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A Review of Computational Models for Falling Liquid Films

  • Avijit Karmakar
  • Sumanta AcharyaEmail author
Chapter
  • 154 Downloads

Abstract

In this chapter, a comprehensive review of numerical studies for falling liquid films over plain flat surfaces and horizontal tubes have been presented in terms of flow hydrodynamics and coupled heat and mass transfer. The early studies on the falling film transport models were based on simplified assumptions, and the reduced equations yielded approximate solutions. Developments in Computational Fluid Dynamics (CFD) led by Professor Spalding at Imperial College since the 1960s have enabled the solution of the full set of equations, and space- and time-accurate solutions. The present review primarily discusses recent studies that are based on the solution of the full set of coupled liquid–gas flow equations and highlights some key observations based on these studies. For liquid film flow over plain flat surfaces, the review highlights the important role of interfacial waves and the associated enhancement in the sensible heat transfer rates. However, the impact of these interfacial waves on coupled heat and mass transfer and the potential interaction of these waves with the gas medium is not fully understood. For film flow over horizontal tubes, the recent literature has made significant progress through full-scale models and employing sharp interface capturing techniques. Time- and space-resolved calculations for falling film evaporation over horizontal tubes are currently limited in the literature, but could reveal key underlying mechanisms and/or assist in developing underlying models related to dry-out conditions.

Nomenclature

C

Species concentration

Cp

Specific heat

d

Tube diameter

D

Mass diffusivity

Fr

Froude number

\({\vec{\text{g}}}\)

Gravity vector

Ga

Modified Galileo number

h

Heat transfer coefficient

ΔH

Enthalpy

k

Thermal conductivity

L

Characteristic length for the film

Le

Lewis number

\(\dot{m}\)

Mass flow rate

\(\dot{m}^{\prime \prime }\)

Diffusion mass flux

\({\hat{\text{n}}}\)

Unit normal to the interface

Nu

Nusselt number

p

Pressure

Pe

Peclet number

Pr

Prandtl number

\({\text{q}}^{\prime \prime }\)

Heat flux

Q

Volume flow rate

Re

Reynolds number

s

Interfacial line coordinate

Sh

Sherwood number

St

Stanton number

Sc

Schmidt number

t

Time

\({\hat{\text{t}}}\)

Unit tangential to the interface

T

Temperature

\({\vec{\text{u}}}\)

Velocity vector

u

Streamwise velocity

v

Transverse velocity

W

Domain width

We

Weber number

x

Streamwise coordinate

y

Transverse coordinate

Y

Mass fraction

Greek

ρ

Density

μ

Dynamic viscosity

δ

Film thickness

σ

Surface tension coefficient

κ

Interface curvature

ν

Kinematic viscosity

τ

Shear stress

Γ

Mass flow rate per unit width

ε

Ratio of length scales

λ

Spacing

Λ

Wavelength

ψ

Stream function

ξ

Moving coordinate

Φ

Thermal energy due to viscous dissipation

θ

Dimensionless temperature

β

Mass transfer coefficient

α

Ratio of domain length to width

ζ

Capillary length

Subscript

abs

Absorption

b

Bulk

cr

Critical

d

Diabatic boundary

evap

Evaporation

g

Gas

gp

Gaseous phase

l

Liquid

N

Nusselt

v

Vapor

w

Wall

W

Wave celerity

Superscript

*

Non-dimensional

i

Order

in

Inlet

T

Transpose

Abbreviations

BL

Boundary Layer

CFD

Computational Fluid Dynamics

MAC

Marker and Cell

OpenFOAM

Open-source Field Operation and Manipulation

SIMPLE

Semi-implicit Method for Pressure-Linked Equations

SIMPLER

Semi-implicit Method for Pressure-Linked Equations Revised

UHF

Uniform Heat Flux

UWT

Uniform Wall Temperature

VOF

Volume of Fluid

2D

Two dimensional

3D

Three dimensional

Notes

Acknowledgements

The authors wish to acknowledge support from a DOE-ARPAE Grant project (DE-AR0000572) under the ARID program through the Electric Power Research Institute (EPRI) as the prime contractor. This financial support is gratefully acknowledged. Numerical simulations undertaken by the authors (Avijit Karmakar and Sumanta Acharya) and reported in this paper used the resources of the Oak Ridge Leadership Computing Facility at the Oak Ridge National Laboratory, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC05-00OR22725.

