scholarly journals Population balance modeling for air–water bubbly flow in a vertical U-bend

2018 ◽  
Vol 10 (4) ◽  
pp. 170-177
Author(s):  
Yichuan Huang ◽  
Hongye Zhu ◽  
Xingtuan Yang ◽  
Jiyuan Tu ◽  
Shengyao Jiang
Keyword(s):  
Tube Wall ◽  
Bubbly Flow ◽  
Population Balance ◽  
Superficial Velocity ◽  
Balance Model ◽  
Outer Side ◽  
Group Model ◽  
Population Balance Modeling ◽  
Buoyant Force ◽  
High Heat Transfer

Bubbly flow in U-bend is widely encountered in two-phase flow systems because of its compactness and high heat transfer coefficient. The modeling of phase distributions, velocity fields, and interfacial area concentration in the U-bend is crucial for the analysis of mass, momentum, and energy transportation processes in the equipment. However, this subject has not received enough attention yet. In this paper, the combination of population balance model and two-fluid model was used in the simulation of air–water bubbly flow in a U-bend with 24 mm inner diameter and 96 mm curvature. The homogeneous multiple size group model was used to solve the population balance equation and reconstruct the bubble size distribution function. The phase distribution at 0°, 90°, and 180° was predicted and the results showed that the superficial velocities of gas and liquid phase were the control parameters. Under higher gas superficial velocity, the buoyant force is dominant and makes the bubbles concentrate on the outer side of the tube wall; while under lower gas superficial velocity, the centrifugal force is dominant and makes the bubbles concentrate on the inner side of the tube wall. These results met well with the experimental results of Usui.

Understanding the Precipitated Calcium Carbonate Flocculation Mechanism Induced by Starch through Population Balance Modeling

2011 ◽  
Vol 236-238 ◽  
pp. 1250-1255
Author(s):  
Yi Zhou Sang ◽  
Nayef M. Al Saifi ◽  
Peter Englezos
Keyword(s):  
Calcium Carbonate ◽  
Population Balance ◽  
Energy Dissipation Rate ◽  
Balance Model ◽  
Collision Efficiency ◽  
Precipitated Calcium Carbonate ◽  
Population Balance Modeling ◽  
Flocculation Mechanism ◽  
Effects Of Temperature ◽  
Breakage Mechanism

The precipitated calcium carbonate (PCC) flocculation kinetics and floc structures induced by cationic tapioca starch were recorded by the Malvern Mastersizer 2000 (Malvern Instruments Inc, Malvern, UK). Of particular interest, a population balance model for PCC flocculation was employed to extract the flocculation constants, namely collision efficiency, magnitude of energy dissipation rate and restructuring rate. The model made an attempt to take aggregation, breakage and flocs restructuring into account simultaneously to describe the PCC flocculation by aggregation and breakage mechanism. Through a response surface methodology (RSM) involving a central composite design, the effects of temperature, polymer dosage, ionic strength, and shear rate on flocculation parameters were investigated in this paper.

scholarly journals Population Balance Modeling and Opinion Dynamics—A Mutually Beneficial Liaison?

Processes ◽  
2018 ◽  
Vol 6 (9) ◽  
pp. 164 ◽  
Author(s):  
Michael Kuhn ◽  
Christoph Kirse ◽  
Heiko Briesen
Keyword(s):  
Opinion Dynamics ◽  
Population Balance ◽  
Initial Distribution ◽  
Balance Model ◽  
Order Moment ◽  
Liquid Droplets ◽  
Population Balance Modeling ◽  
The One ◽  
New Formulation ◽  
Dynamics Problems

