
Notes
-----
Raise :class:`NotImplementedError` if Re isn't in range Re ≤ 5e5
Examples
--------
Selected values from Table 1, pag 195
>>> print("%0.2f" % Morsi(0.1))
240.02
>>> print("%0.2f" % Morsi(1000))
0.46
>>> print("%0.2f" % Morsi(5e4))
0.49
'''
if 0 <= Re < 0.1:
Cd = 24/Re
elif Re < 1:
Cd = 22.73/Re + 0.0903/Re**2 + 3.69
elif Re < 10:
Cd = 29.1667/Re - 3.8889/Re**2 + 1.222
elif Re < 100:
Cd = 46.5/Re - 116.67/Re**2 + 0.6167
elif Re < 1000:
Cd = 98.33/Re - 2778/Re**2 + 0.3644
elif Re < 5000:
Cd = 148.62/Re - 4.75e4/Re**2 + 0.357
elif Re < 10000:
Cd = -490.546/Re + 57.87e4/Re**2 + 0.46
elif Re <= 50000:
Cd = -1662.5/Re + 5.4167e6/Re**2 + 0.5191
else:
raise NotImplementedError("Input out of range 0 < Re < 5e5")
return Cd
[docs]
@refDoc(__doi__, [8, 7])
def Khan(Re, improved=True):
r'''Calculates drag coefficient of a smooth sphere using the method in
[8]_ including the improve in [7]_.
Original correlation:
.. math::
C_d = (2.25Re^{-0.31} + 0.36Re^{0.06})^{3.45}
Brown-Lawler improved version:
.. math::
C_d = (2.49Re^{-0.328} + 0.34Re^{0.067})^{3.18}
Parameters
----------
Re : float
Reynolds number of the sphere, [-]
improved : boolean
Use the improved version from Brown-Lawler
Returns
-------
Cd : float
Drag coefficient [-]
Notes
-----
Raise :class:`NotImplementedError` if Re isn't in range Re ≤ 3e5
Examples
--------
There isn´t testing values but checking a value similar to Barati
correlation would be enough
>>> print("%0.2f" % Khan(1000))
0.49
'''
if Re <= 0 or Re > 3e5:
raise NotImplementedError("Input out of range 0 < Re ≤ 3e5")
if improved:
Cd = (2.49*Re**-0.328 + 0.34*Re**0.067)**3.18
else:
# Eq 15a
Cd = (2.25*Re**-0.31 + 0.36*Re**0.06)**3.45
return Cd
[docs]
@refDoc(__doi__, [9, 7])
def Flemmer(Re, improved=True):
r'''Calculates drag coefficient of a smooth sphere using the method in
[9]_ including the improve in [7]_.
Original correlation:
.. math::
C_d = \frac{24}{Re}10^E
E = 0.261Re^{0.369}-0.105^{0.431} - \frac{0.124}{1+(\log Re)^2}
Brown-Lawler improved version:
.. math::
E = 0.383Re^{0.356}-0.207Re^{0.396} - \frac{0.143}{1+(\log Re)^2}
Parameters
----------
Re : float
Reynolds number of the sphere, [-]
improved : boolean
Use the improved version from Brown-Lawler
Returns
-------
Cd : float
Drag coefficient [-]
Notes
-----
Raise :class:`NotImplementedError` if Re isn't in range Re ≤ 3e5
Examples
--------
There isn´t testing values but checking a value similar to Barati
correlation would be enough
>>> print("%0.2f" % Flemmer(0.1))
247.90
>>> print("%0.2f" % Flemmer(1000))
0.45
>>> print("%0.2f" % Flemmer(5e4))
0.48
'''
if Re <= 0 or Re > 3e5:
raise NotImplementedError("Input out of range 0 < Re ≤ 3e5")
if improved:
E = 0.383*Re**0.356 - 0.207*Re**0.396 - 0.143/(1 + (log10(Re))**2)
else:
E = 0.261*Re**0.369 - 0.105*Re**0.431 - 0.124/(1 + (log10(Re))**2)
return 24/Re*10**E
[docs]
@refDoc(__doi__, [10, 7])
def Haider(Re, improved=True):
r'''Calculates drag coefficient of a smooth sphere using the method in
[10]_ including the improve in [7]_.
