Volume 19, Issue 4 (2019)                   Modares Mechanical Engineering 2019, 19(4): 969-979 | Back to browse issues page

XML Persian Abstract Print


Download citation:
BibTeX | RIS | EndNote | Medlars | ProCite | Reference Manager | RefWorks
Send citation to:

Mirzaparikhany S, Ansari M. A Theoretical Model for Evaporation of Leidenfrost Drop for Prediction of Vapor Layer Thickness under the Drop. Modares Mechanical Engineering. 2019; 19 (4) :969-979
URL: http://journals.modares.ac.ir/article-15-21551-en.html
1- Mechanical Engineering Faculty, Tarbiat Modares University, Tehran, Iran
Abstract:   (421 Views)
In this paper, a theoretical model is proposed for Leidenfrost droplet evaporation by solving the mass, momentum, and energy conservation equations. This model involves a set of four equations, of which the values of vapor layer thickness, evaporation rate on the lower surface of the drop, the volume of evaporating droplet, and temperature distribution in vapor layer are obtained. This set of equation is solved with Fortran code by the predictor-corrector method. The main unknown value in these equations is the vapor layer thickness, which is predicted in every step of simulation and corrected by the balance of forces that act on the drop. In this study, the upper surface of the drop, where contacts with air and the lower surface of droplet, where contacts with the vapor layer are predicted with high accuracy by solving the Young- Laplace equation. The vapor layer thickness obtained from the proposed model is compared with experimental data and encouraging agreement is observed.
Full-Text [PDF 798 kb]   (278 Downloads)    

