Twophase flow voidage (fluids.two_phase_voidage)¶

fluids.two_phase_voidage.
Thom
(x, rhol, rhog, mul, mug)[source]¶ Calculates void fraction in twophase flow according to the model of [1] as given in [2].
\[\alpha = \left[1 + \left(\frac{1x}{x}\right)\left(\frac{\rho_g} {\rho_l}\right)^{0.89}\left(\frac{\mu_l}{\mu_g}\right)^{0.18} \right]^{1}\]Parameters:  x : float
Quality at the specific tube interval []
 rhol : float
Density of the liquid [kg/m^3]
 rhog : float
Density of the gas [kg/m^3]
 mul : float
Viscosity of liquid [Pa*s]
 mug : float
Viscosity of gas [Pa*s]
Returns:  alpha : float
Void fraction (area of gas / total area of channel), []
Notes
Based on experimental data for boiling of water. [3] presents a slightly different model. However, its results are almost identical. A comparison can be found in the unit tests. Neither expression was found in [1] in a brief review.
References
[1] (1, 2, 3) Thom, J. R. S. “Prediction of Pressure Drop during Forced Circulation Boiling of Water.” International Journal of Heat and Mass Transfer 7, no. 7 (July 1, 1964): 70924. doi:10.1016/00179310(64)90002X. [2] (1, 2) Xu, Yu, and Xiande Fang. “Correlations of Void Fraction for Two Phase Refrigerant Flow in Pipes.” Applied Thermal Engineering 64, no. 12 (March 2014): 242–51. doi:10.1016/j.applthermaleng.2013.12.032. [3] (1, 2) Dalkilic, A. S., S. Laohalertdecha, and S. Wongwises. “Effect of Void Fraction Models on the TwoPhase Friction Factor of R134a during Condensation in Vertical Downward Flow in a Smooth Tube.” International Communications in Heat and Mass Transfer 35, no. 8 (October 2008): 92127. doi:10.1016/j.icheatmasstransfer.2008.04.001. Examples
>>> Thom(.4, 800, 2.5, 1E3, 1E5) 0.9801482164042417

fluids.two_phase_voidage.
Zivi
(x, rhol, rhog)[source]¶ Calculates void fraction in twophase flow according to the model of [1] as given in [2] and [3].
\[\alpha = \left[1 + \left(\frac{1x}{x}\right) \left(\frac{\rho_g}{\rho_l}\right)^{2/3}\right]^{1}\]Parameters:  x : float
Quality at the specific tube interval []
 rhol : float
Density of the liquid [kg/m^3]
 rhog : float
Density of the gas [kg/m^3]
Returns:  alpha : float
Void fraction (area of gas / total area of channel), []
Notes
Based on experimental data for boiling of water. More complicated variants of this are also in [1].
References
[1] (1, 2, 3) Zivi, S. M. “Estimation of SteadyState Steam VoidFraction by Means of the Principle of Minimum Entropy Production.” Journal of Heat Transfer 86, no. 2 (May 1, 1964): 24751. doi:10.1115/1.3687113. [2] (1, 2) Xu, Yu, and Xiande Fang. “Correlations of Void Fraction for Two Phase Refrigerant Flow in Pipes.” Applied Thermal Engineering 64, no. 12 (March 2014): 242–51. doi:10.1016/j.applthermaleng.2013.12.032. [3] (1, 2) Dalkilic, A. S., S. Laohalertdecha, and S. Wongwises. “Effect of Void Fraction Models on the TwoPhase Friction Factor of R134a during Condensation in Vertical Downward Flow in a Smooth Tube.” International Communications in Heat and Mass Transfer 35, no. 8 (October 2008): 92127. doi:10.1016/j.icheatmasstransfer.2008.04.001. Examples
>>> Zivi(.4, 800, 2.5) 0.9689339909056356

fluids.two_phase_voidage.
Smith
(x, rhol, rhog)[source]¶ Calculates void fraction in twophase flow according to the model of [1], also given in [2] and [3].
\[\alpha = \left\{1 + \left(\frac{1x}{x}\right) \left(\frac{\rho_g}{\rho_l}\right)\left[K+(1K) \sqrt{\frac{\frac{\rho_l}{\rho_g} + K\left(\frac{1x}{x}\right)} {1 + K\left(\frac{1x}{x}\right)}}\right] \right\}^{1}\]Parameters:  x : float
Quality at the specific tube interval []
 rhol : float
Density of the liquid [kg/m^3]
 rhog : float
Density of the gas [kg/m^3]
Returns:  alpha : float
Void fraction (area of gas / total area of channel), []
Notes
[1] is an easy to read paper and has been reviewed. The form of the expression here is rearranged somewhat differently than in [1] but has been verified to be numerically equivalent. The form of this in [3] is missing a square root on a bracketed term; this appears in multiple papers by the authors.
References
[1] (1, 2, 3, 4) Smith, S. L. “Void Fractions in TwoPhase Flow: A Correlation Based upon an Equal Velocity Head Model.” Proceedings of the Institution of Mechanical Engineers 184, no. 1 (June 1, 1969): 64764. doi:10.1243/PIME_PROC_1969_184_051_02. [2] (1, 2) Xu, Yu, and Xiande Fang. “Correlations of Void Fraction for Two Phase Refrigerant Flow in Pipes.” Applied Thermal Engineering 64, no. 12 (March 2014): 242–51. doi:10.1016/j.applthermaleng.2013.12.032. [3] (1, 2, 3) Dalkilic, A. S., S. Laohalertdecha, and S. Wongwises. “Effect of Void Fraction Models on the TwoPhase Friction Factor of R134a during Condensation in Vertical Downward Flow in a Smooth Tube.” International Communications in Heat and Mass Transfer 35, no. 8 (October 2008): 92127. doi:10.1016/j.icheatmasstransfer.2008.04.001. Examples
>>> Smith(.4, 800, 2.5) 0.959981235534199

fluids.two_phase_voidage.
Fauske
(x, rhol, rhog)[source]¶ Calculates void fraction in twophase flow according to the model of [1], as given in [2] and [3].
\[\alpha = \left[1 + \left(\frac{1x}{x}\right) \left(\frac{\rho_g}{\rho_l}\right)^{0.5}\right]^{1}\]Parameters:  x : float
Quality at the specific tube interval []
 rhol : float
Density of the liquid [kg/m^3]
 rhog : float
Density of the gas [kg/m^3]
Returns:  alpha : float
Void fraction (area of gas / total area of channel), []
Notes
[1] has not been reviewed. However, both [2] and [3] present it the same way.
References
[1] (1, 2, 3) Fauske, H., Critical twophase, steamwater flows, in: Heat Transfer and Fluid Mechanics Institute 1961: Proceedings. Stanford University Press, 1961, p. 7989. [2] (1, 2, 3) Xu, Yu, and Xiande Fang. “Correlations of Void Fraction for Two Phase Refrigerant Flow in Pipes.” Applied Thermal Engineering 64, no. 12 (March 2014): 242–51. doi:10.1016/j.applthermaleng.2013.12.032. [3] (1, 2, 3) Dalkilic, A. S., S. Laohalertdecha, and S. Wongwises. “Effect of Void Fraction Models on the TwoPhase Friction Factor of R134a during Condensation in Vertical Downward Flow in a Smooth Tube.” International Communications in Heat and Mass Transfer 35, no. 8 (October 2008): 92127. doi:10.1016/j.icheatmasstransfer.2008.04.001. Examples
>>> Fauske(.4, 800, 2.5) 0.9226347262627932

fluids.two_phase_voidage.
Chisholm_voidage
(x, rhol, rhog)[source]¶ Calculates void fraction in twophase flow according to the model of [1], as given in [2] and [3].
\[\alpha = \left[1 + \left(\frac{1x}{x}\right)\left(\frac{\rho_g} {\rho_l}\right)\sqrt{1  x\left(1\frac{\rho_l}{\rho_g}\right)} \right]^{1}\]Parameters:  x : float
Quality at the specific tube interval []
 rhol : float
Density of the liquid [kg/m^3]
 rhog : float
Density of the gas [kg/m^3]
Returns:  alpha : float
Void fraction (area of gas / total area of channel), []
Notes
[1] has not been reviewed. However, both [2] and [3] present it the same way.
References
[1] (1, 2, 3) Chisholm, D. “Pressure Gradients due to Friction during the Flow of Evaporating TwoPhase Mixtures in Smooth Tubes and Channels.” International Journal of Heat and Mass Transfer 16, no. 2 (February 1, 1973): 34758. doi:10.1016/00179310(73)90063X. [2] (1, 2, 3) Xu, Yu, and Xiande Fang. “Correlations of Void Fraction for Two Phase Refrigerant Flow in Pipes.” Applied Thermal Engineering 64, no. 12 (March 2014): 242–51. doi:10.1016/j.applthermaleng.2013.12.032. [3] (1, 2, 3) Dalkilic, A. S., S. Laohalertdecha, and S. Wongwises. “Effect of Void Fraction Models on the TwoPhase Friction Factor of R134a during Condensation in Vertical Downward Flow in a Smooth Tube.” International Communications in Heat and Mass Transfer 35, no. 8 (October 2008): 92127. doi:10.1016/j.icheatmasstransfer.2008.04.001. Examples
>>> Chisholm_voidage(.4, 800, 2.5) 0.949525900374774