Original correlation:
.. math::
C_d = \frac{24}{Re} \left(1+0.1806Re^{0.6459}\right) +
\frac{0.4251}{1+\frac{6880.95}{Re}}
Brown-Lawler improved version:
.. math::
C_d = \frac{24}{Re} \left(1+0.15Re^{0.681}\right) +
\frac{0.407}{1+\frac{8710}{Re}}
Parameters
----------
Re : float
Reynolds number of the sphere, [-]
improved : boolean
Use the improved version from Brown-Lawler
Returns
-------
Cd : float
Drag coefficient [-]
Notes
-----
Raise :class:`NotImplementedError` if Re isn't in range Re ≤ 2.6e5
Examples
--------
There isn´t testing values but checking a value similar to Barati
correlation would be enough
>>> print("%0.2f" % Haider(0.1))
247.50
>>> print("%0.2f" % Haider(1000))
0.46
>>> print("%0.2f" % Haider(5e4))
0.46
'''
if Re <= 0 or Re > 2.6e5:
raise NotImplementedError("Input out of range 0 < Re ≤ 2.6e5")
if improved:
# Eq 19 in [7]_
Cd = 24/Re*(1 + 0.15*Re**0.681) + (0.407/(1 + 8710/Re))
else:
# Eq 6 in [10]_
Cd = 24/Re*(1 + 0.1806*Re**0.6459) + (0.4251/(1 + 6880.95/Re))
return Cd
[docs]
@refDoc(__doi__, [11, 7])
def Turton(Re, improved=True):
r'''Calculates drag coefficient of a smooth sphere using the method in
[11]_ including the improve in [7]_.
Original correlation:
.. math::
C_d = \frac{24}{Re} \left(1+0.173Re^{0.657}\right) +
\frac{0.413}{1+\frac{16300}{Re^{1.09}}}
Brown-Lawler improved version:
.. math::
C_d = \frac{24}{Re} \left(1+0.152Re^{0.677}\right) +
\frac{0.417}{1+\frac{5070}{Re^{0.94}}}
Parameters
----------
Re : float
Reynolds number of the sphere, [-]
improved : boolean
Use the improved version from Brown-Lawler
Returns
-------
Cd : float
Drag coefficient [-]
Notes
-----
Raise :class:`NotImplementedError` if Re isn't in range Re ≤ 2e5
Examples
--------
There isn´t testing values but checking a value similar to Barati
correlation would be enough
>>> print("%0.2f" % Turton(0.1))
247.67
>>> print("%0.2f" % Turton(1000))
0.46
>>> print("%0.2f" % Turton(5e4))
0.46
'''
if Re <= 0 or Re > 2e5:
raise NotImplementedError("Input out of range 0 < Re ≤ 2e5")
if improved:
# Eq 17 in [7]_
Cd = 24/Re*(1 + 0.152*Re**0.677) + (0.417/(1 + 5070/Re**0.94))
else:
# Eq 5 in [11]_
Cd = 24/Re*(1 + 0.173*Re**0.657) + (0.413/(1 + 16300/Re**1.09))
return Cd
[docs]
@refDoc(__doi__, [12])
def Concha(Re):
r'''Calculates drag coefficient of a smooth sphere using the method in
[12]_.
.. math::
C_d = 0.284153 \left(1+\frac{9.04}{Re^{1/2}}\right)^2
\sum_{\alpha} B_{\alpha}Re^{\alpha}
Parameters
----------
Re : float
Reynolds number of the sphere, [-]
Returns
-------
Cd : float
Drag coefficient [-]
Notes
-----
Raise :class:`NotImplementedError` if Re isn't in range Re ≤ 3e5
Examples
--------
Selected point from Table I
>>> print("%0.0f" % Concha(0.1))
239
>>> print("%0.2f" % Concha(1000))
0.46
>>> print("%0.2f" % Concha(3e5))
0.20
'''
if Re <= 0 or Re > 3e5:
raise NotImplementedError("Input out of range 0 < Re ≤ 3e5")
Bi = [9.620833e-1, 2.736461e-5, -3.938611e-10, 2.476861e-15,
-7.159345e-21, 7.437237e-27]
# Eq 13
Cd = 0.284153*(1+9.04/Re**0.5)**2 * sum(B*Re**i for i, B in enumerate(Bi))
return Cd
[docs]
@refDoc(__doi__, [13])
def Swamee(Re):
r'''Calculates drag coefficient of a smooth sphere using the method in
[13]_.
.. math::
C_d = 0.5\left\{16\left[\left(\frac{24}{Re}\right)^{1.6} +
\left(\frac{130}{Re}\right)^{0.72}\right]^{2.5} +
\left[\left(\frac{40000}{Re}\right)^2 + 1\right]^{-0.25}\right\}^{0.25}
Parameters
----------
Re : float
Reynolds number of the sphere, [-]
Returns
-------
Cd : float
Drag coefficient [-]
Notes
-----
Raise :class:`NotImplementedError` if Re isn't in range Re ≤ 1.5e5
Examples
--------
There isn´t testing values but checking a value similar to Barati
correlation would be enough
>>> print("%0.2f" % Swamee(0.1))
244.05
>>> print("%0.2f" % Swamee(1000))
0.44
>>> print("%0.2f" % Swamee(5e4))
0.48
'''
if Re <= 0 or Re > 1.5e5:
raise NotImplementedError("Input out of range 0 < Re ≤ 1.5e5")
# Eq 17
Cd = 0.5*(16*((24/Re)**1.6 + (130/Re)**0.72)**2.5
+ ((40000/Re)**2 + 1)**-0.25)**0.25
return Cd
[docs]
@refDoc(__doi__, [14])
def Cheng(Re):
r'''Calculates drag coefficient of a smooth sphere using the method in
[14]_.