References

  1. 1.
    Abdou, M. A. (1999). Exploring novel high power density concepts for attractive fusion systems. Fusion Engineering and Design, 45, 145–167.  https://doi.org/10.1016/S0920-3796(99)00018-6.CrossRefGoogle Scholar
  2. 2.
    Takase K, Yoshida H, Ose Y, et al (2003) Large-scale numerical simulations of multiphase flow behavior in an advanced light-water reactor core. Annual Report of the Earth Simulator Center, April 2004:Google Scholar
  3. 3.
    Sarma, P. K., Vijayalakshmi, B., Mayinger, F., & Kakac, S. (1998). Turbulent film condensation on a horizontal tube with external flow of pure vapors. International Journal of Heat and Mass Transfer, 41, 537–545.  https://doi.org/10.1016/S0017-9310(97)00192-0.CrossRefzbMATHGoogle Scholar
  4. 4.
    Killion, J. D., & Garimella, S. (2004). Simulation of Pendant Droplets and Falling Films in Horizontal Tube Absorbers. Journal of Heat Transfer, 126, 1003.  https://doi.org/10.1115/1.1833364.CrossRefGoogle Scholar
  5. 5.
    Gerendas, M., & Wittig, S. (2001). Experimental and Numerical Investigation on the Evaporation of Shear-Driven Multicomponent Liquid Wall Films. Journal of Engineering for Gas Turbines and Power, 123, 580.  https://doi.org/10.1115/1.1362663.CrossRefGoogle Scholar
  6. 6.
    Yilmaz, E. (2003). Sources and characteristics of oil consumption in a spark-ignition engine (Ph.D. thesis, Massachusetts Institute of Technology)Google Scholar
  7. 7.
    Jebson, R. S., & Chen, H. (1997). Performances of falling film evaporators on whole milk and a comparison with performance on skim milk. Journal of Dairy Research, 64, 57–67.  https://doi.org/10.1017/S0022029996001963.CrossRefGoogle Scholar
  8. 8.
    Brotherton, F. (2002). Alcohol recovery in falling film evaporators. Applied Thermal Engineering, 22, 855–860.  https://doi.org/10.1016/S1359-4311(01)00125-9.CrossRefGoogle Scholar
  9. 9.
    Uche, J., Artal, J., & Serra, L. (2003). Comparison of heat transfer coefficient correlations for thermal desalination units. Desalination, 152, 195–200.  https://doi.org/10.1016/S0011-9164(02)01063-9.CrossRefGoogle Scholar
  10. 10.
    Fulford, G. D. (1964). The Flow of Liquids in Thin Films. Adv Chem Eng, 5, 151–236.  https://doi.org/10.1016/S0065-2377(08)60008-3.CrossRefGoogle Scholar
  11. 11.
    Benjamin, T. B. (1957). Wave formation in laminar flow down an inclined plane. Journal of Fluid Mechanics, 2, 554.  https://doi.org/10.1017/S0022112057000373.MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Park, C. D., & Nosoko, T. (2003). Three-dimensional wave dynamics on a falling film and associated mass transfer. AIChE Journal, 49, 2715–2727.  https://doi.org/10.1002/aic.690491105.CrossRefGoogle Scholar
  13. 13.
    Chang, H.-C. (1994). Wave Evolution on a Falling Film. Annual Review of Fluid Mechanics, 26, 103–136.  https://doi.org/10.1146/annurev.fluid.26.1.103.MathSciNetCrossRefGoogle Scholar
  14. 14.
    Nguyen, L. T., & Balakotaiah, V. (2000). Modeling and experimental studies of wave evolution on free falling viscous films. Physics of Fluids, 12, 2236–2256.  https://doi.org/10.1063/1.1287612.CrossRefzbMATHGoogle Scholar
  15. 15.
    Brackbill, J., Kothe, D., & Zemach, C. (1992). A continuum method for modeling surface tension. Journal of Computational Physics, 100, 335–354.  https://doi.org/10.1016/0021-9991(92)90240-Y.MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Nusselt, W. (1916). Die oberflachenkondensation des wasserdamphes. VDI-Zeitschrift, 60, 541–546.Google Scholar
  17. 17.
    Dietze, G. F., Leefken, A., & Kneer, R. (2008). Investigation of the backflow phenomenon in falling liquid films. Journal of Fluid Mechanics, 595, 435–459.  https://doi.org/10.1017/S0022112007009378.CrossRefzbMATHGoogle Scholar
  18. 18.
    Chang, H. C., Demekhin, E. A., & Kopelevich, D. I. (1993). Nonlinear evolution of waves on a vertically falling film. Journal of Fluid Mechanics, 250, 433–480.  https://doi.org/10.1017/S0022112093001521.MathSciNetCrossRefGoogle Scholar
  19. 19.
    Chang, H. C., Demekhin, E. A., & Kalaidin, E. (1996). Simulation of Noise-Driven Wave Dynamics on a Falling Film. AIChE Journal, 42, 1553–1568.  https://doi.org/10.1002/aic.690420607.CrossRefGoogle Scholar
  20. 20.
    Demekhin, E. A., Kaplan, M. A., & Shkadov, V. Y. (1988). Mathematical models of the theory of viscous liquid films. Fluid Dynamics, 22, 885–893.  https://doi.org/10.1007/BF01050727.CrossRefzbMATHGoogle Scholar
  21. 21.
    Demekhin, E. A., Demekhin, I. A., & Shkadov, V. Y. (1984). Solitons in viscous films flowing down a vertical wall. Fluid Dynamics, 18, 500–507.  https://doi.org/10.1007/BF01090610.MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Benney, D. J. (1966). Long Waves on Liquid Films. Journal of Mathematical Physics, 45, 150–155.  https://doi.org/10.1002/sapm1966451150.MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Gjevik, B. (1970). Occurrence of finite-amplitude surface waves on falling liquid films. Physics of Fluids, 13, 1918–1925.  https://doi.org/10.1063/1.1693186.CrossRefzbMATHGoogle Scholar
