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Add several models for calculating possible definitions for two-phase liquid-gas viscosity
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fluids/two_phase_voidage.py

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@@ -34,7 +34,8 @@
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'Nicklin_Wilkes_Davidson', 'Gregory_Scott', 'Dix',
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'Sun_Duffey_Peng', 'Xu_Fang_voidage', 'Woldesemayat_Ghajar',
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'Lockhart_Martinelli_Xtt', 'two_phase_voidage_experimental',
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'density_two_phase']
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'density_two_phase', 'Beattie_Whalley', 'McAdams', 'Cicchitti',
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'Lin_Kwok', 'Fourar_Bories']
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### Models based on slip ratio
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@@ -407,7 +408,7 @@ def homogeneous(x, rhol, rhog):
407408
Upward Inclined Pipes." International Journal of Multiphase Flow 33,
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no. 4 (April 2007): 347-370. doi:10.1016/j.ijmultiphaseflow.2006.09.004.
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'''
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return 1./(1 + (1-x)/x*(rhog/rhol))
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return 1./(1. + (1-x)/x*(rhog/rhol))
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def Chisholm_Armand(x, rhol, rhog):
@@ -1928,3 +1929,344 @@ def two_phase_voidage_experimental(rho_lg, rhol, rhog):
19281929
no. 1 (October 1, 2008): 106-13.
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'''
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return (rho_lg - rhol)/(rhog - rhol)
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### two-phase viscosity models
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def Beattie_Whalley(x, mul, mug, rhol, rhog):
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r'''Calculates a suggested definition for liquid-gas two-phase flow
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viscosity in internal pipe flow according to the form in [1]_ and shown
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in [2]_ and [3]_.
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.. math::
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\mu_m = \mu_l(1-\alpha_m)(1 + 2.5\alpha_m) + \mu_g\alpha_m
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\alpha_m = \frac{1}{1 + \left(\frac{1-x}{x}\right)\frac{\rho_g}{\rho_l}}
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\text{(homogeneous model)}
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Parameters
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----------
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x : float
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Quality of the gas-liquid flow, [-]
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mul : float
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Viscosity of liquid, [Pa*s]
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mug : float
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Viscosity of gas, [Pa*s]
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rhol : float
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Density of the liquid [kg/m^3]
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rhog : float
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Density of the gas [kg/m^3]
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Returns
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-------
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mu_lg : float
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Liquid-gas viscosity (**a suggested definition, potentially useful
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for empirical work only!**) [Pa*s]
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Notes
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-----
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This model converges to the liquid or gas viscosity as the quality
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approaches either limits.
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Examples
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--------
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>>> Beattie_Whalley(x=0.4, mul=1E-3, mug=1E-5, rhol=850, rhog=1.2)
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1.7363806909512365e-05
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References
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----------
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.. [1] Beattie, D. R. H., and P. B. Whalley. "A Simple Two-Phase Frictional
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Pressure Drop Calculation Method." International Journal of Multiphase
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Flow 8, no. 1 (February 1, 1982): 83-87.
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doi:10.1016/0301-9322(82)90009-X.
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.. [2] Awad, M. M., and Y. S. Muzychka. "Effective Property Models for
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Homogeneous Two-Phase Flows." Experimental Thermal and Fluid Science 33,
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no. 1 (October 1, 2008): 106-13.
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.. [3] Kim, Sung-Min, and Issam Mudawar. "Review of Databases and
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Predictive Methods for Pressure Drop in Adiabatic, Condensing and
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Boiling Mini/Micro-Channel Flows." International Journal of Heat and
1989+
Mass Transfer 77 (October 2014): 74-97.
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doi:10.1016/j.ijheatmasstransfer.2014.04.035.
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'''
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alpha = homogeneous(x, rhol, rhog)
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return mul*(1. - alpha)*(1. + 2.5*alpha) + mug*alpha
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def McAdams(x, mul, mug):
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r'''Calculates a suggested definition for liquid-gas two-phase flow
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viscosity in internal pipe flow according to the form in [1]_ and shown
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in [2]_ and [3]_.
