Complete Evaluation of Cell Mixing and Hydrodynamic Performance of Thin-Layer Cascade Reactor
Complete Evaluation of Cell Mixing and Hydrodynamic Performance of Thin-Layer Cascade Reactor
Akhtar, Shehnaz;Ali, Haider;Park, Cheol Woo
2020-01-21 00:00:00
applied sciences Article Complete Evaluation of Cell Mixing and Hydrodynamic Performance of Thin-Layer Cascade Reactor 1 2 1 , Shehnaz Akhtar , Haider Ali and Cheol Woo Park * School of Mechanical Engineering, Kyungpook National University, 80 Daehakro, Bukgu, Daegu 41566, Korea; shehnazakhtar073@gmail.com Department of Chemical Engineering, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway; haider.ali@ntnu.no * Correspondence: chwoopark@knu.ac.kr; Tel.: +82-53-950-7569; Fax: +82-53-950-6550 Received: 10 December 2019; Accepted: 16 January 2020; Published: 21 January 2020 Abstract: Microalgae are a great source of food and supplements as well as a potential source for the production of biofuels. However, the operational cost must be reduced to allow viable productions of bulk chemicals such as biofuels from microalgae. One approach to minimize the cost is to increase the eciency of the photobioreactor. Photobioreactor eciency is correlated to hydrodynamic mixing, which promotes single cell exposure to sunlight, keeps algae cells in suspension, and homogenizes the distribution of nutrients. Thus, a possible route to enhance the eciency of the photobioreactor can be identified through an improved understanding of the mixing phenomenon. Therefore, for the current thin-layer cascade reactor, two aspects of its performance—namely, cell mixing and hydrodynamic characteristics—are evaluated under varying mass flow rates, slope angles, water depths, and aspect ratios of the channel by using computational fluid dynamics. The resulting model is validated with experimental data. Results reveal that limited cell mixing is achieved in the thin-layer cascade reactor with increased water depth and large aspect ratios. However, cell mixing is significantly increased at high mass flow rates. The increase in the mass flow rate and slope angle results in increased flow velocity and power consumption. Keywords: microalgae; thin layer cascade reactor; residence time; power consumption; cell mixing 1. Introduction Microalgae are small organisms that convert sunlight into energy in the presence of CO and nutrients. Microalgae have been studied intensively in the past because of their application in food, medicines, and compounds for biofuels [1,2]. Dierent mass culture systems have been used for the production of microalgae. Mainly, they are divided into open and closed photobioreactors. Closed photobioreactors are used for high-quality biomass production, but they require greater power consumption, thus making it economically expensive [3]. Open raceway ponds are being widely used for the large-scale culturing of microalgae in the world. The advantages of raceways are their relatively low cost and simple design. However, because of the high culture thickness in raceways (15–30 cm), the photo inhabitation can aect the photosynthesis phenomenon and consequently the algal productivity. They operate at low fluid velocity, and thereby, a paddle wheel is required to keep algal cells in suspension [4,5]. An alternate approach for the mass production of microalgae is a thin-layer cascade reactor first introduced by Dr. Ivan Setlík in the 1960s [6]. A thin-layer cascade reactor is an open system for the commercial-scale cultivation of microalgae [7,8]. A thin-layer cascade (TLC) reactor consists of shallow channels with a thin layer (thickness 10 mm) of algal culture Appl. Sci. 2020, 10, 746; doi:10.3390/app10030746 www.mdpi.com/journal/applsci Appl. Sci. 2020, 10, 746 2 of 15 medium. The thin layer of algal suspension improves light utilization and results in high biomass density (25–35 g/L) [8,9]. Photoinhibition is a major challenge in TLC reactors because it considerably aects the photosynthetic eciency of algal cells and consequently reduces biomass production [9–11]. Light attenuation occurs as the liquid layer becomes thicker in a TLC reactor, which decreases the local light penetration. A steep gradient in light attenuation is expected along the culture depth. Thus, eective culture mixing is necessary to prevent photoinhibition in TLC reactors. Culture mixing also prevents cell sedimentation in the TLC reactor. The increase in layer thickness escalates the chances of cell sedimentation by increasing the residence time of algal cells in a TLC reactor. Precisely, an increase in layer thickness results in a twofold increase in the residence time of algae cells/decrease in algae cell mixing [12,13]. Culture mixing significantly depends on various design parameters of TLC