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Added several more turbulent friction factor in helical tube correlat…
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@CalebBell
CalebBell committed Apr 21, 2017
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269 changes: 263 additions & 6 deletions fluids/friction.py
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Original file line number Diff line number Diff line change
Expand Up @@ -47,7 +47,10 @@
'Brkic_2011_2', 'Fang_2011', 'Blasius', 'von_Karman',
'Prandtl_von_Karman_Nikuradse', 'helical_laminar_fd_White',
'helical_laminar_fd_Mori_Nakayama', 'helical_laminar_fd_Schmidt',
'helical_turbulent_fd_Schmidt', 'helical_turbulent_fd_Mori_Nakayama']
'helical_turbulent_fd_Schmidt', 'helical_turbulent_fd_Mori_Nakayama',
'helical_turbulent_fd_Prasad', 'helical_turbulent_fd_Czop',
'helical_turbulent_fd_Guo', 'helical_turbulent_fd_Ju',
'helical_turbulent_fd_Mandal_Nigam']



Expand Down Expand Up @@ -1797,7 +1800,7 @@ def helical_laminar_fd_White(Re, Di, Dc):
Parameters
----------
Re : float
Reynolds number with `D`=`Di`, [-]
Reynolds number with `D=Di`, [-]
Di : float
Inner diameter of the coil, [m]
Dc : float
Expand Down Expand Up @@ -1839,6 +1842,7 @@ def helical_laminar_fd_White(Re, Di, Dc):
De = 11.6
return fd/(1. - (1. - (11.6/De)**0.45)**(1./0.45))


def helical_laminar_fd_Mori_Nakayama(Re, Di, Dc):
r'''Calculates Darcy friction factor for a fluid flowing inside a curved
pipe such as a helical coil under laminar conditions, using the method of
Expand All @@ -1851,7 +1855,7 @@ def helical_laminar_fd_Mori_Nakayama(Re, Di, Dc):
Parameters
----------
Re : float
Reynolds number with `D`=`Di`, [-]
Reynolds number with `D=Di`, [-]
Di : float
Inner diameter of the coil, [m]
Dc : float
Expand Down Expand Up @@ -1911,7 +1915,7 @@ def helical_laminar_fd_Schmidt(Re, Di, Dc):
Parameters
----------
Re : float
Reynolds number with `D`=`Di`, [-]
Reynolds number with `D=Di`, [-]
Di : float
Inner diameter of the coil, [m]
Dc : float
Expand Down Expand Up @@ -1975,7 +1979,7 @@ def helical_turbulent_fd_Schmidt(Re, Di, Dc, roughness=0):
Parameters
----------
Re : float
Reynolds number with `D`=`Di`, [-]
Reynolds number with `D=Di`, [-]
Di : float
Inner diameter of the coil, [m]
Dc : float
Expand Down Expand Up @@ -2030,7 +2034,7 @@ def helical_turbulent_fd_Mori_Nakayama(Re, Di, Dc):
Parameters
----------
Re : float
Reynolds number with `D`=`Di`, [-]
Reynolds number with `D=Di`, [-]
Di : float
Inner diameter of the coil, [m]
Dc : float
Expand Down Expand Up @@ -2072,6 +2076,259 @@ def helical_turbulent_fd_Mori_Nakayama(Re, Di, Dc):
return 0.3*(Dc/Di)**-0.5*term*(1. + 0.112*term)


def helical_turbulent_fd_Prasad(Re, Di, Dc,roughness=0):
r'''Calculates Darcy friction factor for a fluid flowing inside a curved
pipe such as a helical coil under turbulent conditions, using the method of
Prasad [1]_, also shown in [2]_.
.. math::
f_{curv} = f_{\text{str,turb}}\left[1 + 0.18\left[Re\left(\frac{D_i}
{D_c}\right)^2\right]^{0.25}\right]
Parameters
----------
Re : float
Reynolds number with `D=Di`, [-]
Di : float
Inner diameter of the coil, [m]
Dc : float
Diameter of the helix/coil measured from the center of the tube on one
side to the center of the tube on the other side, [m]
roughness : float, optional
Roughness of pipe wall [m]
Returns
-------
fd : float
Darcy friction factor for a curved pipe [-]
Notes
-----
No range of validity was specified, but the experiments used were with
coil/tube diameter ratios of 17.24 and 34.9, hot water in the tube, and
:math:`1780 < Re < 59500`. At very low curvatures, converges on the
straight pipe result.
Examples
--------
>>> helical_turbulent_fd_Prasad(1E4, 0.01, .2)
0.043313098093994626
References
----------
.. [1] Prasad, B. V. S. S. S., D. H. Das, and A. K. Prabhakar. "Pressure
Drop, Heat Transfer and Performance of a Helically Coiled Tubular
Exchanger." Heat Recovery Systems and CHP 9, no. 3 (January 1, 1989):
249-56. doi:10.1016/0890-4332(89)90008-2.
.. [2] El-Genk, Mohamed S., and Timothy M. Schriener. "A Review and
Correlations for Convection Heat Transfer and Pressure Losses in
Toroidal and Helically Coiled Tubes." Heat Transfer Engineering 0, no. 0
(June 7, 2016): 1-28. doi:10.1080/01457632.2016.1194693.
'''
fd = friction_factor(Re=Re, eD=roughness/Di)
return fd*(1. + 0.18*(Re*(Di/Dc)**2)**0.25)


