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280798 Advanced Computational Modeling of Photosynthetically Active Radiation (PAR) Distribution in Algae Photobioreactors

The development of highly efficient scalable continuous-flow algae photobioreactors (PBRs) could be a major advance towards enabling algae-based biofuel and biorenewable chemicals technology.Conversion of solar energy into chemical energy by photosynthesis is strongly depends on the quantity and quality of light received by microorganisms. Therefore, it is crucial to understand the availability and distribution of light in order to optimize the design and operation of a photobioreactor. In particular, it is important to understand the distribution of photosynthetically active radiation (PAR) for phototrophic microorganisms, which includes wavelengths from 400-700 nm. This radiation is absorbed by various pigments in the organisms, such as chlorophyll, carotenes and xanthophylls, which have different PAR absorption spectra. Despite the fact that only a narrow band of wavelengths are useful for photosynthesis, the most frequently used method for simulating light distribution in PBRs is to employ the Beer-Lambert law to calculate the overall light intensity distribution in one dimension. However, there exist several more advanced CFD techniques to solve the radiation transfer equation, such as the discrete ordinate (DO) and Monte Carlo (MC) methods, which are commonly used in other engineering fields, for example in combustion and HVAC. Although most of these models are used to compute total radiative transfer, in principle they can be extended to include spectral dependencies. Consequently, it is necessary, desirable, and feasible to develop a multidimensional spectral radiation model capable of predicting light distribution in photobioreactors.

In this work we describe a detailed and general numerical method for simulating the spatial distribution of PAR in photobioreactors using the discrete ordinate (DO) method for solving the radiative transfer equation (RTE), which was implemented in a computer program developed using the open source CFD library openFOAM. This non-gray DO implementation divides the radiation spectrum into $N$ wavelength bands, in each of which the treatment of the light is the same as that for the gray DO model.Optical properties of the medium and boundary conditions for the non-gray DO model are applied on a band basis. Thus, the PAR transfer can be modeled by solving RTEs in small wavelength bands in the 400-700 nm wavelength range with a non-gray DO model. In algal cultures, the liquid medium is usually transparent to visible light, and therefore the transport of visible wavelengths are determined mainly by algae cells. The optical properties of the algae cells and the radiative properties of the turbid culture medium were calculated at each wavelength band range using the method developed by Pottier, et.al. 2005, which is based on Mie theory and requires information concerning algal pigmentation, shape, and size distribution. The model was validated in a simple rectangular rector configuration using the experimental data provided in Pottier, et.al. 2005. Subsequently, simulations were carried out in tubular and annular photobioreactor configurations, and implications of the simulation predictions are discussed.

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