Nuclear Engineering and Technology

Korean Nuclear Society (한국원자력학회)
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An explicit approximation of the central angle for the curved interface in double-circle model for horizontal two-phase stratified flow

  • Taehwan Ahn (Department of Mechanical and Process Engineering, ETH Zurich) ;
  • Dongwon Jeong (School of Mechanical Engineering, Pusan National University) ;
  • Jin-Yeong Bak (School of Mechanical Engineering, Pusan National University) ;
  • Jae Jun Jeong (School of Mechanical Engineering, Pusan National University) ;
  • Byongjo Yun (School of Mechanical Engineering, Pusan National University)
  • Received : 2023.10.31
  • Accepted : 2024.03.13
  • Published : 2024.08.25
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Abstract

Stratified flow in horizontal tubes is frequently observed in gas-liquid two-phase flow system. In the two-fluid modeling, it is important to define the interface shape in solving the balance equations to determine the key parameters such as the interfacial transfer terms, void fraction, and pressure drop. A double-circle model is usually introduced to depict the concave-down interface in a horizontal circular tube under the stratified-wavy flow condition. However, calculation of the central angle in the double-circle model, which represents the interfacial curvature, requires an appropriate iterative numerical root-finding scheme to solve the implicit transcendental equation. In this study, an explicit approximate equation has been proposed without requirement of the iterative scheme and numerical instability, which is expected to improve the coding process and computation efficiency in the analysis code with the two-fluid model.

Keywords

Acknowledgement

This work was supported by a 2-Year Research Grant of Pusan National University, South Korea.

References

  1. Y. Taitel, A.E. Dukler, A model for predicting flow regime transitions in horizontal and near horizontal gas-liquid flow, AIChE J. 22 (1) (1976) 47-55. 
  2. D. Biberg, An explicit approximation for the wetted angle in two-Phase stratified pipe flow, Can. J. Chem. Eng. 77 (6) (1999) 1221-1224. 
  3. A.G. Flores, K.E. Crowe, P. Griffith, Gas-phase secondary flow in horizontal, stratified and annular two-phase flow, Int. J. Multiphas. Flow 21 (2) (1995) 207-221. 
  4. T. Fukano, H. Nakagawa, Y. Mori, M. Watanabe, Liquid film formation on the inner surface of the horizontal channel, Nucl. Eng. Des. 175 (1-2) (1997) 3-13. 
  5. N.A. Vlachos, S.V. Paras, A.J. Karabelas, Liquid-to-wall shear stress distribution in stratified/atomization flow, Int. J. Multiphas. Flow 23 (5) (1997) 845-863. 
  6. J.R. Thome, J. El Hajal, A. Cavallini, Condensation in horizontal tubes, part 2: new heat transfer model based on flow regimes, Int. J. Heat Mass Tran. 46 (18) (2003) 3365-3387. 
  7. T. Ahn, J. Moon, B. Bae, J. Jeong, B. Bae, B. Yun, An empirical model of the wetted wall fraction in separated flows of horizontal and inclined pipes, Chem. Eng. Sic. 178 (2018) 260-272. 
  8. X.T. Chen, X.D. Cal, J.P. Brill, Gas-liquid stratified-wavy flow in horizontal pipelines, J. Energy Resour. Technol. 119 (1997) 209-216. 
  9. N. Brauner, D. Moalem Maron, J. Rovinsky, A two-fluid model for stratified flows with curved interfaces, Int. J. Multiphas. Flow 24 (6) (1998) 975-1004. 
  10. W. Meng, X.T. Chen, G.E. Kouba, C. Sarica, J.P. Brill, Experimental study of low-liquid-loading gas-liquid flow in near-horizontal pipes, SPE Prod. Facil. 16 (4) (2001) 240-249. 
  11. S. Badie, C.P. Hale, C.J. Lawrence, G.F. Hewitt, Pressure gradient and holdup in horizontal two-phase gas-liquid flows with low liquid loading, Int. J. Multiphas. Flow 26 (9) (2000) 1525-1543. 
  12. A. Ullmann, N. Brauner, Closure relations for two-fluid models for two-phase stratified smooth and stratified wavy flows, Int. J. Multiphas. Flow 32 (1) (2006) 82-105. 
  13. Y.P. Liu, H. Zhang, S.H. Wang, J. Wang, Effect of binary mixtures of surfactants on horizontal gas-liquid flow with low liquid loading, J. Petrol. Sci. Eng. 68 (3-4) (2009) 235-244. 
  14. T. Ahn, B. Yun, J. Jeong, Void fraction prediction for separated flows in the nearly horizontal tubes, Nucl. Eng. Technol. 47 (6) (2015) 669-677. 
  15. H.Q. Zhang, C. Sarica, A model for wetted-wall fraction and gravity center of liquid film in gas/liquid pipe flow, SPE J. 16 (3) (2011) 692-697. 
  16. T. Ahn, B. Yun, J. Jeong, K. Kang, Y. Park, J. Cheon, D. Jerng, Development of a new condensation model for the nearly-horizontal heat exchanger tube under the steam flowing conditions, Int. J. Heat Mass Tran. 79 (2014) 876-884. 
  17. T. Ahn, J. Kang, B. Bae, J. Jeong, B. Yun, Steam condensation in horizontal and inclined tubes under stratified flow conditions, Int. J. Heat Mass Tran. 141 (2019) 71-87.