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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Research-Article
A Probability Model for Fully Developed Annular Flow in Vertical Pipes: Film Thickness, Interfacial Shear Stress, and Droplet Size Distribution
Ri Zhang,
Ri Zhang
College of Engineering,
Ocean University of China,
Qingdao 266100, China;
Ocean University of China,
Qingdao 266100, China;
State Key Laboratory of Hydraulic Engineering
Simulation and Safety,
Tianjin University,
Tianjin 300072, China
Simulation and Safety,
Tianjin University,
Tianjin 300072, China
Search for other works by this author on:
Haixiao Liu,
Haixiao Liu
State Key Laboratory of Hydraulic Engineering
Simulation and Safety,
Tianjin University,
Tianjin 300072, China;
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
Advanced Ship and Deep-Sea Exploration,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: liuhx@tju.edu.cn
Search for other works by this author on:
Sheng Dong,
Sheng Dong
College of Engineering,
Ocean University of China,
Qingdao 266100, China
Ocean University of China,
Qingdao 266100, China
Search for other works by this author on:
Mingyang Liu
Mingyang Liu
State Key Laboratory of Hydraulic Engineering Simulation and Safety,
Tianjin University,
Tianjin 300072, China
Tianjin University,
Tianjin 300072, China
Search for other works by this author on:
Ri Zhang
College of Engineering,
Ocean University of China,
Qingdao 266100, China;
Ocean University of China,
Qingdao 266100, China;
State Key Laboratory of Hydraulic Engineering
Simulation and Safety,
Tianjin University,
Tianjin 300072, China
Simulation and Safety,
Tianjin University,
Tianjin 300072, China
Haixiao Liu
State Key Laboratory of Hydraulic Engineering
Simulation and Safety,
Tianjin University,
Tianjin 300072, China;
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
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
Ocean University of China,
Qingdao 266100, China
Mingyang Liu
State Key Laboratory of Hydraulic Engineering Simulation and Safety,
Tianjin University,
Tianjin 300072, China
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. Mar 2017, 139(3): 032001 (10 pages)
Published Online: November 16, 2016
Article history
Received:
December 15, 2015
Revised:
September 10, 2016
Citation
Zhang, R., Liu, H., Dong, S., and Liu, M. (November 16, 2016). "A Probability Model for Fully Developed Annular Flow in Vertical Pipes: Film Thickness, Interfacial Shear Stress, and Droplet Size Distribution." ASME. J. Heat Transfer. March 2017; 139(3): 032001. https://doi.org/10.1115/1.4034900
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