Sustainable development and efficient use of energy goes on hand which results in environment pollution minimisation and better socio-economic conditions. The Green energy is now a prime talk all around the globe to ensure zero toxic gas emission as global warming and other hazardous pollution caused by burning of fossil fuels are taking the world to an unstable condition. Also increasing consumption of petro-fuel with rapid growth of transportation and population compared to total deposited amount is leading it on the verge of gradual extinction as it is a depleted source of energy [1] [2] . So in this context, oil extracted from organic matter (biofuel) has attracted the scientist and researchers as it is eco-friendly and sustainable. Biofuel has a great potential to mitigate the continuous demand in every aspects. The mission of negative carbon emission would be fulfilled to a great extent by large scale production of biofuel. Biofuel production may become much more economical than fossil fuel. Extensive research has been carried out for the last five decades regarding the development of the biofuel technology. The developed countries of the world have emphasized and investing money to increase the productivity level of biofuel. So it can be foreseen to be the fuel of future [3] [4] [5] .

Biofuel is referred to as solid, liquid or gaseous compound obtained from organic matter. The main advantage of it over fossil fuel is that it is non-toxic and biodegradable [2] . Biofuel production is categorized into three generations. The first generation biofuel such as soybean, rapeseed, sunflower, palm oil has some environmental limitations as they compete with cultivable land for food production. The second generation biofuel such as agricultural residues, wood residues, non-edible oil or sugarcane has issues of environmental hazard [6] [7] . So to overcome those drawbacks microalgae based biofuel has been appeared as a potential source of biodiesel which ensures the clean energy for better environment.

Microalgae are eukaryotic and prokaryotic photosynthetic microorganisms. They convert water and CO₂ into sugar i.e. lipid and carbohydrate in photosynthesis process by means of sunlight. The sugar contents are subsequently used to extract oil. In the very beginning, microalgae have harvested for some pharmaceutical purposes, waste water treatment, cosmetics and poultry food. As the time passing by, it has got importance in fuel sector due to its almost double productivity level of biomass and it grows 100 times faster than any terrestrial plants. So the challenging task for the researchers is to develop congenial culture system for high productivity of microalgae [8] [9] [10] [11] .

Microalgae culture system requires supply of light, CO₂, nutrients but availability of light is the first and foremost concern. Adequate exposure to light of every cell in the culture system ensures the uniform growth of microalgae, yet it is a challenging task due to proper design consideration of culture system. Generally, two types of culture systems are available such as traditional open pond system and closed photo bioreactor system. The open pond includes shallow big ponds, circular ponds, tanks and raceway pond but raceway pond has been commonly used for culture [12] [13] . The raceway pond method facilitates economic and easier process of culture but has a lot of disadvantages include poor stirring mechanism so mass transfer rate is very low. Hence less mass productivity, insufficient utilization of sunlight close to the bottom surface of pond and contamination risk due to fast growing heterotrophs and predators have hindered the commercial production. On the contrary, the closed photo bioreactor technology is free from those drawbacks to a great extent. But, photobioreactor which is promising to culture of microalgae is still under consideration as better geometric shape and proper growth model are associated with it [14] . Maximum sunlight capturing capacity and minimum space requirement are first and foremost condition in designing a photo bioreactor. Both the outdoor and the indoor cultivation process are in vogue but for large scale production outdoor cultivation is required as to utilize natural source of light. The photo bioreactors such as bubble column, torus, helical and stirred tank have low illuminated surface area. But for outdoor cultivation large illuminated surface area is needed. In this context, U-loop horizontal tubular photo bioreactor is more efficient than other considering their large illumination area and easily scaling up capacity [15] [16] [17] [18] . From this point of view, investigations were limited only to analyse the growth model in case of horizontal u-loop tubular photo bioreactor. In this work we have conducted CFD comparison analysis among different shape horizontal photo bioreactors as simulation plays a vital role to predict the result before going to experiment on a real test bed. We hereby proposed vertically square and hexagonal shape horizontal PBRs besides tubular PBR. As hydrodynamics, light regime, shear stress and pressure distribution are most important parameters to decide which one is the best suited to microalgae growth, so we consider these parameters for result analysis.

In our simulation only the microalgae suspension is considered to obtain fully developed single phase laminar flow with no slip condition at the wall. Here, we have focused on the comparison of fluid behaviour in U-loop portion other than straight part as shear rate and rate of cell damage is high there.

The rest of the paper is organized as follows. The theoretical framework is described in the Section 2; Section 3 describes the methodology of the mathematical model development; results and conclusions are presented in the Section 4 and the Section 5 respectively.

As in this paper, our focus is on the comparative analysis of flow phenomenon for three PBRs, thus we conduct the study in two steps: Mathematical model development and numerical simulation.

During the simulation, the solver was configured as time dependent. For achieving better and comparative results, we ran the simulation for the seventh day of microalgae culture as microalgae growth can clearly be observed from this day. The time range was (540,000, 10, 540,050) seconds. From those analyses significant changes are noticed for three PBR’s. For comparison, we analyse the results for 50 second. The topics of interest in our result analysis include grid independency, velocity distributions, pressure profiles through the ducts curvature and shear stress on the wall of ducts. The shear stress at the middle of the U-loop is the prime concern in this paper as it helps to find out which one is conforming to less cell damage. To identify the fluid behaviour for different profiles the three PBR’s are fragmented in different three cross sections.

As mesh size plays a vital role in case of accuracy, so satisfactory computational accuracy can be achieved by continuously changing the meshes until the results from two trials lead to very close to each other [14] . As we previously discussed about the grid independency, some results regarding velocity magnitude are shown in Figure 4 and Figure 5 for normal and coarse mesh in case of tubular PBR.

In Figure 4(a), for coarse mesh the velocity magnitude is 0.9168 m/s and in Figure 4(b), for coarse mesh it is 0.9316 m/s. The both cross sections are taken at the middle of U-loop. From Figure 5(a) the maximum velocity at straight portion is 0.75 for coarse mesh and from Figure 5(b) it is 0.8 for normal mesh.

In our study, we simulate the flow dynamics of three types of PBR’s and discuss the velocity, pressure and shear stress properties as microalgae endurance capacity depends on them. For all the cases, in the U-loop portion, higher velocity exists than any other parts but always the speed is less and moderate in tubular PBR than others. The velocity distribution in tubular PBR is better suited to the culture of microalgae. As shear stress is mostly important factor for microalgae culture, we have analysed our results especially for U-loop portion and less shear stress is found in tubular shape than rest

of the PBR’s. So from our analysis it can be said that tubular PBR is the best choice for microalgae culture. Though pressure profile is always uniformly decreasing from inlet to outlet for all PBR’s, a little fluctuation is found in U-loop portion as for haphazard distribution of fluid. But the pressure is always less in tubular PBR. So the simulation result of fluid properties velocity, shear stress and pressure indicates that the tubular one shows better agreement for the culture of microalgae.

The authors are gratefully acknowledged for the technical supports to the Centre of Excellence in Mathematics, Department of Mathematics, Mahidol University, Bangkok- 10400, Thailand, and the Simulation Lab, Department of Mathematics, Chittagong University of Engineering & Technology, Chittagong, Bangladesh.

Shahriar, M., Monir, M.I. and Deb, U.K. (2016) Comparative Analysis of Hydrodynamics Behavior of Microalgae Suspension Flow in Circular, Square and Hexagonal Shape Photo Bioreactors. American Journal of Computational Mathematics, 6, 320-335. http://dx.doi.org/10.4236/ajcm.2016.64033