Skip to main content
SpringerLink
Log in

Researches on hydrodynamics of liquid film flow on inclined plate using diffuse-interface method

  • Original
  • Published:
Heat and Mass Transfer Aims and scope Submit manuscript

Abstract

The liquid film flow can consistently remove heat to reduce the pressure and temperature in the containment when a severe accident occurs in reactors. However, due to the various variable factors of the environment, such as angle of wall inclination and physical properties of liquids, the liquid film flow is complex in practice. In order to investigate the influences of inclined angle of plate, contact angle, surface tension and density on the hydrodynamics of liquid film, numerical simulation of liquid film flow on the inclined plate are studied by using the diffuse-interface method. Good agreements of the maximum liquid film thickness and the wave velocity are observed between experiment and simulation, proving that diffuse-interface method can be available to simulate the hydraulic characteristics of the liquid film flow. And the analysis of the influence of the above factors on liquid film flows show that the solitary wave phenomenon can be observed in the simulation; the wettability of liquid film flow becomes worse when the inclined angle and the contact angle increase; the change of contact angle is related to the surface tension; the wettability of the liquid film can be improved by increasing density of the liquid for the condition that the wettability is not good.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16

Similar content being viewed by others

Abbreviations

G :

chemical potential

λ :

mixed energy density

p :

Pressure

μ :

kinematic viscosity

T:

Time

ρ :

fluid density

G:

the acceleration of the gravity

σ :

surface tension coefficient

F st :

surface tension force

ϕ :

phase field variable

u :

velocity field

n :

the unit normal vector

χ :

transferring-regulating parameter

γ :

Mobility

δ:

initial film thickness

ε pf :

interface thickness

References

  1. Wasden FK, Dukler AE (1989) Insights into the hydrodynamics of free falling wavy films. AICHE J 35(2):187–195

    Article  Google Scholar 

  2. Nusselt W (1916) Die OberflachenKondensation des Wasserdamfes. Z Ver D Ing 4:569–575

    Google Scholar 

  3. Kapitza PL (1948) Wave flow of thin layers of a viscous fluid layers. Zh Eksp Theor Fiz 18(1):3–28

    Google Scholar 

  4. Kapitza PL, Kapitza SP (1949) Wave flow of thin liquid layers. Zh. Eksp. Theor. Fiz. 19:105–120

    Google Scholar 

  5. Brauner N et al (1985) Interfacial structure of thin falling films: piecewise modeling of the waves, Physico-Chem. Hydrodynam. 6(1):87–90

    MathSciNet  Google Scholar 

  6. Benilov ES, Chapman SJ, Mcleod JB, Ockendon JR, Zubkov VS (2010) On liquid films on an inclined plate. J Fluid Mech 663:53–69

    Article  MathSciNet  MATH  Google Scholar 

  7. Ambrosini W, Forgione N, Oriolo F, Vigni P, Baessler S (1999) Experimental investigation on wave velocity in a falling film, in: 2nd international symposium on two-phase flow Modelling and experimentation. Pisa, Italy, May 23-26:1999

    Google Scholar 

  8. Ambrosini W, Forgione N, Oriolo F (2002) Statistical characteristics of a water film falling down a flat plate at different inclinations and temperatures, Int. J Multiphas Flow 28(9):1521–1540

    Article  MATH  Google Scholar 

  9. Moran K, Inumaru J, Kawaji M (2002) Instantaneous hydrodynamics of a laminar wavy liquid film. Int J Multiphase Flow 28(5):731–755

    Article  MATH  Google Scholar 

  10. Huang XG, Yang YH, Hu P, Bao K (2014) Experimental study of water–air countercurrent flow characteristics in large scale rectangular channel. Ann Nucl Energy 69:125–133

    Article  Google Scholar 

  11. Du WF, Lu YH, Zhao RC, Chang L, Chang HJ (2018) Film thickness of free falling water flow on a large-scale ellipsoidal surface. Prog Nucl Energy 105:1–7

    Article  Google Scholar 

  12. Mascarenhas N, Mudawar I (2013) Study of the influence of interfacial waves on heat transfer in turbulent falling films. Int J Heat Mass Transf 67(1):1106–1121

