Research Papers: Evaporation, Boiling, and Condensation

A Computational Study on the Effects of Surface Tension and Prandtl Number on Laminar-Wavy Falling-Film Condensation

[+] Author and Article Information
Mahdi Nabil

Department of Mechanical and
Nuclear Engineering,
The Pennsylvania State University,
University Park, PA 16802
e-mail: Mahdi.Nabil@psu.edu

Alexander S. Rattner

Department of Mechanical and
Nuclear Engineering,
The Pennsylvania State University,
236A Reber Building,
University Park, PA 16802
e-mail: Alex.Rattner@psu.edu

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received June 4, 2016; final manuscript received June 4, 2017; published online July 6, 2017. Assoc. Editor: Amitabh Narain.

J. Heat Transfer 139(12), 121501 (Jul 06, 2017) (11 pages) Paper No: HT-16-1356; doi: 10.1115/1.4037062 History: Received June 04, 2016; Revised June 04, 2017

Characterization of wavy film heat and mass transfer is essential for numerous energy-intensive chemical and industrial applications. While surface tension is the underlying cause of film waviness, widely used correlations for falling-film heat transfer do not account for surface tension magnitude as a governing parameter. Furthermore, although the effect of Prandtl number on wavy falling-film heat transfer has been highlighted in some studies, it is not included in most published Nusselt number correlations. Contradictory trends for Nusselt number variation with Prandtl number are found in correlations that do account for such effects. A systematic simulation-based parametric study is performed here to determine the individual effects of Reynolds, Prandtl, capillary, and Jakob numbers on heat transfer in laminar-wavy falling-films. First-principles based volume-of-fluid (VOF) simulations are performed for wavy falling condensation with varying fluid properties and flow rates. A sharp surface tension volumetric force model is employed to predict wavy interface behavior. The numerical model is first validated for smooth falling-film condensation heat transfer and wavy falling-film thickness. The simulation approach is applied to identify Nusselt number trends with Reynolds, Prandtl, capillary, and Jakob numbers. Finally, based on the collected simulation data, a new Nusselt number correlation for laminar-wavy falling-film condensation is proposed.

Copyright © 2017 by ASME
Your Session has timed out. Please sign back in to continue.


