Transactions of the Korean Society of Mechanical Engineers B (대한기계학회논문집B)

The Korean Society of Mechanical Engineers (대한기계학회)
권호 표지
DOI QR코드

DOI QR Code

Comparison of Numerical Results for Laminar Wavy Liquid Film Flows down a Vertical Plate for Various Time-Differencing Schemes for the Volume Fraction Equation

수직평판을 타고 흐르는 층류파동액막류에 대한 체적분율식 시간차분법에 따른 해석 결과 비교

  • Park, Il-Seouk (School of Mechanical Engineering, Kyungpook Nat'l Univ.) ;
  • Kim, Young-Jo (School of Mechanical Engineering, Kyungpook Nat'l Univ.) ;
  • Min, June-Kee (Rolls-Royce University Technology Center, Pusan Nat'l Univ.)
  • 박일석 (경북대학교 기계공학부) ;
  • 김영조 (경북대학교 기계공학부) ;
  • 민준기 (부산대학교 롤스로이스 대학기술센터)
  • Received : 2011.07.06
  • Accepted : 2011.08.17
  • Published : 2011.11.01
Download PDF
⟨ Previous Next ⟩

Abstract

Liquid film flows are classified into waveless laminar, wavy laminar, and turbulent flows depending on the Reynolds number or the flow stability. Since the wavy motions of the film flows are so intricate and nonlinear, studies on them have largely been experimental. Most numerical approaches have been limited to the waveless flow regime. The various free surface-tracking schemes adopted for this problem were used to more accurately estimate the average film thickness, rather than to capture the unsteady wavy motion. In this study, the wavy motions in laminar wavy liquid film flows with Reynolds numbers of 200-1000 were simulated with various numerical schemes based on the volume of fluid (VOF) method for interface tracking. The results from each numerical scheme were compared with the experimental results in terms of the average film thickness, the wave velocity, and the wave amplitude.

액막류는 레이놀즈수 및 유동 안정성에 의해 파동이 없는 층류액막류, 파동을 동반한 층류 액막류 및 난류액막류로 구분된다. 파동액막류는 강한 비선형성에 의해 매우 복잡하여 기존에는 주로 실험적 연구가 진행되었다. 수치적 해석은 주로 파동이 없는 경우에 국한되었으며 여러 가지 자유표면 해석기법을 이용하여 평균액막두께를 예측하였다. 이 연구에서는 층류액막류의 파동현상을 레이놀즈수 20~1000 범위에서 수치해석하였다. 이 때, VOF 자유표면 해석기법에 기반한 여러 가지 수치방법을 비교 연구하였으며 평균액막두께, 파동속도 및 진폭을 실험결과와 비교하였다.

