scholarly journals On the numerical study of isothermal vertical bubbly flow using two population balance approaches

2007 ◽  
Vol 62 (17) ◽  
pp. 4659-4674 ◽  
Author(s):  
Sherman C.P. Cheung ◽  
G.H. Yeoh ◽  
J.Y. Tu
Keyword(s):  
Numerical Study ◽  
Bubbly Flow ◽  
Population Balance

Taylor series expansion scheme applied for solving population balance equation

2018 ◽  
Vol 34 (4) ◽  
pp. 561-594 ◽  
Author(s):  
Mingzhou Yu ◽  
Jianzhong Lin
Keyword(s):  
Series Expansion ◽  
Taylor Series ◽  
Numerical Study ◽  
Rapid Development ◽  
Taylor Series Expansion ◽  
Population Balance ◽  
Population Balance Modeling ◽  
Physicochemical Processes ◽  
Selection Of ◽  
Expansion Scheme

Abstract Population balance equations (PBE) are widely applied to describe many physicochemical processes such as nanoparticle synthesis, chemical processes for particulates, colloid gel, aerosol dynamics, and disease progression. The numerical study for solving the PBE, i.e. population balance modeling, is undergoing rapid development. In this review, the application of the Taylor series expansion scheme in solving the PBE was discussed. The theories, implement criteria, and applications are presented here in a universal form for ease of use. The aforementioned method is mathematically economical and applicable to the combination of fine-particle physicochemical processes and can be used to numerically and pseudo-analytically describe the time evolution of statistical parameters governed by the PBE. This article summarizes the principal details of the method and discusses its application to engineering problems. Four key issues relevant to this method, namely, the optimization of type of moment sequence, selection of Taylor series expansion point, optimization of an order of Taylor series expansion, and selection of terms for Taylor series expansion, are emphasized. The possible direction for the development of this method and its advantages and shortcomings are also discussed.

Transition of Bubbly Flow in Vertical Tubes: Effect of Bubble Size and Tube Diameter

2009 ◽  
Vol 131 (9) ◽  
Author(s):  
A. K. Das ◽  
P. K. Das ◽  
J. R. Thome
Keyword(s):  
Slug Flow ◽  
Bubbly Flow ◽  
Axial Flow ◽  
Population Balance ◽  
Tube Diameter ◽  
Transition Boundary ◽  
Transition Mechanism ◽  
Flow Development ◽  
Wide Range ◽  
Balance Technique

In a companion paper (“Modelling Bubbly Flow by Population Balance Technique Part I: Axial Flow Development and Its Transitions,” ASME J. Fluids Eng), a two fluid model along with a multiclass population balance technique has been used to find out comprehensive criteria for the transition from bubbly to slug flow, primarily through a study of axial flow development. Using the same basic model the transition mechanism has been investigated in the present paper covering a wide range of process parameters. Though the dominating rate of bubble coalescence during the axial development of the flow acts as the main cause for the transition to slug flow, the simultaneous transformation of the radial voidage pattern cannot be overlooked. Appearance of core, intermediate, wall, and two peaks are observed in the radial voidage distribution depending on the phase superficial velocities. A map has been developed indicating the boundaries of the above subregimes. It has been observed that not only the size of the bubbles entering the inlet plane but also the size distribution (monodispersion or bidispersion) changes the voidage peak and shifts the transition boundary. It is interesting to note that the bubbly flow only with a core peak void distribution transforms into slug flow with a change in the operating parameters. Transition boundary is also observed to shift with a change in the tube diameter. The simulation results have been compared with experimental data taken from different sources and very good agreements have been noted.

scholarly journals A numerical study on the estimation of the stable size distribution for a cell population balance model

2018 ◽  
Vol 41 (8) ◽  
pp. 2894-2905 ◽  
Author(s):  
Luis M. Abia ◽  
Óscar Angulo ◽  
Juan Carlos López-Marcos ◽  
Miguel Ángel López-Marcos
Keyword(s):  
Size Distribution ◽  
Cell Population ◽  
Numerical Study ◽  
Population Balance ◽  
Balance Model ◽  
Population Balance Model ◽  
A Cell ◽  
Stable Size Distribution

scholarly journals Experimental and Numerical Study of the Flow and Heat Transfer in a Bubbly Turbulent Flow in a Pipe with Sudden Expansion

Energies ◽  
2019 ◽  
Vol 12 (14) ◽  
pp. 2735 ◽  
Author(s):  
Pavel Lobanov ◽  
Maksim Pakhomov ◽  
Viktor Terekhov
Keyword(s):  
Heat Transfer ◽  
Liquid Velocity ◽  
Numerical Study ◽  
Bubbly Flow ◽  
Fluid Phase ◽  
Reynolds Stress Model ◽  
Sudden Expansion ◽  
Two Phase ◽  
Carrier Fluid ◽  
Carrier Liquid

The flow patterns and heat transfer of a downstream bubbly flow in a sudden pipe expansion are experimentally and numerically studied. Measurements of the bubble size were performed using shadow photography. Fluid phase velocities were measured using a PIV system. The numerical model was employed the Eulerian approach. The set of RANS equations was used for modelling two-phase bubbly flows. The turbulence of the carrier liquid phase was predicted using the Reynolds stress model. The peak of axial and radial fluctuations of the carrier fluid (liquid) velocity in the bubbly flow is observed in the shear layer. The addition of air bubbles resulted in a significant increase in the heat transfer rate (up to 300%). The main enhancement in heat transfer is observed after the point of flow reattachment.

On the Numerical Study of Bubbly Flow Created by Ventilated Cavity

2010 ◽  
Vol 29-32 ◽  
pp. 143-148
Author(s):  
Min Xiang ◽  
S.C.P. Cheung ◽  
Ji Yuan Tu ◽  
Wei Hua Zhang ◽  
Yang Fei
Keyword(s):  
Flow Field ◽  
Void Fraction ◽  
Numerical Study ◽  
Fluid Model ◽  
Bubbly Flow ◽  
Bubble Diameter ◽  
Flow Region ◽  
Valuable Insight ◽  
Two Phase ◽  
Ventilated Cavity

The aim of the study was to develop a numerical model to reproduce the bubbly flow field created by ventilated cavity which includes three different regions. The model was established based on the Eulerian-Eulerian two-fluid model coupled with a population balance approach which is solved by the Homogeneous Multiple-Size-Group (MUSIG) model to predict bubble size distribution. Base on the model, the simulation was carried out at the experimental condition of Su et al. (1995). Firstly three regions were successfully captured proved by the spatial voidage distribution and streamline shape. Then distributions of void fraction and Sauter mean bubble diameter at various sections below the cavity corresponding to three regions respectively were plotted against experimental data. A close agreement was observed in the void fraction distribution which indicates that qualitative details of the structure of the two-phase flow field below the cavity was successfully produced. The Sauter mean bubble diameter in the pipe flow region was under-predicted for about 10%. In conclusion, the proposed model was validated in predicting the multi-region flow field below the ventilated cavity which will provide a valuable insight in designing and controlling of the two phase systems with the detailed flow field information obtained.

Numerical Study on Population Balance Approaches in Modeling of Isothermal Vertical Bubbly Flows

2009 ◽  
pp. 599-604
Author(s):  
Sherman C. P. Cheung ◽  
G. H. Yeoh ◽  
J. Y. Tu ◽  
E. Krepper ◽  
D. Lucas
Keyword(s):  
Numerical Study ◽  
Population Balance ◽  
Bubbly Flows
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