Skip to main content
SpringerLink
Log in

Sensitivity of two-fluid model calculations to two-group drift-flux correlations used in the prediction of interfacial drag

  • Research Article
  • Published:
Experimental and Computational Multiphase Flow Aims and scope Submit manuscript

Abstract

Void fraction prediction of the one-dimensional two-fluid model has been evaluated utilizing a computational tool developed in MATLAB. Various drift-flux correlations, specifically those of Ishii, Kataoka and Ishii, Chexal-Lellouche, Hibiki and Ishii, Shen et al., and Schlegel et al., have been used in the calculation of interfacial drag. The uncertainty in the void fraction prediction by the two-fluid model has been evaluated for each of the specified models under one-group conditions for the gas phase. In addition, several two-group drift-flux models have been implemented for the prediction of interfacial drag, and the accuracy has been compared to the accuracy of the one-group predictions. The results indicate that drift-flux correlations in the same “family” show minor improvements when using updated models. The models of Hibiki and Ishii and Schlegel et al. show the best results of the models included in this study. Some shortcomings were observed for the Chexal-Lellouche correlation. The two-group approach has shown significant error reduction over one-group models. The results highlight the need for properly formulated drift-flux correlations based on physical principles rather than curve fits, as those curve fits can hide compensating errors. Additional data in large diameter pipes, collected with steam-water systems at various pressures, would be extremely valuable for further analysis.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Abbreviations

A :

Area (m2)

C 0 :

Distribution parameter (—)

C D :

Drag coefficient (—)

D :

Diameter (m)

g :

Gravitational acceleration (m/s2)

j :

Volumetric flux (m/s)

M :

Interfacial drag (N/m3)

N :

Number of experiments (—)

P :

Pressure (kPa)

Re:

Reynolds number (—)

r :

Radius (m)

v :

Velocity (m/s)

v gj :

Drift velocity (m/s)

z :

Axial position (m)

α :

Void fraction (—)

Δρ :

Density difference (kg/m3)

ε :

Turbulent dissipation (m2/s3)

μ :

Dynamic viscosity (Pa·s)

ρ :

Density (kg/m3)

σ :

Surface tension (N/m)

1:

Bubble group 1

2:

Bubble group 2

∞:

Asymptotic value

f :

Value for liquid

g :

Value for gas

gs :

Value in the liquid slug

H :

Hydraulic equivalent diameter

i :

Index for experimental condition

j :

Index for measurement location

k :

Index for bubble group

r :

Relative velocity

Sm :

Sauter mean value

z :

Axial direction

< >:

Area average

<< >>:

Void weighted area average

BWR:

Boiling water reactor

CFD:

Computational fluid dynamics

CSAU:

Code scaling, applicability, and uncertainty

IATE:

Interfacial area transport equation

KURRI:

Kyoto University Research Reactor Institute

PIRT:

Phenomena identification and ranking table

PWR:

Pressurized water reactor

SMR:

Small modular reactor

References

  • Andersen, J. G. M., Chu, K. H. 1982. BWR refill-reflood program Task 4.7: Constitutive correlations for shear and heat transfer for the BWR version of TRAC. Technical Report. United States.

  • Atomic Energy Society of Japan. 2008. Standard method for safety evaluation using best estimate code based on uncertainty and scaling analysis with statistical approach. AESJ-SC-S001.

  • Baily, R. V., Zmola P. C., Taylor F. M., Planchet R. J. 1956. Transport of gases through liquid-gas mixture. In: Proceedings of the AIChE New Orleans Meeting.

  • Brooks, C. S., Paranjape, S. S., Ozar, B., Hibiki, T., Ishii, M. 2012. Two-group drift-flux model for closure of the modified two-fluid model. Int J Heat Fluid Flow, 37: 196–208.

    Article  Google Scholar 

  • Carrier, F. 1963. Steam separation technology under the Euroatom Program. Allis-Chalmers Atomic Energy Division. Technical Report ACNP-63021.

  • Chexal, B., et al. 1991. The Chexal-Lellouche void fraction correlation for generalized applications. NSAC-139.

  • Clark, C., Griffiths, M., Chen, S., Hibiki, T., Ishii, M., Ozaki, T., Kinoshita, I., Yoshida, Y. 2014. Drift-flux correlation for rod bundle geometries. Int J Heat Fluid Flow, 48: 1–14.