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.. math::
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\mu_m = \left(\frac{x}{\mu_g} + \frac{1-x}{\mu_l}\right)^{-1}
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Parameters
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----------
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x : float
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Quality of the gas-liquid flow, [-]
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mul : float
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Viscosity of liquid, [Pa*s]
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mug : float
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Viscosity of gas, [Pa*s]
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Returns
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-------
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mu_lg : float
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Liquid-gas viscosity (**a suggested definition, potentially useful
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for empirical work only!**) [Pa*s]
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Notes
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-----
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This model converges to the liquid or gas viscosity as the quality
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approaches either limits.
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2024+
[3]_ states this is the most common definition of two-phase liquid-gas
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viscosity.
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Examples
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--------
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>>> McAdams(x=0.4, mul=1E-3, mug=1E-5)
2030+
2.4630541871921184e-05
2031+
2032+
References
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----------
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.. [1] McAdams, W. H. "Vaporization inside Horizontal Tubes-II Benzene-Oil
2035+
Mixtures." Trans. ASME 39 (1949): 39-48.
2036+
.. [2] Awad, M. M., and Y. S. Muzychka. "Effective Property Models for
2037+
Homogeneous Two-Phase Flows." Experimental Thermal and Fluid Science 33,
2038+
no. 1 (October 1, 2008): 106-13.
2039+
.. [3] Kim, Sung-Min, and Issam Mudawar. "Review of Databases and
2040+
Predictive Methods for Pressure Drop in Adiabatic, Condensing and
2041+
Boiling Mini/Micro-Channel Flows." International Journal of Heat and
2042+
Mass Transfer 77 (October 2014): 74-97.
2043+
doi:10.1016/j.ijheatmasstransfer.2014.04.035.
2044+
'''
2045+
return 1./(x/mug + (1. - x)/mul)
2046+
2047+
2048+
def Cicchitti(x, mul, mug):
2049+
r'''Calculates a suggested definition for liquid-gas two-phase flow
2050+
viscosity in internal pipe flow according to the form in [1]_ and shown
2051+
in [2]_ and [3]_.
2052+
2053+
.. math::
2054+
\mu_m = x\mu_g + (1-x)\mu_l
2055+
2056+
Parameters
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----------
2058+
x : float
2059+
Quality of the gas-liquid flow, [-]
2060+
mul : float
2061+
Viscosity of liquid, [Pa*s]
2062+
mug : float
2063+
Viscosity of gas, [Pa*s]
2064+
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Returns
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-------
2067+
mu_lg : float
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Liquid-gas viscosity (**a suggested definition, potentially useful
2069+
for empirical work only!**) [Pa*s]
2070+
2071+
Notes
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-----
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This model converges to the liquid or gas viscosity as the quality
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approaches either limits.
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Examples
2077+
--------
2078+
>>> Cicchitti(x=0.4, mul=1E-3, mug=1E-5)
2079+
0.0006039999999999999
2080+
2081+
References
2082+
----------
2083+
.. [1] Cicchitti, A., C. Lombardi, M. Silvestri, G. Soldaini, and R.
2084+
Zavattarelli. "Two-Phase Cooling Experiments: Pressure Drop, Heat
2085+
Transfer and Burnout Measurements." Centro Informazioni Studi
2086+
Esperienze, Milan, January 1, 1959.
2087+
.. [2] Awad, M. M., and Y. S. Muzychka. "Effective Property Models for
2088+
Homogeneous Two-Phase Flows." Experimental Thermal and Fluid Science 33,
2089+
no. 1 (October 1, 2008): 106-13.
2090+
.. [3] Kim, Sung-Min, and Issam Mudawar. "Review of Databases and
2091+
Predictive Methods for Pressure Drop in Adiabatic, Condensing and
2092+
Boiling Mini/Micro-Channel Flows." International Journal of Heat and
2093+
Mass Transfer 77 (October 2014): 74-97.
2094+
doi:10.1016/j.ijheatmasstransfer.2014.04.035.
2095+
'''
2096+
return x*mug + (1. - x)*mul
2097+
2098+
2099+
def Lin_Kwok(x, mul, mug):
2100+
r'''Calculates a suggested definition for liquid-gas two-phase flow
2101+
viscosity in internal pipe flow according to the form in [1]_ and shown
2102+
in [2]_ and [3]_.
