Error Analysis of Liquid Holdup Measurement in Gas-Liquid Annular Flow Through Circular Pipes Using High-Speed Camera Method

  • Li Liu (刘莉)
  • Bofeng Bai (白博峰)Email author


Accurate measurement of gas-liquid phase fraction is essential for the proper modelling of the pressure drop, heat transfer coefficient, mass transfer rate and interfacial area in two-phase flows. In this paper, taking the issue of optical distortion into account, an analytical model was proposed to estimate and correct the liquid holdup in gas-liquid annular flow through a circular pipe using high-speed camera method. The error in the liquid holdup measurement generated from different refractive indices among transparent circular pipe, liquid film and air core was firstly theoretically analyzed based on the geometric optics. Experimental tests were then carried out to identify the difference as well as to validate the proposed model. Results indicated that the prediction of the liquid holdup has a good performance with the experimental data (i.e., mean relative error is 4.1%) and the measured liquid holdup is larger than the real one. It was found that the measured liquid holdup is larger than the real one. Generally, when the real liquid holdup gets smaller, the discrepancy between the measured liquid holdup by image and the real liquid holdup becomes more significant. Thus, after measuring the liquid holdup from the images, the value of the measured liquid holdup must be corrected by the present model in order to obtain the real liquid holdup.

Key words

gas-liquid annular flow liquid holdup optical refraction analytical correction 

CLC number

TK 121 

Document code


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    AZZOPARDI B J. Disturbance wave frequencies, velocities and spacing in vertical annular two-phase flow [J]. Nuclear Engineering and Design, 1986, 92(2): 121–133.CrossRefGoogle Scholar
  2. [2]
    SCHUBRING D, ASHWOOD A C, SHEDD T A, et al. Planar laser-induced fluorescence (PLIF) measurements of liquid film thickness in annular flow. Part I: Methods and data [J]. International Journal of Multiphase Flow, 2010, 36(10): 815–824.Google Scholar
  3. [3]
    LIU L, BAI B F. Scaling laws for gas-liquid flow in swirl vane separators [J]. Nuclear Engineering and Design, 2016, 298: 229–239.CrossRefGoogle Scholar
  4. [4]
    LIU L, BAI B F. Generalization of droplet entrainment rate correlation for annular flow considering disturbance wave properties [J]. Chemical Engineering Science, 2017, 164: 279–291.CrossRefGoogle Scholar
  5. [5]
    DEVIA F, FOSSA M. Design and optimisation of impedance probes for void fraction measurements [J]. Flow Measurement and Instrumentation, 2003, 14(4/5): 139–149.CrossRefGoogle Scholar
  6. [6]
    WINKLER J, KILLION J, GARIMELLA S, et al. Void fractions for condensing refrigerant flow in small channels: Part I literature review [J]. International Journal of Refrigeration, 2012, 35(2): 219–245.CrossRefGoogle Scholar
  7. [7]
    CAETANO E F, SHOHAM O, BRILL J P. Upward vertical two-phase flow through an annulus——Part I: Single-phase friction factor, Taylor bubble rise velocity, and flow pattern prediction [J]. Journal of Energy Resources Technology, 1992, 114(1): 1–13.CrossRefGoogle Scholar
  8. [8]
    ODDIE G, SHI H, DURLOFSKY L J, et al. Experimental study of two and three phase flows in large diameter inclined pipes [J]. International Journal of Multiphase Flow, 2003, 29(4): 527–558.CrossRefzbMATHGoogle Scholar
  9. [9]
    KOYAMA S, LEE J, YONEMOTO R. An investigation on void fraction of vapor liquid two-phase flow for smooth and microfin tubes with R134a at adiabatic condition [J]. International Journal of Multiphase Flow, 2004, 30(3): 291–310.CrossRefzbMATHGoogle Scholar
  10. [10]
    VAN NIMWEGEN A T, PORTELA L M, HENKES R A W M. The effect of surfactants on air-water annular and churn flow in vertical pipes. Part 2: Liquid holdup and pressure gradient dynamics [J]. International Journal of Multiphase Flow, 2015, 71: 146–158.Google Scholar
