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Research Papers

Numerical Simulations of Hydrodynamics and Heat Transfer in Wavy Falling Liquid Films on Vertical and Inclined Walls

[+] Author and Article Information
Hongyi Yu

Institute of Technical Thermodynamics,
Technische Universität Darmstadt,
Petersenstr. 17,
Darmstadt 64287, Germany

Tatiana Gambaryan-Roisman

e-mail: gtatiana@ttd.tu-darmstadt.de

Peter Stephan

Institute of Technical Thermodynamics,
Center of Smart Interfaces,
Technische Universität Darmstadt,
Petersenstr. 17,
Darmstadt 64287, Germany

1Present address: Shaanxi Heavy Duty Automobile Co., Ltd., Automotive Engineering R&D Center CAE Department, Xi'an, China.

2Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the Journal of Heat Transfer. Manuscript received August 22, 2012; final manuscript received January 17, 2013; published online September 11, 2013. Assoc. Editor: Sushanta K. Mitra.

J. Heat Transfer 135(10), 101010 (Sep 11, 2013) (9 pages) Paper No: HT-12-1451; doi: 10.1115/1.4024550 History: Received August 22, 2012; Revised January 17, 2013

The flow of thin falling liquid films is unstable to long-wave disturbances. The flow instability leads to development of waves at the liquid–gas interface. The effect of the waves on heat and mass transfer in falling liquid films is a subject of ongoing scientific discussion. In this work, numerical investigation of the wave dynamics has been performed using a modified volume-of-fluid (VOF) method for tracking the free surface. The surface tension is described using the continuum surface force (CSF) model. With low disturbance frequency, solitary waves of large amplitude are developed, which are preceded by low-amplitude capillary waves. With high disturbance frequency, low amplitude sinusoidal waves are developed. The waveforms dependent on the Reynolds number and disturbance frequency are summarized in a form of a regime map. A correlation describing the separation curve between the sinusoidal waves regime and solitary waves regime is proposed. The wave parameters (peak height, length, and propagation speed) are computed from the simulation results and compared with available experimental correlations in a wide range of parameters. The effects of the disturbance frequency and the plane inclination angle on the wave dynamics have been studied. The interaction of waves initiated by simultaneous disturbances of two different frequencies has been investigated. The heat transfer in the wavy film has been simulated for the constant wall temperature boundary condition. The effects of Prandtl number and disturbance frequency on local and global heat transfer parameters have been investigated. It has been shown that the influence of waves on heat transfer is significant for large Prandtl numbers in a specific range of disturbance frequencies.

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References

Figures

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Fig. 1

Comparison of waveforms of (a) the present numerical studies to (b) the Kapitzas' photographs of periodically excited waves

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Fig. 2

Streamlines of a sinusoidal wave in a moving coordinate system

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Fig. 3

Streamlines of a solitary wave in a moving coordinate system

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Fig. 4

Comparison of computed wave speed and wave peak height with experimental results of Nosoko et al. [7]

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Fig. 5

Waveforms for falling film of Re = 20, We = 33.2, β = 90 deg with different disturbance frequencies

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Fig. 6

Map of wavy regimes for a liquid film flow along a vertical wall. (a) Map for water films in the full range of Reynolds numbers used in simulations; (b) map for water and ethanol films, Re < 25

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Fig. 7

Waveforms of film flow with Re = 20, f = 15 Hz at various inclination angles

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Fig. 8

Waveforms for film flow of Re = 20, β = 90 deg at different time instances for disturbance frequencies 27 Hz (starting at t = 0 s) and 35 Hz (starting at the time instance t = 0.5 s)

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Fig. 9

Curves of constant temperature in a sinusoidal wave. Re = 69, β = 90 deg, f = 53 Hz

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Fig. 10

Curves of constant temperature in a solitary wave. Re = 69, β = 90 deg, f = 17.7 Hz

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Fig. 11

The relative average Nusselt number as a function of dimensionless disturbance frequency for Re = 69, β = 90 deg

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