Pendant droplet motion for absorption on horizontal tube banks

https://doi.org/10.1016/j.ijheatmasstransfer.2004.04.032Get rights and content

Abstract

Falling films on internally cooled horizontal tube banks are widely used in the absorbers of absorption heat pumps. Recent literature suggests that the droplets that form on the underside of the tubes play a large part in the absorption process. Flow visualization of aqueous lithium–bromide solutions falling over 15.9 mm OD tubes using high-speed video is presented here. The results illustrate the characteristic droplet evolution pattern, including the axial elongation along the tube, the formation of a primary droplet, trailing liquid thread, and satellite droplets, and the formation of saddle waves due to the spreading lamellae of the primary droplet impacts. In addition, a new image analysis method is developed to quantify the surface area and volume of the droplets during their formation, detachment, fall and impact. Using a semi-automated edge-detection process, a mathematical description of the interface of the droplets is generated for each frame of a sequence. The results show that the surface area and volume of a droplet between the tubes increase until the primary droplet impacts the tube beneath. The surface area and volume both drop sharply after impact as the main liquid inventory of the droplet joins the film surrounding the tube. As the trailing liquid thread breaks into satellite droplets, the surface-area-to-volume ratio reaches a maximum. These results are useful for developing more realistic models of heat and mass transfer in droplets pendant from horizontal tubes.

Introduction

Internally cooled horizontal tube banks over which a liquid film falls due to gravity are used in many applications, in particular in the absorbers of absorption heat pumps. The heat and mass transfer occurring across the film is affected by the details of the flow pattern of the liquid film. In most absorption heat pumps, the liquid flow rate is such that droplets form on the bottom of each tube and fall onto the top of the tube beneath. It has been suggested in the literature that a significant portion of the total absorption occurs on the pendant liquid droplets [1], [2], [3], [4], [5]. In addition, the behavior of the droplets affects the waviness and temporal distribution of the liquid film surrounding the tubes. Thus, understanding the behavior of the droplets is important for the understanding of the overall absorption process on falling films over horizontal tubes. In most models of absorption on horizontal tubes, the effects of droplets are essentially neglected: the film is assumed to be smooth, uniformly distributed, and instantly transported from the bottom of one tube to the top of the next without the possibility of absorption [6], [7], [8]. Previous models of the absorption process on horizontal tubes that have separately considered the role of droplets have been forced to utilize greatly simplified assumptions about the shape of the droplets during formation and fall (as well as oversimplifying the effects of droplet impact) [2], [3]. The evolution of the shape of droplets forming in horizontal tube banks with falling water films has been investigated using high-speed digital photography [5]. This analysis revealed that the flow pattern differed significantly from the idealized pattern often assumed in the literature. The progression of events that characterizes the evolution of droplets in these systems was shown for the case of water falling over a horizontal tube bank with 12.7 mm outside-diameter tubes spaced 25.4 mm apart. The present work extends this analysis to the case of aqueous lithium–bromide solutions, a working fluid pair encountered frequently in absorption heat pumps, falling over a bank of horizontal 15.9 mm diameter tubes spaced 15.9 mm apart, a geometry characteristic of absorber designs used in commercial absorption heat pumps. In addition, a new method for analyzing the shape of the droplet interface is developed, which allows the quantification of droplet surface area and volume during the evolution of a pendant drop. This is accomplished by developing a mathematical description for the coordinates of the interface contained in each of a sequence of high-speed video. This mathematical description is a piecewise-smooth spline function that uniquely minimizes the surface area of the function given the coordinates identified on the droplet interface. Using a known reference dimension from the video, this function can be appropriately integrated to estimate the temporal development of droplet surface area and volume during droplet formation and detachment. This information provides valuable insight and information for accurately modeling the transport processes on pendant droplets.

