Two-phase flow voidage (fluids.two_phase_voidage)

fluids.two_phase_voidage.Thom(x, rhol, rhog, mul, mug)[source]

Calculates void fraction in two-phase flow according to the model of [R11071197] as given in [R11081197].

\[\alpha = \left[1 + \left(\frac{1-x}{x}\right)\left(\frac{\rho_g} {\rho_l}\right)^{0.89}\left(\frac{\mu_l}{\mu_g}\right)^{0.18} \right]^{-1}\]
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. [R11091197] 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 [R11071197] in a brief review.

References

[R11071197](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): 709-24. doi:10.1016/0017-9310(64)90002-X.
[R11081197](1, 2) Xu, Yu, and Xiande Fang. “Correlations of Void Fraction for Two- Phase Refrigerant Flow in Pipes.” Applied Thermal Engineering 64, no. 1-2 (March 2014): 242–51. doi:10.1016/j.applthermaleng.2013.12.032.
[R11091197](1, 2) Dalkilic, A. S., S. Laohalertdecha, and S. Wongwises. “Effect of Void Fraction Models on the Two-Phase 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): 921-27. doi:10.1016/j.icheatmasstransfer.2008.04.001.

Examples

>>> Thom(.4, 800, 2.5, 1E-3, 1E-5)
0.9801482164042417
fluids.two_phase_voidage.Zivi(x, rhol, rhog)[source]

Calculates void fraction in two-phase flow according to the model of [R11101200] as given in [R11111200] and [R11121200].

\[\alpha = \left[1 + \left(\frac{1-x}{x}\right) \left(\frac{\rho_g}{\rho_l}\right)^{2/3}\right]^{-1}\]
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 [R11101200].

References

[R11101200](1, 2, 3) Zivi, S. M. “Estimation of Steady-State Steam Void-Fraction by Means of the Principle of Minimum Entropy Production.” Journal of Heat Transfer 86, no. 2 (May 1, 1964): 247-51. doi:10.1115/1.3687113.
[R11111200](1, 2) Xu, Yu, and Xiande Fang. “Correlations of Void Fraction for Two- Phase Refrigerant Flow in Pipes.” Applied Thermal Engineering 64, no. 1-2 (March 2014): 242–51. doi:10.1016/j.applthermaleng.2013.12.032.
[R11121200](1, 2) Dalkilic, A. S., S. Laohalertdecha, and S. Wongwises. “Effect of Void Fraction Models on the Two-Phase 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): 921-27. 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 two-phase flow according to the model of [R11131203], also given in [R11141203] and [R11151203].

\[\alpha = \left\{1 + \left(\frac{1-x}{x}\right) \left(\frac{\rho_g}{\rho_l}\right)\left[K+(1-K) \sqrt{\frac{\frac{\rho_l}{\rho_g} + K\left(\frac{1-x}{x}\right)} {1 + K\left(\frac{1-x}{x}\right)}}\right] \right\}^{-1}\]
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

[R11131203] is an easy to read paper and has been reviewed. The form of the expression here is rearranged somewhat differently than in [R11131203] but has been verified to be numerically equivalent. The form of this in [R11151203] is missing a square root on a bracketed term; this appears in multiple papers by the authors.

References

[R11131203](1, 2, 3, 4) Smith, S. L. “Void Fractions in Two-Phase Flow: A Correlation Based upon an Equal Velocity Head Model.” Proceedings of the Institution of Mechanical Engineers 184, no. 1 (June 1, 1969): 647-64. doi:10.1243/PIME_PROC_1969_184_051_02.
[R11141203](1, 2) Xu, Yu, and Xiande Fang. “Correlations of Void Fraction for Two- Phase Refrigerant Flow in Pipes.” Applied Thermal Engineering 64, no. 1-2 (March 2014): 242–51. doi:10.1016/j.applthermaleng.2013.12.032.
[R11151203](1, 2, 3) Dalkilic, A. S., S. Laohalertdecha, and S. Wongwises. “Effect of Void Fraction Models on the Two-Phase 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): 921-27. 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 two-phase flow according to the model of [R11161206], as given in [R11171206] and [R11181206].

\[\alpha = \left[1 + \left(\frac{1-x}{x}\right) \left(\frac{\rho_g}{\rho_l}\right)^{0.5}\right]^{-1}\]
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

[R11161206] has not been reviewed. However, both [R11171206] and [R11181206] present it the same way.