reactors, such as channel dimensions and slope angles and flow rates. At high cultural thickness, algae cell mixing can be improved by increasing flow velocity [7]. However, the power required for mixing the suspension increases with the increase in cultural thickness and inclination of the slope [14]. Therefore, TLC reactors with small culture thicknesses are favorable for high biomass densities of microalgae. The small suspension layer limits the night biomass loss by respiration and promotes faster warming of the culture at the start of cultivation, thereby preventing the strong photoinhibition of algal growth [15–17]. The algal productivity is strongly influenced by the inclination angle of the reactor and water depth. Under optimal climate conditions, the increase in channel length and slope angle causes a substantial increase in algal biomass productivity because of the increase in photosynthetic eciency. However, the night biomass loss suciently increases with the increase in culture thickness [14]. The algal productivity in TLC is considerably aected by the surface-to-volume ratio. A TLC reactor unit with a large surface-to-volume ratio is a more ecient system for biomass density (about 30%) as compared to the unit with a small surface-to-volume ratio [8]. However, at low volumes of suspension, the utilization of light energy and algal growth can be increased by vigorous culture mixing [18]. The photon energy received by each cell is also considerably aected by the length of the optical path (thickness of culture layer), the design of the cultivation unit, and the rate of mixing. The highest growth rate and productivity is achieved in cultivation systems with lower microalgae layer thickness. Small culture depth, high flow velocity, and higher slope angles create intensive turbulence, which optimizes the change of light and dark periods of individual cells and results in a higher eciency of light utilization [19,20]. Cultural thickness also plays an important role in the carbonation eciency of TLC. High culture thickness also limits algal growth due to the incomplete absorption of CO because of the short retention time of the gas bubbles [21]. Optimizing culture mixing by selecting the suitable values of these design parameters is necessary to prevent photoinhibition in TLC reactors and consequently enhance biomass production. However, studies investigating the culture mixing in TLC reactors are lacking. The advancement in numerical techniques and the availability of high-quality computers have allowed us to predict complex flow characteristics inside photobioreactors, especially for the cases where the use of an experimental setup is restricted by technical constraints [22]. Recently, Severin et al. [10] performed a numerical simulation to evaluate the eect of volume flow and slope angle on cultural mixing for the main cultivation channel of TLC (i.e., the upper channel). Their results confirmed that mixing could be improved at high volume flows and slope angles. However, their studies do not include a detailed evaluation of hydrodynamic and cell mixing in each compartment of the TLC reactor. Despite its high potential for ecient biomass production, TLC in numerical studies has remained neglected. Moreover, the hydrodynamic is dierent in each compartment of the TLC; the residence time of the algae cell, mixing eciency, energy consumption, and flow field will be dierent in each compartment. Therefore, this study investigates the hydrodynamic performance and algae cell mixing in each compartment of the reactor separately by employing computational fluid dynamics (CFD). Appl. Sci. 2020, 10, 746 3 of 15 residence time of the algae cell, mixing efficiency, energy consumption, and flow field will be different in each compartment. Therefore, this study investigates the hydrodynamic performance and Appl. Sci. 2020, 10, 746 3 of 15 algae cell mixing in each compartment of the reactor separately by employing computational fluid dynamics (CFD). The numerical calculations have been performed by considering different geometrical aspects The numerical calculations have been performed by considering dierent geometrical aspects (channel width, water depth, and inclination of the surface) of the reactor. The results in terms of (channel width, water depth, and inclination of the surface) of the reactor. The results in terms of mixing efficiency and the residence time of algae cells have been discussed to evaluate the mixing mixing eciency and the residence time of algae cells have been discussed to evaluate the mixing phenomenon. For the hydrodynamic characteristics of the TLC reactor, the velocity magnitude and phenomenon. For the hydrodynamic characteristics of the TLC reactor, the velocity magnitude and the the hydraulic power consumption have been evaluated. hydraulic power consumption have been evaluated. 