  11. [11]
    KENDOUSH A A. A comparative study of the various nuclear radiations used for void fraction measurements [J]. Nuclear Engineering and Design, 1992, 137(2): 249–257.CrossRefGoogle Scholar
  12. [12]
    LI Z B, WU Y X, LI D H. Gamma-ray attenuation technique for measuring void fraction in horizontal gasliquid two-phase flow [J]. Nuclear Science and Techniques, 2007, 18(2): 73–76.CrossRefGoogle Scholar
  13. [13]
    BIEBERLE A, HOPPE D, SCHLEICHER E, et al. Void measurement using high resolution gamma-ray computed tomography. Nuclear Engineering and Design, 2011, 241(6): 2086–2092.CrossRefGoogle Scholar
  14. [14]
    ZHANG Z Q, BIEBERLE M, BARTHEL F, et al. Investigation of upward concurrent gas-liquid pipe flow using ultrafast X-ray tomography and wire-mesh sensor [J]. Flow Measurement and Instrumentation, 2013, 32: 111–118.CrossRefGoogle Scholar
  15. [15]
    YANGY C, XIANG Y, CHU GW, et al. A noninvasive X-ray technique for determination of liquid holdup in a rotating packed bed [J]. Chemical Engineering Science, 2015, 138: 244–255.CrossRefGoogle Scholar
  16. [16]
    KAMEI T, SERIZAWA A. Measurement of 2-dimensional local instantaneous liquid film thickness around simulated nuclear fuel rod by ultrasonic transmission technique [J]. Nuclear Engineering and Design, 1998, 184(2/3): 349–362.CrossRefGoogle Scholar
  17. [17]
    ZHAI L S, JIN N D, GAO Z K, et al. The ultrasonic measurement of high water volume fraction in dispersed oil-in-water flows [J]. Chemical Engineering Science, 2013, 94: 271–283.CrossRefGoogle Scholar
  18. [18]
    FIGUEIREDO M M F, GONCALVES J L, NAKASHIMA A M V, et al. The use of an ultrasonic technique and neural networks for identification of the flow pattern and measurement of the gas volume fraction in multiphase flows [J]. Experimental Thermal and Fluid Science, 2016, 70: 29–50.CrossRefGoogle Scholar
  19. [19]
    PRASSER H M, BÖTTERS A, ZSCHAU J. A new electrode-mesh tomograph for gas-liquid flows [J]. Flow Measurement and Instrumentation, 1998, 9(2): 111–119.CrossRefGoogle Scholar
  20. [20]
    HAN H W, ZHU Z F, GABRIEL K. A study on the effect of gas flow-rate on the wave characteristics in twophase gas-liquid annular flow [J]. Nuclear Engineering and Design, 2006, 236(24): 2580–2588.CrossRefGoogle Scholar
  21. [21]
    ZHAO Y J, MARKIDES C N, MATAR O K, et al. Disturbance wave development in two-phase gas-liquid upwards vertical annular flow [J]. International Journal of Multiphase Flow, 2013, 55: 111–129.CrossRefGoogle Scholar
  22. [22]
    VIEIRA R E, KESANA N R, TORRES C F, et al. Experimental investigation of horizontal gas-liquid stratified and annular flow using wire-mesh sensor [J]. Journal of Fluids Engineering, 2014, 136(12): 121301.CrossRefGoogle Scholar
  23. [23]
    WU H, TAN C, DONG X X, et al. Design of a conductance and capacitance combination sensor for water holdup measurement in oil-water two-phase flow [J]. Flow Measurement and Instrumentation, 2015, 46: 218–229.CrossRefGoogle Scholar
  24. [24]
    CHEN X, HAN Y F, REN Y Y, et al. Water holdup measurement of oil-water two-phase flow with low velocity using a coaxial capacitance sensor [J]. Experimental Thermal and Fluid Science, 2017, 81: 244–255.CrossRefGoogle Scholar
  25. [25]
    TRIPLETT K A, GHIAASIAAN S M, ABDELKHALIK S I, et al. Gas-liquid two-phase flow in microchannels——Part II: Void fraction and pressure drop [J]. International Journal of Multiphase Flow, 1999, 25(3): 395–410.CrossRefzbMATHGoogle Scholar
  26. [26]
    KAWAHARA A, CHUNG P M Y, KAWAJI M. Investigation of two-phase flow pattern, void fraction and pressure drop in a microchannel [J]. International Journal of Multiphase Flow, 2002, 28(9): 1411–1435.CrossRefzbMATHGoogle Scholar
  27. [27]