References

[R11161206](1, 2, 3) Fauske, H., Critical two-phase, steam-water flows, in: Heat Transfer and Fluid Mechanics Institute 1961: Proceedings. Stanford University Press, 1961, p. 79-89.
[R11171206](1, 2, 3) Xu, Yu, and Xiande Fang. “Correlations of Void Fraction for Two- Phase Refrigerant Flow in Pipes.” Applied Thermal Engineering 64, no. 1-2 (March 2014): 242–51. doi:10.1016/j.applthermaleng.2013.12.032.
[R11181206](1, 2, 3) Dalkilic, A. S., S. Laohalertdecha, and S. Wongwises. “Effect of Void Fraction Models on the Two-Phase 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): 921-27. 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 two-phase flow according to the model of [R11191209], as given in [R11201209] and [R11211209].

\[\alpha = \left[1 + \left(\frac{1-x}{x}\right)\left(\frac{\rho_g} {\rho_l}\right)\sqrt{1 - x\left(1-\frac{\rho_l}{\rho_g}\right)} \right]^{-1}\]
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

[R11191209] has not been reviewed. However, both [R11201209] and [R11211209] present it the same way.

References

[R11191209](1, 2, 3) Chisholm, D. “Pressure Gradients due to Friction during the Flow of Evaporating Two-Phase Mixtures in Smooth Tubes and Channels.” International Journal of Heat and Mass Transfer 16, no. 2 (February 1, 1973): 347-58. doi:10.1016/0017-9310(73)90063-X.
[R11201209](1, 2, 3) Xu, Yu, and Xiande Fang. “Correlations of Void Fraction for Two- Phase Refrigerant Flow in Pipes.” Applied Thermal Engineering 64, no. 1-2 (March 2014): 242–51. doi:10.1016/j.applthermaleng.2013.12.032.
[R11211209](1, 2, 3) Dalkilic, A. S., S. Laohalertdecha, and S. Wongwises. “Effect of Void Fraction Models on the Two-Phase 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): 921-27. 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 two-phase flow according to the model of [R11221212], as given in [R11231212] and [R11241212].

\[\alpha = \left[1 + \left(\frac{1-x}{x}\right)^{0.72}\left(\frac{\rho_g} {\rho_l}\right)^{0.4}\left(\frac{\mu_l}{\mu_g}\right)^{0.08} \right]^{-1}\]
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

[R11221212] has not been reviewed. However, both [R11231212] and [R11241212] present it the same way, if slightly differently rearranged.

References

[R11221212](1, 2, 3) J.M. Turner, G.B. Wallis, The Separate-cylinders Model of Two-phase Flow, NYO-3114-6, Thayer’s School Eng., Dartmouth College, Hanover, New Hampshire, USA, 1965.
[R11231212](1, 2, 3) Xu, Yu, and Xiande Fang. “Correlations of Void Fraction for Two- Phase Refrigerant Flow in Pipes.” Applied Thermal Engineering 64, no. 1-2 (March 2014): 242–51. doi:10.1016/j.applthermaleng.2013.12.032.
[R11241212](1, 2, 3) Dalkilic, A. S., S. Laohalertdecha, and S. Wongwises. “Effect of Void Fraction Models on the Two-Phase 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): 921-27. doi:10.1016/j.icheatmasstransfer.2008.04.001.

Examples

>>> Turner_Wallis(.4, 800, 2.5, 1E-3, 1E-5)
0.8384824581634625
fluids.two_phase_voidage.homogeneous(x, rhol, rhog)[source]

Calculates void fraction in two-phase flow according to the homogeneous flow model, reviewed in [R11251215], [R11261215], and [R11271215].

\[\alpha = \frac{1}{1 + \left(\frac{1-x}{x}\right)\frac{\rho_g}{\rho_l}}\]
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

[R11251215](1, 2) Xu, Yu, and Xiande Fang. “Correlations of Void Fraction for Two- Phase Refrigerant Flow in Pipes.” Applied Thermal Engineering 64, no. 1-2 (March 2014): 242–51. doi:10.1016/j.applthermaleng.2013.12.032.
[R11261215](1, 2) Dalkilic, A. S., S. Laohalertdecha, and S. Wongwises. “Effect of Void Fraction Models on the Two-Phase 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): 921-27. doi:10.1016/j.icheatmasstransfer.2008.04.001.
[R11271215](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): 347-370. 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 two-phase flow according to the model presented in [R11281218] based on that of [R11291218] as shown in [R11301218], [R11311218], and [R11321218].

\[\alpha = \frac{\alpha_h}{\alpha_h + (1-\alpha_h)^{0.5}}\]
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