  24. 24.
    Lin, S. P. (1974). Finite amplitude side-band stability of a viscous film. Journal of Fluid Mechanics, 63, 417–429.  https://doi.org/10.1017/S0022112074001704.CrossRefzbMATHGoogle Scholar
  25. 25.
    Nakaya, C. (1975). Long waves on a thin fluid layer flowing down an inclined plane. Physics of Fluids, 18, 1407–1412.  https://doi.org/10.1063/1.861037.CrossRefzbMATHGoogle Scholar
  26. 26.
    Takeshi, O. (1999). Surface equation of falling film flows with moderate Reynolds number and large but finite Weber number. Physics of Fluids, 11, 3247–3269.  https://doi.org/10.1063/1.870186.MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Panga, M. K. R., & Balakotaiah, V. (2003). Low-Dimensional Models for Vertically Falling Viscous Films. Physical Review Letters, 90, 4.  https://doi.org/10.1103/PhysRevLett.90.154501.CrossRefGoogle Scholar
  28. 28.
    Kapitza, P. L. (1948). Wave flow of thin layers of viscous liquid. Part I. Free flow. Zhurnal Eksp i Teor Fiz, 18, 3–28.Google Scholar
  29. 29.
    Shkadov, V. Y. (1970). Wave flow regimes of a thin layer of viscous fluid subject to gravity. Fluid Dynamics, 2, 29–34.  https://doi.org/10.1007/BF01024797.MathSciNetCrossRefGoogle Scholar
  30. 30.
    Yu, L. Q., Wasden, F. K., Dukler, A. E., & Balakotaiah, V. (1995). Nonlinear evolution of waves on falling films at high Reynolds numbers. Physics of Fluids, 7, 1886–1902.  https://doi.org/10.1063/1.868503.MathSciNetCrossRefzbMATHGoogle Scholar
  31. 31.
    Ruyer-Quil, C., & Manneville, P. (2000). Improved modeling of flows down inclined planes. European Physical Journal B: Condensed Matter and Complex Systems, 15, 357–369.  https://doi.org/10.1007/s100510051137.CrossRefzbMATHGoogle Scholar
  32. 32.
    Scheid, B., Ruyer-Quil, C., & Manneville, P. (2006). Wave patterns in film flows: modelling and three-dimensional waves.Google Scholar
  33. 33.
    Mudunuri, R. R., & Balakotaiah, V. (2006). Solitary waves on thin falling films in the very low forcing frequency limit. AIChE Journal, 52, 3995–4003.  https://doi.org/10.1002/aic.11015.CrossRefGoogle Scholar
  34. 34.
    Ramaswamy, B., Chippada, S., & Joo, S. W. (1996). A full-scale numerical study of interfacial instabilities in thin-film flows. Journal of Fluid Mechanics, 325, 163–194.  https://doi.org/10.1017/S0022112096008075.CrossRefzbMATHGoogle Scholar
  35. 35.
    Nagasaki, T., Hijikata, K. (1989). A numerical study of interfacial waves on a falling liquid film. In National Heat Transfer Conference (pp. 22–30)Google Scholar
  36. 36.
    Miyara, A. (2000). Numerical simulation of wavy liquid film flowing down on a vertical wall and an inclined wall. International Journal of Thermal Sciences, 39, 1015–1027.  https://doi.org/10.1016/S1290-0729(00)01192-3.CrossRefGoogle Scholar
  37. 37.
    Gao, D., Morley, N. B., & Dhir, V. (2003). Numerical simulation of wavy falling film flow using VOF method. Journal of Computational Physics, 192, 624–642.  https://doi.org/10.1016/j.jcp.2003.07.013.CrossRefzbMATHGoogle Scholar
  38. 38.
    Savage, M. D. (1998). Wave flow of liquid films. Alekseenko, S. V., Nakoryakov, V. E., Pokusaev, B. G., & Fukano, T. (1994). 313 pp. ISBN 1567800 0215. $135. J Fluid Mech 363:348–349.  https://doi.org/10.1017/S002211209821874XCrossRefGoogle Scholar
  39. 39.
    Frenkel, A. L., & Indireshkumar, K. (1996). Derivations and simulations of evolution equations of wavy film flows. In Mathematical modeling and simulation in hydrodynamic stability (pp. 35–81).Google Scholar
  40. 40.
    Ruyer-quil, C. (2012). Instabilities and modeling of falling film flows (Ph.D. thesis, Université Pierre et Marie Curie, Paris, France).Google Scholar
  41. 41.
    Chang, H., Demekhin, E. A. (2002). Complex wave dynamics on thin films. Elsevier Science.Google Scholar
  42. 42.
    Trifonov, Y. Y. (2008). Trifonov_08. 17:30–52.  https://doi.org/10.1134/S1810232808010049.
  43. 43.
    Alekseenko, S. V., Nakoryakov, V. E., & Pokusaev, B. G. (1985). Wave formation on vertical falling liquid films. International Journal of Multiphase Flow, 11, 607–627.  https://doi.org/10.1016/0301-9322(85)90082-5.CrossRefzbMATHGoogle Scholar
  44. 44.
    Panga, M. K., Mudunuri, R. R., & Balakotaiah, V. (2005). Long-wavelength equation for vertically falling films. Physical Review E Statistical Nonlinear, Soft Matter Physics 71.  https://doi.org/10.1103/PhysRevE.71.036310
  45. 45.
    Pumir, A., Manneville, P., & Pomeau, Y. (1983). On solitary waves running down an inclined plane. Journal of Fluid Mechanics, 135, 27–50.  https://doi.org/10.1017/S0022112083002943.CrossRefzbMATHGoogle Scholar
  46. 46.
    Sivashinsky, G. I., & Michelson, D. M. (1980). On irregular wavy flow of a liquid film down a vertical plane. Progress of Theoretical Physics, 63, 2112–2114.  https://doi.org/10.1143/PTP.63.2112.CrossRefGoogle Scholar