    Article  Google Scholar 

  13. Seban R, Faghri A (1978) Wave effects on the transport of falling laminar liquid films. Journal of Heat Transfer-Transactions of the ASME 100(1):1–12

    Article  Google Scholar 

  14. F. Gu, C.J Liu, X.G. Yuan, G.C. Yu, 2004. CFD simulation of liquid film flow on inclined plates, Chem Eng Technol 27 (10), 1099–1104

    Article  Google Scholar 

  15. Martin M, Defraeye T, Derome D, Carmeliet J (2015) A film flow model for analysing gravity-driven, thin wavy fluid films. Int J Multiphase Flow 73:207–216

    Article  MathSciNet  Google Scholar 

  16. Doro EO, Aidun CK (2013) Interfacial waves and the dynamics of backflow in falling liquid films. J Fluid Mech 726:261–284

    Article  MathSciNet  MATH  Google Scholar 

  17. Anderson DM, McFadden GB, Wheeler AA (1998) Diffuse-Interface methods in fluid mechanics, Annu.Rev.fluid. Mech. 30(1):139–165

    MATH  Google Scholar 

  18. Yue P, Feng JJ, Liu C, Shen J (2004) A diffuse-interface method for simulating two-phase flows of complex fluids. J Fluid Mech 515:293–317

    Article  MathSciNet  MATH  Google Scholar 

  19. Wang Y, Cai J (2017) Numerical investigation on bubble evolution during nucleate boiling using diffuse interface method. Int J Heat Mass Transf 112:28–38

    Article  Google Scholar 

  20. Y. Wang and J. Cai, 2017. Numerical Investigation of Bubble Evolution at Different Contact Angles in Nucleate Boiling Based on Diffuse Interface Method, The 17th International Topical Meeting on Nuclear Reactor Thermal Hydraulics (NURETH-17), Xi’an, China, September 3–8, 2017

  21. Wang Y, Cai J, Li Q, Yin H, Yang X (2018) Diffuse Interface simulation of bubble rising process: a comparison of adaptive mesh refinement and arbitrary Lagrange-Euler methods. Heat Mass Transf 54(6):1767–1778

    Article  Google Scholar 

  22. Wang Y, Cai J, Li Q (2018) Numerical simulation of large bubble rising behavior in nuclear reactor using diffuse interface method. Int J Energy Res 42:276–283

    Article  Google Scholar 

  23. Wang C, Cai J (2018) Numerical simulation of bubble rising behavior in liquid LBE using diffuse interface method. Nucl Eng Des 340:219–228

    Article  Google Scholar 

  24. Jiang M, Zhou B, Wang X (2018) Comparisons and validations of contact angle models. Int J Hydrog Energy 43(12):6364–6378

    Article  Google Scholar 

  25. SIkalo S, Wilhelm H-D, Roisman IV, Jakirlic S (2005) Dynamic contact angle of spreading droplets: experiments and simulations. Phys Fluids 17(6):062103

    Article  MATH  Google Scholar 

  26. G. Zhu, J. Yao, L. Zhang, S. Hai, L. Aifen, S Bilal, 2016. Investigation of dynamic contact angle using a direct numerical simulation method. Langmuir, acs.langmuir.6b02543

  27. Johnson MFG, Schluter RA, Miksis MJ, Bankoff SG (1999) Experimental study of rivulet formation on an inclined plate by fluores-cent imaging. J Fluid Mech 394:339

    Article  MATH  Google Scholar 

  28. Nicolaiewsky EMA, Fair JR (1999) Liquid flow over textured surfaces, 1. Contact angles. Ind Eng Chem Res 38(1):284–291

    Article  Google Scholar 

Download references

Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant No. 11675057).

Author information

Authors and Affiliations

  1. School of Electric Power, South China University of Technology, Guangzhou, 510640, China

    Jiejin Cai & Xiongjie Zhuo

Authors
  1. Jiejin Cai
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xiongjie Zhuo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jiejin Cai.

Ethics declarations

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Cai, J., Zhuo, X. Researches on hydrodynamics of liquid film flow on inclined plate using diffuse-interface method. Heat Mass Transfer 56, 1889–1899 (2020). https://doi.org/10.1007/s00231-020-02829-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00231-020-02829-6

Search

Navigation