Simulation of a Bubble Column by Computational Fluid Dynamics and Population Balance Equation Using the Cell Average Method

2017 ◽  
Vol 40 (10) ◽  
pp. 1792-1801 ◽  
Author(s):  
Qian Li ◽  
Jingcai Cheng ◽  
Chao Yang ◽  
Zai-Sha Mao
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Balance Equation ◽  
Average Method ◽  
Bubble Column ◽  
Population Balance ◽  
Population Balance Equation ◽  
Cell Average

scholarly journals Characterization of Simultaneous Evolution of Size and Composition Distributions Using Generalized Aggregation Population Balance Equation

Pharmaceutics ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 1152
Author(s):  
Mehakpreet Singh ◽  
Ashish Kumar ◽  
Saeed Shirazian ◽  
Vivek Ranade ◽  
Gavin Walker
Keyword(s):  
Finite Volume ◽  
Balance Equation ◽  
Numerical Scheme ◽  
Population Balance ◽  
Population Balance Equation ◽  
Finite Volume Scheme ◽  
Average Technique ◽  
Volume Scheme ◽  
Density Prediction ◽  
Cell Average

The application of multi-dimensional population balance equations (PBEs) for the simulation of granulation processes is recommended due to the multi-component system. Irrespective of the application area, numerical scheme selection for solving multi-dimensional PBEs is driven by the accuracy in (size) number density prediction alone. However, mixing the components, i.e., the particles (excipients and API) and the binding liquid, plays a crucial role in predicting the granule compositional distribution during the pharmaceutical granulation. A numerical scheme should, therefore, be able to predict this accurately. Here, we compare the cell average technique (CAT) and finite volume scheme (FVS) in terms of their accuracy and applicability in predicting the mixing state. To quantify the degree of mixing in the system, the sum-square χ2 parameter is studied to observe the deviation in the amount binder from its average. It has been illustrated that the accurate prediction of integral moments computed by the FVS leads to an inaccurate prediction of the χ2 parameter for a bicomponent population balance equation. Moreover, the cell average technique (CAT) predicts the moments with moderate accuracy; however, it computes the mixing of components χ2 parameter with higher precision than the finite volume scheme. The numerical testing is performed for some benchmarking kernels corresponding to which the analytical solutions are available in the literature. It will be also shown that both numerical methods equally well predict the average size of the particles formed in the system; however, the finite volume scheme takes less time to compute these results.

Numerical Calculation of Mass Transfer With Heterogeneous Chemical Reactions in Three-Phase Bubble Columns

2007 ◽  
Author(s):  
Dieter Mewes ◽  
Dierk Wiemann
Keyword(s):  
Balance Equation ◽  
Bubble Column ◽  
Three Dimensional ◽  
Population Balance ◽  
Kernel Functions ◽  
Time Dependent ◽  
Bubble Coalescence ◽  
Population Balance Equation ◽  
Heterogeneous Chemical ◽  
Three Phase

Bubble column reactors are used for several processes in the chemical industry, e.g. hydrogenation or oxidation reactions. At the bottom of the reactor a gaseous phase is dispersed into a continuous liquid phase with suspended particles. The resulting bubble swarm induces three-dimensional, time-dependent velocity and concentration fields, which are predicted numerically. All phases are described by an Eulerian approach. The numerical calculations of the local interfacial area density and the interphase transfer terms for mass and momentum are based on a population balance equation approach which enables an effective way to couple population balance and computational fluid dynamics. In three-phase gas-liquid-solid flow particles with diameters of 100 μm are considered as catalyst for a heterogeneous chemical reaction. The influence of particles on bubble coalescence has been investigated in order to extend an existing model for the kernel functions in the population balance equation describing bubble coalescence and dispersion. The resulting three-dimensional, time-dependent velocity and concentration fields are described and graphically presented for the hydrogenation of anthra-chinone.

scholarly journals Numerical investigation and modelling of the venous injection of sclerosant foam

2019 ◽  
Vol 60 ◽  
pp. C261-C278
Author(s):  
K. C. Wong ◽  
S. W. Armfield ◽  
N. Williamson
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Numerical Investigation ◽  
Size Distribution ◽  
Bubble Size ◽  
Bubble Column ◽  
Population Balance ◽  
Bubble Size Distribution ◽  
Ambient Fluid ◽  
Saphenofemoral Junction