  47. 47.
    Yih, C.-S., & Guha, C. R. (1955). Hydraulic Jump in a Fluid System of Two Layers. Tellus, 7, 358–366.  https://doi.org/10.1111/j.2153-3490.1955.tb01172.x.CrossRefGoogle Scholar
  48. 48.
    Chang, H.-C. (1986). Traveling waves on fluid interfaces: Normal form analysis of the Kuramoto-Sivashinsky equation. Physics of Fluids, 29, 3142.  https://doi.org/10.1063/1.865965.MathSciNetCrossRefzbMATHGoogle Scholar
  49. 49.
    Korteweg, D. J., & de Vries, G. (1895). XLI. On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves. London, Edinburgh, Dublin Philos Mag J Sci, 39, 422–443.  https://doi.org/10.1080/14786449508620739.CrossRefzbMATHGoogle Scholar
  50. 50.
    Petviashvili, V. I., & Tsvelodub, D. Y. (1978, February). Horseshoe-shaped solitons on a flowing viscous film of fluid. In Soviet Physics Doklady (Vol. 23, p. 117).Google Scholar
  51. 51.
    Ruyer-Quil, C., & Manneville, P. (1998). Modeling film flows down inclined planes. European Physical Journal B: Condensed Matter and Complex Systems, 6, 277–292.  https://doi.org/10.1007/s100510050550.CrossRefzbMATHGoogle Scholar
  52. 52.
    Harlow, F. H., Welch, J. E., et al. (1965). Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface. Physics of Fluids, 8, 2182.MathSciNetCrossRefGoogle Scholar
  53. 53.
    Patankar S V, Spalding DB (1972) A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows. Int J Heat Mass Transf 15:1787–1806.  https://doi.org/10.1016/0017-9310(72)90054-3CrossRefGoogle Scholar
  54. 54.
    Van, Doormaal J. P., & Raithby, G. D. (1984). Enhancements of the SIMPLE method for predicting incompressible fluid flows. Numer Heat Transf, 7, 147–163.  https://doi.org/10.1080/01495728408961817.CrossRefzbMATHGoogle Scholar
  55. 55.
    Patankar, S. V. (1981). A calculation procedure for two-dimensional elliptic situations. Numer Heat Transf, 4, 409–425.  https://doi.org/10.1080/01495728108961801.CrossRefGoogle Scholar
  56. 56.
    Issa RI (1986) Solution of the implicitly discretised fluid flow equations by operator-splitting. J Comput Phys 62:40–65.  https://doi.org/10.1016/0021-9991(86)90099-9MathSciNetCrossRefGoogle Scholar
  57. 57.
    Scardovelli R, Tryggvason TAR, Zaleski P (2014) Direct Numerical Simulations of Gas – Liquid Multiphase FlowsGoogle Scholar
  58. 58.
    Artemov, V., Beale, S. B., de Vahl, Davis G., et al. (2009). A tribute to D.B. Spalding and his contributions in science and engineering. International Journal of Heat and Mass Transfer, 52, 3884–3905.  https://doi.org/10.1016/j.ijheatmasstransfer.2009.03.038.CrossRefzbMATHGoogle Scholar
  59. 59.
    Spalding DB (1981) Numerical computation of multi-phase fluid flow and heat transfer. In: In Von Karman Inst. for Fluid Dyn. Numerical Computation of Multi-Phase FlowsGoogle Scholar
  60. 60.
    Hirt, C., & Nichols, B. (1981). Volume of fluid (VOF) method for the dynamics of free boundaries. Journal of Computational Physics, 39, 201–225.  https://doi.org/10.1016/0021-9991(81)90145-5.CrossRefzbMATHGoogle Scholar
  61. 61.
    D. Y (1982) Them dependent multimaterial flow with large fluid distribution. Numer Methods Fluid D 24:Google Scholar
  62. 62.
    Lafaurie, B., Nardone, C., Scardovelli, R., et al. (1994). Modelling merging and fragmentation in multiphase flows with SURFER. Journal of Computational Physics, 113, 134–147.MathSciNetCrossRefGoogle Scholar
  63. 63.
    Sussman, M., & Puckett, E. G. (2000). A Coupled Level Set and Volume-of-Fluid Method for Computing 3D and Axisymmetric Incompressible Two-Phase Flows. Journal of Computational Physics, 162, 301–337.  https://doi.org/10.1006/jcph.2000.6537.MathSciNetCrossRefzbMATHGoogle Scholar
  64. 64.
    Enright D, Fedkiw R, Ferziger J, Mitchell I (2002) A hybrid particle level set method for improved interface capturingGoogle Scholar
  65. 65.
    Hirshburg, R. I., & Florschuetz, L. W. (1982). Laminar Wavy-Film Flow: Part I. Hydrodynamic Analysis. J Heat Transfer, 104, 452.  https://doi.org/10.1115/1.3245114.CrossRefGoogle Scholar
  66. 66.
    Brauner, N., Moalem Maron, D., & Toovey, I. (1987). Characterization of the interfacial velocity in wavy thin films flow. Int Commun Heat Mass Transf, 14, 293–302.  https://doi.org/10.1016/0735-1933(87)90030-3.CrossRefGoogle Scholar
  67. 67.
    Brauner, N. (1989). Modelling of wavy flow in turbulent free falling films. International Journal of Multiphase Flow, 15, 505–520.  https://doi.org/10.1016/0301-9322(89)90050-5.CrossRefzbMATHGoogle Scholar
  68. 68.
    Wasden, F. K., & Dukler, A. E. (1989). Numerical investigation of large wave interactions on free falling films. International Journal of Multiphase Flow, 15, 357–370.  https://doi.org/10.1016/0301-9322(89)90006-2.CrossRefGoogle Scholar
  69. 69.
    Bach, P., & Villadsen, J. (1984). Simulation of the vertical flow of a thin, wavy film using a finite-element method. International Journal of Heat and Mass Transfer, 27, 815–827.  https://doi.org/10.1016/0017-9310(84)90002-4.CrossRefzbMATHGoogle Scholar