    KAWAHARA A, SADATOMI M, OKAYAMA K, et al. Effects of channel diameter and liquid properties on void fraction in adiabatic two-phase flow through microchannels [J]. Heat Transfer Engineering, 2005, 26(3): 13–19.CrossRefGoogle Scholar
  28. [28]
    CHUNG P M Y, KAWAJI M. The effect of channel diameter on adiabatic two-phase flow characteristics in microchannels [J]. International Journal of Multiphase Flow, 2004, 30(7/8): 735–761.CrossRefzbMATHGoogle Scholar
  29. [29]
    ZADRAZIL I, MARKIDES C N. An experimental characterization of liquid films in downwards cocurrent gas-liquid annular flow by particle image and tracking velocimetry [J]. International Journal of Multiphase Flow, 2014, 67: 42–53.CrossRefGoogle Scholar
  30. [30]
    MILKIE J A, GARIMELLA S, MACDONALD M P. Flow regimes and void fractions during condensation of hydrocarbons in horizontal smooth tubes [J]. International Journal of Heat and Mass Transfer, 2016, 92: 252–267.CrossRefGoogle Scholar
  31. [31]
    WUA B, FIROUZI M, MITCHELL T, et al. A critical review of flow maps for gas-liquid flows in vertical pipes and annuli [J]. Chemical Engineering Journal, 2017, 326: 350–377.CrossRefGoogle Scholar
  32. [32]
    LU Q, SURYANARAYANA N V, CHRISTODOULU C. Film thickness measurement with an ultrasonic transducer [J]. Experimental Thermal and Fluid Science, 1993, 7(4): 354–361.CrossRefGoogle Scholar
  33. [33]
    PEDERSEN P C, CAKARESKI Z, HERMANSON J C. Ultrasonic monitoring of film condensation for applications in reduced gravity [J]. Ultrasonics, 2000, 8: 486–490.CrossRefGoogle Scholar
  34. [34]
    MIYA M, WOODMANSEE D E, HANRATTY T J. A model for roll waves in gas-liquid flow [J]. Chemical Engineering Science, 1971, 26(11): 1915–1931.CrossRefGoogle Scholar
  35. [35]
    CONEY M W E. The theory and application of conductance probes for the measurement of liquid film thickness in two-phase flow [J]. Journal of Physics E: Scientific Instruments, 1973, 6(9): 903–910.CrossRefGoogle Scholar
  36. [36]
    AZIZI S, KARIMI H, DARVISHI P. Flow pattern and oil holdup prediction in vertical oil-water twophase flow using pressure fluctuation signal [J]. Iranian Journal of Chemistry and Chemical Engineering, 2017, 36(2): 125–141.Google Scholar
  37. [37]
    SMITH T R, SCHLEGEL J P, HIBIKI T, et al. Twophase flow structure in large diameter pipes [J]. International Journal of Heat and Fluid Flow, 2012, 33(1): 156–167.CrossRefGoogle Scholar
  38. [38]
    PRASSER H M, KREPPER E, LUCAS D. Evolution of the two-phase flow in a vertical tube: Decomposition of gas fraction profiles according to bubble size classes using wire-mesh sensors [J]. International Journal of Thermal Sciences, 2002, 41(1): 17–28.CrossRefGoogle Scholar
  39. [39]
    PRASSER H M, BEYER M, CARL H, et al. Evolution of the structure of a gas-liquid two-phase flow in a large vertical pipe [J]. Nuclear Engineering and Design, 2007, 237(15/16/17): 1848–1861.CrossRefGoogle Scholar
  40. [40]
    SAISORN S, WONGWISES S. The effects of channel diameter on flow pattern, void fraction and pressure drop of two-phase air-water flow in circular microchannels [J]. Experimental Thermal and Fluid Science, 2010, 34(4): 454–462.CrossRefGoogle Scholar
  41. [41]
    MOHAMMADPOUR A, AKHAVAN-BEHABADI M A, EBRAHIMZADEH M, et al. Experimental determination of void fraction in surface aeration using image processing technique [J]. Journal of Mechanical Science and Technology, 2015, 29(6): 2391–2400.CrossRefGoogle Scholar
  42. [42]
    PAN L M, HE H, JU P, et al. Experimental study and modeling of disturbance wave height of vertical annular flow [J]. International Journal of Heat and Mass Transfer, 2015, 89: 165–175.CrossRefGoogle Scholar

Copyright information

© Shanghai Jiaotong University and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Nuclear Science and EngineeringShanghai Jiao Tong UniversityShanghaiChina
  2. 2.State Key Laboratory of Multiphase Flow in Power EngineeringXi’an Jiaotong UniversityXi’anChina

Personalised recommendations