Keywords

References

  1. Min, J. K. and Park, I. S., 2011, "Numerical Study for Laminar Wavy Motions of Liquid Film Flow on Vertical Wall," Int. J. Heat Mass Transfer, Vol. 54, pp. 3256-3266. https://doi.org/10.1016/j.ijheatmasstransfer.2011.04.005
  2. Nusselt, W., 1916, "Die Oberflachen Kondensation des Wasserdampes, Zeitsehrit des Vereines Deutscher Ingenieure," Vol. 60, pp. 541-575.
  3. Faghri, A. and Seban, R. A., 1988, "Heat and Mass Transfer to a Turbulent Liquid Film," Int. J. Heat Mass Transfer, Vol. 31, No. 4, pp. 891-894. https://doi.org/10.1016/0017-9310(88)90145-7
  4. Chun, M. -H. and Kim, K. -T., 1990, "Assessment of the New and Existing Correlations for Laminar and Turbulent Film Condensations on a Vertical Surface," Int. Commun. Heat Mass Transfer, Vol. 17, pp. 431-441. https://doi.org/10.1016/0735-1933(90)90062-O
  5. Park, I. S. and Choi, D. H., "Analysis of LiBr-H2O Film Absorption on a Horizontal Tube," 1996, Trans. of the KSME (B), Vol. 20, No. 2, pp. 670-679.
  6. Grigoreva, N. I. and Nakoryakov, V. E., 1977, "Exact Solution Combined Heat and Mass Transfer Problem During Film Absorption," J. Eng. Phys., Vol. 33, No. 5, pp. 1349-1353. https://doi.org/10.1007/BF00860913
  7. Grossman, G., 1982, "Simultaneous Heat and Mass Transfer in Film Absorption under Laminar Flow," Int. J. Heat Mass Transfer, Vol. 25, No. 3, pp. 357-371.
  8. Andberg, J. W. and Vilet, G. C., 1987, "A Simplified Model for Absorption of Vapors into Liquid Films Flowing over Cooled Horizontal Tubes," ASHRAE Trans., Vol. 93, pp. 2454-2466.
  9. Park, I. S. and Kim, M. Y., 2009, "Numerical Investigation of the Heat and Mass Transfer in a Vertical Tube Evaporator with the Three-Zone Analysis," Int. J. Heat Mass Transfer, Vol. 52, pp. 2599-2606. https://doi.org/10.1016/j.ijheatmasstransfer.2008.12.020
  10. Feddaoui, M., Mir, A. and Belahmidi, E., 2003, "Cocurrent Turbulent Mixed Convection Heat and Mass Transfer in Falling Film of Water inside a Vertical Heated Tube," Int. J. Heat Mass Transfer, Vol. 46, pp. 3499-3509.
  11. Groff, M. K., Ormiston, S. J. and Soliman, H. M., 2007, "Numerical Solution of Film Condensation from Turbulent Flow of Vapor-Gas Mixtures in Vertical Tubes," Int. J. Heat Mass Transfer, Vol. 50, pp. 3899-3912. https://doi.org/10.1016/j.ijheatmasstransfer.2007.02.012
  12. Harlow, F. H. and Welch, J. E., 1965, "Numerical Calculation of Time-Dependent Viscous Incompressible Flow of Fluid with Free Surface," Phys. Fluids, Vol. 8, pp. 2182-2189. https://doi.org/10.1063/1.1761178
  13. Daly, B. J., 1969, "A Technique for Including Surface Tension Effects in Hydrodynamics Calculations," J. Comput. Phys., Vol. 4. Pp. 97-117.
  14. Chan, R. K. C. and Street, R. L., 1970, "A Computer Study of Finite-Amplitude Water Waves," J. Comput. Phys., Vol. 6, pp. 68-94. https://doi.org/10.1016/0021-9991(70)90005-7
  15. The, J. L., Raithby, G. D. and Stubley, G. D., 1994, "Surface-adaptive Finite-Volume Method for Solving Free Surface Flows," Numer. Heat Transfer B, Vol. 6, pp. 367-380.
  16. Lilek, Z., 1965, "Ein Finite-Volume Verfahren Zur Berechnung Von Incompressiblen und Kompressiblen Stromungen in Komplexen Geometrien Mit Beweglichen Randern und Freien Oberflachen," Dissertation, University of Hamburg, Germany.
  17. Muzaferija, S. and Peric, M., 1997, "Compuation of Free-Surface Flows Using the Finite Volume Method and Moving Grids," Numer. Heat Transfer B, Vol. 32, pp. 369-384. https://doi.org/10.1080/10407799708915014
  18. Min, J. K. and Choi, D. H., 1999, "Analysis of the Absorption Process on a Horizontal Tube Using Navier- Stokes Equations with Surface-Tension Effects," Int. J. Heat Mass Transfer, Vol. 42, No. 24, pp. 4567-4578. https://doi.org/10.1016/S0017-9310(99)00104-0
  19. Park, I. S. and Choi, D. H., 2001, "Heat- and Mass- Transfer Analysis for the Condensing Film Flow along a Vertical Grooved Tube," Int. J. Heat Mass Transfer, Vol. 44, No. 22, pp. 4277-4285. https://doi.org/10.1016/S0017-9310(01)00068-0
  20. Park, I. S., 2010, "Numerical Analysis for Flow Heat and Mass Transfer in Film Flow along a Vertical Fluted Tube," Int. J. Heat Mass Transfer, Vol. 53, No. 1-3, pp. 309-319. https://doi.org/10.1016/j.ijheatmasstransfer.2009.09.028
  21. Hirt, C. W. and Nichols, B. D., 1981, "Volume of Fluid(VOF) Method for the Dynamics of Free Boundaries," J. Comput. Phys., Vol. 39, pp. 201-225. https://doi.org/10.1016/0021-9991(81)90145-5
  22. Partom, I. S., 1987, "Application of the VOF Method to the Sloshing of a Fluid in a Partially Filled Cylindrical Container," Int. J. Heat Mass Transfer, Vol. 7, pp. 535-550.
  23. Patankar, S. V., 1980, "Numerical Heat Transfer and Fluid Flow," McGraw-Hill, New York.
  24. Fluent 6.3 Users Guide, 2006, Fluent Inc., Canonsburg.
  25. Youngs, D. L., 1992, "Time-Dependent Multi-Material Flow with Large Fluid Distortion," Numerical Methods for Fluid Dynamics, Academic Press, pp. 273-285.
  26. Takamasa, T. and Hazuku, T., 2000, "Measuring Interfacial Waves on Film Flowing Down a Vertical Plate Wall in the Entry Region Using Laser Focus Displacement Meters," Int. J. Heat Mass Transfer, Vol. 43, pp. 2807-2819. https://doi.org/10.1016/S0017-9310(99)00335-X
  27. Ito, A. and Sasaki, M., 1986, "Breakdown and Formation of a Liquid Film Flowing Down an Inclined Plane," Trans. Jpn. Soc. Mech. Eng., Vol. 52, pp. 1261-1265. https://doi.org/10.1299/kikaib.52.1261

Cited by

  1. Numerical Study of Wavy Film Flow on Vertical Plate Using Different Turbulent Models vol.38, pp.5, 2014, https://doi.org/10.3795/KSME-B.2014.38.5.373