[R11281218](1, 2) Chisholm, Duncan. Two-Phase Flow in Pipelines and Heat Exchangers. Institution of Chemical Engineers, 1983.
[R11291218](1, 2) Armand, Aleksandr Aleksandrovich. The Resistance During the Movement of a Two-Phase System in Horizontal Pipes. Atomic Energy Research Establishment, 1959.
[R11301218](1, 2) Xu, Yu, and Xiande Fang. “Correlations of Void Fraction for Two- Phase Refrigerant Flow in Pipes.” Applied Thermal Engineering 64, no. 1-2 (March 2014): 242–51. doi:10.1016/j.applthermaleng.2013.12.032.
[R11311218](1, 2) Dalkilic, A. S., S. Laohalertdecha, and S. Wongwises. “Effect of Void Fraction Models on the Two-Phase 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): 921-27. doi:10.1016/j.icheatmasstransfer.2008.04.001.
[R11321218](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): 347-370. 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 two-phase flow according to the model presented in [R11331223] as shown in [R11341223], [R11351223], and [R11361223].

\[\alpha = 0.833\alpha_h\]
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

[R11331223](1, 2) Armand, Aleksandr Aleksandrovich. The Resistance During the Movement of a Two-Phase System in Horizontal Pipes. Atomic Energy Research Establishment, 1959.
[R11341223](1, 2) Xu, Yu, and Xiande Fang. “Correlations of Void Fraction for Two- Phase Refrigerant Flow in Pipes.” Applied Thermal Engineering 64, no. 1-2 (March 2014): 242–51. doi:10.1016/j.applthermaleng.2013.12.032.
[R11351223](1, 2) Dalkilic, A. S., S. Laohalertdecha, and S. Wongwises. “Effect of Void Fraction Models on the Two-Phase 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): 921-27. doi:10.1016/j.icheatmasstransfer.2008.04.001.
[R11361223](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): 347-370. 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 two-phase flow according to the model presented in [R11371227] as shown in [R11381227].

\[\alpha = 1 - \left(\frac{1-x}{x}\frac{\rho_g}{\rho_l}\right)^{0.5} \alpha_h^{0.5}\]
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

[R11371227] is in Japanese.

[R11391227] 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

[R11371227](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): 39-46. doi:10.3327/jaesj.5.39.
[R11381227](1, 2) Xu, Yu, and Xiande Fang. “Correlations of Void Fraction for Two- Phase Refrigerant Flow in Pipes.” Applied Thermal Engineering 64, no. 1-2 (March 2014): 242–51. doi:10.1016/j.applthermaleng.2013.12.032.
[R11391227](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): 347-370. 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 two-phase flow according to the model in [R11401230] as shown in [R11411230] and [R11421230].

\[ \begin{align}\begin{aligned}\alpha = 0.81[1 - \exp(-2.2\sqrt{Fr_{tp}})]\alpha_h\\Fr_{tp} = \frac{G_{tp}^2}{gD\rho_{tp}^2}\\\rho_{tp} = \left(\frac{1-x}{\rho_l} + \frac{x}{\rho_g}\right)^{-1}\end{aligned}\end{align} \]
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

[R11401230](1, 2) Guzhov, A. I, Vasiliĭ Andreevich Mamaev, and G. E Odisharii︠a︡. A Study of Transportation in Gas-Liquid Systems. Une Étude Sur Le Transport Des Systèmes Gaz-Liquides. Bruxelles: International Gas Union, 1967.
[R11411230](1, 2) Xu, Yu, and Xiande Fang. “Correlations of Void Fraction for Two- Phase Refrigerant Flow in Pipes.” Applied Thermal Engineering 64, no. 1-2 (March 2014): 242–51. doi:10.1016/j.applthermaleng.2013.12.032. 921-27. doi:10.1016/j.icheatmasstransfer.2008.04.001.
[R11421230](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): 347-370. 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 two-phase flow according to the model presented in [R11441234], also reviewed in [R11451234] and [R11461234]. 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 [R11441234]. Here, the coefficients are distributed for three ranges, > 250 micrometers, 250-75 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

[R11441234](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 Two-Phase Flow Through Microchannels.” Heat Transfer Engineering 26, no. 3 (February 16, 2005): 13-19. doi:10.1080/01457630590907158.
[R11451234](1, 2) Xu, Yu, and Xiande Fang. “Correlations of Void Fraction for Two- Phase Refrigerant Flow in Pipes.” Applied Thermal Engineering 64, no. 1-2 (March 2014): 242–51. doi:10.1016/j.applthermaleng.2013.12.032.
[R11461234](1, 2) Dalkilic, A. S., S. Laohalertdecha, and S. Wongwises. “Effect of Void Fraction Models on the Two-Phase 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): 921-27. doi:10.1016/j.icheatmasstransfer.2008.04.001.