Received: 2018/05/31 | Accepted: 2018/08/5 | Published: 2019/04/6

References
1. Mascarenhas N, Mudawar I. Analytical and computational methodology for modeling spray quenching of solid alloy cylinders. International Journal of Heat and Mass Transfer. 2010;53(25-26):5871-5883. [Link] [DOI:10.1016/j.ijheatmasstransfer.2010.06.055]
2. Guo R, Wu J, Fan H, Zhan X. The effects of spray characteristic on heat transfer during spray quenching of aluminum alloy 2024. Experimental Thermal and Fluid Science. 2016;76:211-220. [Link] [DOI:10.1016/j.expthermflusci.2016.03.025]
3. Dou R, Wen Z, Zhou G. Heat transfer characteristics of water spray impinging on high temperature stainless steel plate with finite thickness. International Journal of Heat and Mass Transfer. 2015;90:376-387. [Link] [DOI:10.1016/j.ijheatmasstransfer.2015.06.079]
4. Gradeck M, Seiler N, Ruyer P, Maillet D. Heat transfer for Leidenfrost drops bouncing onto a hot surface. Experimental Thermal and Fluid Science. 2013;47:14-25. [Link] [DOI:10.1016/j.expthermflusci.2012.10.023]
5. Chatzikyriakou D, Walker SP, Hewitt GF. The contribution of non-wetting droplets to direct cooling of the fuel during PWR post-LOCA reflood. Nuclear Engineering and Design. 2010;240(10):3108-3114. [Link] [DOI:10.1016/j.nucengdes.2010.05.029]
6. Hamdan KS, Kim DE, Moon SK. Droplets behavior impacting on a hot surface above the Leidenfrost temperature. Annals of Nuclear Energy. 2015;80:338-347. [Link] [DOI:10.1016/j.anucene.2015.02.021]
7. Dunand P, Castanet G, Gradeck M, Lemoine F, Maillet D. Heat transfer of droplets impinging onto a wall above the Leidenfrost temperature. Comptes Rendus Mécanique. 2013;341(1-2):75-87. [Link] [DOI:10.1016/j.crme.2012.11.006]
8. Gottfried BS, Lee CJ, Bell KJ. The Leidenfrost phenomenon: Film boiling of liquid droplets on a flat plate. International Journal of Heat and Mass Transfer. 1966;9(11):1167-1188. [Link] [DOI:10.1016/0017-9310(66)90112-8]
9. Mousa MM, Hanafy AE. Evaporation time of liquid droplet on superheating horizontal surface. Alexandria Engineering Journal. 2004;43(4):433-444. [Link]
10. Xie H, Zhou Z. A model for droplet evaporation near Leidenfrost point. International Journal of Heat and Mass Transfer. 2007;50(25-26):5328-5333. [Link] [DOI:10.1016/j.ijheatmasstransfer.2007.03.028]
11. Myers TG, Charpin JPF. A mathematical model of the Leidenfrost effect on an axisymmetric droplet. Physics of Fluids. 2009;21(6):063101. [Link] [DOI:10.1063/1.3155185]
12. Dasgupta A, Chandraker DK, Nayak AK, Vijayan PK. Prediction of vapor film thickness below a Leidenfrost drop. Journal of Heat Transfer. 2015;137(12):124501. [Link] [DOI:10.1115/1.4030909]
13. Sobac B, Rednikov A, Dorbolo S, Colinet P. Leidenfrost effect: Accurate drop shape modeling and refined scaling laws. Physical Review E. 2014;90(5):053011. [Link] [DOI:10.1103/PhysRevE.90.053011]
14. Pomeau Y, Le Berre M, Celestini F, Frisch T. The Leidenfrost effect: From quasi-spherical droplets to puddles. Comptes Rendus Mecanique. 2012;340(11-12):867-881. [Link] [DOI:10.1016/j.crme.2012.10.034]
15. Snoeijer JH, Brunet P, Eggers J. Maximum size of drops levitated by an air cushion. Physical Review E. 2009;79(3):036307. [Link] [DOI:10.1103/PhysRevE.79.036307]
16. Celestini F, Frisch T, Pomeau Y. Take off of small Leidenfrost droplets. Physical Review Letters. 2012;109(3):034501. [Link] [DOI:10.1103/PhysRevLett.109.034501]
17. Biance AL, Clanet Ch, Quéré D. Leidenfrost drops. Physics of Fluids. 2003;15(6):1632-1637. [Link] [DOI:10.1063/1.1572161]
18. Burton JC, Sharpe AL, Van Der Veen RCA, Franco A, Nagel SR. Geometry of the vapor layer under a Leidenfrost drop. Physical Review Letters. 2012;109(7):074301. [Link] [DOI:10.1103/PhysRevLett.109.074301]
19. Hassebrook A, Kruse C, Wilson Ch, Anderson T, Zuhlke C, Alexander D, et al. Effects of droplet diameter and fluid properties on the Leidenfrost temperature of polished and micro/nanostructured surfaces. Journal of Heat Transfer. 2016;138(5):051501. [Link] [DOI:10.1115/1.4032291]
20. Hassebrook A, Kruse C, Wilson Ch, Anderson T, Zuhlke C, Alexander D, et al. Effects of droplet diameter on the Leidenfrost temperature of laser processed multiscale structured surfaces. 14th Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems (ITherm), 27-30 May, 2014, Orlando, Florida, USA. Piscataway: IEEE; 2014. [Link] [DOI:10.1109/ITHERM.2014.6892316]
21. Quéré D. Leidenfrost dynamics. Annual Review of Fluid Mechanics. 2013;45:197-215. [Link] [DOI:10.1146/annurev-fluid-011212-140709]
22. Oosthuizen PH, Naylor D. An introduction to convective heat transfer analysis. New Yourk: WCB/McGraw Hill; 1999. [Link]
23. Kays WM, Crawford ME, Weigand B. Convective heat and mass transfer. 4th Edition. New York: Mc Graw-Hill Higher Education; 2005. [Link]
24. Heydarinejhad Gh. Advanced fluid mechanics. 2nd Edition. Tehran: Tarbiat Modares Univercity; 2015. [Persian] [Link]
25. Alois AR, Rincón AF. Young-laplace equation in convenient polar coordinates and its implementation in matlab. Revista Colombiana de Química. 2010;39(3):413-425. [Link]
26. Del Rıo OI, Neumann AW. Axisymmetric drop shape analysis: Computational methods for the measurement of interfacial properties from the shape and dimensions of pendant and sessile drops. Journal of Colloid and Interface Science. 1997;196(2):136-147. [Link] [DOI:10.1006/jcis.1997.5214]

Add your comments about this article : Your username or Email:
CAPTCHA