.. math::
C_d = \frac{24}{Re}\left(1+0.27Re\right)^{0.43} +
0.47\left[1-\exp\left(-0.04Re^{0.38}\right)\right]
Parameters
----------
Re : float
Reynolds number of the sphere, [-]
Returns
-------
Cd : float
Drag coefficient [-]
Notes
-----
Raise :class:`NotImplementedError` if Re isn't in range Re ≤ 2e5
Examples
--------
There isn´t testing values but checking a value similar to Barati
correlation would be enough
>>> print("%0.2f" % Cheng(0.1))
242.77
>>> print("%0.2f" % Cheng(1000))
0.47
>>> print("%0.2f" % Cheng(5e4))
0.46
'''
if Re <= 0 or Re > 2e5:
raise NotImplementedError("Input out of range 0 < Re ≤ 2e5")
# Eq 1
Cd = 24/Re*(1 + 0.27*Re)**0.43 + 0.47*(1 - exp(-0.04*Re**0.38))
return Cd
[docs]
@refDoc(__doi__, [15])
def Terfous(Re):
r'''Calculates drag coefficient of a smooth sphere using the method in
[15]_.
.. math::
C_d = 2.689 + \frac{21.683}{Re} + \frac{0.131}{Re^2}
- \frac{10.616}{Re^{0.1}} + \frac{12.216}{Re^{0.2}}
Parameters
----------
Re : float
Reynolds number of the sphere, [-]
Returns
-------
Cd : float
Drag coefficient [-]
Notes
-----
Raise :class:`NotImplementedError` if Re isn't in range 0.1 ≤ Re ≤ 5e4
Examples
--------
There isn´t testing values but checking a value similar to Barati
correlation would be enough
>>> print("%0.2f" % Terfous(0.1))
238.62
>>> print("%0.2f" % Terfous(1000))
0.46
>>> print("%0.2f" % Terfous(5e4))
0.49
'''
if Re < 0.1 or Re > 2e5:
raise NotImplementedError("Input out of range 0.1 < Re ≤ 5e4")
# Eq 4
Cd = 2.689 + 21.683/Re + 0.131/Re**2 - 10.616/Re**0.1 + 12.216/Re**0.2
return Cd
[docs]
def Mikhailov(Re):
r'''Calculates drag coefficient of a smooth sphere using the method in
[16]_.
For 0.1 < Re < 10:
.. math::
C_d = \frac{3808\left[(1617933/2030) + (178861/1063)Re +
(1219/1084)Re^2\right]}
{681Re\left[(77531/422) + (13529/976)Re - (1/71154)Re^2\right]}
For 10 < Re < 1.183e5:
.. math::
C_d = \frac{777\left[(669806/875) + (114976/1155)Re +
(707/1380)Re^2\right]}
{646Re\left[(32869/952) + (924/643)Re - (1/385718)Re^2\right]}
Parameters
----------
Re : float
Reynolds number of the sphere, [-]
Returns
-------
Cd : float
Drag coefficient [-]
Notes
-----
Raise :class:`NotImplementedError` if Re isn't in range 0.1 ≤ Re ≤ 118300
Examples
--------
Selected points from Table 1, pag 434
>>> print("%0.2f" % Mikhailov(0.1))
245.85
>>> print("%0.2f" % Mikhailov(1))
27.35
>>> print("%0.3f" % Mikhailov(101))
1.064
>>> print("%0.4f" % Mikhailov(1e3))
0.5016
>>> print("%0.4f" % Mikhailov(1e5))
0.5241
'''
if 0.1 <= Re < 10:
Cd = 3808*((1617933/2030) + (178861/1063)*Re + (1219/1084)*Re**2) / \
(681*Re*((77531/422) + (13529/976)*Re - (1/71154)*Re**2))
elif Re < 118300:
# There are a typo in the last sum sign of equation
Cd = 777*((669806/875) + (114976/1155)*Re + (707/1380)*Re**2) / \
(646*Re*((32869/952) + (924/643)*Re - (1/385718)*Re**2))
else:
raise NotImplementedError("Input out of range 0.1 < Re ≤ 1.183e5")
return Cd
[docs]
def dragSphere(Re, method=None):
"""Function general for the drag coeficient for smooth spheres
Parameters
----------
Re : float
Reynolds number of the sphere, [-]
method : str
Name of method to use
Returns
-------
Cd : float
Drag coefficient [-]
"""
if method is None:
method = Clift
func = getattr(sys.modules[__name__], method)
try:
return func(Re)
except NotImplementedError:
return Clift(Re)
f_list = (Barati, Clift, Ceylan, Almedeij, Morrison, Morsi, Khan, Flemmer,
Haider, Turton, Concha, Swamee, Cheng, Terfous, Mikhailov)