    Article  Google Scholar 

  • Dave, A., Manera, A., Beyer, M., Lucas, D. 2015. Evaluating performance of two-group interfacial area transport equation for large diameter pipes. In: Proceedings of the 16th International Topical Meeting on Nuclear Reactor Thermal Hydraulics.

  • Division of Risk Assessment and Projects. 2007. TRACE 5.0 Theory Manual. Office of Nuclear Regulatory Research, United States Nuclear Regulatory Commission.

  • Griffiths, M. J., Schlegel, J. P., Clark, C., Chen, S. W., Hibiki, T., Ishii, M., Kinoshita, I., Yoshida, Y. 2014. Uncertainty evaluation of the Chexal-Lellouche correlation for void fraction in rod bundles. Prog Nucl Energ, 74: 143–153.

    Article  Google Scholar 

  • Hall, W. H., Prueter, W. P., Thorne, T. L., Wall, J. R. 1988. High pressure steam/water void fraction profiles in large diameter vertical tubes. In: Proceedings of the Thermal Hydraulics of Nuclear Steam Generators/Heat Exchangers.

  • Hanson, R. G., Wilson, G. E., Ortiz, M. G., Griggs, D. P. 1992. Development of a phenomena identification and ranking table (PIRT) for a postulated double-ended guillotine break in a production reactor. Nucl Eng Des, 136: 335–346.

    Article  Google Scholar 

  • Hashemi, A., Kim, J. H., Sursock, J. P. 1986. Effect of diameter and geometry on two-phase flow regimes and carry-over in a model PWR hot leg. In: Proceedings of the 8th International Heat Transfer Conference.

  • Hibiki, T., Ishii, M. 2000. Experimental study on hot-leg U-bend two-phase natural circulation in a loop with a large diameter pipe. Nucl Eng Des, 195: 69–84.

    Article  Google Scholar 

  • Hibiki, T., Ishii, M. 2001. Effect of inlet geometry on hot-leg U-bend two-phase natural circulation in a loop with a large diameter pipe. Nucl Eng Des, 203: 209–228.

    Article  Google Scholar 

  • Hibiki, T., Ishii, M. 2003. One-dimensional drift-flux model for two-phase flow in a large diameter pipe. Int J Heat Mass Trans, 46: 1773–1790.

    Article  Google Scholar 

  • Hills, J. H. 1976. The operation of a bubble column at high throughputs: I. Gas holdup measurements. Chem Eng J, 12: 89–99.

    Article  Google Scholar 

  • Inoue, Y. 2001. Measurement of interfacial area concentration of gas-liquid two-phase flows in a large diameter pipe. Ph.D. Thesis. Kyoto University, Japan.

    Google Scholar 

  • Ishii, M. 1977. One-dimensional drift-flux model and constitutive equations for relative motion between phases in various two-phase flow regimes. ANL-77-47, USA.

  • Ishii, M., Hibiki, T. 2010. Thermo-Fluid Dynamics of Two-Phase Flow, 2nd edn. Springer.

  • Kataoka, I., Ishii, M. 1987. Drift-flux model for large diameter pipe and new correlation for pool void fraction. Int J Heat Mass Trans, 30: 1927–1939.

    Article  Google Scholar 

  • Kim, S., Fu, X. Y., Wang, X., Ishii, M. 2000. Development of the miniaturized four-sensor conductivity probe and the signal processing scheme. Int J Heat Mass Trans, 43: 4101–4118.

    Article  Google Scholar 

  • Larson, T. K., Moody, F. J., Wilson, G. E., Brown, W. L., Frepoli, C., Hartz, J., Woods, B. G., Oriani, L. 2007. Iris small break loca phenomena identification and ranking table (PIRT). Nucl Eng Des, 237: 618–626.

    Article  Google Scholar 

  • Manera, A., Ozar, B., Paranjape, S., Ishii, M., Prasser, H. M. 2009. Comparison between wire-mesh sensors and conductive needle-probes for measurements of two-phase flow parameters. Nucl Eng Des, 239: 1718–1724.

    Article  Google Scholar 

  • Ohnuki, A., Akimoto, H. 2000. Experimental study on transition of flow pattern and phase distribution in upward air-water two-phase flow along a large vertical pipe. Int J Multiphase Flow, 26: 367–386.

