A numerical model coupling bubble flow, light transfer, cell motion and growth kinetics for real timescale microalgae cultivation and its applications in flat plate photobioreactors

A comprehensive numerical model based on volume-of-fluid (VOF) is established in this paper for the simulation of multiphysical process of the microalgae cultivation in photobioreactors (PBRs). The comprehensive numerical model is composed of the following four models: (1) a free-surface lattice Boltzmann model for VOF simulations of bubble flow, (2) a discrete ordinate model for collimated light transfer, (3) a Lagrangian model for cell motion, and (4) a kinetic model for microalgae growth. A temporal extrapolation scheme is proposed first to extend the simulation in small time steps into the real timescale. The growths of microalgae in a two-dimensional flat plat PBR are then simulated by the model. The effects of the gas hold-up, bubble distribution, light intensity and light/dark history on the growth of microalgae are further studied in detail. The result showed that the average growth rate can be adopted for the whole PBR. The non-uniform distribution of bubbles attenuates the positive effects of bubbles on increasing light intensity inside the PBRs. Meanwhile, the simulation with the average flow field without fluctuations can lead to non-uniform distributions of cells and errors in prediction the microalgae growth due to the centrifugal effects. The residence time distribution (RTD) of cells in the PBR is almost uniform under the condition studied, and the simulation results with RTD are close to the results with cell tracking. Finally, an improved structure of flat plat PBRs with horizontal deflectors is proposed. The results demonstrated that the inserted deflectors can increase the gas hold-ups and the uniformity of gas distributions. These effects lead to higher light intensity in the PBR, which increases the growth rate of the microalgae.