2. T 2. TLC LC Desc Description ription an and d M Mathematical athematical Mod Modeling eling A three A three-dimensional -dimensional TLC TLC rre eactor actor as as desc described ribed by by [1 [11 1]] was was u used sed in in tthis his st study udy.. Th The e re reactor actor had had a a channel channel lengt length h (L) o (L) of f 4 m 4 m and a ch and a channel annel width (W) of width (W) of 1 m 1 m ((Figur Figure e 1 1)). . The re The reactor actor consist consists s o of f an an up upper per channel in channel inclined clined in in the horizontal direction connected the horizontal direction connected by a by a flow flow rev reversal ersal mo module dule to the lowe to the lower r c channel hannel in t in the he oppos opposite ite direct direction. ion. The fi The first rst mod module ule in t in the he reactor i reactor is s the the iinlet nlet modul module, e, whi which ch di distributes stributes the the wa water ter over the wi over the width dth of of the upper cha the upper channel. nnel. The Thea angle ngle of of the theiinlet nlet m module odule to the to theupper pl upper plate ate was 55 was 55°. . At the end of the upper ch At the end of the upper channel, annel, a a dr drip ip edge edge (length: (length: 5 cm, 5 cm, angle angle t to o the vertical: 10°) was de the vertical: 10 ) was designed signed ffor or smooth flow i smooth flow into nto the reversal the reversal modul module. e. The bottom The bottom of the flow of the flow reversal module w reversal module was as sloped in the sloped in the direct direction ion o of f tthe he flow t flow to o as assur sure e grav gravity-driven ity-driven fflow low t to o the lower c the lower channel. hannel. The flow of the w The flow of the water ater was was accord according ing to to the described the described order of the order of the module modules s of t of the he reactor. T reactor. The he length of t length of the he upper an upper and d lower lower channel channel was was kept kept constant, constantand , and the the inclination inclination angle, angl water e, water depth, depth, an and width d wof idth o the rfeactor the rewer actor e varied were v (T aable ried (T 1).able 1). (a) (b) Figure 1. Figure 1. Com Computational putational mmodel odel of thin-lay of thin-layer er cas cascade cade (TL (TLC) C) used used in thi in sthis stud study y (a) xy-vi (a) xy-view ew and ( and b) xyz-vi (b) xyz-view ew. . Table 1. Summary of important parameters of the thin-layer cascade reactor used in this study. Table 1. Summary of important parameters of the thin-layer cascade reactor used in this study. Parameters Value Parameters Value Slope angle 1 ; 2 ; 3 Slope angle 1°; 2°; 3° Depth ratio 5.6 mm; 7.5 mm; 10 mm Depth ratio 5.6 mm; 7.5 mm; 10 mm Aspect ratio 180; 260; 340 Aspect ratio 180; 260; 340 Mass flow rate 1.6–3.6 kg/s Mass flow rate 1.6–3.6 kg/s 2.1. Hydrodynamic Modeling 2.1. Hydrodynamic Modeling The open channel flow behavior is evaluated based on the Reynolds number and hydraulic The open channel flow behavior is evaluated based on the Reynolds number and hydraulic diameter (D ), which are given below: diameter (𝐷 ), which are given below: 4dW D = (1) 2d + W 4𝑑𝑊 (1) 𝐷 = 2𝑑 + D𝑊 U Re = (2) 𝜌𝐷 𝑈 = (2) where W represents the channel width (m), d is the channel or water depth (m), and U denotes the average water velocity (m/s). Water was taken as the working fluid with a density () 1000 (kg/m ) and viscosity () of 0.001 (Pa. s). The flow behavior in the TLC reactor was turbulent with a 𝑅𝑒 Appl. Sci. 2020, 10, 746 4 of 15 Reynolds number, ranging from 6300 to 14,200 [23–25]. The geometrical eects were studied by using a dimensionless number, depth ratio, and aspect ratio (AR), as given below: Channel width AR = . Channel depth The hydraulic power required for mixing is the product of the flow rate Q (m /s), cultural density 3 2 (kg/m ), gravity constant g (m/s ), and head loss. For the case of the cascade reactor with an inclined surface of length L (m), the hydraulic power E (W/m ) is given by: E = gLQI (3) where I represent the inclination angle of the surface. Q is the product of liquid velocity U (m/s), thickness of algal suspension d (m) and width of the reactor W (m). Thus, the hydraulic power per unit area (W/m ) is given by [14,26]. E /WL = gUdI (4) The k-! turbulence model was adopted to model the turbulence in an open channel. The simulation of turbulent flow with a k-! model requires an initial velocity U , initial turbulent intensity I and o T turbulent length scale L as a boundary condition. U = AU (5) ( ) I = 0.16 Re (6) L = 0.07D (7) where U represent the initial velocity (m/s), A is the cross-sectional area (m ), and U denotes the average velocity (m/s). The continuity equation for k-! turbulence model is given as follows: r.