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In the microalgae based biofuel technology, two main cultivation methods are available such as the Open pond system and the Closed photo bioreactor (PBR). The primary advantages of utilizing open raceway ponds are low production and maintenance cost. Though the open raceway ponds have been adjudged potentially cost effective, so many surrounding issues are involved to produce microalgae at a large scale that could make microalgae fuel cost competitive with the conventional petro oil. Many researchers have been studied so far to increase the efficiency of the cultivation methods without providing a proper mathematical model of flow dynamics inside the open raceway ponds. This paper presents a mathematical model to analyze the flow behavior of an open pond culture focusing the mixing factors by using a paddlewheel while the paddlewheel have its own unique dynamic characteristics. From our simulation we observed that the paddlewheel plays a vital role in mixing and the growth of microalgae. The velocity profiles, shear stress distributions are also studied at different parts of an open pond culture for a microalgae suspension.

The demand of energy and the Green House Effect (GHE) are the main two problems of the present world. In the 21^{st} century it has become unbearable with the time passing by. So to mitigate the GHE, the global warming problems and the depletion of fossil fuels, we need to find out an alternative energy sources to meet these massive problems over the next five decades [_{2} from the environment and treatment of the waste water [_{2} from the environment which helps to reduce global warming issue because it has ability to tolerate gas pollutions than most other toxic chemicals [

Generally, biofuels are categorized in three generations. The first generation biofuels are crops plants such as sugar beet, sugar cane, palm oil, vegetables oil, soybean, animal fats etc. The second generation biofuels are non-edible parts of plants [

At present new technologies and culture systems have been developed to produce biofuel from the microalgae. It is assumed to be the best source to meet the energy demand and to reduce the pressure on the petroleum based oil. Many researchers have accepted considerable interest in microalgae biofuel as a substitute of the fossil fuel. To get the best productivity from the microalgae, they have to go through rigorous cultivation process [

Microalgae are unicellular, photosynthetic microscopic organisms. They are very small plants generally size from 1 - 50 micrometers and have no leaves or roots [

The open cultivation system has been used since 1950s. At present four major types of open pond are used such as raceway ponds, tanks, big ponds and circular ponds. They are different in their shapes, sizes and construction materials. One is the unmixed tank where nutrients and water are applied but have no mixing. In this system production is very low. Another system is called thin layer reactor where a paddle wheel controls the whole culture flow and surface to volume ratio is high [

Flow dynamics of the microalgae suspension can be obtained by the computational fluid dynamics method. Generally in the channel, the flow is assumed to be laminar flow to prevent the mortality rate of the cells in suspension and can be formulated by the Navier Stocks equation. Because of laminar flow the characteristics of flow field are Newtonian and fluid particle movement is absence near the wall of the domain. Thus on the wall no slip condition at the channels may be considered. Different velocities are occurring at the different portions of the flow for the variation of wall share rate [_{2} and other antioxidant properties in the suspension. In the algae suspension mixture various parameters are affected which are studied numerically.

The rest of our paper is organized as follows. In Section 2 mathematical model and mesh design are established for the computational geometry. In Section 3, a single phase laminar flow model is established and numerical simulation results are analyzed. Finally a brief conclusion for this study is described in Section 4.

The main goal of this study is to improve our understanding of the flow dynamics of microalgae suspension by using single phase fluid model for an open pond system. Generally, in this system the paddlewheel controls the mixing velocity and prevent sedimentation. So the phenomenon due to the rotation of the paddle wheel is also our concern in this simulation study.

In our study, the dimensions of the geometry are considered as per from the traditional raceway pond cultivation system. It is 10,000 mm in length and 2000 mm in width. The curvature radius of the inner periphery is about 1133 mm. The semicircular baffles on the both sides are about 600 mm in radius. Its depth is about 500 mm [

The computational domain is placed horizontally along XY axis and Z axis is perpendicular to the flow. The surface area is 98.33 m^{2} while the working volume is 23.29 m^{3}. In our simulation fine mesh design is considered with 673,800 elements and 489,180 degrees of freedom.

Mesh elements | No. of elements |
---|---|

Vertex elements | 40 |

Boundary elements | 36,605 |

Domain elements | 345,844 |

Edge elements | 1551 |

Name | Values | Description |
---|---|---|

9.8 m/s^{2} | Gravity acceleration | |

0.001 Pa.s | Water viscosity | |

0.55 | Constant parameter | |

200 | Constant parameter | |

1 | Constant parameter | |

0.063 [1/h] | Maximum growth rate |

The microalgae suspension inside the open pond is considered as an incompressible single phase Newtonian fluid. The flow of the suspension is governed by the continuity equation and the Navier-Stokes equation, which are as follows:

∂ ρ ∂ t + ∇ ⋅ ( ρ u ) = 0 (1)

ρ ∂ u ∂ t + ρ ( u ⋅ ∇ ) u = ∇ ⋅ [ − P I + τ ] + F (2)

where ρ is the density of the suspension, u is the velocity, p is the pressure, τ is the viscous stress tensor, F is the volume force, I is the unit matrix.

