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Investigation of Flow Dynamics for a Microalgae Suspension in an Open Pond System ()

^{1}Department of Mathematics, Marine Fisheries Academy, Chittagong, Bangladesh.

^{2}Department of Mathematics, Chittagong University of Engineering and Technology, Chittagong, Bangladesh.

^{3}Department of Mechanical Engineering, Chittagong University of Engineering and Technology, Chittagong, Bangladesh.

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*American Journal of Computational Mathematics*,

**7**, 195-207. doi: 10.4236/ajcm.2017.73018.

1. Introduction

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 [1] . Now, a day’s biofuel is considered as one of the most alternative to fossil fuel in transportation sectors and has the capability to meet the energy demand as an alternative to gaseous and other liquids [2] . There are several advantages to produce biodiesel from microalgae such as capacity of fixing CO_{2} from the environment and treatment of the waste water [3] . Microalgae can mitigate CO_{2} from the environment which helps to reduce global warming issue because it has ability to tolerate gas pollutions than most other toxic chemicals [4] .

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 [5] . But in both cases, they yield a large cultivable area. Third generation biofuels are refers to various bio oil, biodiesel, renewable oil etc. Microalgae are the third generation biofuels which have no disadvantages like the first and the second generation biofuels [6] .

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 [7] . There are two types of culture systems. One is the traditional and simplest open pond system and the other is the closed photo bioreactors. Closed photo bioreactors are also many types: vertical column, flat panel, torus etc. They require small cultivable area, but the disadvantages are complicated mechanism to construct, operational cost and investment is high. Open pond facilitates mass cultivation of microalgae with cheap investment and operational expenses compared to closed system [8] . Between them the open pond systems are easy to construct and capital expense is low [9] .

Microalgae are unicellular, photosynthetic microscopic organisms. They are very small plants generally size from 1 - 50 micrometers and have no leaves or roots [10] . It is found in aquatic environments, damp places or shallow water sources [11] . Algae are constituted by carbohydrates, Nucleic Acids, Fats and proteins. Algae type microorganisms contain 40 percent fatty acids. These fatty acids can be turned into biodiesel [12] . This biodiesel has much popularity because it is nontoxic and almost has no effect in environment. There are different colors and groups of microalgae based on their taxonomy and it helps to mitigate surplus Carbon dioxide from the environment. To produce the chemical energy from the solar energy microalgae play a vital role promising biodiesel to their proficient absorption [13] . Nowadays microalgae have varied applications in food industries, chemical sector, pharmaceutical, and different poultry industries [14] . Generally three ingredients are needed for algae growth including Carbon-dioxide, Water and Sunlight [15] . Among them the sunlight is mandatory to support nutrients functioning properly [16] . To ensure the highest productivity from cultivation the sunlight reaching the suspension system must be kept within the tolerance level [17] .

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 [18] . Now a day’s raceway pond system is most common which is the artificial, cheapest and established in different crop production areas. It looks like an oval-shaped and generally 0.3 m deep with recirculation channel built in concrete or plastic line. Depending on the size of a raceway pond, bends flow is guided by baffles placed. Paddlewheel maintains the flow continuity during daylight and prevents sedimentation. There are eight flat blades in a paddlewheel generally adjusted with the depth of the raceway pond. It works as like as propellers which divides the flow into two section [19] .

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 [20] . In this study we focus on the dynamic behavior of the paddlewheel approve the adequate movement by mixing of CO_{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.

2. Mathematical Model

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.

2.1. Geometry

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 [21] . The blade of the paddle wheel is in length 520 mm and the thickness is 0.2 mm. Figure 1 shows the dimension of the computational domain of algae suspension in the raceway pond. Figure 2 and Figure 3 show the CAD model raceway pond and the paddlewheel respectively.

Figure 1. Dimensions of the algae suspension domain in the raceway pond.

Figure 2. A CAD model of the raceway pond.

Figure 3. Design of a paddle wheel (dimensions are in cm).

2.2. Computational Domain and Meshes

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. Figure 4 and Figure 5 shows the computational domain and mesh design of the algae suspension respectively. The Table 1 shows the elements of mesh design while in the Table 2 shows the parameters of microalgae suspension.

Figure 4. The computational domain of the algae suspension in the pond.

Figure 5. A fine mesh design of the computational domain.

Table 1. Number elements of mesh design for the computational domain.

Table 2. The parameters used in our simulation.