Hewitt, G. F. , Shires, G. L. , and Bott, T. R. , 1994, Process Heat Transfer, CRC Press, Boca Raton, FL.
Srikhirin, P. , Aphornratana, S. , and Chungpaibulpatana, S. , 2001, “ A Review of Absorption Refrigeration Technologies,” Renewable Sustainable Energy Rev., 5(4), pp. 343–372. [CrossRef]
Ribatski, G. , and Jacobi, A. M. , 2005, “ Falling-Film Evaporation on Horizontal Tubes—A Critical Review,” Int. J. Refrig., 28(5), pp. 635–653. [CrossRef]
Goodykoontz, J. H. , and Dorsch, R. G. , 1966, “ Local Heat-Transfer Coefficients for Condensation of Steam in Vertical Downflow Within a 5/8-Inch-Diameter Tube,” National Aeronautics and Space Administration (NASA), Washington, DC, Technical Note No. D-3326.
Chun, K. R. , and Seban, R. A. , 1971, “ Heat Transfer to Evaporating Liquid Films,” ASME J. Heat Transfer, 93(4), pp. 391–396. [CrossRef]
Fujita, T. , and Ueda, T. , 1978, “ Heat Transfer to Falling Liquid Films and Film Breakdown I: Subcooled Liquid Films,” Int. J. Heat Mass Transfer, 21(2), pp. 97–108. [CrossRef]
Karapantsios, T. D. , Kostoglou, M. , and Karabelas, A. J. , 1995, “ Local Condensation Rates of Steam-Air Mixtures in Direct Contact With a Falling Liquid Film,” Int. J. Heat Mass Transfer, 38(5), pp. 779–794. [CrossRef]
Peterson, P. F. , Schrock, V. E. , and Kuhn, S. Z. , 1997, “ Recent Experiments for Laminar and Turbulent Film Heat Transfer in Vertical Tubes,” Nucl. Eng. Des., 175(1), pp. 157–166. [CrossRef]
Kirkbride, C. G. , 1934, “ Heat Transfer by Condensing Vapor on Vertical Tubes,” Ind. Eng. Chem., 26(4), pp. 425–428. [CrossRef]
Al-Sibai, F. , Leefken, A. , and Renz, U. , 2002, “ Local and Instantaneous Distribution of Heat Transfer Rates Through Wavy Films,” Int. J. Therm. Sci., 41(7), pp. 658–663. [CrossRef]
Morioka, I. , Kiyota, M. , and Nakao, R. , 1993, “ Absorption of Water Vapor Into a Film of Aqueous Solution of LiBr Falling Along a Vertical Pipe,” JSME Int. J., Ser. B, 36(2), pp. 351–356. [CrossRef]
Miller, W. A. , and Keyhani, M. , 2001, “ The Correlation of Simultaneous Heat and Mass Transfer Experimental Data for Aqueous Lithium Bromide Vertical Falling Film Absorption,” ASME J. Sol. Energy Eng., 123(1), pp. 30–42. [CrossRef]
Miller, W. A. , and Keyhani, M. , 2001, The Effect of Roll Waves on the Hydrodynamics of Falling Films Observed in Vertical Column Absorbers, ASME Advanced Energy Systems Division (Publication), New York, pp. 45–56.
Patnaik, V. , and Perez-Blanco, H. , 1996, “ A Study of Absorption Enhancement by Wavy Film Flows,” Int. J. Heat Fluid Flow, 17(1), pp. 71–77. [CrossRef]
Yan, Y.-Y. , Lio, H.-C. , and Lin, T.-F. , 1999, “ Condensation Heat Transfer and Pressure Drop of Refrigerant R134a in a Plate Heat Exchanger,” Int. J. Heat Mass Transfer, 42(6), pp. 993–1006. [CrossRef]
Dukler, A. E. , 1959, “Fluid Mechanics and Heat Transfer in Vertical Falling Film Systems,” Chem. Eng. Prog. Symp. Ser., 56(30), pp. 1–10.
Gimbutis, G. I. , 1982, “ Local Heat Exchange in the Film Condensation of a Stationary Vapor on a Vertical Surface,” J. Eng. Phys., 43(3), pp. 974–979.
Butterworth, D. , 1983, Heat Exchanger Design Handbook, Hemisphere, Washington, DC.
Chen, S. L. , Gerner, F. M. , and Tien, C. L. , 1987, “ General Film Condensation Correlations,” Exp. Heat Transfer, 1(2), pp. 93–107. [CrossRef]
Uehara, H. , and Kinoshita, E. , 1994, “ Wave and Turbulent Film Condensation on a Vertical Surface Correlation for Local Heat Transfer Coefficient,” Trans. Jpn. Soc. Mech. Eng., 60(577), pp. 3109–3116. [CrossRef]
Alhusseini, A. A. , Tuzla, K. , and Chen, J. C. , 1998, “ Falling Film Evaporation of Single Component Liquids,” Int. J. Heat Mass Transfer, 41(12), pp. 1623–1632. [CrossRef]
Arndt, S. , and Scholl, S. , 2011, “ Evaporation of Single Component Viscous Liquids in a Metal Falling Film Evaporator,” Heat Mass Transfer, 47(8), pp. 963–971. [CrossRef]
Nusselt, W. , 1916, “ The Surface Condensation of Water Vapour,” VDI Z., 60, pp. 541–546.
Stuhltrager, E. , Miyara, A. , and Uehara, H. , 1995, “ Flow Dynamics and Heat Transfer of a Condensate Film on a Vertical Wall—II. Flow Dynamics and Heat Transfer,” Int. J. Heat Mass Transfer, 38(15), pp. 2715–2722. [CrossRef]
Miyara, A. , 2001, “ Flow Dynamics and Heat Transfer of Wavy Condensate Film,” ASME J. Heat Transfer, 123(3), pp. 492–500. [CrossRef]
Raach, H. , and Mitrovic, J. , 2007, “ Simulation of Heat and Mass Transfer in a Multi-Effect Distillation Plant for Seawater Desalination,” Desalination, 204(1–3), pp. 416–422. [CrossRef]
Rattner, A. S. , and Garimella, S. , 2014, “ Simple Mechanistically Consistent Formulation for Volume-of-Fluid Based Computations of Condensing Flows,” ASME J. Heat Transfer, 136(7), p. 071501. [CrossRef]
Hirt, C. W. , and Nichols, B. D. , 1981, “ Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries,” J. Comput. Phys., 39(1), pp. 201–225. [CrossRef]
The OpenFOAM Foundation, 2015, “ OpenFOAM 2.4.0,” The OpenFOAM Foundation Ltd., London, http://openfoam.com/
Hardt, S. , and Wondra, F. , 2008, “ Evaporation Model for Interfacial Flows Based on a Continuum-Field Representation of the Source Terms,” J. Comput. Phys., 227(11), pp. 5871–5895. [CrossRef]