fluids.two_phase_voidage.
Turner_Wallis
(x, rhol, rhog, mul, mug)[source]¶ Calculates void fraction in twophase flow according to the model of [1], as given in [2] and [3].
\[\alpha = \left[1 + \left(\frac{1x}{x}\right)^{0.72}\left(\frac{\rho_g} {\rho_l}\right)^{0.4}\left(\frac{\mu_l}{\mu_g}\right)^{0.08} \right]^{1}\]Parameters:  x : float
Quality at the specific tube interval []
 rhol : float
Density of the liquid [kg/m^3]
 rhog : float
Density of the gas [kg/m^3]
 mul : float
Viscosity of liquid [Pa*s]
 mug : float
Viscosity of gas [Pa*s]
Returns:  alpha : float
Void fraction (area of gas / total area of channel), []
Notes
[1] has not been reviewed. However, both [2] and [3] present it the same way, if slightly differently rearranged.
References
[1] (1, 2, 3) J.M. Turner, G.B. Wallis, The Separatecylinders Model of Twophase Flow, NYO31146, Thayer’s School Eng., Dartmouth College, Hanover, New Hampshire, USA, 1965. [2] (1, 2, 3) Xu, Yu, and Xiande Fang. “Correlations of Void Fraction for Two Phase Refrigerant Flow in Pipes.” Applied Thermal Engineering 64, no. 12 (March 2014): 242–51. doi:10.1016/j.applthermaleng.2013.12.032. [3] (1, 2, 3) Dalkilic, A. S., S. Laohalertdecha, and S. Wongwises. “Effect of Void Fraction Models on the TwoPhase Friction Factor of R134a during Condensation in Vertical Downward Flow in a Smooth Tube.” International Communications in Heat and Mass Transfer 35, no. 8 (October 2008): 92127. doi:10.1016/j.icheatmasstransfer.2008.04.001. Examples
>>> Turner_Wallis(.4, 800, 2.5, 1E3, 1E5) 0.8384824581634625

fluids.two_phase_voidage.
homogeneous
(x, rhol, rhog)[source]¶ Calculates void fraction in twophase flow according to the homogeneous flow model, reviewed in [1], [2], and [3].
\[\alpha = \frac{1}{1 + \left(\frac{1x}{x}\right)\frac{\rho_g}{\rho_l}}\]Parameters:  x : float
Quality at the specific tube interval []
 rhol : float
Density of the liquid [kg/m^3]
 rhog : float
Density of the gas [kg/m^3]
Returns:  alpha : float
Void fraction (area of gas / total area of channel), []
References
[1] (1, 2) Xu, Yu, and Xiande Fang. “Correlations of Void Fraction for Two Phase Refrigerant Flow in Pipes.” Applied Thermal Engineering 64, no. 12 (March 2014): 242–51. doi:10.1016/j.applthermaleng.2013.12.032. [2] (1, 2) Dalkilic, A. S., S. Laohalertdecha, and S. Wongwises. “Effect of Void Fraction Models on the TwoPhase Friction Factor of R134a during Condensation in Vertical Downward Flow in a Smooth Tube.” International Communications in Heat and Mass Transfer 35, no. 8 (October 2008): 92127. doi:10.1016/j.icheatmasstransfer.2008.04.001. [3] (1, 2) Woldesemayat, Melkamu A., and Afshin J. Ghajar. “Comparison of Void Fraction Correlations for Different Flow Patterns in Horizontal and Upward Inclined Pipes.” International Journal of Multiphase Flow 33, no. 4 (April 2007): 347370. doi:10.1016/j.ijmultiphaseflow.2006.09.004. Examples
>>> homogeneous(.4, 800, 2.5) 0.995334370139969

fluids.two_phase_voidage.
Chisholm_Armand
(x, rhol, rhog)[source]¶ Calculates void fraction in twophase flow according to the model presented in [1] based on that of [2] as shown in [3], [4], and [5].
\[\alpha = \frac{\alpha_h}{\alpha_h + (1\alpha_h)^{0.5}}\]Parameters:  x : float
Quality at the specific tube interval []
 rhol : float
Density of the liquid [kg/m^3]
 rhog : float
Density of the gas [kg/m^3]
Returns:  alpha : float
Void fraction (area of gas / total area of channel), []
References
[1] (1, 2) Chisholm, Duncan. TwoPhase Flow in Pipelines and Heat Exchangers. Institution of Chemical Engineers, 1983. [2] (1, 2) Armand, Aleksandr Aleksandrovich. The Resistance During the Movement of a TwoPhase System in Horizontal Pipes. Atomic Energy Research Establishment, 1959. [3] (1, 2) Xu, Yu, and Xiande Fang. “Correlations of Void Fraction for Two Phase Refrigerant Flow in Pipes.” Applied Thermal Engineering 64, no. 12 (March 2014): 242–51. doi:10.1016/j.applthermaleng.2013.12.032. [4] (1, 2) Dalkilic, A. S., S. Laohalertdecha, and S. Wongwises. “Effect of Void Fraction Models on the TwoPhase Friction Factor of R134a during Condensation in Vertical Downward Flow in a Smooth Tube.” International Communications in Heat and Mass Transfer 35, no. 8 (October 2008): 92127. doi:10.1016/j.icheatmasstransfer.2008.04.001. [5] (1, 2) Woldesemayat, Melkamu A., and Afshin J. Ghajar. “Comparison of Void Fraction Correlations for Different Flow Patterns in Horizontal and Upward Inclined Pipes.” International Journal of Multiphase Flow 33, no. 4 (April 2007): 347370. doi:10.1016/j.ijmultiphaseflow.2006.09.004. Examples
>>> Chisholm_Armand(.4, 800, 2.5) 0.9357814394262114

fluids.two_phase_voidage.
Armand
(x, rhol, rhog)[source]¶ Calculates void fraction in twophase flow according to the model presented in [1] as shown in [2], [3], and [4].
\[\alpha = 0.833\alpha_h\]Parameters:  x : float
Quality at the specific tube interval []
 rhol : float
Density of the liquid [kg/m^3]
 rhog : float
Density of the gas [kg/m^3]
Returns:  alpha : float
Void fraction (area of gas / total area of channel), []
References
[1] (1, 2) Armand, Aleksandr Aleksandrovich. The Resistance During the Movement of a TwoPhase System in Horizontal Pipes. Atomic Energy Research Establishment, 1959. [2] (1, 2) Xu, Yu, and Xiande Fang. “Correlations of Void Fraction for Two Phase Refrigerant Flow in Pipes.” Applied Thermal Engineering 64, no. 12 (March 2014): 242–51. doi:10.1016/j.applthermaleng.2013.12.032. [3] (1, 2) Dalkilic, A. S., S. Laohalertdecha, and S. Wongwises. “Effect of Void Fraction Models on the TwoPhase Friction Factor of R134a during Condensation in Vertical Downward Flow in a Smooth Tube.” International Communications in Heat and Mass Transfer 35, no. 8 (October 2008): 92127. doi:10.1016/j.icheatmasstransfer.2008.04.001. [4] (1, 2) Woldesemayat, Melkamu A., and Afshin J. Ghajar. “Comparison of Void Fraction Correlations for Different Flow Patterns in Horizontal and Upward Inclined Pipes.” International Journal of Multiphase Flow 33, no. 4 (April 2007): 347370. doi:10.1016/j.ijmultiphaseflow.2006.09.004. Examples
>>> Armand(.4, 800, 2.5) 0.8291135303265941

fluids.two_phase_voidage.
Nishino_Yamazaki
(x, rhol, rhog)[source]¶ Calculates void fraction in twophase flow according to the model presented in [1] as shown in [2].
\[\alpha = 1  \left(\frac{1x}{x}\frac{\rho_g}{\rho_l}\right)^{0.5} \alpha_h^{0.5}\]Parameters:  x : float
Quality at the specific tube interval []
 rhol : float
Density of the liquid [kg/m^3]
 rhog : float
Density of the gas [kg/m^3]
Returns:  alpha : float
Void fraction (area of gas / total area of channel), []
Notes
[1] is in Japanese.
[3] either shows this model as iterative in terms of voidage, or forgot to add a H subscript to its second voidage term; the second is believed more likely.
References
[1] (1, 2, 3) Nishino, Haruo, and Yasaburo Yamazaki. “A New Method of Evaluating Steam Volume Fractions in Boiling Systems.” Journal of the Atomic Energy Society of Japan / Atomic Energy Society of Japan 5, no. 1 (1963): 3946. doi:10.3327/jaesj.5.39. [2] (1, 2) Xu, Yu, and Xiande Fang. “Correlations of Void Fraction for Two Phase Refrigerant Flow in Pipes.” Applied Thermal Engineering 64, no. 12 (March 2014): 242–51. doi:10.1016/j.applthermaleng.2013.12.032. [3] (1, 2) Woldesemayat, Melkamu A., and Afshin J. Ghajar. “Comparison of Void Fraction Correlations for Different Flow Patterns in Horizontal and Upward Inclined Pipes.” International Journal of Multiphase Flow 33, no. 4 (April 2007): 347370. doi:10.1016/j.ijmultiphaseflow.2006.09.004. Examples
>>> Nishino_Yamazaki(.4, 800, 2.5) 0.931694583962682