In this contribution, we aim to show that opinion dynamics and population balance modeling can benefit from an exchange of problems and methods. To support this claim, the Deffuant-Weisbuch model, a classical approach in opinion dynamics, is formulated as a population balance model. This new formulation is subsequently analyzed in terms of moment equations, and conservation of the first and second order moment is shown. Exemplary results obtained by our formulation are presented and agreement with the original model is found. In addition, the influence of the initial distribution is studied. Subsequently, the Deffuant-Weisbuch model is transferred to engineering and interpreted as mass transfer between liquid droplets which results in a more flexible formulation compared to alternatives from the literature. On the one hand, it is concluded that the transfer of opinion-dynamics problems to the domain of population balance modeling offers some interesting insights as well as stimulating challenges for the population-balance community. On the other hand, it is inferred that population-balance methods can contribute to the solution of problems in opinion dynamics. In a broad outlook, some further possibilities of how the two fields can possibly benefit from a close interaction are outlined.

scholarly journals Population Balance Modeling and Opinion Dynamics -- A Mutually Beneficial Liaison?

2018 ◽  
Author(s):  
Michael Kuhn ◽  
Christoph Kirse ◽  
Heiko Briesen
Keyword(s):  
Opinion Dynamics ◽  
Population Balance ◽  
Initial Distribution ◽  
Balance Model ◽  
Order Moment ◽  
Liquid Droplets ◽  
Population Balance Modeling ◽  
The One ◽  
New Formulation ◽  
Dynamics Problems

In this contribution, we aim to show that opinion dynamics and population balance modeling can benefit from an exchange of problems and methods. To support this claim, the Deffuant-Weisbuch model, a classical approach in opinion dynamics, is formulated as a population balance model. This new formulation is subsequently analyzed in terms of moment equations, and conservation of the first and second order moment is shown. Exemplary results obtained by our formulation are presented and agreement with the original model is found. Also the influence of the initial distribution is studied. Additionally, the Deffuant-Weisbuch model is transferred to engineering and interpreted as mass transfer between liquid droplets which results in a more flexible formulation compared to alternatives from the literature. On the one hand, it is concluded that the transfer of opinion-dynamics problems to the domain of population balance modeling offers some interesting insights as well as stimulating challenges for the population-balance community. On the other hand, it is inferred that population-balance methods can contribute to the solution of problems in opinion dynamics. In a broad outlook, some further possibilities of how the two fields can possibly benefit from a close interaction are outlined.

Population Balance Modeling of Polydispersed Bubbly Flow in Continuous-Casting Using Multiple-Size-Group Approach

2014 ◽  
Vol 46 (1) ◽  
pp. 406-420 ◽  
Author(s):  
Zhongqiu Liu ◽  
Linmin Li ◽  
Fengsheng Qi ◽  
Baokuan Li ◽  
Maofa Jiang ◽  
...  
Keyword(s):  
Continuous Casting ◽  
Bubbly Flow ◽  
Population Balance ◽  
Size Group ◽  
Group Approach ◽  
Population Balance Modeling

scholarly journals Comparison of One Dimensional and Two Dimensional Population Balance Model for Optimization of a Crystallization Process

2021 ◽  
Author(s):  
Tamar Rosenbaum ◽  
Victoria Mbachu ◽  
Niall Mitchell ◽  
John Gamble ◽  
Patricia Cho ◽  
...  
Keyword(s):  
Aspect Ratio ◽  
Crystallization Process ◽  
Population Balance ◽  
Seed Morphology ◽  
Balance Model ◽  
Population Balance Model ◽  
Two Dimensional ◽  
Population Balance Modeling ◽  
One Dimensional ◽  
The Impact

In this work, the advantage of two-dimensional population balance modeling (2D PBM) for a needle-shaped API is highlighted by comparing the one-dimensional population balance model (1D PBM) developed for an antisolvent crystallization with the 2D PBM. The API utilized for this work had extremely slow desupersaturation, and was not able to achieve solubility concentration despite a ~50 h seed bed age. While the 1D PBM is useful in optimizing the crystallization process to enhance desupersaturation, it is unable to match the particle size quantiles well. 2D PBM was necessary to probe the impact of crystallization process parameters on particle aspect ratio (AR). Simulations utilizing the 2D PBM indicated that regardless of antisolvent addition rate or seed morphology, the final material would still be high aspect ratio. This knowledge saved the investment of much time and efforts in trying to minimize particle AR with changes in crystallization processing parameters alone.

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