A stochastic Lagrangian approach for simulating the effect of turbulent mixing on algae growth rate in a photobioreactor

It is well known that mixing caused by fluid turbulence can cause significantly increased growth rate of algae in photobioreactor flows under certain conditions. In general, flows in which the light penetrates into only a small fraction of the reactor flow field have the largest growth rate enhancement in the presence of fluid mixing. The current paper seeks to develop a computationally efficient prediction method for algae growth rate in practical photobioreactors using a combination of commercially available RANS turbulence models and a stochastic Lagrangian model for the turbulence fluctuations. The stochastic Lagrangian algae growth rate model is first validated by comparison with simulations of algae growth rate obtained by direct numerical simulation of homogeneous turbulence. We then demonstrate the stochastic Lagrangian model approach for prediction of algae growth rate in turbulent pipe flow, which is representative of the primary photoreaction component in many tubular algae production facilities. The results illustrate how algae growth rate increases as the pipe flow Reynolds number is increased.