fluids.two_phase_voidage.
Guzhov
(x, rhol, rhog, m, D)[source]¶ Calculates void fraction in twophase flow according to the model in [1] as shown in [2] and [3].
\[ \begin{align}\begin{aligned}\alpha = 0.81[1  \exp(2.2\sqrt{Fr_{tp}})]\alpha_h\\Fr_{tp} = \frac{G_{tp}^2}{gD\rho_{tp}^2}\\\rho_{tp} = \left(\frac{1x}{\rho_l} + \frac{x}{\rho_g}\right)^{1}\end{aligned}\end{align} \]Parameters:  x : float
Quality at the specific tube interval []
 rhol : float
Density of the liquid [kg/m^3]
 rhog : float
Density of the gas [kg/m^3]
 m : float
Mass flow rate of both phases, [kg/s]
 D : float
Diameter of the channel, [m]
Returns:  alpha : float
Void fraction (area of gas / total area of channel), []
References
[1] (1, 2) Guzhov, A. I, Vasiliĭ Andreevich Mamaev, and G. E Odisharii︠a︡. A Study of Transportation in GasLiquid Systems. Une Étude Sur Le Transport Des Systèmes GazLiquides. Bruxelles: International Gas Union, 1967. [2] (1, 2) Xu, Yu, and Xiande Fang. “Correlations of Void Fraction for Two Phase Refrigerant Flow in Pipes.” Applied Thermal Engineering 64, no. 12 (March 2014): 242–51. doi:10.1016/j.applthermaleng.2013.12.032. 92127. doi:10.1016/j.icheatmasstransfer.2008.04.001. [3] (1, 2) Woldesemayat, Melkamu A., and Afshin J. Ghajar. “Comparison of Void Fraction Correlations for Different Flow Patterns in Horizontal and Upward Inclined Pipes.” International Journal of Multiphase Flow 33, no. 4 (April 2007): 347370. doi:10.1016/j.ijmultiphaseflow.2006.09.004. Examples
>>> Guzhov(.4, 800, 2.5, 1, .3) 0.7626030108534588

fluids.two_phase_voidage.
Kawahara
(x, rhol, rhog, D)[source]¶ Calculates void fraction in twophase flow according to the model presented in [1], also reviewed in [2] and [3]. This expression is for microchannels.
\[\alpha = \frac{C_1 \alpha_h^{0.5}}{1  C_2\alpha_h^{0.5}}\]Parameters:  x : float
Quality at the specific tube interval []
 rhol : float
Density of the liquid [kg/m^3]
 rhog : float
Density of the gas [kg/m^3]
 D : float
Diameter of the channel, [m]
Returns:  alpha : float
Void fraction (area of gas / total area of channel), []
Notes
C1 and C2 were constants for different diameters. Only diameters of 100 and 50 mircometers were studied in [1]. Here, the coefficients are distributed for three ranges, > 250 micrometers, 25075 micrometers, and < 75 micrometers.
The Armand model is used for the first, C1 and C2 are 0.03 and 0.97 for the second, and C1 and C2 are 0.02 and 0.98 for the third.
References
[1] (1, 2, 3) Kawahara, A., M. Sadatomi, K. Okayama, M. Kawaji, and P. M.Y. Chung. “Effects of Channel Diameter and Liquid Properties on Void Fraction in Adiabatic TwoPhase Flow Through Microchannels.” Heat Transfer Engineering 26, no. 3 (February 16, 2005): 1319. doi:10.1080/01457630590907158. [2] (1, 2) Xu, Yu, and Xiande Fang. “Correlations of Void Fraction for Two Phase Refrigerant Flow in Pipes.” Applied Thermal Engineering 64, no. 12 (March 2014): 242–51. doi:10.1016/j.applthermaleng.2013.12.032. [3] (1, 2) Dalkilic, A. S., S. Laohalertdecha, and S. Wongwises. “Effect of Void Fraction Models on the TwoPhase Friction Factor of R134a during Condensation in Vertical Downward Flow in a Smooth Tube.” International Communications in Heat and Mass Transfer 35, no. 8 (October 2008): 92127. doi:10.1016/j.icheatmasstransfer.2008.04.001. Examples
>>> Kawahara(.4, 800, 2.5, 100E6) 0.9276148194410238

fluids.two_phase_voidage.
Baroczy
(x, rhol, rhog, mul, mug)[source]¶ Calculates void fraction in twophase flow according to the model of [1] as given in [2], [3], and [4].
\[\alpha = \left[1 + \left(\frac{1x}{x}\right)^{0.74}\left(\frac{\rho_g} {\rho_l}\right)^{0.65}\left(\frac{\mu_l}{\mu_g}\right)^{0.13} \right]^{1}\]Parameters:  x : float
Quality at the specific tube interval []
 rhol : float
Density of the liquid [kg/m^3]
 rhog : float
Density of the gas [kg/m^3]
 mul : float
Viscosity of liquid [Pa*s]
 mug : float
Viscosity of gas [Pa*s]
Returns:  alpha : float
Void fraction (area of gas / total area of channel), []
References
[1] (1, 2) Baroczy, C. Correlation of liquid fraction in twophase flow with applications to liquid metals, Chem. Eng. Prog. Symp. Ser. 61 (1965) 179191. [2] (1, 2) Xu, Yu, and Xiande Fang. “Correlations of Void Fraction for Two Phase Refrigerant Flow in Pipes.” Applied Thermal Engineering 64, no. 12 (March 2014): 242–51. doi:10.1016/j.applthermaleng.2013.12.032. [3] (1, 2) Dalkilic, A. S., S. Laohalertdecha, and S. Wongwises. “Effect of Void Fraction Models on the TwoPhase Friction Factor of R134a during Condensation in Vertical Downward Flow in a Smooth Tube.” International Communications in Heat and Mass Transfer 35, no. 8 (October 2008): 92127. doi:10.1016/j.icheatmasstransfer.2008.04.001. [4] (1, 2) Woldesemayat, Melkamu A., and Afshin J. Ghajar. “Comparison of Void Fraction Correlations for Different Flow Patterns in Horizontal and Upward Inclined Pipes.” International Journal of Multiphase Flow 33, no. 4 (April 2007): 347370. doi:10.1016/j.ijmultiphaseflow.2006.09.004. Examples
>>> Baroczy(.4, 800, 2.5, 1E3, 1E5) 0.9453544598460807

fluids.two_phase_voidage.
Tandon_Varma_Gupta
(x, rhol, rhog, mul, mug, m, D)[source]¶ Calculates void fraction in twophase flow according to the model of [1] also given in [2], [3], and [4].
For 50 < Rel < 1125:
\[\alpha = 1 1.928Re_l^{0.315}[F(X_{tt})]^{1} + 0.9293Re_l^{0.63} [F(X_{tt})]^{2}\]For Rel > 1125:
\[\alpha = 1 0.38 Re_l^{0.088}[F(X_{tt})]^{1} + 0.0361 Re_l^{0.176} [F(X_{tt})]^{2}\]\[F(X_{tt}) = 0.15[X_{tt}^{1} + 2.85X_{tt}^{0.476}]\]Parameters:  x : float
Quality at the specific tube interval []
 rhol : float
Density of the liquid [kg/m^3]
 rhog : float
Density of the gas [kg/m^3]
 mul : float
Viscosity of liquid [Pa*s]
 mug : float
Viscosity of gas [Pa*s]
 m : float
Mass flow rate of both phases, [kg/s]
 D : float
Diameter of the channel, [m]
Returns:  alpha : float
Void fraction (area of gas / total area of channel), []
Notes
[1] does not specify how it defines the liquid Reynolds number. [2] disagrees with [3] and [4]; the later variant was selected, with:
\[Re_l = \frac{G_{tp}D}{\mu_l}\]The lower limit on Reynolds number is not enforced.
References
[1] (1, 2, 3) Tandon, T. N., H. K. Varma, and C. P. Gupta. “A Void Fraction Model for Annular TwoPhase Flow.” International Journal of Heat and Mass Transfer 28, no. 1 (January 1, 1985): 191198. doi:10.1016/00179310(85)900213. [2] (1, 2, 3) Xu, Yu, and Xiande Fang. “Correlations of Void Fraction for Two Phase Refrigerant Flow in Pipes.” Applied Thermal Engineering 64, no. 12 (March 2014): 242–51. doi:10.1016/j.applthermaleng.2013.12.032. [3] (1, 2, 3) Dalkilic, A. S., S. Laohalertdecha, and S. Wongwises. “Effect of Void Fraction Models on the TwoPhase Friction Factor of R134a during Condensation in Vertical Downward Flow in a Smooth Tube.” International Communications in Heat and Mass Transfer 35, no. 8 (October 2008): 92127. doi:10.1016/j.icheatmasstransfer.2008.04.001. [4] (1, 2, 3) Woldesemayat, Melkamu A., and Afshin J. Ghajar. “Comparison of Void Fraction Correlations for Different Flow Patterns in Horizontal and Upward Inclined Pipes.” International Journal of Multiphase Flow 33, no. 4 (April 2007): 347370. doi:10.1016/j.ijmultiphaseflow.2006.09.004. Examples
>>> Tandon_Varma_Gupta(.4, 800, 2.5, 1E3, 1E5, m=1, D=0.3) 0.9228265670341428

fluids.two_phase_voidage.
Harms
(x, rhol, rhog, mul, mug, m, D)[source]¶ Calculates void fraction in twophase flow according to the model of [1] also given in [2] and [3].
\[ \begin{align}\begin{aligned}\alpha = \left[1  10.06Re_l^{0.875}(1.74 + 0.104Re_l^{0.5})^2 \left(1.376 + \frac{7.242}{X_{tt}^{1.655}}\right)^{0.5}\right]^2\\Re_l = \frac{G_{tp}(1x)D}{\mu_l}\end{aligned}\end{align} \]Parameters:  x : float
Quality at the specific tube interval []
 rhol : float
Density of the liquid [kg/m^3]
 rhog : float
Density of the gas [kg/m^3]
 mul : float
Viscosity of liquid [Pa*s]
 mug : float
Viscosity of gas [Pa*s]
 m : float
Mass flow rate of both phases, [kg/s]
 D : float
Diameter of the channel, [m]
Returns:  alpha : float
Void fraction (area of gas / total area of channel), []
Notes
[1] has been reviewed.
References
[1] (1, 2, 3) Tandon, T. N., H. K. Varma, and C. P. Gupta. “A Void Fraction Model for Annular TwoPhase Flow.” International Journal of Heat and Mass Transfer 28, no. 1 (January 1, 1985): 191198. doi:10.1016/00179310(85)900213. [2] (1, 2) Xu, Yu, and Xiande Fang. “Correlations of Void Fraction for Two Phase Refrigerant Flow in Pipes.” Applied Thermal Engineering 64, no. 12 (March 2014): 242–51. doi:10.1016/j.applthermaleng.2013.12.032. [3] (1, 2) Dalkilic, A. S., S. Laohalertdecha, and S. Wongwises. “Effect of Void Fraction Models on the TwoPhase Friction Factor of R134a during Condensation in Vertical Downward Flow in a Smooth Tube.” International Communications in Heat and Mass Transfer 35, no. 8 (October 2008): 92127. doi:10.1016/j.icheatmasstransfer.2008.04.001. Examples
>>> Harms(.4, 800, 2.5, 1E3, 1E5, m=1, D=0.3) 0.9653289762907554