Examples

>>> Kawahara(.4, 800, 2.5, 100E-6)
0.9276148194410238
fluids.two_phase_voidage.Baroczy(x, rhol, rhog, mul, mug)[source]

Calculates void fraction in two-phase flow according to the model of [R11471237] as given in [R11481237], [R11491237], and [R11501237].

\[\alpha = \left[1 + \left(\frac{1-x}{x}\right)^{0.74}\left(\frac{\rho_g} {\rho_l}\right)^{0.65}\left(\frac{\mu_l}{\mu_g}\right)^{0.13} \right]^{-1}\]
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

[R11471237](1, 2) Baroczy, C. Correlation of liquid fraction in two-phase flow with applications to liquid metals, Chem. Eng. Prog. Symp. Ser. 61 (1965) 179-191.
[R11481237](1, 2) Xu, Yu, and Xiande Fang. “Correlations of Void Fraction for Two- Phase Refrigerant Flow in Pipes.” Applied Thermal Engineering 64, no. 1-2 (March 2014): 242–51. doi:10.1016/j.applthermaleng.2013.12.032.
[R11491237](1, 2) Dalkilic, A. S., S. Laohalertdecha, and S. Wongwises. “Effect of Void Fraction Models on the Two-Phase 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): 921-27. doi:10.1016/j.icheatmasstransfer.2008.04.001.
[R11501237](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): 347-370. doi:10.1016/j.ijmultiphaseflow.2006.09.004.

Examples

>>> Baroczy(.4, 800, 2.5, 1E-3, 1E-5)
0.9453544598460807
fluids.two_phase_voidage.Tandon_Varma_Gupta(x, rhol, rhog, mul, mug, m, D)[source]

Calculates void fraction in two-phase flow according to the model of [R11511241] also given in [R11521241], [R11531241], and [R11541241].

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

[R11511241] does not specify how it defines the liquid Reynolds number. [R11521241] disagrees with [R11531241] and [R11541241]; the later variant was selected, with:

\[Re_l = \frac{G_{tp}D}{\mu_l}\]

The lower limit on Reynolds number is not enforced.

References

[R11511241](1, 2, 3) Tandon, T. N., H. K. Varma, and C. P. Gupta. “A Void Fraction Model for Annular Two-Phase Flow.” International Journal of Heat and Mass Transfer 28, no. 1 (January 1, 1985): 191-198. doi:10.1016/0017-9310(85)90021-3.
[R11521241](1, 2, 3) Xu, Yu, and Xiande Fang. “Correlations of Void Fraction for Two- Phase Refrigerant Flow in Pipes.” Applied Thermal Engineering 64, no. 1-2 (March 2014): 242–51. doi:10.1016/j.applthermaleng.2013.12.032.
[R11531241](1, 2, 3) Dalkilic, A. S., S. Laohalertdecha, and S. Wongwises. “Effect of Void Fraction Models on the Two-Phase 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): 921-27. doi:10.1016/j.icheatmasstransfer.2008.04.001.
[R11541241](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): 347-370. doi:10.1016/j.ijmultiphaseflow.2006.09.004.

Examples

>>> Tandon_Varma_Gupta(.4, 800, 2.5, 1E-3, 1E-5, m=1, D=0.3)
0.9228265670341428
fluids.two_phase_voidage.Harms(x, rhol, rhog, mul, mug, m, D)[source]

Calculates void fraction in two-phase flow according to the model of [R11551245] also given in [R11561245] and [R11571245].

\[ \begin{align}\begin{aligned}\alpha = \left[1 - 10.06Re_l^{-0.875}(1.74 + 0.104Re_l^{0.5})^2 \left(1.376 + \frac{7.242}{X_{tt}^{1.655}}\right)^{-0.5}\right]^2\\Re_l = \frac{G_{tp}(1-x)D}{\mu_l}\end{aligned}\end{align} \]
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

[R11551245] has been reviewed.