def helical_turbulent_fd_Czop (Re, Di, Dc):
r'''Calculates Darcy friction factor for a fluid flowing inside a curved
pipe such as a helical coil under turbulent conditions, using the method of
Czop [1]_, also shown in [2]_.
.. math::
f_{curv} = 0.096De^{-0.1517}
Parameters
----------
Re : float
Reynolds number with `D=Di`, [-]
Di : float
Inner diameter of the coil, [m]
Dc : float
Diameter of the helix/coil measured from the center of the tube on one
side to the center of the tube on the other side, [m]
Returns
-------
fd : float
Darcy friction factor for a curved pipe [-]
Notes
-----
Valid for :math:`2\times10^4 < Re < 1.5\times10^{5}`. Does not use a
straight pipe correlation, and so will not converge on the
straight pipe result at very low curvature.
Examples
--------
>>> helical_turbulent_fd_Czop(1E4, 0.01, .2)
0.02979575250574106
References
----------
.. [1] Czop, V., D. Barbier, and S. Dong. "Pressure Drop, Void Fraction and
Shear Stress Measurements in an Adiabatic Two-Phase Flow in a Coiled
Tube." Nuclear Engineering and Design 149, no. 1 (September 1, 1994):
323-33. doi:10.1016/0029-5493(94)90298-4.
.. [2] El-Genk, Mohamed S., and Timothy M. Schriener. "A Review and
Correlations for Convection Heat Transfer and Pressure Losses in
Toroidal and Helically Coiled Tubes." Heat Transfer Engineering 0, no. 0
(June 7, 2016): 1-28. doi:10.1080/01457632.2016.1194693.
'''
De = Dean(Re=Re, Di=Di, D=Dc)
return 0.096*De**-0.1517


def helical_turbulent_fd_Guo(Re, Di, Dc):
r'''Calculates Darcy friction factor for a fluid flowing inside a curved
pipe such as a helical coil under turbulent conditions, using the method of
Guo [1]_, also shown in [2]_.
.. math::
f_{curv} = 0.638Re^{-0.15}\left(\frac{D_i}{D_c}\right)^{0.51}
Parameters
----------
Re : float
Reynolds number with `D=Di`, [-]
Di : float
Inner diameter of the coil, [m]
Dc : float
Diameter of the helix/coil measured from the center of the tube on one
side to the center of the tube on the other side, [m]
Returns
-------
fd : float
Darcy friction factor for a curved pipe [-]
Notes
-----
Valid for :math:`2\times10^4 < Re < 1.5\times10^{5}`. Does not use a
straight pipe correlation, and so will not converge on the
straight pipe result at very low curvature.
Examples
--------
>>> helical_turbulent_fd_Guo(2E5, 0.01, .2)
0.022189161013253147
References
----------
.. [1] Guo, Liejin, Ziping Feng, and Xuejun Chen. "An Experimental
Investigation of the Frictional Pressure Drop of Steam–water Two-Phase
Flow in Helical Coils." International Journal of Heat and Mass Transfer
44, no. 14 (July 2001): 2601-10. doi:10.1016/S0017-9310(00)00312-4.
.. [2] El-Genk, Mohamed S., and Timothy M. Schriener. "A Review and
Correlations for Convection Heat Transfer and Pressure Losses in
Toroidal and Helically Coiled Tubes." Heat Transfer Engineering 0, no. 0
(June 7, 2016): 1-28. doi:10.1080/01457632.2016.1194693.
'''
return 0.638*Re**-0.15*(Di/Dc)**0.51