fluids.two_phase_voidage.
Domanski_Didion
(x, rhol, rhog, mul, mug)[source]¶ Calculates void fraction in twophase flow according to the model of [1] also given in [2] and [3].
if Xtt < 10:
\[\alpha = (1 + X_{tt}^{0.8})^{0.378}\]Otherwise:
\[\alpha = 0.823 0.157\ln(X_{tt})\]Parameters:  x : float
Quality at the specific tube interval []
 rhol : float
Density of the liquid [kg/m^3]
 rhog : float
Density of the gas [kg/m^3]
 mul : float
Viscosity of liquid [Pa*s]
 mug : float
Viscosity of gas [Pa*s]
Returns:  alpha : float
Void fraction (area of gas / total area of channel), []
Notes
[1] has been reviewed. [2] gives an exponent of 0.38 instead of 0.378 as is in [1]. [3] describes only the novel half of the correlation. The portion for Xtt > 10 is novel; the other is said to be from their 31st reference, Wallis.
There is a discontinuity at Xtt = 10.
References
[1] (1, 2, 3, 4) Domanski, Piotr, and David A. Didion. “Computer Modeling of the Vapor Compression Cycle with Constant Flow Area Expansion Device.” Report. UNT Digital Library, May 1983. [2] (1, 2, 3) Xu, Yu, and Xiande Fang. “Correlations of Void Fraction for Two Phase Refrigerant Flow in Pipes.” Applied Thermal Engineering 64, no. 12 (March 2014): 242–51. doi:10.1016/j.applthermaleng.2013.12.032. [3] (1, 2, 3) Dalkilic, A. S., S. Laohalertdecha, and S. Wongwises. “Effect of Void Fraction Models on the TwoPhase Friction Factor of R134a during Condensation in Vertical Downward Flow in a Smooth Tube.” International Communications in Heat and Mass Transfer 35, no. 8 (October 2008): 92127. doi:10.1016/j.icheatmasstransfer.2008.04.001. Examples
>>> Domanski_Didion(.4, 800, 2.5, 1E3, 1E5) 0.9355795597059169

fluids.two_phase_voidage.
Graham
(x, rhol, rhog, mul, mug, m, D, g=9.80665)[source]¶ Calculates void fraction in twophase flow according to the model of [1] also given in [2] and [3].
\[ \begin{align}\begin{aligned}\alpha = 1  \exp\{1  0.3\ln(Ft)  0.0328[\ln(Ft)]^2\}\\Ft = \left[\frac{G_{tp}^2 x^3}{(1x)\rho_g^2gD}\right]^{0.5}\\\alpha = 0 \text{ for } F_t \le 0.01032\end{aligned}\end{align} \]Parameters:  x : float
Quality at the specific tube interval []
 rhol : float
Density of the liquid [kg/m^3]
 rhog : float
Density of the gas [kg/m^3]
 mul : float
Viscosity of liquid [Pa*s]
 mug : float
Viscosity of gas [Pa*s]
 m : float
Mass flow rate of both phases, [kg/s]
 D : float
Diameter of the channel, [m]
 g : float, optional
Acceleration due to gravity, [m/s^2]
Returns:  alpha : float
Void fraction (area of gas / total area of channel), []
Notes
[1] has been reviewed. [2] does not list that the expression is not real below a certain value of Ft.
References
[1] (1, 2, 3) Graham, D. M. “Experimental Investigation of Void Fraction During Refrigerant Condensation.” ACRC Technical Report 135. Air Conditioning and Refrigeration Center. College of Engineering. University of Illinois at UrbanaChampaign., December 1997. [2] (1, 2, 3) Xu, Yu, and Xiande Fang. “Correlations of Void Fraction for Two Phase Refrigerant Flow in Pipes.” Applied Thermal Engineering 64, no. 12 (March 2014): 242–51. doi:10.1016/j.applthermaleng.2013.12.032. [3] (1, 2) Dalkilic, A. S., S. Laohalertdecha, and S. Wongwises. “Effect of Void Fraction Models on the TwoPhase Friction Factor of R134a during Condensation in Vertical Downward Flow in a Smooth Tube.” International Communications in Heat and Mass Transfer 35, no. 8 (October 2008): 92127. doi:10.1016/j.icheatmasstransfer.2008.04.001. Examples
>>> Graham(.4, 800, 2.5, 1E3, 1E5, m=1, D=0.3) 0.6403336287530644

fluids.two_phase_voidage.
Yashar
(x, rhol, rhog, mul, mug, m, D, g=9.80665)[source]¶ Calculates void fraction in twophase flow according to the model of [1] also given in [2] and [3].
\[ \begin{align}\begin{aligned}\alpha = \left[1 + \frac{1}{Ft} + X_{tt}\right]^{0.321}\\Ft = \left[\frac{G_{tp}^2 x^3}{(1x)\rho_g^2gD}\right]^{0.5}\end{aligned}\end{align} \]Parameters:  x : float
Quality at the specific tube interval []
 rhol : float
Density of the liquid [kg/m^3]
 rhog : float
Density of the gas [kg/m^3]
 mul : float
Viscosity of liquid [Pa*s]
 mug : float
Viscosity of gas [Pa*s]
 m : float
Mass flow rate of both phases, [kg/s]
 D : float
Diameter of the channel, [m]
 g : float, optional
Acceleration due to gravity, [m/s^2]
Returns:  alpha : float
Void fraction (area of gas / total area of channel), []
Notes
[1] has been reviewed; both [2] and [3] give it correctly.
References
[1] (1, 2, 3) Yashar, D. A., M. J. Wilson, H. R. Kopke, D. M. Graham, J. C. Chato, and T. A. Newell. “An Investigation of Refrigerant Void Fraction in Horizontal, Microfin Tubes.” HVAC&R Research 7, no. 1 (January 1, 2001): 6782. doi:10.1080/10789669.2001.10391430. [2] (1, 2, 3) Xu, Yu, and Xiande Fang. “Correlations of Void Fraction for Two Phase Refrigerant Flow in Pipes.” Applied Thermal Engineering 64, no. 12 (March 2014): 242–51. doi:10.1016/j.applthermaleng.2013.12.032. [3] (1, 2, 3) Dalkilic, A. S., S. Laohalertdecha, and S. Wongwises. “Effect of Void Fraction Models on the TwoPhase Friction Factor of R134a during Condensation in Vertical Downward Flow in a Smooth Tube.” International Communications in Heat and Mass Transfer 35, no. 8 (October 2008): 92127. doi:10.1016/j.icheatmasstransfer.2008.04.001. Examples
>>> Yashar(.4, 800, 2.5, 1E3, 1E5, m=1, D=0.3) 0.7934893185789146

fluids.two_phase_voidage.
Huq_Loth
(x, rhol, rhog)[source]¶ Calculates void fraction in twophase flow according to the model of [1], also given in [2], [3], and [4].
\[\alpha = 1  \frac{2(1x)^2}{1  2x + \left[1 + 4x(1x)\left(\frac {\rho_l}{\rho_g}1\right)\right]^{0.5}}\]Parameters:  x : float
Quality at the specific tube interval []
 rhol : float
Density of the liquid [kg/m^3]
 rhog : float
Density of the gas [kg/m^3]
Returns:  alpha : float
Void fraction (area of gas / total area of channel), []
Notes
[1] has been reviewed, and matches the expressions given in the reviews [2], [3], and [4]; the form of the expression is rearranged somewhat differently.
References
[1] (1, 2, 3) Huq, Reazul, and John L. Loth. “Analytical TwoPhase Flow Void Prediction Method.” Journal of Thermophysics and Heat Transfer 6, no. 1 (January 1, 1992): 13944. doi:10.2514/3.329. [2] (1, 2, 3) Xu, Yu, and Xiande Fang. “Correlations of Void Fraction for Two Phase Refrigerant Flow in Pipes.” Applied Thermal Engineering 64, no. 12 (March 2014): 242–51. doi:10.1016/j.applthermaleng.2013.12.032. [3] (1, 2, 3) Dalkilic, A. S., S. Laohalertdecha, and S. Wongwises. “Effect of Void Fraction Models on the TwoPhase Friction Factor of R134a during Condensation in Vertical Downward Flow in a Smooth Tube.” International Communications in Heat and Mass Transfer 35, no. 8 (October 2008): 92127. doi:10.1016/j.icheatmasstransfer.2008.04.001. [4] (1, 2, 3) Woldesemayat, Melkamu A., and Afshin J. Ghajar. “Comparison of Void Fraction Correlations for Different Flow Patterns in Horizontal and Upward Inclined Pipes.” International Journal of Multiphase Flow 33, no. 4 (April 2007): 347370. doi:10.1016/j.ijmultiphaseflow.2006.09.004. Examples
>>> Huq_Loth(.4, 800, 2.5) 0.9593868838476147

