Location Effect of Free Surface on the Toroidal Vorticity of a Cell Bioreactor

ABSTRACT This numerical study focuses on the development of secondary recirculation zones in viscous, incompressible, rotating flows. Two main objectives are pursued: extending Karl Buhler's reference cavity and analyzing the influence of upstream boundary conditions on the evolution of reverse flow. To this end, several spherical‐bottom configurations are studied using a finite‐volume approach in order to characterize the behavior of fully open flows under the combined effects of the radius ratio (1.48 ≤ α ≤ 2) and the Reynolds number (766 ≤ Re ≤ 2757). The results reveal that the size and the number of the recirculation region strongly depend on the imposed thermal gradient for the concentric hemispherical annular cavity. Specifically, a positive Rayleigh number () suppresses the reverse axial zone, while a negative Rayleigh number () reinforces it. Beyond these findings, a refined modeling framework is proposed, capable of accurately predicting both the onset and behavior of recirculating regions. Furthermore, the study provides a comprehensive analysis of vortex breakdown dynamics, offering new insights into their formation and evolution across different flow regimes. The reliability of the proposed model is further confirmed through validation against experimental data, demonstrating its robustness and applicability to real‐world scenarios. These outcomes carry important implications for fluid mechanics, as they deepen the understanding of turbulence and contribute to the design of more efficient engineering systems as well as the optimization of industrial processes. Finally, the model shows strong potential for bioengineering applications by creating an environment with minimal cavity velocity that supports cell growth, while reducing energy consumption and preserving cell viability.