(u) = 0. (8) The momentum equation derived from the Bernoulli equation is given as follows: h i du + (u.r)u = r. l + (u + ) r + ru + F (9) T u dt where F represents the body force (N/m ), u is the velocity vector (m/s), and I represents the identity matrix. The k-! approach uses two equations to represent the turbulence properties of the flow. The first equation begins with the turbulent kinetic energy k, which determines the energy in the turbulence, and the second equation begins with turbulent dissipation rate !, which determines the scale of turbulence. The governing equations of the turbulent kinetic energy and turbulent dissipation rate for k-! turbulence model are as follows: h i @k + (u.r)k = r. + rk + P !k (10) k 0 @t @! ! + (u.r)! = r.[( + )] + P ! (11) t ! k 0 @t k where and represent the Prandtl numbers for the dissipation rate and kinetic energy, respectively. The typical values of the model constant used in the present study are given as = 0.55, = 0.5, = 0.5, and = 0.09. The turbulent viscosity defined by the k-! turbulence model is given by: = (12) ! Appl. Sci. 2020, 10, 746 5 of 15 where is the turbulent viscosity (Pa. s), ! denotes the dissipation rate (1/s), k represents the turbulent 2 2 3 kinetic energy (m /s ), and is the density of water (kg/m ). The production term is given as follows: h i P = ru : ru + ru . (13) 2.2. Algae Cell Modeling The productivity of microalgae is strongly aected by hydrodynamic mixing, which ensures single cell exposure to light, even the distribution of nutrients, the prevention of sedimentation, and an enhanced utilization of CO . The mixing phenomenon is well explained by the cell distribution inside the reactor. The criterion that determines whether the algae cells follow the fluid stream is called the Stokes number, which is defined as follows: S = (14) p p = (15) where denotes the relaxation time of algae cells (s), d represents the algae cell diameter (m), and p p p is the density of algae cells (kg/m ). A single-cell spherical shaped Chlorella specie, with an algae cell diameter d = 7 m and density = 864 (kg/m ) was used in this study [27]. The calculated Stokes number is less than 1, which means that chlorella cells may follow the fluid stream without aecting the fluid flow in the mixing process [28]. The motion of the algae particles in the reactor can be traced by Newton’s second law of motion. The fluid exerts drag force on the particles, and this drag force can be calculated by using Stokes’ law, provided that the cell Reynolds number is less than 1(Re << 1). The governing equations for the algae cell tracing are as follows: d u = F U u (16) d p dt dx = u (17) dt U u d p p p Re = (18) F = (19) p p where u denotes the chlorella cell velocity (m/s), x is the position vector of algae cells (m), and F p p represents the drag force (N). The density of the released particles is normalized to the magnitude of the fluid velocity at the inlet. This means that more particles are released where the inlet velocity is highest, and fewer particles are released where the velocity field is low. A user-defined auxiliary dependent variable R with a set value of 1 was defined to evaluate the mixing and residence time of particles. This variable solves first-order dierential equations by using the Euler method with defined initial values to calculate the mixing and residence time of algae particles. The following are the governing equations for residence time and mixing length: t2 R (t) = Rdt (20) t1 s2 M (s) = Rds (21) s1 Appl. Sci. 2020, 10, 746 6 of 15 where R represents the residence time (s), M is the mixing length (m), t and t show the time steps t l 1 2 of algae particles at the inlet and outlet of the reactor, and s and s represent the direction of algae 1 2 particle motion at the inlet and outlet, respectively. 3. Numerical Details Numerical computations were performed using the commercial software COMSOL-Multiphysics (V 5.3a). The complete reactor was discretized into a physics-based free tetrahedral mesh. Mesh independence analysis was performed to choose a mesh that ensures a high accuracy of results at a low computational cost by considering three dierent levels of mesh refinement: fine mesh (523,359 domain elements and 352,730 boundary elements), normal mesh (134,183 domain elements and 91,130 boundary elements), and coarse mesh (60,175 domain elements and 3456 boundary elements). The average velocity on the entire reactor volume is computed for all three cases (Table 2). The variation in the CFD predictions is marginal. Consequently, the normal mesh with 134,183 domain elements and 91,130 boundary elements was adopted for all further simulations. Table 