fluids.two_phase_voidage.
Kopte_Newell_Chato
(x, rhol, rhog, mul, mug, m, D, g=9.80665)[source]¶ Calculates void fraction in twophase flow according to the model of [1] also given in [2].
\[ \begin{align}\begin{aligned}\alpha = 1.045  \exp\{1  0.342\ln(Ft)  0.0268[\ln(Ft)]^2 + 0.00597[\ln(Ft)]^3\}\\Ft = \left[\frac{G_{tp}^2 x^3}{(1x)\rho_g^2gD}\right]^{0.5}\\\alpha = \alpha_h \text{ for } F_t \le 0.044\end{aligned}\end{align} \]Parameters:  x : float
Quality at the specific tube interval []
 rhol : float
Density of the liquid [kg/m^3]
 rhog : float
Density of the gas [kg/m^3]
 mul : float
Viscosity of liquid [Pa*s]
 mug : float
Viscosity of gas [Pa*s]
 m : float
Mass flow rate of both phases, [kg/s]
 D : float
Diameter of the channel, [m]
 g : float, optional
Acceleration due to gravity, [m/s^2]
Returns:  alpha : float
Void fraction (area of gas / total area of channel), []
Notes
[1] has been reviewed. If is recommended this expression not be used above Ft values of 454.
References
[1] (1, 2, 3) Kopke, H. R. “Experimental Investigation of Void Fraction During Refrigerant Condensation in Horizontal Tubes.” ACRC Technical Report 142. Air Conditioning and Refrigeration Center. College of Engineering. University of Illinois at UrbanaChampaign., August 1998. [2] (1, 2) Xu, Yu, and Xiande Fang. “Correlations of Void Fraction for Two Phase Refrigerant Flow in Pipes.” Applied Thermal Engineering 64, no. 12 (March 2014): 242–51. doi:10.1016/j.applthermaleng.2013.12.032. Examples
>>> Kopte_Newell_Chato(.4, 800, 2.5, 1E3, 1E5, m=1, D=0.3) 0.6864466770087425

fluids.two_phase_voidage.
Steiner
(x, rhol, rhog, sigma, m, D, g=9.80665)[source]¶ Calculates void fraction in twophase flow according to the model of [1] also given in [2] and [3].
\[ \begin{align}\begin{aligned}\alpha = \frac{x}{\rho_g}\left[C_0\left(\frac{x}{\rho_g} + \frac{1x} {\rho_l}\right) +\frac{v_{gm}}{G} \right]^{1}\\v_{gm} = \frac{1.18(1x)}{\rho_l^{0.5}}[g\sigma(\rho_l\rho_g)]^{0.25}\\C_0 = 1 + 0.12(1x)\end{aligned}\end{align} \]Parameters:  x : float
Quality at the specific tube interval []
 rhol : float
Density of the liquid [kg/m^3]
 rhog : float
Density of the gas [kg/m^3]
 sigma : float
Surface tension of liquid [N/m]
 m : float
Mass flow rate of both phases, [kg/s]
 D : float
Diameter of the channel, [m]
 g : float, optional
Acceleration due to gravity, [m/s^2]
Returns:  alpha : float
Void fraction (area of gas / total area of channel), []
Notes
[1] has been reviewed.
References
[1] (1, 2, 3) Gesellschaft, V. D. I., ed. VDI Heat Atlas. 2nd edition. Berlin; New York:: Springer, 2010. [2] (1, 2) Xu, Yu, and Xiande Fang. “Correlations of Void Fraction for Two Phase Refrigerant Flow in Pipes.” Applied Thermal Engineering 64, no. 12 (March 2014): 242–51. doi:10.1016/j.applthermaleng.2013.12.032. [3] (1, 2) Dalkilic, A. S., S. Laohalertdecha, and S. Wongwises. “Effect of Void Fraction Models on the TwoPhase Friction Factor of R134a during Condensation in Vertical Downward Flow in a Smooth Tube.” International Communications in Heat and Mass Transfer 35, no. 8 (October 2008): 92127. doi:10.1016/j.icheatmasstransfer.2008.04.001. Examples
>>> Steiner(0.4, 800., 2.5, sigma=0.02, m=1, D=0.3) 0.895950181381335

fluids.two_phase_voidage.
Rouhani_1
(x, rhol, rhog, sigma, m, D, g=9.80665)[source]¶ Calculates void fraction in twophase flow according to the model of [1] as given in [2] and [3].
\[ \begin{align}\begin{aligned}\alpha = \frac{x}{\rho_g}\left[C_0\left(\frac{x}{\rho_g} + \frac{1x} {\rho_l}\right) +\frac{v_{gm}}{G} \right]^{1}\\v_{gm} = \frac{1.18(1x)}{\rho_l^{0.5}}[g\sigma(\rho_l\rho_g)]^{0.25}\\C_0 = 1 + 0.2(1x)\end{aligned}\end{align} \]Parameters:  x : float
Quality at the specific tube interval []
 rhol : float
Density of the liquid [kg/m^3]
 rhog : float
Density of the gas [kg/m^3]
 sigma : float
Surface tension of liquid [N/m]
 m : float
Mass flow rate of both phases, [kg/s]
 D : float
Diameter of the channel, [m]
 g : float, optional
Acceleration due to gravity, [m/s^2]
Returns:  alpha : float
Void fraction (area of gas / total area of channel), []
Notes
The expression as quoted in [2] and [3] could not be found in [1].
References
[1] (1, 2, 3) Rouhani, S. Z, and E Axelsson. “Calculation of Void Volume Fraction in the Subcooled and Quality Boiling Regions.” International Journal of Heat and Mass Transfer 13, no. 2 (February 1, 1970): 38393. doi:10.1016/00179310(70)901146. [2] (1, 2, 3) Xu, Yu, and Xiande Fang. “Correlations of Void Fraction for Two Phase Refrigerant Flow in Pipes.” Applied Thermal Engineering 64, no. 12 (March 2014): 242–51. doi:10.1016/j.applthermaleng.2013.12.032. [3] (1, 2, 3) Woldesemayat, Melkamu A., and Afshin J. Ghajar. “Comparison of Void Fraction Correlations for Different Flow Patterns in Horizontal and Upward Inclined Pipes.” International Journal of Multiphase Flow 33, no. 4 (April 2007): 347370. doi:10.1016/j.ijmultiphaseflow.2006.09.004. Examples
>>> Rouhani_1(0.4, 800., 2.5, sigma=0.02, m=1, D=0.3) 0.8588420244136714

fluids.two_phase_voidage.
Rouhani_2
(x, rhol, rhog, sigma, m, D, g=9.80665)[source]¶ Calculates void fraction in twophase flow according to the model of [1] as given in [2] and [3].
\[ \begin{align}\begin{aligned}\alpha = \frac{x}{\rho_g}\left[C_0\left(\frac{x}{\rho_g} + \frac{1x} {\rho_l}\right) +\frac{v_{gm}}{G} \right]^{1}\\v_{gm} = \frac{1.18(1x)}{\rho_l^{0.5}}[g\sigma(\rho_l\rho_g)]^{0.25}\\C_0 = 1 + 0.2(1x)(gD)^{0.25}\left(\frac{\rho_l}{G_{tp}}\right)^{0.5}\end{aligned}\end{align} \]Parameters:  x : float
Quality at the specific tube interval []
 rhol : float
Density of the liquid [kg/m^3]
 rhog : float
Density of the gas [kg/m^3]
 sigma : float
Surface tension of liquid [N/m]
 m : float
Mass flow rate of both phases, [kg/s]
 D : float
Diameter of the channel, [m]
 g : float, optional
Acceleration due to gravity, [m/s^2]
Returns:  alpha : float
Void fraction (area of gas / total area of channel), []
Notes
The expression as quoted in [2] and [3] could not be found in [1].
References
[1] (1, 2, 3) Rouhani, S. Z, and E Axelsson. “Calculation of Void Volume Fraction in the Subcooled and Quality Boiling Regions.” International Journal of Heat and Mass Transfer 13, no. 2 (February 1, 1970): 38393. doi:10.1016/00179310(70)901146. [2] (1, 2, 3) Xu, Yu, and Xiande Fang. “Correlations of Void Fraction for Two Phase Refrigerant Flow in Pipes.” Applied Thermal Engineering 64, no. 12 (March 2014): 242–51. doi:10.1016/j.applthermaleng.2013.12.032. [3] (1, 2, 3) Woldesemayat, Melkamu A., and Afshin J. Ghajar. “Comparison of Void Fraction Correlations for Different Flow Patterns in Horizontal and Upward Inclined Pipes.” International Journal of Multiphase Flow 33, no. 4 (April 2007): 347370. doi:10.1016/j.ijmultiphaseflow.2006.09.004. Examples
>>> Rouhani_2(0.4, 800., 2.5, sigma=0.02, m=1, D=0.3) 0.44819733138968865

