A theoretical analysis of the hydrodynamic influence on the growth of microalgae in the photobioreactors with simple growth kinetics

This work presents a theoretical analysis for understanding the influence of hydrodynamics on the growth of microalgae in the photobioreactor (PBR). In the analysis, it is assumed that the growth rate is determined by the instantaneous light intensity and the light distribution is not influenced by the hydrodynamics. It is proved that the average growth rate over the tracked particles and the volume-averaged growth rate are the same if the average spatial distribution function (SDF) of the particles is included. In addition, the fluid kinematics shows that the SDF is related to the Jacobian or volumetric change ratio of the particle trajectories. For single-phase flows, the SDF should be uniform. The analysis justifies the conclusion that if the PBR is well-mixed and the dynamic growth kinetics are not included, the growth rate is only influenced by the light condition and the geometry of the PBR, but is not influenced by the hydrodynamics. The theoretical analysis is validated by the CFD simulations of the average growth rates of Taylor vortex PBR with single-phase flows, bubble column PBR and airlift PBRs with two-phase flows. It is also found that the particles tend to accumulate near the wall or boundary regions in the Lagrangian particle tracking method. This artificial effect is contrary to the theoretical analysis and can generate errors when predicting the growth rate. Therefore, further validations and examinations are needed for the numerical models.