Section snippets

Previous studies

The phenomenon of droplet formation has been studied for hundreds of years. According to the review by Eggers [9], droplet formation was first mentioned in scientific literature in 1686 by Mariotte [10]. Investigating the formation of droplets from fluid jets, Savart in 1833 [11], Plateau in 1849 [12], and the famous works of Rayleigh in 1879 [13], [14] laid much of the foundation for modern understanding of the formation of droplets. In 1908, Worthington published “A Study of Splashes” which

Experimental setup

The bank of horizontal tubes used in the present study was a single column of nine copper tubes 15.9 mm in diameter and approximately 500 mm long. With the primary focus being an understanding of fluid flow, the apparatus did not include any provision for absorption or heat transfer. The tube center-to-center spacing was 31.8 mm, providing a 15.9 mm tube-to-tube distance. The fluid used was surfactant-free aqueous lithium–bromide (53.44% LiBr by weight, see Table 1 for a summary of

Progression of the interface

The departure of the flow patterns from the idealized patterns assumed in the literature was described in detail by Killion and Garimella [5] for water. The flow patterns with aqueous LiBr exhibit similar characteristics. Fig. 3 shows the typical evolution of a droplet from the early formation through detachment and subsequent impact on the tube below. The early formation is the result of film instabilities but is often driven or accelerated substantially by the arrival of a supply of liquid

Image analysis

The qualitative description above reveals the significant differences between the actual behavior of the droplets and what is often assumed when attempting to model the role of droplets in the absorption process. The droplets rarely, if ever, resemble a sphere or spherical section, and it is clear that the liquid thread and satellite droplets are a significant aspect of the overall process. In addition, the impact and spreading of the droplets generates a non-uniform liquid distribution along

Results

The horizontal lines in Fig. 5 show various limits used to analyze the droplet surface area and volume discussed below. The spline fit to the interface is shown as a light solid curve. The times are referenced to the moment of impact (actually the moment when the droplet first crosses the lower boundary) as time 0. This is because the impact event provides a convenient point of synchronization for aligning the results of several analyses. Fig. 6 shows the results of the analysis of surface

Conclusions

Droplet formation and impact is widely studied, particularly in axisymmetric cases such as formation from a jet and impact onto a flat surface. However, in the application of interest, namely the absorbers of absorption heat pumps, the droplet behavior differs from the axisymmetric case because it occurs in a bank of horizontal tubes surrounded by falling liquid films. Using high-speed, high-resolution video, the behavior of falling films of aqueous lithium–bromide over horizontal-tube banks

Acknowledgements

The authors gratefully acknowledge the support of the National Science Foundation through grant number 9875010, ASHRAE through a Grant-in-Aid, and John Dickerson, Noah Hughes and Matt Bradshaw of Engineering Computing Support Services at Iowa State University.

References (52)

  • S.K Choudhury et al.

    Absorption of vapors into liquid films flowing over cooled horizontal tubes

  • Z. Lu, D. Li, S. Li, B. Yu-Chi, A semi-empirical model of the falling film absorption outside horizontal tubes, in:...
  • J Eggers

    Nonlinear dynamics and breakup of free-surface flows

    Rev. Mod. Phys.

    (1997)
  • E Mariotte

    Traite' Du Mouvement Des Eaux Et Des Autres Corps Fluids

    (1686)
  • F Savart

    Memoire sur la Constitution des Veines Liquides Lancees par des Orifices Circulaires en Mince Paroi

    Annal. Chim.

    (1833)
  • J Plateau

    Acad. Sci. Bruxelles. Mem.

    (1849)
  • L.J.W.S Rayleigh

    On the instability of jets

    Proc. London Math. Soc.

    (1879)
  • L.J.W.S Rayleigh

    On the capillary phenomena of jets

    Proc. Roy. Soc. London: A

    (1879)
  • A.M Worthington

    A Study of Splashes

    (1908)
  • H.E. Edgerton, 1957. Milk Drop Coronet, Cambridge, MA. Available from...
  • R Clift et al.

    Bubbles, Drops, and Particles

    (1978)
  • A Frohn et al.

    Dynamics of Droplets, in Experimental Fluid Mechanics

    (2000)
  • D.B Bogy

    Drop formation in a circular liquid jet

    Ann. Rev. Fluid Mech.

    (1979)
  • A.L Yarin

    Free Liquid Jets and Films: Hydrodynamics and Rheology

    (1993)
  • S Middleman

    Modeling Axisymmetric Flows: Dynamics of Films, Jets, and Drops

    (1995)
  • H.E Edgerton et al.

    Studies in drop formation as revealed by the high-speed motion camera

    J. Phys. Chem.

    (1937)
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