2103+
2104+
.. math::
2105+
\mu_m = \frac{\mu_l \mu_g}{\mu_g + x^{1.4}(\mu_l - \mu_g)}
2106+
2107+
Parameters
2108+
----------
2109+
x : float
2110+
Quality of the gas-liquid flow, [-]
2111+
mul : float
2112+
Viscosity of liquid, [Pa*s]
2113+
mug : float
2114+
Viscosity of gas, [Pa*s]
2115+
2116+
Returns
2117+
-------
2118+
mu_lg : float
2119+
Liquid-gas viscosity (**a suggested definition, potentially useful
2120+
for empirical work only!**) [Pa*s]
2121+
2122+
Notes
2123+
-----
2124+
This model converges to the liquid or gas viscosity as the quality
2125+
approaches either limits.
2126+
2127+
Examples
2128+
--------
2129+
>>> Lin_Kwok(x=0.4, mul=1E-3, mug=1E-5)
2130+
3.515119398126066e-05
2131+
2132+
References
2133+
----------
2134+
.. [1] Lin, S., C. C. K. Kwok, R. -Y. Li, Z. -H. Chen, and Z. -Y. Chen.
2135+
"Local Frictional Pressure Drop during Vaporization of R-12 through
2136+
Capillary Tubes." International Journal of Multiphase Flow 17, no. 1
2137+
(January 1, 1991): 95-102. doi:10.1016/0301-9322(91)90072-B.
2138+
.. [2] Awad, M. M., and Y. S. Muzychka. "Effective Property Models for
2139+
Homogeneous Two-Phase Flows." Experimental Thermal and Fluid Science 33,
2140+
no. 1 (October 1, 2008): 106-13.
2141+
'''
2142+
return mul*mug/(mug + x**1.4*(mul - mug))
2143+
2144+
2145+
def Fourar_Bories(x, mul, mug, rhol, rhog):
2146+
r'''Calculates a suggested definition for liquid-gas two-phase flow
2147+
viscosity in internal pipe flow according to the form in [1]_ and shown
2148+
in [2]_ and [3]_.
2149+
2150+
.. math::
2151+
\mu_m = \rho_m\left(\sqrt{x\nu_g} + \sqrt{(1-x)\nu_l}\right)^2
2152+
2153+
Parameters
2154+
----------
2155+
x : float
2156+
Quality of the gas-liquid flow, [-]
2157+
mul : float
2158+
Viscosity of liquid, [Pa*s]
2159+
mug : float
2160+
Viscosity of gas, [Pa*s]
2161+
rhol : float
2162+
Density of the liquid, [kg/m^3]
2163+
rhog : float
2164+
Density of the gas, [kg/m^3]
2165+
2166+
Returns
2167+
-------
2168+
mu_lg : float
2169+
Liquid-gas viscosity (**a suggested definition, potentially useful
2170+
for empirical work only!**) [Pa*s]
2171+
2172+
Notes
2173+
-----
2174+
This model converges to the liquid or gas viscosity as the quality
2175+
approaches either limits.
2176+
2177+
This was first expressed in the equalivalent form as follows:
2178+
2179+
.. math::
2180+
\mu_m = \rho_m\left(x\nu_g + (1-x)\nu_l + 2\sqrt{x(1-x)\nu_g\nu_l}
2181+
\right)
2182+
2183+
Examples
2184+
--------
2185+
>>> Fourar_Bories(x=0.4, mul=1E-3, mug=1E-5, rhol=850, rhog=1.2)
2186+
2.127617150298565e-05
2187+
2188+
References
2189+
----------
2190+
.. [1] Fourar, M., and S. Bories. "Experimental Study of Air-Water
2191+
Two-Phase Flow through a Fracture (Narrow Channel)." International
2192+
Journal of Multiphase Flow 21, no. 4 (August 1, 1995): 621-37.
2193+
doi:10.1016/0301-9322(95)00005-I.
2194+
.. [2] Awad, M. M., and Y. S. Muzychka. "Effective Property Models for
2195+
Homogeneous Two-Phase Flows." Experimental Thermal and Fluid Science 33,
2196+
no. 1 (October 1, 2008): 106-13.