def helical_turbulent_fd_Ju(Re, Di, Dc,roughness=0):
r'''Calculates Darcy friction factor for a fluid flowing inside a curved
pipe such as a helical coil under turbulent conditions, using the method of
Ju et al. [1]_, also shown in [2]_.
.. math::
f_{curv} = f_{\text{str,turb}}\left[1 +0.11Re^{0.23}\left(\frac{D_i}
{D_c}\right)^{0.14}\right]
Parameters
----------
Re : float
Reynolds number with `D=Di`, [-]
Di : float
Inner diameter of the coil, [m]
Dc : float
Diameter of the helix/coil measured from the center of the tube on one
side to the center of the tube on the other side, [m]
roughness : float, optional
Roughness of pipe wall [m]
Returns
-------
fd : float
Darcy friction factor for a curved pipe [-]
Notes
-----
Claimed to be valid for all turbulent conditions with :math:`De>11.6`.
At very low curvatures, converges on the straight pipe result.
Examples
--------
>>> helical_turbulent_fd_Ju(1E4, 0.01, .2)
0.04945959480770937
References
----------
.. [1] Ju, Huaiming, Zhiyong Huang, Yuanhui Xu, Bing Duan, and Yu Yu.
"Hydraulic Performance of Small Bending Radius Helical Coil-Pipe."
Journal of Nuclear Science and Technology 38, no. 10 (October 1, 2001):
826-31. doi:10.1080/18811248.2001.9715102.
.. [2] El-Genk, Mohamed S., and Timothy M. Schriener. "A Review and
Correlations for Convection Heat Transfer and Pressure Losses in
Toroidal and Helically Coiled Tubes." Heat Transfer Engineering 0, no. 0
(June 7, 2016): 1-28. doi:10.1080/01457632.2016.1194693.
'''
fd = friction_factor(Re=Re, eD=roughness/Di)
return fd*(1. + 0.11*Re**0.23*(Di/Dc)**0.14)


def helical_turbulent_fd_Mandal_Nigam(Re, Di, Dc, roughness=0):
r'''Calculates Darcy friction factor for a fluid flowing inside a curved
pipe such as a helical coil under turbulent conditions, using the method of
Mandal and Nigam [1]_, also shown in [2]_.
.. math::
f_{curv} = f_{\text{str,turb}} [1 + 0.03{De}^{0.27}]
Parameters
----------
Re : float
Reynolds number with `D=Di`, [-]
Di : float
Inner diameter of the coil, [m]
Dc : float
Diameter of the helix/coil measured from the center of the tube on one
side to the center of the tube on the other side, [m]
roughness : float, optional
Roughness of pipe wall [m]
Returns
-------
fd : float
Darcy friction factor for a curved pipe [-]
Notes
-----
Claimed to be valid for all turbulent conditions with
:math:`2500 < De < 15000`. At very low curvatures, converges on the
straight pipe result.
Examples
--------
>>> helical_turbulent_fd_Mandal_Nigam(1E4, 0.01, .2)
0.03831658117115902
References
----------
.. [1] Mandal, Monisha Mridha, and K. D. P. Nigam. "Experimental Study on
Pressure Drop and Heat Transfer of Turbulent Flow in Tube in Tube
Helical Heat Exchanger." Industrial & Engineering Chemistry Research 48,
no. 20 (October 21, 2009): 9318-24. doi:10.1021/ie9002393.
.. [2] El-Genk, Mohamed S., and Timothy M. Schriener. "A Review and
Correlations for Convection Heat Transfer and Pressure Losses in
Toroidal and Helically Coiled Tubes." Heat Transfer Engineering 0, no. 0
(June 7, 2016): 1-28. doi:10.1080/01457632.2016.1194693.
'''
De = Dean(Re=Re, Di=Di, D=Dc)
fd = friction_factor(Re=Re, eD=roughness/Di)
return fd*(1. + 0.03*De**0.27)


# Data from the Handbook of Hydraulic Resistance, 4E, in format (min, max, avg)
# roughness in m; may have one, two, or three of the values.
seamless_other_metals = {'Commercially smooth': (1.5E-6, 1.0E-5, None)}
Expand Down
27 changes: 27 additions & 0 deletions tests/test_friction.py
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Original file line number Diff line number Diff line change
Expand Up @@ -182,3 +182,30 @@ def test_helical_turbulent_fd_Mori_Nakayama():
# but is otherwise correct.
fd = helical_turbulent_fd_Mori_Nakayama(1E4, 0.01, .2)
assert_allclose(fd, 0.037311802071379796)


def test_helical_turbulent_fd_Prasad():
# Checks out, formula in [2]_ is the same as in [1]_!
fd = helical_turbulent_fd_Prasad(1E4, 0.01, .2)
assert_allclose(fd, 0.043313098093994626)
assert_allclose(helical_turbulent_fd_Prasad(1E4, 0.01, 1E20), friction_factor(1E4))

def test_helical_turbulent_fd_Czop():
fd = helical_turbulent_fd_Czop(1E4, 0.01, .2)
assert_allclose(fd, 0.02979575250574106)

def test_helical_turbulent_fd_Guo():
fd = helical_turbulent_fd_Guo(2E5, 0.01, .2)
assert_allclose(fd, 0.022189161013253147)


def test_helical_turbulent_fd_Ju():
fd = helical_turbulent_fd_Ju(1E4, 0.01, .2)
assert_allclose(fd, 0.04945959480770937)
assert_allclose(helical_turbulent_fd_Ju(1E4, 0.01, 1E80), friction_factor(1E4))


def test_helical_turbulent_fd_Mandal_Nigam():
fd = helical_turbulent_fd_Mandal_Nigam(1E4, 0.01, .2)
assert_allclose(fd, 0.03831658117115902)
assert_allclose(helical_turbulent_fd_Mandal_Nigam(1E4, 0.01, 1E80), friction_factor(1E4))

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