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.

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Fig. 1

Phase change flow solver algorithm

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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

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Fig. 3

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

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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.

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Fig. 5

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

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Fig. 6

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

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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.

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Fig. 8

Predicted trends of Nusselt number variation with capillary number

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Fig. 9

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

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Fig. 10

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




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