    Article  Google Scholar 

  • Ohnuki, A., Akimoto, H., Sudo, Y. 1995. Flow pattern and its transition in gas-liquid two-phase flows along a large vertical pipe. In: Proceedings of the 2nd International Conference on Multiphase Flow.

  • Omebere-Iyari, N. K., Azzopardi, B. J., Lucas, D., Beyer, M., Prasser, H. M. 2008. The characteristics of gas/liquid flow in large risers at high pressures. Int J Multiphase Flow, 34: 461–476.

    Article  Google Scholar 

  • Ortiz, M. G., Ghan, L. S. 1992. Uncertainty analysis of minimum vessel liquid inventory during a small-break LOCA in a B W Plant: An application of the CSAU methodology using the RELAP5/MOD3 computer code. Technical Report. Office of Scientific and Technical Information, United States.

    Google Scholar 

  • Ozaki, T., Tsukamoto, N., Nakamura, R., Miyaji, T., Suzuki, R., Hibiki, T. 2016. Effect of compensation error in drift-flux parameters on predictions of thermal-hydraulic parameters in nuclear safety system analysis codes. Prog Nucl Energ, 88: 398–411.

    Article  Google Scholar 

  • Prasser, H. M., Beyer, M., Böttger, A., Carl, H., Lucas, D., Schaffrath, A., Schütz, P., Weiss, F. P., Zschau, J. 2005. Influence of the pipe diameter on the structure of the gas-liquid interface in a vertical two-phase pipe flow. Nucl Technol, 152: 3–22.

    Article  Google Scholar 

  • Prasser, H. M., Beyer, M., Carl, H., Gregor, S., Lucas, D., Pietruske, H., Schütz, P., Weiss, F. P. 2007. Evolution of the structure of a gas-liquid two-phase flow in a large vertical pipe. Nucl Eng Des, 237: 1848–1861.

    Article  Google Scholar 

  • Saito, M. et al. 1998. Dispersion characteristics of gas-liquid two-phase pools. In: Proceedings of the 6th International Conference on Nuclear Engineering.

  • Sawant, P., Schelegel, J., Paranjape, S., Ozar, B., Hibiki, T., Ishii, M. 2008. Flow regime identification in large diameter pipe. In: Proceedings of the 16th International Conference on Nuclear Engineering: 341–351.

  • Schlegel, J. P., Hibiki, T., Ishii, M. 2015. Two-group modeling of interfacial area transport in large diameter channels. Nucl Eng Des, 293: 75–86.

    Article  Google Scholar 

  • Schlegel, J. P., Hibiki, T., Shen, X., Appathurai, S., Subramani, H. 2017. Prediction of interfacial area transport in a coupled two-fluid model computation. J Nucl Sci Tech, 54: 58–73.

    Article  Google Scholar 

  • Schlegel, J. P., Macke, C. J., Hibiki, T., Ishii, M. 2013. Modified distribution parameter for churn-turbulent flows in large diameter channels. Nucl Eng Des, 263: 138–150.

    Article  Google Scholar 

  • Schlegel, J. P., Miwa, S., Chen, S., Hibiki, T., Ishii, M. 2012. Experimental study of two-phase flow structure in large diameter pipes. Exp Therm Fluid Sci, 41: 12–22.

    Article  Google Scholar 

  • Schlegel, J. P., Sawant, P., Paranjape, S., Ozar, B., Hibiki, T., Ishii, M. 2009. Void fraction and flow regime in adiabatic upward two-phase flow in large diameter vertical pipes. Nucl Eng Des, 239: 2864–2874.

    Article  Google Scholar 

  • Schlegel, J. P., Sharma, S., Cuenca, R. M., Hibiki, T., Ishii, M. 2014. Local flow structure beyond bubbly flow in large diameter channels. Int J Heat Fluid Flow, 47: 42–56.

    Article  Google Scholar 

  • Shawkat, M. E., Ching, C. Y., Shoukri, M. 2008. Bubble and liquid turbulence characteristics of bubbly flow in a large diameter vertical pipe. Int J Multiphase Flow, 34: 767–785.

    Article  Google Scholar 

  • Shen, X., Hibiki, T., Nakamura, H. 2015. Bubbly-to-cap bubbly flow transition in a long-26m vertical large diameter pipe at low liquid flow rate. Int J Heat Fluid Fl, 52: 140–155.

