Comprehensive computational model for combining fluid hydrodynamics, light transport and biomass growth in a Taylor vortex algal photobioreactor: Lagrangian approach
Introduction
In order to optimize the design and to reliably scale up photobioreactors, it is necessary to accurately simulate the complex interplay between physical, chemical and biological phenomenon that occur on multiple-time and length scales. For example, Fig. 1 depicts some important relationships between hydrodynamics, mass transport, radiation transport, and algal growth kinetics. However, obtaining quantitatively accurate and reliable models for each of the fundamental processes governing global reactor performance can be challenging or computationally expensive. For example, accurate simulation of fluid mixing and mass transport requires at a minimum the use of validated gas–liquid fluid flow simulations. Accurate simulation of radiation transport in photobioreactors is also a difficult and computationally expensive endeavor for realistic geometries involving curved reactor walls (Kong and Vigil, 2014).
In addition to challenges associated with developing suitable models for fluid flow, radiation transport, and microorganism growth, an efficient computational scheme for capturing the interplay between these processes is required. A comprehensive model should in principle account for all mutual interactions between these basic processes. However, several justifiable assumptions can significantly reduce computational costs, for example by neglecting the effect of biomass loading on hydrodynamics. However other phenomena, particularly insofar as they impact the amount and manner of light delivery to microorganisms, must be carefully simulated as irradiance of microorganisms is known to be the most critical factor affecting photobioreactor performance. Specifically, fluid mixing patterns that shuttle microorganisms periodically between light and dark regions of the reactor can substantially enhance both biomass productivity and light utilization efficiency (Hu and Richmond, 1996, Ugwu et al., 2005, Sobczuk et al., 2006, Kong and Vigil, 2013). Consequently, the essential elements of a comprehensive model of photobioreactor performance should include (a) accurate prediction of radiation distribution in the reactor as a function of biomass concentration, (b) a photosynthetic growth model that accounts for temporal variations in light exposure experienced by microorganisms, and (c) a hydrodynamic model capable of accurately predicting flow patterns, mixing, and the spatial trajectories of microorganisms.
The most common approach for integrating hydrodynamic, radiative, and kinetic growth models to predict global reactor behavior is to (1) compute velocity fields in the reactor, (2) compute microorganism spatial trajectories (Lagrangian particle tracking), (3) generate temporal light exposure trajectories by mapping microorganism position-time data to predictions for the photon flux obtained from a radiation model, and (4) use light exposure trajectories to integrate an algal biomass kinetic growth equation. However, as has been demonstrated by Pruvost et al. (2008), such an approach requires that the Lagrangian particle tracks be consistent with a spatially uniform distribution of biomass for consistency with energy conservation. Although others have made use of the Lagrangian simulation approach to simulate photobioreactor performance, the coupling of detailed multiscale sub-models for hydrodynamics, radiation transport, and algal growth kinetics into a comprehensive modeling tool is novel. Furthermore, the use of experimentally validated and rigorous hydrodynamic and radiation transport sub-models enables analysis and new insights into limitations and weaknesses of the Lagrangian simulation approach. The comprehensive model described here is applied for the first time to a reactor with more complex hydrodynamics and distribution of radiative flux than is found in more familiar flat panel or tubular reactors.
Section snippets
Gas–liquid two-phase flow CFD model
In this work, our previously validated two-fluid flow model was used to simulate multiphase flow dynamics in a Taylor vortex reactor (Gao et al., 2015a, Gao et al., 2015c, Gao et al., 2016). Microalgal growth in this high biomass concentration system is not limited by gas–liquid interphase mass transfer, and therefore no interphase mass transfer model is required (Gao et al., 2015b, Ramezani et al., 2015). The axisymmetric equations of continuity and conservation of momentum equations are given
Growth rate model parameters
The PSU model parameters that appear in Eqs. (13a), (13b), (14), (15) are species specific, and have not previously been reported for Chlorella vulgaris, which is the organism used to generate experimental data for comparison with our model predictions. Consequently, experimental data obtained by Dauta et al. (1990), who investigated the growth rate of Chlorella vulgaris over a wide range of light intensities was used to fit the PSU model parameters using the method developed by Wu and Merchuk
Flow hydrodynamics
Example contour plots for instantaneous simulated liquid phase stream function and gas volume fraction are shown in Fig. 3 for typical Taylor vortex photobioreactor operating conditions with an inner cylinder rotation speed of 400 rpm and air flow rate of 0.05 vvm (85 mL/min). It is obvious from Fig. 3(a) that toroidal vortices are formed in the narrow annular gap, wherein fluid circulates between the inner and outer cylinder walls. Because algal cells have a small Stokes number, they closely
Conclusion
A Lagrangian approach was used to simulate biomass growth curves in a Taylor vortex algal photobioreactor. Direct comparison of simulation predictions with corresponding experimental data for biomass growth curves demonstrates that the computational model correctly predicts that biomass can be more rapidly produced by increasing the Taylor vortex reactor inner cylinder rotation speed. Although the over-predictions of biomass concentration in the later stages may be partly explained by nutrient
Acknowledgements
Financial support was provided for this work by National Science Foundation grant CBET-1236676.
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