  70. 70.
    Kheshgi, H. S., & Scriven, L. E. (1987). Disturbed film flow on a vertical plate. Physics of Fluids, 30, 990–997.  https://doi.org/10.1063/1.866286.CrossRefGoogle Scholar
  71. 71.
    Malamataris, N. T., & Papanastasiou, T. C. (1991). Unsteady Free Surface Flows on Truncated Domains. Industrial and Engineering Chemistry Research, 30, 2211–2219.  https://doi.org/10.1021/ie00057a025.CrossRefGoogle Scholar
  72. 72.
    Salamon, T. R., Armstrong, R. C., & Brown, R. A. (1994). Traveling waves on vertical films: Numerical analysis using the finite element method. Physics of Fluids, 6, 2202–2220.  https://doi.org/10.1063/1.868222.CrossRefzbMATHGoogle Scholar
  73. 73.
    Kiyota, M., Morioka, I., & Kiyoi, M. (1994). Numerical Analysis of Waveforms of Falling Films. Trans Japan Soc Mech Eng Ser B, 60, 4177–4184.  https://doi.org/10.1299/kikaib.60.4177.CrossRefGoogle Scholar
  74. 74.
    Rohlfs, W., Rietz, M., & Scheid, B. (2018). WaveMaker: The three-dimensional wave simulation tool for falling liquid films. SoftwareX, 7, 211–216.  https://doi.org/10.1016/j.softx.2018.07.003.CrossRefGoogle Scholar
  75. 75.
    Dietze, G. F., Rohlfs, W., Nährich, K., et al. (2014). Three-dimensional flow structures in laminar falling liquid films. Journal of Fluid Mechanics, 743, 75–123.  https://doi.org/10.1017/jfm.2013.679.CrossRefGoogle Scholar
  76. 76.
    Nusselt, W. (1923). Der wärmeaustausch am berieselungskühler. VDI-Zeitschrift, 67, 206–210.Google Scholar
  77. 77.
    Kays, W. M., & Crawford, M. E. (1980). Convective heat and mass transfer. Limited: McGraw-Hill Ryerson.Google Scholar
  78. 78.
    Limberg, H. (1973). Wärmeübergang an turbulente und laminare rieselfilme. International Journal of Heat and Mass Transfer, 16, 1691–1702.  https://doi.org/10.1016/0017-9310(73)90162-2.CrossRefzbMATHGoogle Scholar
  79. 79.
    Brauer, H. (1971). Stoffaustausch einschließlich chemischer Reaktion. Aarau: Verlag Sauerländer.Google Scholar
  80. 80.
    Hirshburg, R. I., & Florschuetz, L. W. (1982). Laminar Wavy-Film Flow: Part II. Condensation and Evaporation. J Heat Transfer, 104, 459.  https://doi.org/10.1115/1.3245115.CrossRefGoogle Scholar
  81. 81.
    Jayanti, S., & Hewitt, G. F. (1996). Hydrodynamics and heat transfer of wavy thin film flow. International Journal of Heat and Mass Transfer, 40, 179–190.  https://doi.org/10.1016/S0017-9310(96)00016-6.CrossRefzbMATHGoogle Scholar
  82. 82.
    Miyara, A. (1999). Numerical analysis on flow dynamics and heat transfer of falling liquid films with interfacial waves. Heat and Mass Transfer, 35, 298–306.  https://doi.org/10.1007/s002310050328.CrossRefGoogle Scholar
  83. 83.
    Kunugi, T., & Kino, C. (2005). DNS of falling film structure and heat transfer via MARS method. Computers & Structures, 83, 455–462.  https://doi.org/10.1016/j.compstruc.2004.08.018.CrossRefGoogle Scholar
  84. 84.
    Yu, H., Gambaryan-Roisman, T., & Stephan, P. (2013). Numerical Simulations of Hydrodynamics and Heat Transfer in Wavy Falling Liquid Films on Vertical and Inclined Walls. Journal of Heat Transfer, 135, 101010.  https://doi.org/10.1115/1.4024550.CrossRefGoogle Scholar
  85. 85.
    Kawae, N., Shigechi, T., Kanemaru, K., & Yamada, T. (1980). Water vapor evaporation into laminar film flow of a lithium bromide-water solution (influence of variable properties and inlet film thickness on absorption mass transfer rate). Heat Transf - Japanese Res, 18, 58–70.Google Scholar
  86. 86.
    Grossman, G. (1983). Simultaneous heat and mass transfer in film absorption under laminar flow. International Journal of Heat and Mass Transfer, 26, 357–371.  https://doi.org/10.1016/0017-9310(83)90040-6.CrossRefGoogle Scholar
  87. 87.
    Grossman, G. (1986). No Title. Houstan: Gulf Publishing Company.Google Scholar
  88. 88.
    Ramadane, A., Aoufoussi, Z., & Le Goff, H. (1992). Experimental investigation and modeling of gas-liquid absorption with a high thermal effect. Institution of Chemical Engineers Symposium Series, 1, A451–A459.Google Scholar
  89. 89.
    Ibrahim, G., Nabhan, M. B., & Anabtawi, M. (1995). An investigation into a falling film type cooling tower. International Journal of Refrigeration, 18, 557–564.  https://doi.org/10.1016/0140-7007(96)81783-X.CrossRefGoogle Scholar
  90. 90.
    Nakoryakov VE, Grigor’eva NI (1980) Calculation of heat and mass transfer in nonisothermal absorption on the initial portion of a downflowing film. Theor Found Chem Eng 14:305–309Google Scholar
  91. 91.
    Patnaik, V., & Perez-Blanco, H. (1996). A study of absorption enhancement by wavy film flows. International Journal of Heat and Fluid Flow, 17, 71–77.  https://doi.org/10.1016/0142-727X(95)00076-3.CrossRefGoogle Scholar
  92. 92.
    Sabir, H., Suen, K. O., & Vinnicombe, G. A. (1996). Investigation of effects of wave motion on the performance of a falling film absorber. International Journal of Heat and Mass Transfer, 39, 2463–2472.  https://doi.org/10.1016/0017-9310(95)00336-3.CrossRefzbMATHGoogle Scholar
