scholarly journals Hybrid Approach for Mixing Time Characterization and Scale-Up in Geometrical Nonsimilar Stirred Vessels Equipped with Eccentric Multi-Impeller Systems—An Industrial Perspective

Processes ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 880
Author(s):  
Michael C. Martinetz ◽  
Florian Kaiser ◽  
Martin Kellner ◽  
Dominik Schlosser ◽  
Andreas Lange ◽  
...  

Multipurpose stirring and blending vessels equipped with various impeller systems are indispensable in the pharmaceutical industry because of the high flexibility necessary during multiproduct manufacturing. On the other hand, process scale-up and scale-down during process development and transfer from bench or pilot to manufacturing scale, or the design of so-called scale-down models (SDMs), is a difficult task due to the geometrical differences of used vessels. The present work comprises a hybrid approach to predict mixing times from pilot to manufacturing scale for geometrical nonsimilar vessels equipped with single top, bottom or multiple eccentrically located impellers. The developed hybrid approach is based on the experimental characterization of mixing time in the dedicated equipment and evaluation of the vessel-averaged energy dissipation rate employing computational fluid dynamics (CFD) using single-phase steady-state simulations. Obtained data are consequently used to develop a correlation of mixing time as a function of vessel filling volume and vessel-averaged energy dissipation rate, which enables the prediction of mixing times in specific vessels based on the process parameters. Predicted mixing times are in good agreement with those simulated using time-dependent CFD simulations for tested operating conditions.

1994 ◽  
Vol 5 (4) ◽  
pp. 537-557 ◽  
Author(s):  
M. Bertsch ◽  
R. Dal Passo ◽  
R. Kersner

We study the semi-empirical b—ε model which describes the time evolution of turbulent spots in the case of equal diffusivity of the turbulent energy density b and the energy dissipation rate ε. We prove that the system of two partial differential equations possesses a solution, and that after some time this solution exhibits self-similar behaviour, provided that the system has self-similar solutions. The existence of such self-similar solutions depends upon the value of a parameter of the model.


2016 ◽  
Vol 46 (2) ◽  
pp. 461-481 ◽  
Author(s):  
Magdalena D. Anguelova ◽  
Paul A. Hwang

AbstractActive and total whitecap fractions quantify the spatial extent of oceanic whitecaps in different lifetime stages. Total whitecap fraction W includes both the dynamic foam patches of the initial breaking and the static foam patches during whitecap decay. Dynamic air–sea processes in the upper ocean are best parameterized in terms of active whitecap fraction WA associated with actively breaking crests. The conventional intensity threshold approach used to extract WA from photographs is subjective, which contributes to the wide spread of WA data. A novel approach of obtaining WA from energy dissipation rate ε is proposed. An expression for WA is derived in terms of energy dissipation rate WA(ε) on the basis of the Phillips concept of breaking crest length distribution. This approach allows more objective determination of WA using the breaker kinematic and dynamic properties yet avoids the use of measuring breaking crest distribution from photographs. The feasibility of using WA(ε) is demonstrated with one possible implementation using buoy data and a parametric model for the energy dissipation rate. Results from WA(ε) are compared to WA from photographic data. Sensitivity analysis quantifies variations in WA estimates caused by different parameter choices in the WA(ε) expression. The breaking strength parameter b has the greatest influence on the WA(ε) estimates, followed by the breaker minimal speed and bubble persistence time. The merits and caveats of the novel approach, possible improvements, and implications for using the WA(ε) expression to extract WA from satellite-based radiometric measurements of W are discussed.


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