2. Mesh independence test (m 2.4 kg/s, d = 5.6 mm, slope = 1 ) for velocity averaged on the entire reactor volume. No of Mesh Elements U (m/s) (523,359) 0.5165 (134,191) 0.5128 (60,175) 0.5110 In COMSOL-Multiphysics (V 5.3a), the k-! model with a time-dependent solver was used to simulate the flow. At the inlet, the mass flow rate was varied, and the atmospheric boundary condition (1.0 atm) was assigned at the outlet. No slip boundary condition was applied to the sidewalls and the bottom of the reactor. The slip boundary condition was adapted to the open surfaces of the reactor. Particle tracing for the fluid flow was chosen to investigate the algae cell mixing. A total of 0.2 million particles based on cell density were introduced at the inlet of the reactor. Flow field parameters obtained from the reactor analysis were used to analyze the flow mixing and residence time of algae particles. All simulations were run for 100 s with a step size of 1 s. All numerical calculations were carried out at an Intel Core i7-3370 3.90 GHz processor with a 16 GB RAM operating system. The solver takes approximately 13 and 24 h to achieve complete convergence of the solution for the flow field and 0.2 million algae particles, respectively. 4. Results and Discussion In order to confirm the accuracy of the applied model, the results of this study were compared with the experimental results of [11]. The results of this study were in reasonable agreement with the experimental results, thereby verifying the present numerical methodology. A close agreement exists between the present numerical calculations of velocity with the experimental results at lower mass flow rates, where the maximum percentage error was limited to 4.6% and 5.4% at a mass flow rate of 1.6 kg/s and 2 kg/s. However, at a high mass flow rate, the predicted values of velocity deviate from the experimental values considerably, where the maximum percentage error was 18.59% and 18.89% at a flow rate of 2.4 and 2.8 kg/s, respectively (Figure 2). Appl. Sci. 2020, 10, 746 7 of 15 Appl. Sci. 2020, 10, 746 7 of 15 Figure 2. Comparison of the present study with the experimental results of Apel et al. [11]. Figure 2. Comparison of the present study with the experimental results of Apel et al. [11]. The hydrodynamic performance and algae cell mixing features of a thin-layer cascade reactor The hydrodynamic performance and algae cell mixing features of a thin-layer cascade reactor have been evaluated by using computational fluid dynamics. The hydrodynamic performance based have been evaluated by using computational fluid dynamics. The hydrodynamic performance based on the proposed numerical methodology was evaluated by computing the hydrodynamic properties, on the proposed numerical methodology was evaluated by computing the hydrodynamic properties, namely, the power consumption and velocity magnitude. In addition to the variation in mass flow namely, the power consumption and velocity magnitude. In addition to the variation in mass flow rate, geometric parameters such as the channel depth, channel width, and slope angle were the main rate, geometric parameters such as the channel depth, channel width, and slope angle were the main criteria for the calculation of these properties. Moreover, the algae cell mixing characteristics of the criteria for the calculation of these properties. Moreover, the algae cell mixing characteristics of the TLC reactor were also evaluated based on the residence time and mixing eciency of the reactor with TLC reactor were also evaluated based on the residence time and mixing efficiency of the reactor with the variation in the above-mentioned geometric properties of the reactor. the variation in the above-mentioned geometric properties of the reactor. 4.1. Mixing Performance of TLC Reactor 4.1. Mixing Performance of TLC Reactor Mixing in outdoor cultures of microalgae is essential to prevent cells from settling and sticking Mixing in outdoor cultures of microalgae is essential to prevent cells from settling and sticking to the bottom, to break down the diusional gradients of essential nutrients, and to ensure uniform to the bottom, to break down the diffusional gradients of essential nutrients, and to ensure uniform exposure to sunlight. The mixing length of the algae particles which account for the combined exposure to sunlight. The mixing length of the algae particles which account for the combined streamwise and transversal movement of the algal cell at any given instant can be calculated using streamwise and transversal movement of the algal cell at any given instant can be calculated using Equation (21) [27]. The mixing length is the approximate distance covered by the algae particles Equation (21) [27]. The mixing length is the