Multi-Dimensional Singular Value Decomposition of Scale-Varying CFD Data: Analyzing Scale-Up Effects in Fermentation Processes

The scale-up of processes with complex fluid flow presents significant challenges in process engineering, particularly in fermentation. Computational fluid dynamics (CFD) is a crucial tool for accurately modelling the hydrodynamic environment in bioreactors and understanding the effects of scale-up. This study utilizes Higher Order SVD (HOSVD), which is the multidimensional extension of Singular Value Decomposition (SVD), to identify the dominant structures (modes) of fluid flow in CFD data of fermentation process simulations. Similarly to Proper Orthogonal Decomposition (POD), also based on SVD, this method can be used to identify the dominant structures of fluid flow, and additionally explore the scale parameter space. As a first test case, we examined five scales of a reciprocally shaken flask bioreactor, from 125 mL to 10 L, specified using basic empirical scale-up rules. Results indicate a common set of spatial modes across all scales, thus confirming that the scale-up method assures some dynamic similarity. However, the relative importance of these common spatial modes changes sensibly across process scales. The main spatial mode that represents the large recirculating flow in the flask can account for 19.8% of the data variability for the 125 mL scale but only 11.7% for the 10 L scale case. In this larger scale, one needs a larger number of modes to capture flow dynamics, thus showing an increase in flow complexity. These findings illustrate the impact of scale on fluid dynamics in a particular bioreactor flow but also provide a proof of concept for this methodology.