References

[R11551245](1, 2, 3) Tandon, T. N., H. K. Varma, and C. P. Gupta. “A Void Fraction Model for Annular Two-Phase Flow.” International Journal of Heat and Mass Transfer 28, no. 1 (January 1, 1985): 191-198. doi:10.1016/0017-9310(85)90021-3.
[R11561245](1, 2) Xu, Yu, and Xiande Fang. “Correlations of Void Fraction for Two- Phase Refrigerant Flow in Pipes.” Applied Thermal Engineering 64, no. 1-2 (March 2014): 242–51. doi:10.1016/j.applthermaleng.2013.12.032.
[R11571245](1, 2) Dalkilic, A. S., S. Laohalertdecha, and S. Wongwises. “Effect of Void Fraction Models on the Two-Phase 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): 921-27. doi:10.1016/j.icheatmasstransfer.2008.04.001.

Examples

>>> Harms(.4, 800, 2.5, 1E-3, 1E-5, m=1, D=0.3)
0.9653289762907554
fluids.two_phase_voidage.Domanski_Didion(x, rhol, rhog, mul, mug)[source]

Calculates void fraction in two-phase flow according to the model of [R11581248] also given in [R11591248] and [R11601248].

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

[R11581248] has been reviewed. [R11591248] gives an exponent of -0.38 instead of -0.378 as is in [R11581248]. [R11601248] 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

[R11581248](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.
[R11591248](1, 2, 3) Xu, Yu, and Xiande Fang. “Correlations of Void Fraction for Two- Phase Refrigerant Flow in Pipes.” Applied Thermal Engineering 64, no. 1-2 (March 2014): 242–51. doi:10.1016/j.applthermaleng.2013.12.032.
[R11601248](1, 2, 3) Dalkilic, A. S., S. Laohalertdecha, and S. Wongwises. “Effect of Void Fraction Models on the Two-Phase 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): 921-27. doi:10.1016/j.icheatmasstransfer.2008.04.001.

Examples

>>> Domanski_Didion(.4, 800, 2.5, 1E-3, 1E-5)
0.9355795597059169
fluids.two_phase_voidage.Graham(x, rhol, rhog, mul, mug, m, D, g=9.80665)[source]

Calculates void fraction in two-phase flow according to the model of [R11611251] also given in [R11621251] and [R11631251].

\[ \begin{align}\begin{aligned}\alpha = 1 - \exp\{-1 - 0.3\ln(Ft) - 0.0328[\ln(Ft)]^2\}\\Ft = \left[\frac{G_{tp}^2 x^3}{(1-x)\rho_g^2gD}\right]^{0.5}\\\alpha = 0 \text{ for } F_t \le 0.01032\end{aligned}\end{align} \]
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

[R11611251] has been reviewed. [R11621251] does not list that the expression is not real below a certain value of Ft.

References

[R11611251](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 Urbana-Champaign., December 1997.
[R11621251](1, 2, 3) Xu, Yu, and Xiande Fang. “Correlations of Void Fraction for Two- Phase Refrigerant Flow in Pipes.” Applied Thermal Engineering 64, no. 1-2 (March 2014): 242–51. doi:10.1016/j.applthermaleng.2013.12.032.
[R11631251](1, 2) Dalkilic, A. S., S. Laohalertdecha, and S. Wongwises. “Effect of Void Fraction Models on the Two-Phase 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): 921-27. doi:10.1016/j.icheatmasstransfer.2008.04.001.

Examples

>>> Graham(.4, 800, 2.5, 1E-3, 1E-5, 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 two-phase flow according to the model of [R11641254] also given in [R11651254] and [R11661254].

\[ \begin{align}\begin{aligned}\alpha = \left[1 + \frac{1}{Ft} + X_{tt}\right]^{-0.321}\\Ft = \left[\frac{G_{tp}^2 x^3}{(1-x)\rho_g^2gD}\right]^{0.5}\end{aligned}\end{align} \]
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

[R11641254] has been reviewed; both [R11651254] and [R11661254] give it correctly.

References

[R11641254](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): 67-82. doi:10.1080/10789669.2001.10391430.
[R11651254](1, 2, 3) Xu, Yu, and Xiande Fang. “Correlations of Void Fraction for Two- Phase Refrigerant Flow in Pipes.” Applied Thermal Engineering 64, no. 1-2 (March 2014): 242–51. doi:10.1016/j.applthermaleng.2013.12.032.
[R11661254](1, 2, 3) Dalkilic, A. S., S. Laohalertdecha, and S. Wongwises. “Effect of Void Fraction Models on the Two-Phase 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): 921-27. doi:10.1016/j.icheatmasstransfer.2008.04.001.