approximate distance covered by the algae particles while while moving from the inlet to outlet of the reactor at any given instant. To account for the combined moving from the inlet to outlet of the reactor at any given instant. To account for the combined streamwise and transversal mixing of algae particles, the mixing eciency in terms of algae cells streamwise and transversal mixing of algae particles, the mixing efficiency in terms of algae cells received at the outlet boundary of the reactor after going through the mixing process at the last time received at the outlet boundary of the reactor after going through the mixing process at the last time step were calculated. step were calculated. A high value of mass flow rate increases the degree of mixing, coupled with an increase in the A high value of mass flow rate increases the degree of mixing, coupled with an increase in the number of algae cells reaching the outlet (Figure 3a). These findings are consistent with the results of number of algae cells reaching the outlet (Figure 3a). These findings are consistent with the results of Severin et al. [10]. The increase in mass flow rate promotes a larger number of particles to undergo the Severin et al. [10]. The increase in mass flow rate promotes a larger number of particles to undergo mixing process due to the beneficial eect of turbulence. This situation shows that, to some degree, the the mixing process due to the beneficial effect of turbulence. This situation shows that, to some mixing can be managed simply by adjusting the fluid velocities in the reactor [7]. However, high mass degree, the mixing can be managed simply by adjusting the fluid velocities in the reactor [7]. flow rates consequently can require high power consumption. Moreover, the concentration of algal However, high mass flow rates consequently can require high power consumption. Moreover, the cells at the outlet of the upper channel is greater in comparison to the lower channel (Figure 3a). The concentration of algal cells at the outlet of the upper channel is greater in comparison to the lower most possible reason for the acquired results can be attributed to the geometric height to which the channel (Figure 3a). The most possible reason for the acquired results can be attributed to the suspension is delivered onto the upper channel of the reactor, leading to increased cell concentrations geometric height to which the suspension is delivered onto the upper channel of the reactor, leading and improved mixing [4]. to increased cell concentrations and improved mixing [4]. Appl. Sci. 2020, 10, 746 8 of 15 Appl. Sci. 2020, 10, 746 8 of 15 Appl. Sci. 2020, 10, 746 8 of 15 (a) (b) Figure 3. (a) Effect of mass flow rate on mixing efficiency at a water depth of 5.6 mm and slope angle (a) (b) of 1°. (b) Effect of channel width/channel depth on mixing efficiency of the complete reactor at a mass Figure Figure 3 3. .( a (a ) ) E Ef ect fect of of mass mass flow flow rate rate on on mixing mixine g effic ciency ienc at y a a twater a watdepth er depof th 5.6 of 5. mm 6 mm a and slope nd sloangle pe anof gle flow rate of 2.4 kg/s, water depth of 5.6 mm, and slope angle of 1°. 1 of 1°. ( . (b) E b ) ect Effect of channel of channel w width idth/channel dep /channel depth t on h on mixing mixing e ef ciency ficiency of of the the complete reacto complete reactor at r at a a mass mass flow flow rate rate of of 2 2.4.4 kg kg/s, water /s, water depth depth of 5.6 of 5.6 mm, mm, and and slope slope angle angle of 1° of 1 . . A twofold decrease in mixing is observed with the increase in the AR from 180 to 340 (Figure 3b). An increase in channel width decreases the concentration of algae particles at the outlet of the A twofold decrease in mixing is observed with the increase in the AR from 180 to 340 (Figure 3b). A twofold decrease in mixing is observed with the increase in the AR from 180 to 340 (Figure reactor because of the increased reactor volume, thereby indicating that particles find more space to An increase in channel width decreases the concentration of algae particles at the outlet of the reactor 3b). An increase in channel width decreases the concentration of algae particles at the outlet of the move and mix in the reactor. It can be stated that a variation in geometry cause variations in the because of the increased reactor volume, thereby indicating that particles find more space to move and reactor because of the increased reactor volume, thereby indicating that particles find more space to hydrodynamic properties of the reactor, which affect the mixing phenomenon of the cells [29]. A TLC mix in the reactor. It can be stated that a variation in geometry cause variations in the hydrodynamic move and mix in the reactor. It can be