A numerical study of the motion of algal cells in a representative thin-layer-cascade (TLC) photobioreactor is presented. The goal is to determine the time scale associated with the light/dark (L/D) cycle seen by the cells during their turbulent motion in the liquid culture. Owing to the limited reliability of the available numerical results which deal with time-averaged quantities and thus lack time-resolved information, the present study is based upon the Direct Numerical Simulation of the Navier-Stokes equations, a reliable but consequently expensive numerical approach which does not incur in turbulence modelling errors. Indeed, the simulation is successfully validated in terms of averaged velocity with experimental data. The availability of full temporal information allows algae cells to be followed in time along their trajectories. A large number (up to a million) of tracers is placed in the flow to mimic the algae cell. Their trajectories are statistically studied and linked to the turbulent mixing. Results indicate that, in a typical TLC reactor designed to mimic an experimental setup, cells undergo an L/D cycle with a time scale in the range 0.1–2 s. Such time scale, albeit much longer than the typical time scale of the photosynthesis, significantly benefits the productivity of the algae compared to a steady illumination.

提出了一个代表性的薄层级联（TLC）光生物反应器中藻类细胞运动的数值研究。目的是确定与细胞在液体培养物中的湍流运动过程中看到的明/暗（L / D）周期相关的时间标度。由于处理时间平均量的可用数值结果的可靠性有限，因此缺乏时间分辨的信息，因此本研究基于Navier-Stokes方程的直接数值模拟，这是一种可靠的但因此昂贵的数值方法。不会引起湍流建模错误。确实，该模拟已成功地通过平均速度与实验数据进行了验证。完整的时间信息的可用性允许藻类细胞沿着其轨迹及时追踪。大量（多达一百万个）示踪剂被放置在流中以模拟藻类细胞。对它们的轨迹进行了统计研究，并将其与湍流混合联系在一起。结果表明，在设计用来模拟实验装置的典型TLC反应器中，细胞经历L / D循环，时间范围为0.1–2 s。这种时间尺度虽然比光合作用的典型时间尺度长得多，但与稳定照明相比，极大地有利于藻类的生产力。