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Research Papers: Heat and Mass Transfer

A Probability Model for Fully Developed Annular Flow in Vertical Pipes: Film Thickness, Interfacial Shear Stress, and Droplet Size Distribution

[+] Author and Article Information
Ri Zhang

College of Engineering,
Ocean University of China,
Qingdao 266100, China;
State Key Laboratory of Hydraulic Engineering
Simulation and Safety,
Tianjin University,
Tianjin 300072, China

Haixiao Liu

State Key Laboratory of Hydraulic Engineering
Simulation and Safety,
Tianjin University,
Tianjin 300072, China;
Collaborative Innovation Center for
Advanced Ship and Deep-Sea Exploration,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: liuhx@tju.edu.cn

Sheng Dong

College of Engineering,
Ocean University of China,
Qingdao 266100, China

Mingyang Liu

State Key Laboratory of Hydraulic Engineering Simulation and Safety,
Tianjin University,
Tianjin 300072, China

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received December 15, 2015; final manuscript received September 10, 2016; published online November 16, 2016. Assoc. Editor: Milind A. Jog.

J. Heat Transfer 139(3), 032001 (Nov 16, 2016) (10 pages) Paper No: HT-15-1793; doi: 10.1115/1.4034900 History: Received December 15, 2015; Revised September 10, 2016

The movement and distribution of each phase in annular flow can be considered as random events at a microscopic level. Hence, a probability analysis is appropriate to estimate the morphological features and mechanical characteristics of annular flow from a macroscopic scale. In the present work, three characteristic parameters including the film thickness, interfacial shear stress, and characteristic droplet size are predicted by a probability model as the statistical results of abundant samples. The film thickness can be directly calculated as one of the solutions to the basic equations of annular flow. The interfacial shear stress is estimated as a combination of the frictional and dragging components. The droplet size distribution is obtained using a method of undetermined coefficients. These characteristic parameters are well verified by comparing with the experimental data available in the literature. It is demonstrated that the probability model can accurately calculate the film thickness and maximum droplet size, but the predictions of the interfacial shear stress and mean droplet size are relatively coarse. Furthermore, the effects on the film thickness and Sauter mean diameter of other parameters are discussed in detail. Finally, some important phenomena observed in experiments are interpreted by the probability model.

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References

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Figures

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Fig. 1

The decomposition of interfacial shear stress

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Fig. 2

Generation of the droplet with the maximum size

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Fig. 3

Comparison of film thickness between the probability model and experiments [3032]

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Fig. 4

Effects of parameters on predicting the film thickness: (a) film thickness versus superficial gas velocity [3032], (b) film thickness versus superficial liquid velocity [30], (c) film thickness versus gas density, (d) film thickness versus liquid density, (e) film thickness versus gas viscosity, (f) film thickness versus surface tension, and (g) film thickness versus pipe diameter

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Fig. 5

Comparison of interfacial shear stresses between the probability model and experiments [30,34,35]

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Fig. 6

Comparison of characteristic droplet sizes between the probability model and experiments: (a) 14 cases from Ref. [16], (b) 45 cases from Ref. [36], and (c) six cases from Ref. [26]

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Fig. 7

Effects of parameters on the Sauter mean diameter prediction [36]: (a) Sauter mean diameter versus superficial gas velocity and (b) Sauter mean diameter versus superficial liquid velocity

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Fig. 8

Comparison of probability density distributions of droplet size between the probability model and experiments: (a) one case from Ref. [16], (b) one case from Ref. [36], and (c) one case from Ref. [26]

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