stated that a variation in geometry cause variations in the reactor with a small AR and faster flow rates are suitable for microalgae cultivation because of the properties of the reactor, which aect the mixing phenomenon of the cells [29]. A TLC reactor with a hydrodynamic properties of the reactor, which affect the mixing phenomenon of the cells [29]. A TLC significant increase in the cell mixing, provided that the mechanical structure of the algae cells is not small AR and faster flow rates are suitable for microalgae cultivation because of the significant increase reactor with a small AR and faster flow rates are suitable for microalgae cultivation because of the damaged [28,30]. in the cell mixing, provided that the mechanical structure of the algae cells is not damaged [28,30]. significant increase in the cell mixing, provided that the mechanical structure of the algae cells is not damaged [28,30]. Residence Time Residence Time The residence time of algae cells has a vital importance in the design of the photobioreactor. The Residence Time The residence time of algae cells has a vital importance in the design of the photobioreactor. The residence time or retention time of the algae cells is the total time traveled by the particles from the residence time or retention time of the algae cells is the total time traveled by the particles from the The residence time of algae cells has a vital importance in the design of the photobioreactor. The inlet to the outlet of the reactor. The effect of mass flow rate, water depth, and AR on residence time inlet to the outlet of the reactor. The eect of mass flow rate, water depth, and AR on residence time is residence time or retention time of the algae cells is the total time traveled by the particles from the is plotted separately for each compartment of the reactor (Figure 4a–c). The algae particles need more plotted separately for each compartment of the reactor (Figure 4a–c). The algae particles need more inlet to the outlet of the reactor. The effect of mass flow rate, water depth, and AR on residence time time to move from the inlet to the outlet boundary of the reactor when lower mass flow rates are time to move from the inlet to the outlet boundary of the reactor when lower mass flow rates are is plotted separately for each compartment of the reactor (Figure 4a–c). The algae particles need more adopted (Figure 4a). However, faster flow rates reduced the residence time by increasing the flow adopted (Figure 4a). However, faster flow rates reduced the residence time by increasing the flow time to move from the inlet to the outlet boundary of the reactor when lower mass flow rates are velocity. The higher flow velocity in the lower channel resulted in a larger residence time of algae velocity. The higher flow velocity in the lower channel resulted in a larger residence time of algae adopted (Figure 4a). However, faster flow rates reduced the residence time by increasing the flow particles in the lower channel in comparison with the upper channel. particles in the lower channel in comparison with the upper channel. velocity. The higher flow velocity in the lower channel resulted in a larger residence time of algae particles in the lower channel in comparison with the upper channel. (a) (b) Figure 4. Cont. (a) (b) Appl. Sci. 2020, 10, 746 9 of 15 Appl. Sci. 2020, 10, 746 9 of 15 (c) Figure Figure 4. 4. (a (a )) E Ef ect fect of of mass mass flo flow w rate on re rate on residence sidence time time at a at a water depth of water depth of 5.6 mm and 5.6 mm andslo slope pe angle of angle of 1°. ( 1 .b () Residen b) Residence ce time for various water depths at a ma time for various water depths at a mass ss f flow low rate of 2 rate of 2.4 .4 kg kg/s and slope /s and slope angle angle of 1°. of 1 . (c()cResidence ) Residence ti t me ime for diff for dierent erent cha channel nnel width/channel depth ratios at width/channel depth ratios at a mass a flow massrate flow rate of 2. of 2.4 kg/s, water 4 kg/s, depth water depth of of 5.6 mm, 5.6 mm, and slope angle of and slope angle of 1 . 