fluids.two_phase_voidage.
Nicklin_Wilkes_Davidson
(x, rhol, rhog, m, D, g=9.80665)[source]¶ Calculates void fraction in twophase flow according to the model of [1] as given in [2] and [3].
\[ \begin{align}\begin{aligned}\alpha = \frac{x}{\rho_g}\left[C_0\left(\frac{x}{\rho_g} + \frac{1x} {\rho_l}\right) +\frac{v_{gm}}{G} \right]^{1}\\v_{gm} = 0.35\sqrt{gD}\\C_0 = 1.2\end{aligned}\end{align} \]Parameters:  x : float
Quality at the specific tube interval []
 rhol : float
Density of the liquid [kg/m^3]
 rhog : float
Density of the gas [kg/m^3]
 m : float
Mass flow rate of both phases, [kg/s]
 D : float
Diameter of the channel, [m]
 g : float, optional
Acceleration due to gravity, [m/s^2]
Returns:  alpha : float
Void fraction (area of gas / total area of channel), []
References
[1] (1, 2) D. Nicklin, J. Wilkes, J. Davidson, “Twophase flow in vertical tubes”, Trans. Inst. Chem. Eng. 40 (1962) 6168. [2] (1, 2) Xu, Yu, and Xiande Fang. “Correlations of Void Fraction for Two Phase Refrigerant Flow in Pipes.” Applied Thermal Engineering 64, no. 12 (March 2014): 242–51. doi:10.1016/j.applthermaleng.2013.12.032. [3] (1, 2) Woldesemayat, Melkamu A., and Afshin J. Ghajar. “Comparison of Void Fraction Correlations for Different Flow Patterns in Horizontal and Upward Inclined Pipes.” International Journal of Multiphase Flow 33, no. 4 (April 2007): 347370. doi:10.1016/j.ijmultiphaseflow.2006.09.004. Examples
>>> Nicklin_Wilkes_Davidson(0.4, 800., 2.5, m=1, D=0.3) 0.6798826626721431

fluids.two_phase_voidage.
Gregory_Scott
(x, rhol, rhog)[source]¶ Calculates void fraction in twophase flow according to the model of [1] as given in [2] and [3].
\[ \begin{align}\begin{aligned}\alpha = \frac{x}{\rho_g}\left[C_0\left(\frac{x}{\rho_g} + \frac{1x} {\rho_l}\right) +\frac{v_{gm}}{G} \right]^{1}\\v_{gm} = 0\\C_0 = 1.19\end{aligned}\end{align} \]Parameters:  x : float
Quality at the specific tube interval []
 rhol : float
Density of the liquid [kg/m^3]
 rhog : float
Density of the gas [kg/m^3]
Returns:  alpha : float
Void fraction (area of gas / total area of channel), []
References
[1] (1, 2) Gregory, G. A., and D. S. Scott. “Correlation of Liquid Slug Velocity and Frequency in Horizontal Cocurrent GasLiquid Slug Flow.” AIChE Journal 15, no. 6 (November 1, 1969): 93335. doi:10.1002/aic.690150623. [2] (1, 2) Xu, Yu, and Xiande Fang. “Correlations of Void Fraction for Two Phase Refrigerant Flow in Pipes.” Applied Thermal Engineering 64, no. 12 (March 2014): 242–51. doi:10.1016/j.applthermaleng.2013.12.032. [3] (1, 2) Woldesemayat, Melkamu A., and Afshin J. Ghajar. “Comparison of Void Fraction Correlations for Different Flow Patterns in Horizontal and Upward Inclined Pipes.” International Journal of Multiphase Flow 33, no. 4 (April 2007): 347370. doi:10.1016/j.ijmultiphaseflow.2006.09.004. Examples
>>> Gregory_Scott(0.4, 800., 2.5) 0.8364154370924108

fluids.two_phase_voidage.
Dix
(x, rhol, rhog, sigma, m, D, g=9.80665)[source]¶ Calculates void fraction in twophase flow according to the model of [1] as given in [2] and [3].
\[ \begin{align}\begin{aligned}\alpha = \frac{x}{\rho_g}\left[C_0\left(\frac{x}{\rho_g} + \frac{1x} {\rho_l}\right) +\frac{v_{gm}}{G} \right]^{1}\\v_{gm} = 2.9\left(g\sigma\frac{\rho_l\rho_g}{\rho_l^2}\right)^{0.25}\\C_0 = \frac{v_{sg}}{v_m}\left[1 + \left(\frac{v_{sl}}{v_{sg}}\right) ^{\left(\left(\frac{\rho_g}{\rho_l}\right)^{0.1}\right)}\right]\\v_{gs} = \frac{mx}{\rho_g \frac{\pi}{4}D^2}\\v_{ls} = \frac{m(1x)}{\rho_l \frac{\pi}{4}D^2}\\v_m = v_{gs} + v_{ls}\end{aligned}\end{align} \]Parameters:  x : float
Quality at the specific tube interval []
 rhol : float
Density of the liquid [kg/m^3]
 rhog : float
Density of the gas [kg/m^3]
 sigma : float
Surface tension of liquid [N/m]
 m : float
Mass flow rate of both phases, [kg/s]
 D : float
Diameter of the channel, [m]
 g : float, optional
Acceleration due to gravity, [m/s^2]
Returns:  alpha : float
Void fraction (area of gas / total area of channel), []
Notes
Has formed the basis for several other correlations.
References
[1] (1, 2) Gary Errol. Dix. “Vapor Void Fractions for Forced Convection with Subcooled Boiling at Low Flow Rates.” Thesis. University of California, Berkeley, 1971. [2] (1, 2) Xu, Yu, and Xiande Fang. “Correlations of Void Fraction for Two Phase Refrigerant Flow in Pipes.” Applied Thermal Engineering 64, no. 12 (March 2014): 242–51. doi:10.1016/j.applthermaleng.2013.12.032. [3] (1, 2) Woldesemayat, Melkamu A., and Afshin J. Ghajar. “Comparison of Void Fraction Correlations for Different Flow Patterns in Horizontal and Upward Inclined Pipes.” International Journal of Multiphase Flow 33, no. 4 (April 2007): 347370. doi:10.1016/j.ijmultiphaseflow.2006.09.004. Examples
>>> Dix(0.4, 800., 2.5, sigma=0.02, m=1, D=0.3) 0.8268737961156514

fluids.two_phase_voidage.
Sun_Duffey_Peng
(x, rhol, rhog, sigma, m, D, P, Pc, g=9.80665)[source]¶ Calculates void fraction in twophase flow according to the model of [1] as given in [2] and [3].
\[ \begin{align}\begin{aligned}\alpha = \frac{x}{\rho_g}\left[C_0\left(\frac{x}{\rho_g} + \frac{1x} {\rho_l}\right) +\frac{v_{gm}}{G} \right]^{1}\\v_{gm} = 1.41\left[\frac{g\sigma(\rho_l\rho_g)}{\rho_l^2}\right]^{0.25}\\C_0 = \left(0.82 + 0.18\frac{P}{P_c}\right)^{1}\end{aligned}\end{align} \]Parameters:  x : float
Quality at the specific tube interval []
 rhol : float
Density of the liquid [kg/m^3]
 rhog : float
Density of the gas [kg/m^3]
 sigma : float
Surface tension of liquid [N/m]
 m : float
Mass flow rate of both phases, [kg/s]
 D : float
Diameter of the channel, [m]
 P : float
Pressure of the fluid, [Pa]
 Pc : float
Critical pressure of the fluid, [Pa]
 g : float, optional
Acceleration due to gravity, [m/s^2]
Returns:  alpha : float
Void fraction (area of gas / total area of channel), []
References
[1] (1, 2) K.H. Sun, R.B. Duffey, C.M. Peng, A thermalhydraulic analysis of core uncover, in: Proceedings of the 19th National Heat Transfer Conference, Experimental and Analytical Modeling of LWR Safety Experiments, 1980, pp. 110. Orlando, Florida, USA. [2] (1, 2) Xu, Yu, and Xiande Fang. “Correlations of Void Fraction for Two Phase Refrigerant Flow in Pipes.” Applied Thermal Engineering 64, no. 12 (March 2014): 242–51. doi:10.1016/j.applthermaleng.2013.12.032. [3] (1, 2) Woldesemayat, Melkamu A., and Afshin J. Ghajar. “Comparison of Void Fraction Correlations for Different Flow Patterns in Horizontal and Upward Inclined Pipes.” International Journal of Multiphase Flow 33, no. 4 (April 2007): 347370. doi:10.1016/j.ijmultiphaseflow.2006.09.004. Examples
>>> Sun_Duffey_Peng(0.4, 800., 2.5, sigma=0.02, m=1, D=0.3, P=1E5, Pc=7E6) 0.7696546506515833

fluids.two_phase_voidage.
Xu_Fang_voidage
(x, rhol, rhog, m, D, g=9.80665)[source]¶ Calculates void fraction in twophase flow according to the model developed in the review of [1].
\[\alpha = \left[1 + \left(1 + 2Fr_{lo}^{0.2}\alpha_h^{3.5}\right)\left( \frac{1x}{x}\right)\left(\frac{\rho_g}{\rho_l}\right)\right]^{1}\]Parameters:  x : float
Quality at the specific tube interval []
 rhol : float
Density of the liquid [kg/m^3]
 rhog : float
Density of the gas [kg/m^3]
 m : float
Mass flow rate of both phases, [kg/s]
 D : float
Diameter of the channel, [m]
 g : float, optional
Acceleration due to gravity, [m/s^2]
Returns:  alpha : float
Void fraction (area of gas / total area of channel), []
Notes
Claims an AARD of 5.0%, and suitability for any flow regime, mini and micro channels, adiabatic, evaporating, or condensing flow, and for Frlo from 0.02 to 145, rhog/rhol from 0.0040.153, and x from 0 to 1.
References
[1] (1, 2) Xu, Yu, and Xiande Fang. “Correlations of Void Fraction for Two Phase Refrigerant Flow in Pipes.” Applied Thermal Engineering 64, no. 12 (March 2014): 242–51. doi:10.1016/j.applthermaleng.2013.12.032. Examples
>>> Xu_Fang_voidage(0.4, 800., 2.5, m=1, D=0.3) 0.9414660089942093