2.3. Governing Equations

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:

$\frac{\partial \rho}{\partial t}+\nabla \cdot \left(\rho u\right)=0$ (1)

$\rho \frac{\partial u}{\partial t}+\rho \left(u\cdot \nabla \right)u=\nabla \cdot \left[-PI+\tau \right]+F$ (2)

where $\rho $ is the density of the suspension, $u$ is the velocity, $p$ is the pressure, $\tau $ 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

$s=\frac{1}{2}\left(\nabla u+{\left(\nabla u\right)}^{\text{T}}\right)$

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

$\tau =2\mu s-\frac{2}{3}\mu \left(\nabla \cdot u\right)I$ (4)

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

$\rho \nabla \cdot u=0,$ (6)

and the Equation (2) becomes

$\rho \frac{\partial u}{\partial t}+\rho \left(u\cdot \nabla \right)u=-\nabla pI+\nabla \cdot \left(\mu \left(\nabla u+{\left(\nabla u\right)}^{\text{T}}\right)\right)-\frac{2}{3}\mu \left(\nabla \cdot u\right)I+F.$ (7)

Equation (7) can be written in the simplest form

$\rho \frac{\partial u}{\partial t}+\rho \left(u\cdot \nabla \right)u=\nabla \cdot \left[-pI+\mu \left(\nabla u+{\left(\nabla u\right)}^{\text{T}}\right)\right]+F.$ (8)

Equation (8) can be written in the form

$\rho \frac{\partial u}{\partial t}+\rho \left(u\cdot \nabla \right)u=\nabla \cdot \sigma +pg.$ (9)

where $\sigma $ is the stress tensor and $g$ is the gravity. The stress tensor $\sigma $ can be expressed as

$\sigma =-pI+2\eta D\left(v\right)$ (10)

where $\eta $ is the viscosity of the fluid, $D\left(\nu \right)$ rate of deformation. The viscosity in Equation (10) is determined by

$\eta \left(t\right)={\eta}_{0}{\eta}_{r}\left(t\right).$ (11)

The relative viscosity
${\eta}_{r}\left(t\right)$ relating to the concentration is then used and determined by ^{ }

${\eta}_{r}\left(t\right)=1+\in c\left(t\right),$ (12)

where $\in $ is the Einsteins coefficient [22] . The concentration function c(t) in Equation (12) is given by the following logistic Equation [23] .

$c\left(t\right)={c}_{0}+\frac{A}{1+B{\text{e}}^{\mu t}},$ (13)

where $\mu $ is the constant growth rate of microalgae cells and ${C}_{0}$ is the initial.

Concentration of the suspension and A, B are constants.

2.4. Boundary Condition

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

$\left[-pI+\mu \left(\nabla u+{\left(\nabla u\right)}^{\text{T}}\right)\right]n=-{f}_{0}n.$ (14)

3. Numerical Results and Discussion

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.

Figure 6 represents the velocity profile at three different layers of the computational domain. It is found that the velocity magnitude is too much low at the lower layer (a) of the suspension because of friction between the domain boundary and lower layer fluid of the flow. In (b) shows that the velocity profile at the upper layer where the flow is in contact with the air. As a result the velocity is little bit higher compared to the lower layer. In (c) the highest velocity magnitude is observed in the middle layer of the domain compared to the upper and the lower layer flow. It is also velocity is generally found that the high in the straight portion of the pond. This profile shows that the inlet velocity is gradually increasing at the straight part of the raceway pond and decreasing at the U-loop area.

The velocity distribution graphs are shown in the Figure 7. We observed that when the flow passes through the straight part of the tube it form a parabolic shape in (a). However, the parabolic shape of the velocity is distorted around U-loop area which shown in (b).

In Figure 8, the shear stresses of the three layers have been observed from three different cross sections in one of the inner baffle’s walls along the U-loop portion. The high share stress is found in the middle layer compared to the upper and lower layer of the flow. Through the pattern of the curves of the share rate is same at all three layers; initially a sharp up and sharp fall in found.

Figure 6. The velocity magnitude at three different layers of the computational domain of the suspension flow. (a) The velocity profile at lower the portion of the suspension; (b) The velocity profile at the upper portion of the suspension; (c) The velocity profile at the middle portion of the suspension.

Figure 7. The velocity profile at different cross section of the straight part and the U-loop portion. (a) Velocity profile at a cross section of the stright portion of the domain; (b) The velocity profile at a cross section of the U-loop portion.

A uniform pressure drop at U-loop portion is shown in Figure 9. This phenomenon implies high pressure concentration profile during last moment in suspension. Figure 10 represents the graph of growth concentration of microalgae cell on the seventh day from 06.00 am to 18.00 pm. From our simulation we observed that the growth concentration of microalgae cell is increased slowly with time.

Figure 8. The share rate distribution along the raceway pond.

Figure 9. The pressure profile for the entire raceway pond.

4. Conclusion

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

Figure 10. The growth concentration graph of microalgae cell.

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.

Acknowledgements

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.

Conflicts of Interest

The authors declare no conflicts of interest.

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