# Void Fraction

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## Abstract

This chapter first presents parametric analysis of the void fraction and then provides a brief review of some of the modeling techniques for determination of the void fraction and recommendation of well-scrutinized void fraction correlations, followed by an illustrative example.

## Keywords

Two-phase flow Gas-liquid Flow pattern Horizontal and vertical flow Upward and downward inclined flow Void fraction Pipe orientation Phase flow rates Fluid properties Pipe diameter Drift flux model Distribution parameter Drift velocity Modeling Correlations## References

- Abdulkadir M, Hernandez-Perez V, Sharaf S, Lowndes IS, Azzopardi BJ (2010) Experimental investigation of phase distributions of two-phase air–silicone oil flow in a vertical pipe. World Acad Sci Eng Technol 37:52–59Google Scholar
- Bendiksen KH (1984) An experimental investigation of the motion of long bubbles in inclined tubes. Int J Multiphase Flow 10:467–483CrossRefGoogle Scholar
- Bhagwat SM, Ghajar AJ (2014) A flow pattern independent drift flux model based void fraction correlation for a wide range of gas-liquid two-phase flow. Int J Multiphase Flow 59:186–205CrossRefGoogle Scholar
- Bowers CD, Hrnjak PS (2010) Determination of void fraction in separated two-phase flows using optical techniques, International Refrigeration and Air-Conditioning Conference, Purdue University, pp 2293–2302Google Scholar
- Chen XT, Cai XD, Brill JP (1997) Gas liquid stratified wavy flow in horizontal pipelines. J Energy Resour Technol 119:209–216CrossRefGoogle Scholar
- Colebrook CF (1939) Turbulent flow in pipes, with particular reference to the transition between the smooth and rough pipe laws. J Inst Civil Eng 11:1938–1939CrossRefGoogle Scholar
- Das G, Das PK, Purohit NK, Mitra AK (2002) Liquid holdup in concentric annuli during cocurrent gas–liquid upflow. Can J Chem Eng 80:153–157CrossRefGoogle Scholar
- Dix GE (1971) Vapor void fractions for forced convection with subcooled boiling at low flow rates, Report NEDO-10491, General Electric CoGoogle Scholar
- Ghajar AJ, Bhagwat SM (2014b) Flow patterns, void fraction and pressure drop in gas-liquid two-phase flow at different pipe orientations. In: Frontiers and progress in multiphase flow. Springer Int. Publishing, Cham, Chapter 4, pp 157–212CrossRefGoogle Scholar
- Ghajar AJ, Bhagwat SM (2017) Gas-liquid flow in ducts. In: Michaelides EE, Crowe CT, Schwarzkopf JD (eds) Handbook of multiphase flow, 2nd edn. CRC Press/Taylor & Francis, Boca Rotan, pp 287–356, Chapter 3Google Scholar
- Godbole PV, Tang CC, Ghajar AJ (2011) Comparison of void fraction correlations for different flow patterns in upward vertical two-phase flow. Heat Transfer Eng 32(10):843–860CrossRefGoogle Scholar
- Gokcal B (2008) An experimental and theoretical investigation of slug flow for high oil viscosity in horizontal pipes, Ph.D. Thesis. University of TulsaGoogle Scholar
- Gokcal B, Al-Sarkhi A, Sarica C (2009) Effects of high oil viscosity on drift velocity for horizontal and upward inclined pipes. SPE Proj Fac & Const 4:32–40Google Scholar
- Gomez L, Shoham O, Schmidt Z, Choshki R, Northug T (2000) Unified mechanistic model for steady state two-phase flow: horizontal to upward vertical flow. SPE 5:339–350CrossRefGoogle Scholar
- Hamersma PJ, Hart J (1987) A pressure drop correlation for gas-liquid pipe flow with a small liquid holdup. Chem Eng Sci 42:1187–1196CrossRefGoogle Scholar
- Hart J, Hamersma PJ, Fortuin JMH (1989) Correlations predicting frictional pressure drop and liquid holdup during horizontal gas-liquid pipe flow with a small liquid holdup. Int J Multiphase Flow 15:947–964CrossRefGoogle Scholar
- Hashemi A, Kim JH, Sursock JP (1986) Effect of diameter and geometry on two-phase flow regimes and carryover in model PWR hot leg, Eighth international heat transfer conference, pp 2443–2451Google Scholar
- Hibiki T, Ishii M (2003) One-dimensional drift flux model and constitutive equations for relative motion between phases in various two-phase flow regimes. Int J Heat Mass Transf 46:4935–4948CrossRefGoogle Scholar
- Hills JH (1976) The operation of a bubble column at high throughputs part 1: gas holdup measurements. Chem Eng J 12:89–99CrossRefGoogle Scholar