fluids.two_phase_voidage.
Woldesemayat_Ghajar
(x, rhol, rhog, sigma, m, D, P, angle=0, g=9.80665)[source]¶ Calculates void fraction in twophase flow according to the model of [1].
\[ \begin{align}\begin{aligned}\alpha = \frac{v_{gs}}{v_{gs}\left(1 + \left(\frac{v_{ls}}{v_{gs}} \right)^{\left(\frac{\rho_g}{\rho_l}\right)^{0.1}}\right) + 2.9\left[\frac{gD\sigma(1+\cos\theta)(\rho_l\rho_g)} {\rho_l^2}\right]^{0.25}(1.22 + 1.22\sin\theta)^{\frac{P}{P_{atm}}}}\\v_{gs} = \frac{mx}{\rho_g \frac{\pi}{4}D^2}\\v_{ls} = \frac{m(1x)}{\rho_l \frac{\pi}{4}D^2}\end{aligned}\end{align} \]Parameters:  x : float
Quality at the specific tube interval []
 rhol : float
Density of the liquid [kg/m^3]
 rhog : float
Density of the gas [kg/m^3]
 sigma : float
Surface tension of liquid [N/m]
 m : float
Mass flow rate of both phases, [kg/s]
 D : float
Diameter of the channel, [m]
 P : float
Pressure of the fluid, [Pa]
 angle : float
Angle of the channel with respect to the horizontal (vertical = 90), [degrees]
 g : float, optional
Acceleration due to gravity, [m/s^2]
Returns:  alpha : float
Void fraction (area of gas / total area of channel), []
Notes
Strongly recommended.
References
[1] (1, 2) Woldesemayat, Melkamu A., and Afshin J. Ghajar. “Comparison of Void Fraction Correlations for Different Flow Patterns in Horizontal and Upward Inclined Pipes.” International Journal of Multiphase Flow 33, no. 4 (April 2007): 347370. doi:10.1016/j.ijmultiphaseflow.2006.09.004. Examples
>>> Woldesemayat_Ghajar(0.4, 800., 2.5, sigma=0.2, m=1, D=0.3, P=1E6, angle=45) 0.7640815513429202

fluids.two_phase_voidage.
Lockhart_Martinelli_Xtt
(x, rhol, rhog, mul, mug, pow_x=0.9, pow_rho=0.5, pow_mu=0.1, n=None)[source]¶ Calculates the LockhartMartinelli Xtt twophase flow parameter in a general way according to [2]. [1] is said to describe this. However, very different definitions of this parameter have been used elsewhere. Accordingly, the powers of each of the terms can be set. Alternatively, if the parameter n is provided, the powers for viscosity and phase fraction will be calculated from it as shown below.
\[ \begin{align}\begin{aligned}X_{tt} = \left(\frac{1x}{x}\right)^{0.9} \left(\frac{\rho_g}{\rho_l} \right)^{0.5}\left(\frac{\mu_l}{\mu_g}\right)^{0.1}\\X_{tt} = \left(\frac{1x}{x}\right)^{(2n)/2} \left(\frac{\rho_g} {\rho_l}\right)^{0.5}\left(\frac{\mu_l}{\mu_g}\right)^{n/2}\end{aligned}\end{align} \]Parameters:  x : float
Quality at the specific tube interval []
 rhol : float
Density of the liquid [kg/m^3]
 rhog : float
Density of the gas [kg/m^3]
 mul : float
Viscosity of liquid [Pa*s]
 mug : float
Viscosity of gas [Pa*s]
 pow_x : float, optional
Power for the phase ratio (1x)/x, []
 pow_rho : float, optional
Power for the density ratio rhog/rhol, []
 pow_mu : float, optional
Power for the viscosity ratio mul/mug, []
 n : float, optional
Number to be used for calculating pow_x and pow_mu if provided, []
Returns:  Xtt : float
Xtt LockhartMartinelli twophase flow parameter []
Notes
Xtt is best regarded as an empirical parameter. If used, n is often 0.2 or 0.25.
References
[1] (1, 2) Lockhart, R. W. & Martinelli, R. C. (1949), “Proposed correlation of data for isothermal twophase, twocomponent flow in pipes”, Chemical Engineering Progress 45 (1), 3948. [2] (1, 2) Woldesemayat, Melkamu A., and Afshin J. Ghajar. “Comparison of Void Fraction Correlations for Different Flow Patterns in Horizontal and Upward Inclined Pipes.” International Journal of Multiphase Flow 33, no. 4 (April 2007): 347370. doi:10.1016/j.ijmultiphaseflow.2006.09.004. Examples
>>> Lockhart_Martinelli_Xtt(0.4, 800, 2.5, 1E3, 1E5) 0.12761659240532292

fluids.two_phase_voidage.
two_phase_voidage_experimental
(rho_lg, rhol, rhog)[source]¶ Calculates the void fraction for twophase liquidgas pipeflow. If the weight of fluid in a pipe pipe could be measured and the volume of the pipe were known, an effective density of the twophase mixture could be calculated. This is directly relatable to the void fraction of the pipe, a parameter used to predict the pressure drop. This function converts that measured effective twophase density to void fraction for use in developing correlations.
\[\alpha = \frac{\rho_m  \rho_l}{\rho_g  \rho_l}\]Parameters:  rho_lg : float
Twophase effective density [kg/m^3]
 rhol : float
Density of the liquid [kg/m^3]
 rhog : float
Density of the gas [kg/m^3]
Returns:  alpha : float
Void fraction (area of gas / total area of channel), []
References
[1] Awad, M. M., and Y. S. Muzychka. “Effective Property Models for Homogeneous TwoPhase Flows.” Experimental Thermal and Fluid Science 33, no. 1 (October 1, 2008): 10613. Examples
>>> two_phase_voidage_experimental(481.0, 800, 2.5) 0.4

fluids.two_phase_voidage.
density_two_phase
(alpha, rhol, rhog)[source]¶ Calculates the “effective” density of fluid in a liquidgas flow. If the weight of fluid in a pipe pipe could be measured and the volume of the pipe were known, an effective density of the twophase mixture could be calculated. This is directly relatable to the void fraction of the pipe, a parameter used to predict the pressure drop. This function converts void fraction to effective twophase density.
\[\rho_m = \alpha \rho_g + (1\alpha)\rho_l\]Parameters:  alpha : float
Void fraction (area of gas / total area of channel), []
 rhol : float
Density of the liquid [kg/m^3]
 rhog : float
Density of the gas [kg/m^3]
Returns:  rho_lg : float
Twophase effective density [kg/m^3]
Notes
THERE IS NO THERMODYNAMIC DEFINITION FOR THIS QUANTITY. DO NOT USE THIS VALUE IN SINGLEPHASE CORRELATIONS.
References
[1] Awad, M. M., and Y. S. Muzychka. “Effective Property Models for Homogeneous TwoPhase Flows.” Experimental Thermal and Fluid Science 33, no. 1 (October 1, 2008): 10613. Examples
>>> density_two_phase(.4, 800, 2.5) 481.0

fluids.two_phase_voidage.
Beattie_Whalley
(x, mul, mug, rhol, rhog)[source]¶ Calculates a suggested definition for liquidgas twophase flow viscosity in internal pipe flow according to the form in [1] and shown in [2] and [3].
\[ \begin{align}\begin{aligned}\mu_m = \mu_l(1\alpha_m)(1 + 2.5\alpha_m) + \mu_g\alpha_m\\\alpha_m = \frac{1}{1 + \left(\frac{1x}{x}\right)\frac{\rho_g}{\rho_l}} \text{(homogeneous model)}\end{aligned}\end{align} \]Parameters:  x : float
Quality of the gasliquid flow, []
 mul : float
Viscosity of liquid, [Pa*s]
 mug : float
Viscosity of gas, [Pa*s]
 rhol : float
Density of the liquid [kg/m^3]
 rhog : float
Density of the gas [kg/m^3]
Returns:  mu_lg : float
Liquidgas viscosity (a suggested definition, potentially useful for empirical work only!) [Pa*s]
Notes
This model converges to the liquid or gas viscosity as the quality approaches either limits.
References
[1] (1, 2) Beattie, D. R. H., and P. B. Whalley. “A Simple TwoPhase Frictional Pressure Drop Calculation Method.” International Journal of Multiphase Flow 8, no. 1 (February 1, 1982): 8387. doi:10.1016/03019322(82)90009X. [2] (1, 2) Awad, M. M., and Y. S. Muzychka. “Effective Property Models for Homogeneous TwoPhase Flows.” Experimental Thermal and Fluid Science 33, no. 1 (October 1, 2008): 10613. [3] (1, 2) Kim, SungMin, and Issam Mudawar. “Review of Databases and Predictive Methods for Pressure Drop in Adiabatic, Condensing and Boiling Mini/MicroChannel Flows.” International Journal of Heat and Mass Transfer 77 (October 2014): 7497. doi:10.1016/j.ijheatmasstransfer.2014.04.035. Examples
>>> Beattie_Whalley(x=0.4, mul=1E3, mug=1E5, rhol=850, rhog=1.2) 1.7363806909512365e05

fluids.two_phase_voidage.
McAdams
(x, mul, mug)[source]¶ Calculates a suggested definition for liquidgas twophase flow viscosity in internal pipe flow according to the form in [1] and shown in [2] and [3].
\[\mu_m = \left(\frac{x}{\mu_g} + \frac{1x}{\mu_l}\right)^{1}\]Parameters:  x : float
Quality of the gasliquid flow, []
 mul : float
Viscosity of liquid, [Pa*s]
 mug : float
Viscosity of gas, [Pa*s]
Returns:  mu_lg : float
Liquidgas viscosity (a suggested definition, potentially useful for empirical work only!) [Pa*s]
Notes
This model converges to the liquid or gas viscosity as the quality approaches either limits.
[3] states this is the most common definition of twophase liquidgas viscosity.
References
[1] (1, 2) McAdams, W. H. “Vaporization inside Horizontal TubesII BenzeneOil Mixtures.” Trans. ASME 39 (1949): 3948. [2] (1, 2) Awad, M. M., and Y. S. Muzychka. “Effective Property Models for Homogeneous TwoPhase Flows.” Experimental Thermal and Fluid Science 33, no. 1 (October 1, 2008): 10613. [3] (1, 2, 3) Kim, SungMin, and Issam Mudawar. “Review of Databases and Predictive Methods for Pressure Drop in Adiabatic, Condensing and Boiling Mini/MicroChannel Flows.” International Journal of Heat and Mass Transfer 77 (October 2014): 7497. doi:10.1016/j.ijheatmasstransfer.2014.04.035. Examples
>>> McAdams(x=0.4, mul=1E3, mug=1E5) 2.4630541871921184e05