Sclerosant foam, a mixture of a surfactant liquid and air, is injected directly into varicose veins as a treatment that causes the vein to collapse. This investigation develops a model that will allow the medical specialist to visualise how the sclerosant foam will interact with the blood and behave within the vein. The process is simulated using a multiphase computational fluid dynamics model with the sclerosant foam considered as a two-phase non-Newtonian power law viscosity liquid. The governing multiphase equations are solved using an Eulerian⁠–⁠Eulerian approach coupled with a population balance model to predict the bubble size distribution within the flow field. The computational results demonstrate similar flow characteristics and flow features to an available set of experimental results. The model predicts the mixing layers between the sclerosant foam and the ambient fluid, and the sclerosant liquid and the ambient fluid, as well as the sclerosant liquid coverage on the vein wall and the bubble size distribution within the vein. These quantities are of interest to medical specialists allowing them to assess the treatment feasibility and safety before treating the patients. References S. Ali Mirjalili, J. C. Muirhead, and M. D. Stringer. Redefining the surface anatomy of the saphenofemoral junction in vivo. Clin. Anat., 27(6):915–919, 2014. doi:10.1002/ca.22386. E. Cameron, T. Chen, D. E. Connor, M. Behnia, and K. Parsi. Sclerosant foam structure is strongly influenced by liquid air fraction. Eur. J. Vasc. Endo. Surg., 46:488–494, 2013. doi:10.1016/j.ejvs.2013.07.013. P. Coleridge-Smith. Saphenous ablation: Sclerosant or sclerofoam? Semin. Vasc. Surg., 18:19–24, 2005. doi:10.1053/j.semvascsurg.2004.12.007. J.-J. Guex. Complications and side-effects of foam sclerotherapy. Phlebology, 24:270–274, 2009. doi:10.1258/phleb.2009.009049. Ansys Inc. ANSYS FLUENT 12.0 population balance module manual. ANSYS, 2010. URL https://www.afs.enea.it/project/neptunius/docs/fluent/html/popbal/main_pre.htm. F. Ren, N. A. Noda, T. Ueda, Y. Sano, Y. Takase, T. Umekage, Y. Yonezawa, and H. Tanaka. CFD-PMB coupled simulation of a nanobubble generator with honeycomb structure. volume 372 of IOP Conference Series: Materials Science and Engineering, page 012012, June 2018. doi:10.1088/1757-899X/372/1/012012. P. Souroullas, R. Barnes, G. Smith, S. Nandhra, D. Carradice, and I. Chetter. The classic saphenofemoral junction and its anatomical variations. Phlebology, 32(3):172–178, 2017. doi:10.1177/0268355516635960. A. H. Syed, M. Boulet, T. Melchiori, and J. M. Lavoie. CFD simulations of an air-water bubble column: Effect of Luo coalescence parameter and breakup kernels. Front. Chem., 5(68):1–16, 2017. doi:10.3389/fchem.2017.00068. T. Wang and J. Wang. Numerical simulation of gas-liquid mass transfer in bubble column with a CFD-PBM coupled model. Chem. Eng. Sci., 62:7107–7118, 2007. doi:10.1016/j.ces.2007.08.033. M. R. Watkins. Deactivation of sodium tetradecyl sulphate injection by blood proteins. Euro. J. Vasc. Endo. Surg., 41(4): 521–525, 2011. doi:10.1016/j.ejvs.2010.12.012. K. Wong. Experimental and numerical investigation and modelling of sclerosant foam. PhD thesis, University of Sydney, 2018. K. Wong, T. Chen, D. E. Connor, M. Behnia, and K. Parsi. Basic physiochemical and rheological properties of detergent sclerosants. Phlebology, 30(5):339–349, 2015. doi:10.1177/0268355514529271. K. C. Wong, T. Chen, D. E. Connor, M. Behnia, and K. Parsi. Computational fluid dynamics of liquid and foam sclerosant injection in a vein model. Appl. Mech. Mater., 553:293–298, 2014. doi:10.4028/www.scientific.net/AMM.553.293.

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