Application of extended quadrature method of moments for simulation of bubbly flow and mass transfer in gas‐liquid stirred tanks

Modeling and Simulation of Photobioreactors with Computational Fluid Dynamics—A Comprehensive Review

Computational Fluid Dynamics (CFD) have been frequently applied to model the growth conditions in photobioreactors, which are affected in a complex way by multiple, interacting physical processes. We review common photobioreactor types and discuss the processes occurring therein as well as how these processes have been considered in previous CFD models. The analysis reveals that CFD models of photobioreactors do often not consider state-of-the-art modeling approaches. As a comprehensive photobioreactor model consists of several sub-models, we review the most relevant models for the simulation of fluid flows, light propagation, heat and mass transfer and growth kinetics as well as state-of-the-art models for turbulence and interphase forces, revealing their strength and deficiencies. In addition, we review the population balance equation, breakage and coalescence models and discretization methods since the predicted bubble size distribution critically depends on them. This comprehensive overview of the available models provides a unique toolbox for generating CFD models of photobioreactors. Directions future research should take are also discussed, mainly consisting of an extensive experimental validation of the single models for specific photobioreactor geometries, as well as more complete and sophisticated integrated models by virtue of the constant increase of the computational capacity.

Influence of Interfacial Force Models and Population Balance Models on the kLa Value in Stirred Bioreactors

Optimal oxygen supply is vitally important for the cultivation of aerobically growing cells, as it has a direct influence on cell growth and product formation. A process engineering parameter directly related to oxygen supply is the volumetric oxygen mass transfer coefficient kLa. It is the influences on kLa and computing time of different interfacial force and population balance models in stirred bioreactors that have been evaluated in this study. For this investigation, the OpenFOAM 7 open-source toolbox was utilized. Firstly, the Euler–Euler model with a constant bubble diameter was applied to a 2L scale bioreactor to statistically examine the influence of different interfacial models on the kLa value. It was shown that the kL model and the constant bubble diameter have the greatest influence on the calculated kLa value. To eliminate the problem of a constant bubble diameter and to take effects such as bubble breakup and coalescence into account, the Euler–Euler model was coupled with population balance models (PBM). For this purpose, four coalescence and five bubble breakup models were examined. Ultimately, it was established that, for all of the models tested, coupling computational fluid dynamics (CFD) with PBM resulted in better agreement with the experimental data than using the Euler–Euler model. However, it should be noted that the higher accuracy of the PBM coupled models requires twice the computation time.

Investigation of the flow patterns and power requirements in agitated systems: effects of the design of baffles and vessel base

The flow patterns and power consumption of a six-blade Rushton turbine (RT) in a cylindrical vessel are characterized in this paper. We focus on the effects of the shape of the vessel base by studying two cases: a conical and a dished shape. In addition, the effects of the height of the vessel base (h2) are explored and four cases are considered, namely: h2/D = 1/10, 1/6, 1/5 and 1/3 (D: vessel diameter). In the second part of our investigation, a new design of baffles (a triangular-shaped baffle) is suggested and a comparison is made between the performance of the standard and the triangular baffles. The main findings revealed that the conical shape of the vessel base provides a slight enhancement in the axial circulation at almost the same power input for the dished bottomed vessel. For Re < 2 × 104, the power required by both types of baffles is the same; however, above this value of Re, a reduction by about 4% in power consumption is given by the standard baffles. Also, and for all shapes of baffles and vessel bases, a reduction in power consumption may be obtained by increasing the height of the vessel base.

Approximate Moment Methods for Population Balance Equations in Particulate and Bioengineering Processes

Population balance modeling is an established framework to describe the dynamics of particle populations in disperse phase systems found in a broad field of industrial, civil, and medical applications. The resulting population balance equations account for the dynamics of the number density distribution functions and represent (systems of) partial differential equations which require sophisticated numerical solution techniques due to the general lack of analytical solutions. A specific class of solution algorithms, so-called moment methods, is based on the reduction of complex models to a set of ordinary differential equations characterizing dynamics of integral quantities of the number density distribution function. However, in general, a closed set of moment equations is not found and one has to rely on approximate closure methods. In this contribution, a concise overview of the most prominent approximate moment methods is given.

Modeling of Non-Newtonian Flow in an Inverted Cone Foam Breaker

Foam formation is a widespread phenomenon and often a serious problem in fermentation processes. Inverted cones used as mechanical foam breakers are rotating devices that pump the fluid up and pulverize it at the edge. The shearing and centrifugal actions of such geometries can help to control foaming. In this study, a model was developed using Computational Fluid Dynamics (CFD), based on the non-Newtonian properties of foam, to describe and explain the action of inverted cones as foam breakers.