The strain rate tensor related to the velocity is given by the following equation

s = 1 2 ( ∇ u + ( ∇ u ) T )

The viscous stress tensor in Equation (2) is given by

τ = 2 μ s − 2 3 μ ( ∇ ⋅ u ) I (4)

When the temperature variations in a flow are small, a single phase fluid can often be assumed as incompressible, that is ρ is constant or nearly constant. This is the case for all liquids under normal conditions and also for gases at low velocity. For constant ρ the continuity Equation (1) becomes

ρ ∇ ⋅ u = 0 , (6)

and the Equation (2) becomes

ρ ∂ u ∂ t + ρ ( u ⋅ ∇ ) u = − ∇ p I + ∇ ⋅ ( μ ( ∇ u + ( ∇ u ) T ) ) − 2 3 μ ( ∇ ⋅ u ) I + F . (7)

Equation (7) can be written in the simplest form

ρ ∂ u ∂ t + ρ ( u ⋅ ∇ ) u = ∇ ⋅ [ − p I + μ ( ∇ u + ( ∇ u ) T ) ] + F . (8)

Equation (8) can be written in the form

ρ ∂ u ∂ t + ρ ( u ⋅ ∇ ) u = ∇ ⋅ σ + p g . (9)

where σ is the stress tensor and g is the gravity. The stress tensor σ can be expressed as

σ = − p I + 2 η D ( v ) (10)

where η is the viscosity of the fluid, D ( ν ) rate of deformation. The viscosity in Equation (10) is determined by

η ( t ) = η 0 η r ( t ) . (11)

The relative viscosity η r ( t ) relating to the concentration is then used and determined by ^{ }

η r ( t ) = 1 + ∈ c ( t ) , (12)

where ∈ is the Einsteins coefficient [

c ( t ) = c 0 + A 1 + B e μ t , (13)

where μ is the constant growth rate of microalgae cells and C 0 is the initial.

Concentration of the suspension and A, B are constants.

In our study the adequate boundary conditions are important factor for the suspension. In our model no slip boundary condition is considered in inner side of the boundary wall. i.e. u = 0 . In the inlet u = u 0 and the normal stress at the outlet can be described by the following equation

[ − p I + μ ( ∇ u + ( ∇ u ) T ) ] n = − f 0 n . (14)

The main goal of our simulation is to investigate the flow dynamics for an open pond system while the microalgae suspension circulates under the action of paddlewheel. Here we have used the COMSOL multiphysics simulation software version 4.2a to carry out our simulation. As we have taken time depended study, the time interval was [0, 100, 3600] and the results are analyzed for the last time step. The inlet velocity of was taken as U_{in} = 0.5 ms^{−1} for the suspension flow.

The velocity distribution graphs are shown in the

In

A uniform pressure drop at U-loop portion is shown in

In this study we analyzed the flow behavior of microalgae suspension in an open raceway pond system. The total surface area of the computational domain is 98.33 m^{2} and the volume is 23.29 m^{3}. In our simulation a fine mesh design is considered with 673,800 elements and 489,180 degrees of freedom for grid sensitive analysis. From our simulation we found that the velocity of the suspension generally high in the middle part of the computational domain. The velocity

magnitude is too much low at the lower layer of the suspension because of friction between boundary of the domain and lower layer of the flow. At the upper layer the flow is in contact with the air. As a result velocity is little bit higher compared to the lower layer. We also observed that this velocity is high at the straight portion than the U-loop portion in raceway pond. Consequently, the share rate distribution is responded with the flow velocity. The upper share rate is found in the middle of the domain compared to the lower and middle layers. A uniform pressure drop is found for the entire domain except a little fluctuation around U-loop area. We also found a good response for the cell growth by considering the increment of concentration of the suspension.

The authors thankfully acknowledge 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 and Technology, Chittagong-4349, Bangladesh.

Singha, N.B., Deb, U.K. and Shahriar, M. (2017) Investigation of Flow Dynamics for a Microalgae Suspension in an Open Pond System. American Journal of Computational Mathematics, 7, 195-207. https://doi.org/10.4236/ajcm.2017.73018