Applying Computational Fluid Dynamics Technology in Bioprocesses-Part 2 - Computational fluid dynamics can resolve performance problems. - BioPharm International


Applying Computational Fluid Dynamics Technology in Bioprocesses-Part 2
Computational fluid dynamics can resolve performance problems.

BioPharm International
Volume 23, Issue 5


The published literature on the liquid-phase mixing in a turbulent flow regime presents mathematical models and experimental techniques for determining mixing time, and reveals the effects of the hardware configuration on the mixing performance.24 Mixing is very important for cell culture and fermentation because non-ideal mixing can lead to concentration gradients in nutrients, oxygen, and pH, among others. These gradients are likely to influence cellular behavior, growth, or process yield. Moving oxygen-limiting zones in large fed-batch bioreactors, a result of poor mixing, induce both metabolic and stress responses, which may account for the reduced biomass yield on scale-up and altered physiological properties of cells grown under large-scale conditions.25 CFD has been used to investigate mixing performance in stirred-tanks because it overcomes the limitations of classical reactor flow models, such as compartment and recirculation models.26–33 One of the applications is to understand local runaways and the quenching of runaway reactions in a tank under imperfect mixing conditions in an effort to develop operating protocols that prevent runaways in stirred reactors.9

Figure 1
CFD also can provide a reliable prediction of mixing time.26–32,34 After a flow field is set up, an unsteady solution of a tracer transport equation leads to the prediction of the evolution of the tracer concentration inside the tank over time. Figure 1 shows the typical profiles of tracer concentration in a stirred-tank in CFD simulations when a Reynolds Average Navier-Stokes (RANS) model is used. The procedure to obtain the mixing time in CFD simulations is similar to the experimental approach.35 Tracer is added and monitors are turned to trace the concentration of the tracer at randomly chosen locations in the tank. Although it is hard for a RANS-based CFD model to exactly match the transient responses recorded by experimental conductivity probes, the predicted mixing time is in agreement with experiments, especially for single-phase flow. The curve of tracer response predicted by LES was found to be in better agreement with the experimental curve because of the LES's capability of accurately capturing the scalar fluctuations in the tank.36,32

The measured mixing time depends on the location of the added tracer.29,35,37 The simulation should be in agreement with experimental values and empirical predictions as long as the addition point is kept away from the wall. In addition, accurately predicting the mean flow-field is key to successfully predicting the mixing time.28,38,39 Mixing time as a function of agitation speed is also plotted in Figure 1. The simulations can provide correlations of the mixing time to operating and geometry parameters such as agitation speed (N), impeller diameter (D), tank diameter (T), and power number of the impeller (P 0), as indicated by the solid line in the plot. This information can greatly help the scale-up and scale-down processes if the mixing time is the primary concern.

The presence of solid particles will dramatically change the flow characteristics in agitated tanks. CFD simulations can provide detailed insight into the behavior of particles and how the liquid flow is altered by the presence of particles.40 The presence of solids in a fluid actually slows down the mixing process, sometimes by more than 10-fold that of a single-phase state.41 LES confirmed that particles heavier than the fluid tend to rise slowly to the top in unbaffled, tall, turbulently stirred-tanks.42

CFD simulations have been widely applied to investigate the multi-phase mixing (resuspension) process in an agitated or sparged tank, using either the Euler–Euler approach for dense systems or the Euler–Lagrange approach for dilute-to-moderate dense systems, the former being more popular than the latter because it is less demanding on computation resources. The two-fluid (Euler–Euler) approach can determine the flow pattern and the concentration field in a dense solid–liquid suspension in industrial vessels, when a kinetic theory of granular flow for the solid stress and the solid pressure is adopted, taking into account particle–particle interactions.43 Predictions for solid distribution in an industrial crystallizer show agreement with experiments for several agitation speeds and mean concentrations.

The two-fluid model, in conjunction with the slide-mesh algorithm, also is used to model the resuspension process in stirred-tanks.44,45 The model is not only able to predict the formation of the clear liquid layer in the upper part of the tank, but also can provide quantitative agreement with experimental data on suspension height. The model also can predict the critical impeller speed over a wide range of design and operating conditions, e.g., solid loading (0.34–15% wt), different impeller designs (Rushton turbine, pitched blade down- and up-flow turbines),45 solid particle sizes (120–1,000 mm) and for various superficial gas velocities (0–10 mm/s). However, it has been observed that the drag coefficient may sometimes need to be fine-tuned to match the available experimental data.46

The performed studies demonstrate that the Euler–Euler approach, when applied to multi-phase flows without consideration for bubble coalescence or break-up, can agree with experiments, particularly when the bubble-flow is dominant.47 When bubble breakup and coalescence are accounted for, and bubble size distribution is important, many researchers have used population balance models to model the spatial evolution of gas bubbles in bioreactors.48–50 The mechanisms responsible for bubble coalescence and breakage are complex and not yet fully understood. For turbulent flows, most models formulate the kernel functions for the bubble coalescence according to random collision driven by turbulence and wake entrainment and the kernel functions for bubble breakage to turbulent eddies.50

Figure 2
Although a uniformly mixed flow-field is optimal, CFD simulations indicate that full homogeneity of the gas–liquid mixture may never be achieved.51 Figure 2 shows the distribution of bubbles in a production-scale cell culture bioreactor, which is strongly dependent on the impeller type, sparger design, agitation rate, and sparging rate.

Power draw, another important parameter for bioreactor operation, depends primarily on the impeller geometry and fluid dynamics around the impeller blades.52 CFD provides a convenient and reliable tool to calibrate the power number of the impellers and the power consumption for a given bioreactor using the torque on the impeller surface and shaft. For a multiple impeller system, the calculated overall power number is less than the value expected if each of the impellers had the same power number as the single ones because of interference between adjacent impellers.53 Power usage for a sparged tank depends on bubble coalescence, generally lower than the ungassed case.54

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