Kunkelmann, C. , and Stephan, P. , 2009, “ CFD Simulation of Boiling Flows Using the Volume-of-Fluid Method Within OpenFOAM,” Numer. Heat Transfer, 56(8), pp. 631–646. [CrossRef]
Subramaniam, V. , and Garimella, S. , 2009, “ From Measurements of Hydrodynamics to Computation of Species Transport in Falling Films,” Int. J. Refrig., 32(4), pp. 607–626. [CrossRef]
Fang, C. , David, M. , Rogacs, A. , and Goodson, K. , 2010, “ Volume of Fluid Simulation of Boiling Two-Phase Flow in a Vapor-Venting Microchannel,” Front. Heat Mass Transfer, 1(1), p. 013002.
Weller, H. G. , 2002, “ Derivation, Modelling, and Solution of the Conditionally Averaged Two-Phase Flow Equations,” Nabla Ltd., Technical Report No. TR/HGW/02.
Kissling, K. , Springer, J. , Jasak, H. , Schutz, S. , Urban, K. , Piesche, M. , Schütz, S. , Urban, K. , and Piesche, M. , 2010, “ A Coupled Pressure Based Solution Algorithm Based on the Volume-of-Fluid Approach for Two or More Immiscible Fluids,” Fifth European Conference on Computational Fluid Dynamics (ECCOMAS CFD), Lisbon, Portugal, June 14–17. https://www.uni-ulm.de/fileadmin/website_uni_ulm/mawi.inst.070/urban/papers/ECCOMASCFD2010paperfinal.pdf
Esmaeeli, A. , and Tryggvason, G. , 2004, “ Computations of Film Boiling—Part I: Numerical Method,” Int. J. Heat Mass Transfer, 47(25), pp. 5451–5461. [CrossRef]
Deshpande, S. S. , Anumolu, L. , and Trujillo, M. F. , 2012, “ Evaluating the Performance of the Two-Phase Flow Solver InterFoam,” Comput. Sci. Discovery, 5(1), p. 014016.
Marschall, H. , Hinterberger, K. , Schuler, C. , Habla, F. , Hinrichsen, O. , Schüler, C. , Habla, F. , Hinrichsen, O. , Schuler, C. , Habla, F. , and Hinrichsen, O. , 2012, “ Numerical Simulation of Species Transfer Across Fluid Interfaces in Free-Surface Flows Using OpenFOAM,” Chem. Eng. Sci., 78, pp. 111–127. [CrossRef]
Rusche, H. , 2002, “ Computational Fluid Dynamics of Dispersed Two-Phase Flows at High Phase Fractions,” Ph.D. thesis, Imperial College of Science, Technology and Medicine, London. http://powerlab.fsb.hr/ped/kturbo/OpenFOAM/docs/HenrikRuschePhD2002.pdf
Yang, Z. , Peng, X. F. , and Ye, P. , 2008, “ Numerical and Experimental Investigation of Two Phase Flow During Boiling in a Coiled Tube,” Int. J. Heat Mass Transfer, 51(5–6), pp. 1003–1016. [CrossRef]
Yuan, M. H. , Yang, Y. H. , Li, T. S. , and Hu, Z. H. , 2008, “ Numerical Simulation of Film Boiling on a Sphere With a Volume of Fluid Interface Tracking Method,” Int. J. Heat Mass Transfer, 51(7–8), pp. 1646–1657. [CrossRef]
Onishi, H. , Kawamura, M. , Tada, Y. , and Takimoto, A. , 2013, “ Numerical Analysis on Heat Transfer Characteristics of Looped Minichannel Using Phase-Change VOF Method,” ASME Paper No. ICNMM2013-73184.
Brackbill, J. U. , Kothe, D. B. , and Zemach, C. , 1992, “ A Continuum Method for Modeling Surface-Tension,” J. Comput. Phys., 100(2), pp. 335–354. [CrossRef]
Raeini, A. Q. Q. , Blunt, M. J. J. , and Bijeljic, B. , 2012, “ Modelling Two-Phase Flow in Porous Media at the Pore Scale Using the Volume-of-Fluid Method,” J. Comput. Phys., 231(17), pp. 5653–5668. [CrossRef]
Patankar, S. V. , 1980, Numerical Heat Transfer and Fluid Flow, Taylor & Francis Group, New York.
Ye, X. , Yan, W. , Jiang, Z. , and Li, C. , 2002, “ Hydrodynamics of Free-Falling Turbulent Wavy Films and Implications for Enhanced Heat Transfer,” Heat Transfer Eng., 23(1), pp. 48–60. [CrossRef]
Nabil, M. , and Rattner, A. S. , 2016, “ InterThermalPhaseChangeFoam—A Framework for Two-Phase Flow Simulations With Thermally Driven Phase Change,” SoftwareX, 5, pp. 216–226. [CrossRef]
Hopf, L. , 1910, “ Turbulenz bei Einem Flusse,” Ann. Phys., 337(9), pp. 777–808. [CrossRef]
Kapitza, P. L. , and Kapitza, S. P. , 1949, “ Wave Flow of Thin Layers of Viscous Liquids—Part III: Experimental Research of a Wave Flow Regime,” Zh. Eksp. Teor. Fiz., 19, pp. 105–120.
Dukler, A. E. , 1959, “ Dynamics of Vertical Falling Film Systems,” Chem. Eng. Prog., 55(10), pp. 62–67.
Feind, F. , 1960, “ Falling Liquid Films With Countercurrent Air Flow in Vertical Tubes,” VDI-Forschungsh., 481, p. 26.
Edwards, D. K. , Mills, A. F. , and Denny, V. E. , 1979, Transfer Processes: An Introduction to Diffusion, Convention, and Radiation, McGraw-Hill, New York.
Ishigai, S. , Nakanisi, S. , Koizumi, T. , and Oyabu, Z. , 1972, “ Hydrodynamics and Heat Transfer of Vertical Falling Liquid Films—Part 1: Classification of Flow Regimes,” Bull. JSME, 15(83), pp. 594–602. [CrossRef]
Fulford, G. D. , 1964, “ The Flow of Liquids in Thin Films,” Adv. Chem. Eng., 5, pp. 151–236.
Phan, L. , and Narain, A. , 2007, “ Nonlinear Stability of the Classical Nusselt Problem of Film Condensation and Wave Effects,” ASME J. Appl. Mech., 74(2), pp. 279–290. [CrossRef]
Naik, R. , Narain, A. , and Mitra, S. , 2016, “ Steady and Unsteady Simulations for Annular Internal Condensing Flows—Part I: Algorithm and Its Accuracy,” Numer. Heat Transfer, Part B, 69(6), pp. 473–494. [CrossRef]
Naik, R. , and Narain, A. , 2016, “ Steady and Unsteady Simulations for Annular Internal Condensing Flows—Part II: Instability and Flow Regime Transitions,” Numer. Heat Transfer, Part B, 69(6), pp. 495–510. [CrossRef]