Examples

>>> Yashar(.4, 800, 2.5, 1E-3, 1E-5, m=1, D=0.3)
0.7934893185789146
fluids.two_phase_voidage.Huq_Loth(x, rhol, rhog)[source]

Calculates void fraction in two-phase flow according to the model of [R11671257], also given in [R11681257], [R11691257], and [R11701257].

\[\alpha = 1 - \frac{2(1-x)^2}{1 - 2x + \left[1 + 4x(1-x)\left(\frac {\rho_l}{\rho_g}-1\right)\right]^{0.5}}\]
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

[R11671257] has been reviewed, and matches the expressions given in the reviews [R11681257], [R11691257], and [R11701257]; the form of the expression is rearranged somewhat differently.

References

[R11671257](1, 2, 3) Huq, Reazul, and John L. Loth. “Analytical Two-Phase Flow Void Prediction Method.” Journal of Thermophysics and Heat Transfer 6, no. 1 (January 1, 1992): 139-44. doi:10.2514/3.329.
[R11681257](1, 2, 3) Xu, Yu, and Xiande Fang. “Correlations of Void Fraction for Two- Phase Refrigerant Flow in Pipes.” Applied Thermal Engineering 64, no. 1-2 (March 2014): 242–51. doi:10.1016/j.applthermaleng.2013.12.032.
[R11691257](1, 2, 3) Dalkilic, A. S., S. Laohalertdecha, and S. Wongwises. “Effect of Void Fraction Models on the Two-Phase 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): 921-27. doi:10.1016/j.icheatmasstransfer.2008.04.001.
[R11701257](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): 347-370. 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 two-phase flow according to the model of [R11711261] also given in [R11721261].

\[ \begin{align}\begin{aligned}\alpha = 1.045 - \exp\{-1 - 0.342\ln(Ft) - 0.0268[\ln(Ft)]^2 + 0.00597[\ln(Ft)]^3\}\\Ft = \left[\frac{G_{tp}^2 x^3}{(1-x)\rho_g^2gD}\right]^{0.5}\\\alpha = \alpha_h \text{ for } F_t \le 0.044\end{aligned}\end{align} \]
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

[R11711261] has been reviewed. If is recommended this expression not be used above Ft values of 454.

References

[R11711261](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 Urbana-Champaign., August 1998.
[R11721261](1, 2) Xu, Yu, and Xiande Fang. “Correlations of Void Fraction for Two- Phase Refrigerant Flow in Pipes.” Applied Thermal Engineering 64, no. 1-2 (March 2014): 242–51. doi:10.1016/j.applthermaleng.2013.12.032.

Examples

>>> Kopte_Newell_Chato(.4, 800, 2.5, 1E-3, 1E-5, 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 two-phase flow according to the model of [R11731263] also given in [R11741263] and [R11751263].

\[ \begin{align}\begin{aligned}\alpha = \frac{x}{\rho_g}\left[C_0\left(\frac{x}{\rho_g} + \frac{1-x} {\rho_l}\right) +\frac{v_{gm}}{G} \right]^{-1}\\v_{gm} = \frac{1.18(1-x)}{\rho_l^{0.5}}[g\sigma(\rho_l-\rho_g)]^{0.25}\\C_0 = 1 + 0.12(1-x)\end{aligned}\end{align} \]
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

[R11731263] has been reviewed.

References

[R11731263](1, 2, 3) Gesellschaft, V. D. I., ed. VDI Heat Atlas. 2nd edition. Berlin; New York:: Springer, 2010.
[R11741263](1, 2) Xu, Yu, and Xiande Fang. “Correlations of Void Fraction for Two- Phase Refrigerant Flow in Pipes.” Applied Thermal Engineering 64, no. 1-2 (March 2014): 242–51. doi:10.1016/j.applthermaleng.2013.12.032.
[R11751263](1, 2) Dalkilic, A. S., S. Laohalertdecha, and S. Wongwises. “Effect of Void Fraction Models on the Two-Phase 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): 921-27. 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 two-phase flow according to the model of [R11761266] as given in [R11771266] and [R11781266].

\[ \begin{align}\begin{aligned}\alpha = \frac{x}{\rho_g}\left[C_0\left(\frac{x}{\rho_g} + \frac{1-x} {\rho_l}\right) +\frac{v_{gm}}{G} \right]^{-1}\\v_{gm} = \frac{1.18(1-x)}{\rho_l^{0.5}}[g\sigma(\rho_l-\rho_g)]^{0.25}\\C_0 = 1 + 0.2(1-x)\end{aligned}\end{align} \]
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 [R11771266] and [R11781266] could not be found in [R11761266].

