A Review of Computational Models for Falling Liquid Films

  • Avijit Karmakar
  • Sumanta AcharyaEmail author


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.



Species concentration


Specific heat


Tube diameter


Mass diffusivity


Froude number


Gravity vector


Modified Galileo number


Heat transfer coefficient




Thermal conductivity


Characteristic length for the film


Lewis number


Mass flow rate

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

Diffusion mass flux


Unit normal to the interface


Nusselt number




Peclet number


Prandtl number

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

Heat flux


Volume flow rate


Reynolds number


Interfacial line coordinate


Sherwood number


Stanton number


Schmidt number




Unit tangential to the interface




Velocity vector


Streamwise velocity


Transverse velocity


Domain width


Weber number


Streamwise coordinate


Transverse coordinate


Mass fraction





Dynamic viscosity


Film thickness


Surface tension coefficient


Interface curvature


Kinematic viscosity


Shear stress


Mass flow rate per unit width


Ratio of length scales






Stream function


Moving coordinate


Thermal energy due to viscous dissipation


Dimensionless temperature


Mass transfer coefficient


Ratio of domain length to width


Capillary length









Diabatic boundary






Gaseous phase










Wave celerity












Boundary Layer


Computational Fluid Dynamics


Marker and Cell


Open-source Field Operation and Manipulation


Semi-implicit Method for Pressure-Linked Equations


Semi-implicit Method for Pressure-Linked Equations Revised


Uniform Heat Flux


Uniform Wall Temperature


Volume of Fluid


Two dimensional


Three dimensional



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.


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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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