  93. 93.
    Habib, H. M., & Wood, B. D. (2001). Simultaneous Heat and Mass Transfer in Film Absorption With the Presence of Non-Absorbable Gases. Journal of Heat Transfer, 123, 984.  https://doi.org/10.1115/1.1370523.CrossRefGoogle Scholar
  94. 94.
    Karami, S., & Farhanieh, B. (2009). A numerical study on the absorption of water vapor into a film of aqueous LiBr falling along a vertical plate. Heat and Mass Transfer, 46, 197–207.  https://doi.org/10.1007/s00231-009-0557-y.CrossRefGoogle Scholar
  95. 95.
    Chow, L. C., & Chung, J. N. (1983). Evaporation of water into a laminar stream of air and superheated steam. International Journal of Heat and Mass Transfer, 26, 373–380.  https://doi.org/10.1016/0017-9310(83)90041-8.CrossRefzbMATHGoogle Scholar
  96. 96.
    Schröppel, J., & Thiele, F. (1983). On the calculation of momentum, heat, and mass transfer in laminar and turbulent boundary layer flows along a vaporizing liquid film. Numer Heat Transf, 6, 475–496.  https://doi.org/10.1080/01495728308963101.CrossRefzbMATHGoogle Scholar
  97. 97.
    Yan, W. M., Tsay, Y. L., & Lin, T. F. (1989). Simultaneous heat and mass transfer in laminar mixed convection flows between vertical parallel plates with asymmetric heating. International Journal of Heat and Fluid Flow, 10, 262–269.  https://doi.org/10.1016/0142-727X(89)90045-3.CrossRefGoogle Scholar
  98. 98.
    Yan, W.-M. (1992). Effects of film evaporation on laminar mixed convection heat and mass transfer in a vertical channel. International Journal of Heat and Mass Transfer, 35, 3419–3429.  https://doi.org/10.1016/0017-9310(92)90228-K.CrossRefGoogle Scholar
  99. 99.
    Tsay, Y. L., Lin, T. F., & Yan, W. M. (1990). Cooling of a falling liquid film through interfacial heat and mass transfer. International Journal of Multiphase Flow, 16, 853–865.  https://doi.org/10.1016/0301-9322(90)90008-7.CrossRefzbMATHGoogle Scholar
  100. 100.
    Tsay, Y. L., & Lin, T. F. (1995). Evaporation of a heated falling liquid film into a laminar gas stream. Exp Therm Fluid Sci, 11, 61–71.  https://doi.org/10.1016/0894-1777(94)00112-L.CrossRefGoogle Scholar
  101. 101.
    Debbissi, C., Orfi, J., & Ben, Nasrallah S. (2001). Evaporation of water by free convection in a vertical channel including effects of wall radiative propeties. International Journal of Heat and Mass Transfer, 44, 811–826.  https://doi.org/10.1016/S0017-9310(00)00125-3.CrossRefzbMATHGoogle Scholar
  102. 102.
    Debbissi, C., Orfi, J., & Ben Nasrallah, S. (2003). Evaporation of water by free or mixed convection into humid air and superheated steam. International Journal of Heat and Mass Transfer, 46, 4703–4715.  https://doi.org/10.1016/S0017-9310(03)00092-9.CrossRefzbMATHGoogle Scholar
  103. 103.
    Feddaoui, M., Mir, A., & Belahmidi, E. (2003). Numerical simulation of mixed convection heat and mass transfer with liquid film cooling along an insulated vertical channel. Heat Mass Transf und Stoffuebertragung, 39, 445–453.  https://doi.org/10.1007/s00231-002-0340-9.CrossRefzbMATHGoogle Scholar
  104. 104.
    Ren, C., & Wan, Y. (2016). A new approach to the analysis of heat and mass transfer characteristics for laminar air flow inside vertical plate channels with falling water film evaporation. International Journal of Heat and Mass Transfer, 103, 1017–1028.  https://doi.org/10.1016/j.ijheatmasstransfer.2016.07.109.CrossRefGoogle Scholar
  105. 105.
    Wan, Y., Ren, C., Xing, L., & Yang, Y. (2017). Analysis of heat and mass transfer characteristics in vertical plate channels with falling film evaporation under uniform heat flux/uniform wall temperature boundary conditions. International Journal of Heat and Mass Transfer, 108, 1279–1284.  https://doi.org/10.1016/j.ijheatmasstransfer.2016.12.110.CrossRefGoogle Scholar
  106. 106.
    Schlottke, J., & Weigand, B. (2008). Direct numerical simulation of evaporating droplets. Journal of Computational Physics, 227, 5215–5237.  https://doi.org/10.1016/j.jcp.2008.01.042.MathSciNetCrossRefzbMATHGoogle Scholar
  107. 107.
    Hu, X., & Jacobi, A. M. (1996). The Intertube Falling Film: Part 1—Flow Characteristics, Mode Transitions, and Hysteresis. Journal of Heat Transfer, 118, 616.  https://doi.org/10.1115/1.2822676.CrossRefGoogle Scholar
  108. 108.
    Mitrovic, J. (2005). Flow structures of a liquid film falling on horizontal tubes. Chemical Engineering and Technology, 28, 684–694.  https://doi.org/10.1002/ceat.200500064.CrossRefGoogle Scholar
  109. 109.
    Roques, J. F., Dupont, V., & Thome, J. R. (2002). Falling Film Transitions on Plain and Enhanced Tubes. Journal of Heat Transfer, 124, 491.  https://doi.org/10.1115/1.1458017.CrossRefGoogle Scholar
  110. 110.
    Mohamed, A. M. I. (2007). Flow behavior of liquid falling film on a horizontal rotating tube. Exp Therm Fluid Sci, 31, 325–332.  https://doi.org/10.1016/j.expthermflusci.2006.05.004.CrossRefGoogle Scholar