References

[R11761266](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): 383-93. doi:10.1016/0017-9310(70)90114-6.
[R11771266](1, 2, 3) Xu, Yu, and Xiande Fang. “Correlations of Void Fraction for Two- Phase Refrigerant Flow in Pipes.” Applied Thermal Engineering 64, no. 1-2 (March 2014): 242–51. doi:10.1016/j.applthermaleng.2013.12.032.
[R11781266](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): 347-370. 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 two-phase flow according to the model of [R11791269] as given in [R11801269] and [R11811269].

\[ \begin{align}\begin{aligned}\alpha = \frac{x}{\rho_g}\left[C_0\left(\frac{x}{\rho_g} + \frac{1-x} {\rho_l}\right) +\frac{v_{gm}}{G} \right]^{-1}\\v_{gm} = \frac{1.18(1-x)}{\rho_l^{0.5}}[g\sigma(\rho_l-\rho_g)]^{0.25}\\C_0 = 1 + 0.2(1-x)(gD)^{0.25}\left(\frac{\rho_l}{G_{tp}}\right)^{0.5}\end{aligned}\end{align} \]
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 [R11801269] and [R11811269] could not be found in [R11791269].

References

[R11791269](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): 383-93. doi:10.1016/0017-9310(70)90114-6.
[R11801269](1, 2, 3) Xu, Yu, and Xiande Fang. “Correlations of Void Fraction for Two- Phase Refrigerant Flow in Pipes.” Applied Thermal Engineering 64, no. 1-2 (March 2014): 242–51. doi:10.1016/j.applthermaleng.2013.12.032.
[R11811269](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): 347-370. 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 two-phase flow according to the model of [R11821272] as given in [R11831272] and [R11841272].

\[ \begin{align}\begin{aligned}\alpha = \frac{x}{\rho_g}\left[C_0\left(\frac{x}{\rho_g} + \frac{1-x} {\rho_l}\right) +\frac{v_{gm}}{G} \right]^{-1}\\v_{gm} = 0.35\sqrt{gD}\\C_0 = 1.2\end{aligned}\end{align} \]
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

[R11821272](1, 2) D. Nicklin, J. Wilkes, J. Davidson, “Two-phase flow in vertical tubes”, Trans. Inst. Chem. Eng. 40 (1962) 61-68.
[R11831272](1, 2) Xu, Yu, and Xiande Fang. “Correlations of Void Fraction for Two- Phase Refrigerant Flow in Pipes.” Applied Thermal Engineering 64, no. 1-2 (March 2014): 242–51. doi:10.1016/j.applthermaleng.2013.12.032.
[R11841272](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): 347-370. 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 two-phase flow according to the model of [R11851275] as given in [R11861275] and [R11871275].

\[ \begin{align}\begin{aligned}\alpha = \frac{x}{\rho_g}\left[C_0\left(\frac{x}{\rho_g} + \frac{1-x} {\rho_l}\right) +\frac{v_{gm}}{G} \right]^{-1}\\v_{gm} = 0\\C_0 = 1.19\end{aligned}\end{align} \]
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

[R11851275](1, 2) Gregory, G. A., and D. S. Scott. “Correlation of Liquid Slug Velocity and Frequency in Horizontal Cocurrent Gas-Liquid Slug Flow.” AIChE Journal 15, no. 6 (November 1, 1969): 933-35. doi:10.1002/aic.690150623.
[R11861275](1, 2) Xu, Yu, and Xiande Fang. “Correlations of Void Fraction for Two- Phase Refrigerant Flow in Pipes.” Applied Thermal Engineering 64, no. 1-2 (March 2014): 242–51. doi:10.1016/j.applthermaleng.2013.12.032.
[R11871275](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): 347-370. 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 two-phase flow according to the model of [R11881278] as given in [R11891278] and [R11901278].

\[ \begin{align}\begin{aligned}\alpha = \frac{x}{\rho_g}\left[C_0\left(\frac{x}{\rho_g} + \frac{1-x} {\rho_l}\right) +\frac{v_{gm}}{G} \right]^{-1}\\v_{gm} = 2.9\left(g\sigma\frac{\rho_l-\rho_g}{\rho_l^2}\right)^{0.25}\\C_0 = \frac{v_{sg}}{v_m}\left[1 + \left(\frac{v_{sl}}{v_{sg}}\right) ^{\left(\left(\frac{\rho_g}{\rho_l}\right)^{0.1}\right)}\right]\\v_{gs} = \frac{mx}{\rho_g \frac{\pi}{4}D^2}\\v_{ls} = \frac{m(1-x)}{\rho_l \frac{\pi}{4}D^2}\\v_m = v_{gs} + v_{ls}\end{aligned}\end{align} \]
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