- Inoue Y (2001) Measurement of interfacial area concentration of gas–liquid two-phase flow in a large diameter pipe, M.S. Thesis, Graduate School of Energy Science, Kyoto UniversityGoogle Scholar
- Inoue A, Kurosu T, Aoki T, Yagi M, Misutake T, Morooka S (1995) Void fraction distribution in BWR fuel assembly and evaluation of subchannel code. J Nucl Sci Technol 32:629–640CrossRefGoogle Scholar
- Ishii M (1977) One-dimensional drift flux model and constitutive equations for relative motion between phases in various two-phase flow regimes, Argonne National Laboratory, pp 77–47Google Scholar
- Jeyachandra BC (2011) Effect of pipe inclination on flow characteristics of high viscosity oil gas two-phase flow, Ph.D. Thesis, University of TulsaGoogle Scholar
- Kaji M, Azzopardi BJ (2010) The effect of pipe diameter on the structure of gas-liquid flow in vertical pipes. Int J Multiphase Flow 36:303–313CrossRefGoogle Scholar
- Kataoka I, Ishii M (1987) Drift flux model for large diameter pipe and new correlation for pool void fraction. Int J Heat Mass Transf 30:1927–1939CrossRefGoogle Scholar
- Keinath B (2012) Void fraction, pressure drop and heat transfer in high pressure condensing flows through microchannels, Ph.D. Thesis, Georgia Institute of TechnologyGoogle Scholar
- Liu W, Tamai H, Takase K (2013) Pressure drop and void fraction in steam–water two-phase flow at high pressure. J Heat Transf 135:1–13Google Scholar
- Marchaterre JF (1956) The effect of pressure on boiling density in multiple rectangular channels, Report ANL-5522, Argonne National LabsGoogle Scholar
- Marchaterre JF, Petrick M, Lottes PA, Weatherland RJ, Flinn WS (1960) Natural and forced circulation boiling studies, Report ANL-5735, Argonne National LabsGoogle Scholar
- Mukherjee H (1979) An experimental study of inclined two-phase flow, Ph.D. Thesis, University of TulsaGoogle Scholar
- Nicklin DJ, Wilkes JO, Davidson JF (1962) Two-phase flow in vertical tubes. Trans Inst Chem Eng 40:61–68Google Scholar
- Oshinowo O (1971) Two-phase flow in a vertical tube coil, Ph.D. Thesis, University of Toronto, CanadaGoogle Scholar
- Rouhani SZ, Axelsson E (1970) Calculation of void volume fraction in the subcooled and quality boiling regions. Int J Heat Mass Transf 13:383–393CrossRefGoogle Scholar
- Sacks PS (1975) Measured characteristics of adiabatic and condensing single component two- phase flow of refrigerant in a 0.377 inch diameter horizontal tube, ASME Winter Annual Meeting, Houston, 75WA/HT-24, pp 1–12Google Scholar
- Schlegel J, Hibiki T, Ishii M (2010) Development of a comprehensive set of drift flux constitutive models for pipes of various hydraulic diameters. Prog Nucl Energy 52:666–677CrossRefGoogle Scholar
- Shedd TA (2010) Void fraction and pressure drop measurements for refrigerant R410a flows in small diameter tubes, Technical Report AHRTI 20110-01Google Scholar
- Shoukri M, Hassan I, Gerges I (2003) Two-phase bubbly flow structure in large diameter vertical pipe. Can J Chem Eng 81:205–211CrossRefGoogle Scholar
- Taitel Y, Dukler AE (1976) A model for predicting flow regime transitions in horizontal and near horizontal gas-liquid flow. AICHE J 22:47–55CrossRefGoogle Scholar
- Wallis GB (1969) One-dimensional two-phase flow. McGraw-Hill, New YorkGoogle Scholar
- Woldesemayat MA, Ghajar AJ (2007) Comparison of void fraction correlations for different flow patterns in horizontal and upward inclined pipes. Int J Multiphase Flow 33:347–370CrossRefGoogle Scholar
- Wongwises S, Pipathttakul M (2006) Flow pattern, pressure drop and void fraction of gas–liquid two-phase flow in an inclined narrow annular channel. Exp Thermal Fluid Sci 30:345–354CrossRefGoogle Scholar
- Xiong R, Chung JN (2006) Size effect on adiabatic gas-liquid two-phase flow map and void fraction in micro-channels, Proceedings of Int. Mech. Eng. Congress and Exposition, ChicagoGoogle Scholar
- Zuber N, Findlay J (1965) Average volume concentration in two-phase systems. ASME J Heat Transf 87:453–468CrossRefGoogle Scholar

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© The Author(s), under exclusive license to Springer Nature Switzerland AG 2020