  111. 111.
    Ruan, B., Jacobi, A. M., & Li, L. (2009). Effects of a countercurrent gas flow on falling-film mode transitions between horizontal tubes. Exp Therm Fluid Sci, 33, 1216–1225.  https://doi.org/10.1016/j.expthermflusci.2009.07.009.CrossRefGoogle Scholar
  112. 112.
    Lewis, D. J. (1950). The Instability of Liquid Surfaces when Accelerated in a Direction Perpendicular to their Planes. II. Proc R Soc A Math Phys Eng Sci, 202, 81–96.  https://doi.org/10.1098/rspa.1950.0086.CrossRefGoogle Scholar
  113. 113.
    Richard Bellman, R. H. P. (1953). Effects of surface tension and viscosity on Taylor instability.Google Scholar
  114. 114.
    Maron-Moalem, D., Sideman, S., & Dukler, A. E. (1978). Dripping characteristics in a horizontal tube film evaporator. Desalination, 27, 117–127.  https://doi.org/10.1016/S0011-9164(00)88106-0.CrossRefGoogle Scholar
  115. 115.
    Ganic, E. N., & Roppo, M. N. (1980). An Experimental Study of Falling Liquid Film Breakdown on a Horizontal Cylinder During Heat Transfer. Journal of Heat Transfer, 102, 342.  https://doi.org/10.1115/1.3244285.CrossRefGoogle Scholar
  116. 116.
    Hu, X., & Jacobi, A. M. (1998). Departure-site spacing for liquid droplets and jets falling between horizontal circular tubes. Exp Therm Fluid Sci, 16, 322–331.  https://doi.org/10.1016/S0894-1777(97)10031-0.CrossRefGoogle Scholar
  117. 117.
    Rayleigh, L. (1878). On the instability of jets. Proceedings of London Mathematical Society s1-10:4–13.  https://doi.org/10.1112/plms/s1-10.1.4.MathSciNetCrossRefGoogle Scholar
  118. 118.
    Eggers, J., Villermaux, E. (2008). Physics of liquid jets. Reports Program Physics, 71.  https://doi.org/10.1088/0034-4885/71/3/036601.CrossRefGoogle Scholar
  119. 119.
    Killion, J. D., & Garimella, S. (2004). Pendant droplet motion for absorption on horizontal tube banks. International Journal of Heat and Mass Transfer, 47, 4403–4414.  https://doi.org/10.1016/j.ijheatmasstransfer.2004.04.032.CrossRefGoogle Scholar
  120. 120.
    Chen, X., Shen, S., Wang, Y., et al. (2015). Measurement on falling film thickness distribution around horizontal tube with laser-induced fluorescence technology. International Journal of Heat and Mass Transfer, 89, 707–713.  https://doi.org/10.1016/j.ijheatmasstransfer.2015.05.016.CrossRefGoogle Scholar
  121. 121.
    Jafar, F., Thorpe, G., & Turan, O. F. (2007). Liquid Film Falling on Horizontal Circular Cylinders. 16th Australasian Fluid Mechanics Conference (pp. 1193–1200). Queensland, Australia: Gold Coast.Google Scholar
  122. 122.
    Sun, F., Xu, S., & Gao, Y. (2012). Numerical simulation of liquid falling film on horizontal circular tubes. Front Chem Sci Eng, 6, 322–328.  https://doi.org/10.1007/s11705-012-1296-z.CrossRefGoogle Scholar
  123. 123.
    Qiu, Q., Zhu, X., Mu, L., & Shen, S. (2015). Numerical study of falling film thickness over fully wetted horizontal round tube. International Journal of Heat and Mass Transfer, 84, 893–897.  https://doi.org/10.1016/j.ijheatmasstransfer.2015.01.024.CrossRefGoogle Scholar
  124. 124.
    Qiu, Q., Meng, C., Quan, S., & Wang, W. (2017). 3-D simulation of flow behaviour and film distribution outside a horizontal tube. International Journal of Heat and Mass Transfer, 107, 1028–1034.  https://doi.org/10.1016/j.ijheatmasstransfer.2016.11.009.CrossRefGoogle Scholar
  125. 125.
    Chen, J., Zhang, R., & Niu, R. (2015). Numerical simulation of horizontal tube bundle falling film flow pattern transformation. Renewable Energy, 73, 62–68.  https://doi.org/10.1016/j.renene.2014.08.007.CrossRefGoogle Scholar
  126. 126.
    Li, M., Lu, Y., Zhang, S., & Xiao, Y. (2016). A numerical study of effects of counter-current gas flow rate on local hydrodynamic characteristics of falling films over horizontal tubes. Desalination, 383, 68–80.  https://doi.org/10.1016/j.desal.2016.01.016.CrossRefGoogle Scholar
  127. 127.
    Fiorentino, M., & Starace, G. (2016). Numerical investigations on two-phase flow modes in evaporative condensers. Applied Thermal Engineering, 94, 777–785.  https://doi.org/10.1016/j.applthermaleng.2015.10.099.CrossRefGoogle Scholar
  128. 128.
    Ding, H., Xie, P., Ingham, D., et al. (2018). Flow behaviour of drop and jet modes of a laminar falling film on horizontal tubes. International Journal of Heat and Mass Transfer, 124, 929–942.  https://doi.org/10.1016/j.ijheatmasstransfer.2018.03.111.CrossRefGoogle Scholar
  129. 129.
    Killion, J. D., & Garimella, S. (2003). Gravity-driven flow of liquid films and droplets in horizontal tube banks. International Journal of Refrigeration, 26, 516–526.  https://doi.org/10.1016/S0140-7007(03)00009-4.CrossRefGoogle Scholar
  130. 130.
    Yung, D., Lorenz, J. J., & Ganic, E. N. (1980). Vapor/liquid interaction and entrainment in falling film evaporators. Journal of Heat Transfer, 102, 20.  https://doi.org/10.1115/1.3244242.CrossRefGoogle Scholar
