This study describes the development and validation of Computational Fluid Dynamics (CFD) methodology for the simulation of dispersed two-phase flows. A two-fluid (Euler-Euler) methodology previously developed at Imperial College is adapted to high phase fractions. It employs averaged mass and momentum conservation equations to describe the time-dependent motion of both phases and, due to the averaging process, requires additional models for the inter-phase momentum transfer and turbulence for closure. The continuous phase turbulence is represented using a two-equation k − ε−turbulence model which contains additional terms to account for the effects of the dispersed on the continuous phase turbulence. The Reynolds stresses of the dispersed phase are calculated by relating them to those of the continuous phase through a turbulence response function. The inter-phase momentum transfer is determined from the instantaneous forces acting on the dispersed phase, comprising drag, lift and virtual mass. These forces are phase fraction dependent and in this work revised modelling is put forward in order to capture the phase fraction dependency of drag and lift. Furthermore, a correlation for the effect of the phase fraction on the turbulence response function is proposed. The revised modelling is based on an extensive survey of the existing literature. The conservation equations are discretised using the finite-volume method and solved in a solution procedure, which is loosely based on the PISO algorithm, adapted to the solution of the two-fluid model. Special techniques are employed to ensure the stability of the procedure when the phase fraction is high or changing rapidely. Finally, assessment of the methodology is made with reference to experimental data for gas-liquid bubbly flow in a sudden enlargement of a circular pipe and in a plane mixing layer. Additionally, Direct Numerical Simulations (DNS) are performed using an interface-capturing methodology in order to gain insight into the dynamics of free rising bubbles, with a view towards use in the longer term as an aid in the development of inter-phase momentum transfer models for the two-fluid methodology. The direct numerical simulation employs the mass and momentum conservation equations in their unaveraged form and the topology of the interface between the two phases is determined as part of the solution. A novel solution procedure, similar to that used for the two-fluid model, is used for the interface-capturing methodology, which allows calculation of air bubbles in water. Two situations are investigated: bubbles rising in a stagnant liquid and in a shear flow. Again, experimental data are used to verify the computational results.

Computational fluid dynamics of dispersed two-phase flows at high phase fractions

High cell-density culture of Escherichia coli

http://dbkgroup.org/Papers/davey_kell_micrev96.pdf

Flow cytometry and cell sorting of heterogeneous microbial populations: the importance of single-cell analyses.

Bubble-size distributions and flow fields in bubble columns are calculated numerically. The population balance is simplified and reduced to a balance equation for the average bubble volume. Models developed predict the rate of bubble breakup and coalescence based on physical principles. The flow fields are numerically calculated for bubble columns with cylindrical cross sections using the Euler-Euler method. The newly derived balance equations for the average bubble volumes are implemented into a commercial CFD code. The solutions of the balance equation for high superficial gas velocities result mainly in two fractions: one for the fraction with small and the other for the fraction with large bubble diameters. Both are considered pseudocontinuous phases, in addition to the liquid phase. The calculated flow fields are characterized by several large-scale vortices. The local volume fractions of gas and liquid are locally inhomogeneous and highly time-dependent. The time-averaged flow field is axisymmetric and stationary. The calculated volume fractions, velocities, and bubble-size distributions agree well with existing and previously published experimental results for bubble columns up to 0.3 m in diameter.

Bubble‐Size distributions and flow fields in bubble columns

https://hal.archives-ouvertes.fr/hal-01394969/document

Measuring techniques in gas–liquid and gas–liquid–solid reactors

Bioprocess optimization and control: Application of hybrid modelling

Process models are used to formulate knowledge about process behaviour. They are applied, e.g., to predict the process' future behaviour and for state estimation when reliable on-line measuring techniques to monitor the key variables of the process are not available. There are different sources of information available for modelling, which provide process knowledge in different representations. Some elements or aspects may be described by physically based mathematical models and others by heuristically obtained rules of thumb, while some information may still be hidden in the process data recorded during previous runs of the process. Heuristic rules are conveniently processed with fuzzy expert systems, while artificial neural networks present themselves as a powerful tool for uncovering the information within the process data without the need to transform the information into one of the other representations. Artificial neural networks and fuzzy technology are increasingly being employed for modelling biotechnological processes, thus extending the traditional way of process modelling by mathematical equations. However, a sufficiently comprehensive combination of all these techniques has not yet been put forward. Here, we present a simple way of combining all the available knowledge relating to a given process. In a case study, we demonstrate the development of a hybrid model for state estimation and prediction on the example of a yeast production process. The model was validated during a cultivation performed in a standard pilot-scale fermenter.

Hybrid modelling of yeast production processes – combination of a priori knowledge on different levels of sophistication

Fuzzy-aided neural network for real-time state estimation and process prediction in the alcohol formation step of production-scale beer brewing

Using measurement data in bioprocess modelling and control

A new simple strategy for a reliable and robust automatic control of the specific growth rate in fed-batch cultivation processes is presented. Its advantages over model supported control is that the algorithm only needs a minimum of information about the process. Moreover, it is independent of the specific microorganism, the cultivation phase and the biomass level. Also, only a minimum of soft- and hardware is required. Hence, the approach is attractive for industrial production processes that do not have specialized instrumentation. Its accuracy is comparable with model supported control and thus sufficient for most industrial applications. Simulations and experimental tests of the technique performed for the example of a fed-batch cultivation of E. coli demonstrate a good controller performance for various cultivation conditions and process disturbances. Preferred applications will be production systems where the productivity is critically dependent on the growth rate, e.g. in recombinant protein or antibiotic productions.

Andreas Lübbert

Papers

Bioprocess optimization and control: Application of hybrid modelling

Hybrid modelling of yeast production processes – combination of a priori knowledge on different levels of sophistication

Fuzzy-aided neural network for real-time state estimation and process prediction in the alcohol formation step of production-scale beer brewing

Using measurement data in bioprocess modelling and control

Automatic control of the specific growth rate in fed-batch cultivation processes based on an exhaust gas analysis