    Article  Google Scholar 

  • Shen, X., Mishima, K., Nakamura, H. 2010. Flow-induced void fraction transition phenomenon in two-phase flow. In: Proceedings of the 18th International Conference on Nuclear Engineering: 597–604.

  • Shi, S., Wu, Z., Liu, Z., Schlegel, J. P., Brooks, C. S., Eoh, J., Yan, Y., Liu, Y., Yang, W. S., Ishii, M. 2015. Experimental study of natural circulation instability with void reactivity feedback during startup transients for a BWR-type SMR. Prog Nucl Energ, 83: 73–81.

    Article  Google Scholar 

  • Smith, T. R., Schlegel, J. P., Hibiki, T., Ishii, M. 2012. Two-phase flow structure in large diameter pipes. Int J Heat Fluid Fl, 33: 156–167.

    Article  Google Scholar 

  • Spore, J. W., Jolly-Woodruff, S. J., Knight, T. K., Lin, J. C., Nelson, R. A., Pasamehmetoglu, K. O., Steinke, R. G., Unal, C. 1993. TRAC-PF1/MOD2, Vol. 1: Theory manual. LA-12031-M, Vol. I, NUREG/CR-5673, USA.

  • Styrikovich, M. A., Kutateladze, S. S. 1976. Hydrodynamics of liquid-gas system. Energy, 196.

  • Sun, X., Ishii, M., Kelly, J. M. 2003. Modified two-fluid model for the two-group interfacial area transport equation. Ann Nucl Energ, 30: 1601–1622.

    Article  Google Scholar 

  • Talley, J. D., Kim, S., Mahaffy, J., Bajorek, S. M., Tien, K. 2011. Implementation and evaluation of one-group interfacial area transport equation in TRACE. Nucl Eng Des, 241: 865–873.

    Article  Google Scholar 

  • Talley, J. D., Worosz, T., Kim, S., Bajorek, S. M., Tien, K. 2013. Effect of bubble interactions on the prediction of interfacial area in TRACE. Nucl Eng Des, 264: 135–145.

    Article  Google Scholar 

  • Technical Program Group. 1989. Quantifying reactor safety margins: Application of CSAU to a LBLOCA. NUREG/CR-5249.

  • Thermal Hydraulics Group. 1998. Relap5/Mod3 code manual. Vol. I: Code structure, system models and solution methods. RELAP5/MOD3.2.2Beta, USA.

  • Wilson, G. E., Boyack, B. E. 1998. The role of the PIRT process in experiments, code development and code applications associated with reactor safety analysis. Nucl Eng Des, 186: 23–37.

    Article  Google Scholar 

  • Wilson, J. F., Grenda, R. J., Patterson, J. F. 1961. Steam volume fraction in a bubbling two-phase mixture. Transactions of the American Nuclear Society, 4: 356–357.

    Google Scholar 

  • Worosz, T. 2015. Ph.D. Thesis. Penn State University.

  • Yeoh, G. H. 2019. Thermal hydraulic considerations of nuclear reactor systems: Past, present and future challenges. Exp Comput Multiphase Flow, 1: 3–27.

    Article  Google Scholar 

  • Zuber, N., Findlay, J. A. 1965. Average volumetric concentration in two-phase flow systems. J Heat Trans, 87: 453–468.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mining and Nuclear Engineering, Missouri University of Science and Technology, 301 W 14th St, Rolla, MO, 65401, USA

    Alexander Swearingen & Joshua P. Schlegel

  2. School of Nuclear Engineering, Purdue University, 516 Northwestern Ave, West Lafayette, IN, 47907, USA

    Takashi Hibiki

Authors
  1. Alexander Swearingen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Joshua P. Schlegel
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Takashi Hibiki
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Joshua P. Schlegel.

Additional information

Declaration of competing interest

The authors have no competing interests to declare that are relevant to the content of this article.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Swearingen, A., Schlegel, J.P. & Hibiki, T. Sensitivity of two-fluid model calculations to two-group drift-flux correlations used in the prediction of interfacial drag. Exp. Comput. Multiph. Flow 4, 318–335 (2022). https://doi.org/10.1007/s42757-021-0106-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s42757-021-0106-6

Keywords

Search

Navigation