  131. 131.
    Ribatski, G., & Jacobi, A. M. (2005). Falling-film evaporation on horizontal tubes—A critical review. International Journal of Refrigeration, 28, 635–653.  https://doi.org/10.1016/j.ijrefrig.2004.12.002.CrossRefGoogle Scholar
  132. 132.
    Ribatski, G., & Thome, J. R. (2007). Two-phase flow and heat transfer across horizontal tube bundles-a review. Heat Transfer Engineering, 28, 508–524.  https://doi.org/10.1080/01457630701193898.CrossRefGoogle Scholar
  133. 133.
    Hu, X., & Jacobi, A. M. (1996). The intertube falling film: Part 2—Mode effects on sensible heat transfer to a falling liquid film. Journal of Heat Transfer, 118, 626.  https://doi.org/10.1115/1.2822678.CrossRefGoogle Scholar
  134. 134.
    Luo, L. C., Zhang, G. M., Pan, J. H., & Tian, M. C. (2013). Flow and heat transfer characteristics of falling water film on horizontal circular and non-circular cylinders. Journal of Hydrodynamics, 25, 404–414.  https://doi.org/10.1016/S1001-6058(11)60379-0.CrossRefGoogle Scholar
  135. 135.
    Jafar, F. A., Thorpe, G. R., & Turan, Ö. F. (2014). Liquid film falling on horizontal plain cylinders: Numerical study of heat transfer in unsaturated porous media. International Journal for Computational Methods in Engineering Science and Mechanics, 15, 101–109.  https://doi.org/10.1080/15502287.2013.874056.MathSciNetCrossRefGoogle Scholar
  136. 136.
    Karmakar, A., & Acharya, S. (2017). Heat transfer characteristics of falling film over horizontal tubes—A numerical study. In: 55th AIAA Aerospace Sciences Meeting. American Institute of Aeronautics and Astronautics, Grapevine, TexasGoogle Scholar
  137. 137.
    Andberg, J. W., & Vliet, G. C. (1983). Design guidelines for water-lithium bromide absorbers. ASHRAE Trans 89, 220–232Google Scholar
  138. 138.
    Andberg, J. W. (1986). Absorption of vapors into liquid films flowing over cooled horizontal tubes, Ph.D. thesis. Texas University, Austin (USA)Google Scholar
  139. 139.
    Choudhury, S. K., Nishiguchi, A., Hisajima, D., et al. (1993). Absorption of vapors into liquid films flowing over cooled horizontal tubes. ASHRAE Transaction, 99, 81–89.Google Scholar
  140. 140.
    Min, J. K., & Choi, D. H. (1999). Analysis of the absorption process on a horizontal tube using Navier-Stokes equations with surface-tension effects. International Journal of Heat and Mass Transfer, 42, 4567–4578.  https://doi.org/10.1016/S0017-9310(99)00104-0.CrossRefzbMATHGoogle Scholar
  141. 141.
    Jeong, S., & Garimella, S. (2002). Falling-film and droplet mode heat and mass transfer in a horizontal tube LiBr/water absorber. International Journal of Heat and Mass Transfer, 45, 1445–1458.  https://doi.org/10.1016/S0017-9310(01)00262-9.CrossRefGoogle Scholar
  142. 142.
    Subramaniam, V., & Garimella, S. (2009). From measurements of hydrodynamics to computation of species transport in falling films. International Journal of Refrigeration, 32, 607–626.  https://doi.org/10.1016/j.ijrefrig.2009.02.008.CrossRefGoogle Scholar
  143. 143.
    Subramaniam, V., & Garimella, S. (2014). Numerical study of heat and mass transfer in lithium bromide-water falling films and droplets. International Journal of Refrigeration, 40, 211–226.  https://doi.org/10.1016/j.ijrefrig.2013.07.025.CrossRefGoogle Scholar
  144. 144.
    Harikrishnan, L., Maiya, M. P., & Tiwari, S. (2011). Investigations on heat and mass transfer characteristics of falling film horizontal tubular absorber. International Journal of Heat and Mass Transfer, 54, 2609–2617.  https://doi.org/10.1016/j.ijheatmasstransfer.2011.01.024.CrossRefGoogle Scholar
  145. 145.
    Hosseinnia, S. M., Naghashzadegan, M., & Kouhikamali, R. (2017). CFD simulation of water vapor absorption in laminar falling film solution of water-LiBr—Drop and jet modes. Applied Thermal Engineering, 115, 860–873.  https://doi.org/10.1016/j.applthermaleng.2017.01.022.CrossRefGoogle Scholar
  146. 146.
    Kocamustafaogullari, G., & Chen, I. Y. (1988). Falling film heat transfer analysis on a bank of horizontal tube evaporator. AIChE Journal, 34, 1539–1549.  https://doi.org/10.1002/aic.690340916.CrossRefGoogle Scholar
  147. 147.
    Liu, Z. H., Zhu, Q. Z., & Chen, Y. M. (2002). Evaporation heat transfer of falling water film on a horizontal tube bundle. Heat Transfer Asian Research, 31, 42–55.  https://doi.org/10.1002/htj.10016.CrossRefGoogle Scholar
  148. 148.
    Abraham, R., & Mani, A. (2015). Heat transfer characteristics in horizontal tube bundles for falling film evaporation in multi-effect desalination system. Desalination, 375, 129–137.  https://doi.org/10.1016/j.desal.2015.06.018.CrossRefGoogle Scholar

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© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.Mechanical, Materials and Aerospace Engineering DepartmentIllinois Institute of TechnologyChicagoUSA

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