Grahic Jump Location
Fig. 1

Phase change flow solver algorithm

Grahic Jump Location
Fig. 2

(a) Schematic of the computational geometry, (b) internal mesh structure and a close view of the mesh structure within the film region, and (c) initial film thickness within the computational mesh

Grahic Jump Location
Fig. 3

Wall heat flux and film Reynolds number results from mesh independence study

Grahic Jump Location
Fig. 4

Average wavy falling-film thickness compared with available empirical correlations. Smooth-film analytic model of Nusselt [23] and Hopf [48] included for reference.

Grahic Jump Location
Fig. 5

Trends of Nusselt number with Reynolds number from present simulation study and prior empirical correlations

Grahic Jump Location
Fig. 6

Trends of Nusselt number with Prandtl number compared with empirical correlations at: (a) Re = 75, (b) Re = 767, and (c) Re = 1371

Grahic Jump Location
Fig. 7

Profiles of wavy falling-film at three different Re (corresponding to middle data point of each capillary number sweep in Fig. 8). These profiles are stretched in the x direction by 30% to highlight the wavy film profile. In this figure, y-axis represents the variable “y” and the long-time mean film thickness δ(y)—as represented by the dark-shaded region—has developed nonuniformities (in y-direction) due to wave effects.

Grahic Jump Location
Fig. 8

Predicted trends of Nusselt number variation with capillary number

Grahic Jump Location
Fig. 9

Comparison of Nusselt number values predicted with proposed correlation and simulation results

Grahic Jump Location
Fig. 10

The Nusselt number values for smooth falling-film condensation versus analytical predictions



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In