[R11881278](1, 2) Gary Errol. Dix. “Vapor Void Fractions for Forced Convection with Subcooled Boiling at Low Flow Rates.” Thesis. University of California, Berkeley, 1971.
[R11891278](1, 2) Xu, Yu, and Xiande Fang. “Correlations of Void Fraction for Two- Phase Refrigerant Flow in Pipes.” Applied Thermal Engineering 64, no. 1-2 (March 2014): 242–51. doi:10.1016/j.applthermaleng.2013.12.032.
[R11901278](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): 347-370. 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 two-phase flow according to the model of [R11911281] as given in [R11921281] and [R11931281].

\[ \begin{align}\begin{aligned}\alpha = \frac{x}{\rho_g}\left[C_0\left(\frac{x}{\rho_g} + \frac{1-x} {\rho_l}\right) +\frac{v_{gm}}{G} \right]^{-1}\\v_{gm} = 1.41\left[\frac{g\sigma(\rho_l-\rho_g)}{\rho_l^2}\right]^{0.25}\\C_0 = \left(0.82 + 0.18\frac{P}{P_c}\right)^{-1}\end{aligned}\end{align} \]
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

[R11911281](1, 2) K.H. Sun, R.B. Duffey, C.M. Peng, A thermal-hydraulic analysis of core uncover, in: Proceedings of the 19th National Heat Transfer Conference, Experimental and Analytical Modeling of LWR Safety Experiments, 1980, pp. 1-10. Orlando, Florida, USA.
[R11921281](1, 2) Xu, Yu, and Xiande Fang. “Correlations of Void Fraction for Two- Phase Refrigerant Flow in Pipes.” Applied Thermal Engineering 64, no. 1-2 (March 2014): 242–51. doi:10.1016/j.applthermaleng.2013.12.032.
[R11931281](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): 347-370. 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 two-phase flow according to the model developed in the review of [R11941284].

\[\alpha = \left[1 + \left(1 + 2Fr_{lo}^{-0.2}\alpha_h^{3.5}\right)\left( \frac{1-x}{x}\right)\left(\frac{\rho_g}{\rho_l}\right)\right]^{-1}\]
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 0.004-0.153, and x from 0 to 1.

References

[R11941284](1, 2) Xu, Yu, and Xiande Fang. “Correlations of Void Fraction for Two- Phase Refrigerant Flow in Pipes.” Applied Thermal Engineering 64, no. 1-2 (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 two-phase flow according to the model of [R11951285].

\[ \begin{align}\begin{aligned}\alpha = \frac{v_{gs}}{v_{gs}\left(1 + \left(\frac{v_{ls}}{v_{gs}} \right)^{\left(\frac{\rho_g}{\rho_l}\right)^{0.1}}\right) + 2.9\left[\frac{gD\sigma(1+\cos\theta)(\rho_l-\rho_g)} {\rho_l^2}\right]^{0.25}(1.22 + 1.22\sin\theta)^{\frac{P}{P_{atm}}}}\\v_{gs} = \frac{mx}{\rho_g \frac{\pi}{4}D^2}\\v_{ls} = \frac{m(1-x)}{\rho_l \frac{\pi}{4}D^2}\end{aligned}\end{align} \]
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

[R11951285](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): 347-370. 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 Lockhart-Martinelli Xtt two-phase flow parameter in a general way according to [R11971286]. [R11961286] 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.

\[ \begin{align}\begin{aligned}X_{tt} = \left(\frac{1-x}{x}\right)^{0.9} \left(\frac{\rho_g}{\rho_l} \right)^{0.5}\left(\frac{\mu_l}{\mu_g}\right)^{0.1}\\X_{tt} = \left(\frac{1-x}{x}\right)^{(2-n)/2} \left(\frac{\rho_g} {\rho_l}\right)^{0.5}\left(\frac{\mu_l}{\mu_g}\right)^{n/2}\end{aligned}\end{align} \]
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 (1-x)/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 Lockhart-Martinelli two-phase flow parameter [-]

Notes

Xtt is best regarded as an empirical parameter. If used, n is often 0.2 or 0.25.

References

[R11961286](1, 2) Lockhart, R. W. & Martinelli, R. C. (1949), “Proposed correlation of data for isothermal two-phase, two-component flow in pipes”, Chemical Engineering Progress 45 (1), 39-48.
[R11971286](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): 347-370. doi:10.1016/j.ijmultiphaseflow.2006.09.004.

Examples

>>> Lockhart_Martinelli_Xtt(0.4, 800, 2.5, 1E-3, 1E-5)
0.12761659240532292