2197+
.. [3] Aung, NZ, and T. Yuwono. "Evaluation of Mixture Viscosity Models in
2198+
the Prediction of Two-Phase Flow Pressure Drops." ASEAN Journal on
2199+
Science and Technology for Development 29, no. 2 (2012).
2200+
'''
2201+
rhom = 1./(x/rhog + (1. - x)/rhol)
2202+
nul = mul/rhol # = nu_mu_converter(rho=rhol, mu=mul)
2203+
nug = mug/rhog # = nu_mu_converter(rho=rhog, mu=mug)
2204+
return rhom*((x*nug)**0.5 + ((1. - x)*nul)**0.5)**2
2205+
2206+
2207+
def Duckler(x, mul, mug, rhol, rhog):
2208+
r'''Calculates a suggested definition for liquid-gas two-phase flow
2209+
viscosity in internal pipe flow according to the form in [1]_ and shown
2210+
in [2]_, [3]_, and [4]_.
2211+
2212+
.. math::
2213+
\mu_m = \frac{\frac{x\mu_g}{\rho_g} + \frac{(1-x)\mu_l}{\rho_l} }
2214+
{\frac{x}{\rho_g} + \frac{(1-x)}{\rho_l} }
2215+
2216+
Parameters
2217+
----------
2218+
x : float
2219+
Quality of the gas-liquid flow, [-]
2220+
mul : float
2221+
Viscosity of liquid, [Pa*s]
2222+
mug : float
2223+
Viscosity of gas, [Pa*s]
2224+
rhol : float
2225+
Density of the liquid, [kg/m^3]
2226+
rhog : float
2227+
Density of the gas, [kg/m^3]
2228+
2229+
Returns
2230+
-------
2231+
mu_lg : float
2232+
Liquid-gas viscosity (**a suggested definition, potentially useful
2233+
for empirical work only!**) [Pa*s]
2234+
2235+
Notes
2236+
-----
2237+
This model converges to the liquid or gas viscosity as the quality
2238+
approaches either limits.
2239+
2240+
This has also been expressed in the following form:
2241+
2242+
.. math::
2243+
\mu_m = \rho_m \left[x\left(\frac{\mu_g}{\rho_g}\right)
2244+
+ (1 - x)\left(\frac{\mu_l}{\rho_l}\right)\right]
2245+
2246+
According to the homogeneous definition of two-phase density.
2247+
2248+
Examples
2249+
--------
2250+
>>> Duckler(x=0.4, mul=1E-3, mug=1E-5, rhol=850, rhog=1.2)
2251+
1.2092040385066917e-05
2252+
2253+
References
2254+
----------
2255+
.. [1] Fourar, M., and S. Bories. "Experimental Study of Air-Water
2256+
Two-Phase Flow through a Fracture (Narrow Channel)." International
2257+
Journal of Multiphase Flow 21, no. 4 (August 1, 1995): 621-37.
2258+
doi:10.1016/0301-9322(95)00005-I.
2259+
.. [2] Awad, M. M., and Y. S. Muzychka. "Effective Property Models for
2260+
Homogeneous Two-Phase Flows." Experimental Thermal and Fluid Science 33,
2261+
no. 1 (October 1, 2008): 106-13.
2262+
.. [3] Kim, Sung-Min, and Issam Mudawar. "Review of Databases and
2263+
Predictive Methods for Pressure Drop in Adiabatic, Condensing and
2264+
Boiling Mini/Micro-Channel Flows." International Journal of Heat and
2265+
Mass Transfer 77 (October 2014): 74-97.
2266+
doi:10.1016/j.ijheatmasstransfer.2014.04.035.
2267+
.. [4] Aung, NZ, and T. Yuwono. "Evaluation of Mixture Viscosity Models in
2268+
the Prediction of Two-Phase Flow Pressure Drops." ASEAN Journal on
2269+
Science and Technology for Development 29, no. 2 (2012).
2270+
'''
2271+
return (x*mug/rhog + (1. - x)*mul/rhol)/(x/rhog + (1. - x)/rhol)
2272+

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