fluids.two_phase_voidage.
Cicchitti
(x, mul, mug)[source]¶ Calculates a suggested definition for liquidgas twophase flow viscosity in internal pipe flow according to the form in [1] and shown in [2] and [3].
\[\mu_m = x\mu_g + (1x)\mu_l\]Parameters:  x : float
Quality of the gasliquid flow, []
 mul : float
Viscosity of liquid, [Pa*s]
 mug : float
Viscosity of gas, [Pa*s]
Returns:  mu_lg : float
Liquidgas viscosity (a suggested definition, potentially useful for empirical work only!) [Pa*s]
Notes
This model converges to the liquid or gas viscosity as the quality approaches either limits.
References
[1] (1, 2) Cicchitti, A., C. Lombardi, M. Silvestri, G. Soldaini, and R. Zavattarelli. “TwoPhase Cooling Experiments: Pressure Drop, Heat Transfer and Burnout Measurements.” Centro Informazioni Studi Esperienze, Milan, January 1, 1959. [2] (1, 2) Awad, M. M., and Y. S. Muzychka. “Effective Property Models for Homogeneous TwoPhase Flows.” Experimental Thermal and Fluid Science 33, no. 1 (October 1, 2008): 10613. [3] (1, 2) Kim, SungMin, and Issam Mudawar. “Review of Databases and Predictive Methods for Pressure Drop in Adiabatic, Condensing and Boiling Mini/MicroChannel Flows.” International Journal of Heat and Mass Transfer 77 (October 2014): 7497. doi:10.1016/j.ijheatmasstransfer.2014.04.035. Examples
>>> Cicchitti(x=0.4, mul=1E3, mug=1E5) 0.0006039999999999999

fluids.two_phase_voidage.
Lin_Kwok
(x, mul, mug)[source]¶ Calculates a suggested definition for liquidgas twophase flow viscosity in internal pipe flow according to the form in [1] and shown in [2] and [3]_.
\[\mu_m = \frac{\mu_l \mu_g}{\mu_g + x^{1.4}(\mu_l  \mu_g)}\]Parameters:  x : float
Quality of the gasliquid flow, []
 mul : float
Viscosity of liquid, [Pa*s]
 mug : float
Viscosity of gas, [Pa*s]
Returns:  mu_lg : float
Liquidgas viscosity (a suggested definition, potentially useful for empirical work only!) [Pa*s]
Notes
This model converges to the liquid or gas viscosity as the quality approaches either limits.
References
[1] (1, 2) Lin, S., C. C. K. Kwok, R. Y. Li, Z. H. Chen, and Z. Y. Chen. “Local Frictional Pressure Drop during Vaporization of R12 through Capillary Tubes.” International Journal of Multiphase Flow 17, no. 1 (January 1, 1991): 95102. doi:10.1016/03019322(91)90072B. [2] (1, 2) Awad, M. M., and Y. S. Muzychka. “Effective Property Models for Homogeneous TwoPhase Flows.” Experimental Thermal and Fluid Science 33, no. 1 (October 1, 2008): 10613. Examples
>>> Lin_Kwok(x=0.4, mul=1E3, mug=1E5) 3.515119398126066e05

fluids.two_phase_voidage.
Fourar_Bories
(x, mul, mug, rhol, rhog)[source]¶ Calculates a suggested definition for liquidgas twophase flow viscosity in internal pipe flow according to the form in [1] and shown in [2] and [3].
\[\mu_m = \rho_m\left(\sqrt{x\nu_g} + \sqrt{(1x)\nu_l}\right)^2\]Parameters:  x : float
Quality of the gasliquid flow, []
 mul : float
Viscosity of liquid, [Pa*s]
 mug : float
Viscosity of gas, [Pa*s]
 rhol : float
Density of the liquid, [kg/m^3]
 rhog : float
Density of the gas, [kg/m^3]
Returns:  mu_lg : float
Liquidgas viscosity (a suggested definition, potentially useful for empirical work only!) [Pa*s]
Notes
This model converges to the liquid or gas viscosity as the quality approaches either limits.
This was first expressed in the equalivalent form as follows:
\[\mu_m = \rho_m\left(x\nu_g + (1x)\nu_l + 2\sqrt{x(1x)\nu_g\nu_l} \right)\]References
[1] (1, 2) Fourar, M., and S. Bories. “Experimental Study of AirWater TwoPhase Flow through a Fracture (Narrow Channel).” International Journal of Multiphase Flow 21, no. 4 (August 1, 1995): 62137. doi:10.1016/03019322(95)00005I. [2] (1, 2) Awad, M. M., and Y. S. Muzychka. “Effective Property Models for Homogeneous TwoPhase Flows.” Experimental Thermal and Fluid Science 33, no. 1 (October 1, 2008): 10613. [3] (1, 2) Aung, NZ, and T. Yuwono. “Evaluation of Mixture Viscosity Models in the Prediction of TwoPhase Flow Pressure Drops.” ASEAN Journal on Science and Technology for Development 29, no. 2 (2012). Examples
>>> Fourar_Bories(x=0.4, mul=1E3, mug=1E5, rhol=850, rhog=1.2) 2.127617150298565e05

fluids.two_phase_voidage.
liquid_gas_voidage
(x, rhol, rhog, D=None, m=None, mul=None, mug=None, sigma=None, P=None, Pc=None, angle=0, g=9.80665, Method=None, AvailableMethods=False)[source]¶ This function handles calculation of twophase liquidgas voidage for flow inside channels. 29 calculation methods are available, with varying input requirements. A correlation will be automatically selected if none is specified. The full list of correlation can be obtained with the AvailableMethods flag.
If no correlation is selected, the following rules are used, with the earlier options attempted first:
 TODO: defaults
Parameters:  x : float
Quality of fluid, []
 rhol : float
Liquid density, [kg/m^3]
 rhog : float
Gas density, [kg/m^3]
 D : float, optional
Diameter of pipe, [m]
 m : float, optional
Mass flow rate of fluid, [kg/s]
 mul : float, optional
Viscosity of liquid, [Pa*s]
 mug : float, optional
Viscosity of gas, [Pa*s]
 sigma : float, optional
Surface tension, [N/m]
 P : float, optional
Pressure of fluid, [Pa]
 Pc : float, optional
Critical pressure of fluid, [Pa]
 angle : float, optional
Angle of the channel with respect to the horizontal (vertical = 90), [degrees]
 g : float, optional
Acceleration due to gravity, [m/s^2]
Returns:  alpha : float
Void fraction (area of gas / total area of channel), []
 methods : list, only returned if AvailableMethods == True
List of methods which can be used to calculate twophase liquidgas voidage with the given inputs.
Other Parameters:  Method : string, optional
A string of the function name to use, as in the dictionary two_phase_voidage_correlations.
 AvailableMethods : bool, optional
If True, function will consider which methods which can be used to calculate twophase liquidgas voidage with the given inputs and return them as a list instead of performing a calculation.
Examples
>>> liquid_gas_voidage(m=0.6, x=0.1, rhol=915., rhog=2.67, mul=180E6, mug=14E6, ... sigma=0.0487, D=0.05) 0.9744097632663492

fluids.two_phase_voidage.
gas_liquid_viscosity
(x, mul, mug, rhol=None, rhog=None, Method=None, AvailableMethods=False)[source]¶ This function handles the calculation of twophase liquidgas viscosity. Six calculation methods are available; three of them require only x, mul, and mug; the other three require rhol and rhog as well.
The ‘McAdams’ method will be used if no method is specified. The full list of correlation can be obtained with the AvailableMethods flag.
ALL OF THESE METHODS ARE ONLY SUGGESTED DEFINITIONS, POTENTIALLY USEFUL FOR EMPERICAL WORK ONLY!
Parameters:  x : float
Quality of fluid, []
 mul : float
Viscosity of liquid, [Pa*s]
 mug : float
Viscosity of gas, [Pa*s]
 rhol : float, optional
Liquid density, [kg/m^3]
 rhog : float, optional
Gas density, [kg/m^3]
Returns:  mu_lg : float
Liquidgas viscosity (a suggested definition, potentially useful for empirical work only!) [Pa*s]
 methods : list, only returned if AvailableMethods == True
List of methods which can be used to calculate twophase liquidgas viscosity with the given inputs.
Other Parameters:  Method : string, optional
A string of the function name to use, as in the dictionary liquid_gas_viscosity_correlations.
 AvailableMethods : bool, optional
If True, function will consider which methods which can be used to calculate twophase liquidgas viscosity with the given inputs and return them as a list instead of performing a calculation.
Notes
All of these models converge to the liquid or gas viscosity as the quality approaches either limits. Other definitions have been proposed, such as using only liquid viscosity.
These values cannot just be plugged into single phase correlations!
Examples
>>> gas_liquid_viscosity(x=0.4, mul=1E3, mug=1E5, rhol=850, rhog=1.2, Method='Duckler') 1.2092040385066917e05 >>> gas_liquid_viscosity(x=0.4, mul=1E3, mug=1E5) 2.4630541871921184e05