1°. The residence time is strongly influenced by the geometrical aspects of TLC, as evidenced by The residence time is strongly influenced by the geometrical aspects of TLC, as evidenced by the the longer time spent by the algae cells in the reactor with the increased water depth and AR due to longer time spent by the algae cells in the reactor with the increased water depth and AR due to the the increase in reactor volume (Figure 4b,c). The particle tracing methodology in this study does not increase in reactor volume (Figure 4b,c). The particle tracing methodology in this study does not include particle fluid interaction because the computed Stokes number of the algae particles was small. include particle fluid interaction because the computed Stokes number of the algae particles was Therefore, the algae cells follow the fluid stream. The lack of this interaction resists a proportional small. Therefore, the algae cells follow the fluid stream. The lack of this interaction resists a increase in cell residence time with the number of particles introduced at the inlet [25,31]. The residence proportional increase in cell residence time with the number of particles introduced at the inlet time of algae greatly aects the mixing process; a large residence time slows down the mixing process. [25,31]. The residence time of algae greatly affects the mixing process; a large residence time slows Thus, a reactor with a small AR, water depth, and faster flow rates is a suitable option for microalgae down the mixing process. Thus, a reactor with a small AR, water depth, and faster flow rates is a cultivation because of the shorter residence time involved and the good distribution of nutrients, suitable option for microalgae cultivation because of the shorter residence time involved and the sunlight, and CO [32]. good distribution of nutrients, sunlight, and CO2 [32]. 4.2. Hydrodynamic Performance of TLC Reactor 4.2. Hydrodynamic Performance of TLC Reactor 4.2.1. Velocity Magnitude 4.2.1. Velocity Magnitude Microalgae cultivation is velocity sensitive. Thus, an estimation of proper velocity is essential Microalgae cultivation is velocity sensitive. Thus, an estimation of proper velocity is essential neither to provide the settlement of algae cells at the bottom of the reactor nor to be sheared. Liquid neither to provide the settlement of algae cells at the bottom of the reactor nor to be sheared. Liquid velocity is the measure of liquid flow and the extent of turbulence in the reactor. Some degree of velocity is the measure of liquid flow and the extent of turbulence in the reactor. Some degree of turbulence is required in the reactor to ensure that all cells are frequently exposed to light for eective turbulence is required in the reactor to ensure that all cells are frequently exposed to light for effective photosynthesis [33]. photosynthesis [33]. With the increase in mass flow rate and slope angle, an increase in velocity is observed (Figure 5a,d). With the increase in mass flow rate and slope angle, an increase in velocity is observed (Figure The increase in liquid volume with the increase in water depth and AR causes a substantial reduction 5a,d). The increase in liquid volume with the increase in water depth and AR causes a substantial in the flow velocity (Figure 5b,c). The increase in velocity is more significant at a higher mass flow rate reduction in the flow velocity (Figure 5b,c). The increase in velocity is more significant at a higher and particularly at a high slope angle where a sharp increase in velocity is observed. This trend is mass flow rate and particularly at a high slope angle where a sharp increase in velocity is observed. confirmed in Figure 5d. Theses finding indicate that with increased flow velocity (either due to slope This trend is confirmed in Figure 5d. Theses finding indicate that with increased flow velocity (either or mass flow rate), better mixing can be achieved [11,34]. Therefore, to achieve high velocities for the due to slope or mass flow rate), better mixing can be achieved [11,34]. Therefore, to achieve high good mixing of algae cells, TLC reactors with a small AR and water depth and inclined at a higher velocities for the good mixing of algae cells, TLC reactors with a small AR and water depth and slope angle are a good choice. inclined at a higher slope angle are a good choice. Appl. Sci. 2020, 10, 746 10 of 15 Appl. Sci. 2020, 10, 746 10 of 15 Appl. Sci. 2020, 10, 746 10 of 15 (a) (b) (a) (b) (c) (d) (c) (d) Figure 5. Velocity magnitude (a) for different mass flow rates at a water depth of 5.6 mm and slope Figure 5. Velocity magnitude (a) for different mass flow rates at a water depth of 5.6 mm and slope Figure 5. Velocity magnitude (a) for dierent mass flow rates at a water depth of 5.6 mm and slope angle of 2°, (b) for various channel width/channel depth ratios at a mass flow rate of 2.4 kg/s and angle of 2°, (b) for various channel width/channel depth ratios at a mass flow rate of 2.4 kg/s and angle of 2 , (b) for various channel width/channel depth ratios at a mass flow rate of 2.4 kg/s and slope slope angle of 1°, (c) for various water depths at a mass flow rate of 2.4 kg/s and slope angle of 1°, and slope angle of 1°, (c) for various water depths at a mass flow rate of 2.4 kg/s and slope angle of 1°, and angle of 1 , (c) for various water depths at a mass flow rate of 2.4 kg/s and slope angle of 1 , and (d) for (d) for (d) for differen differen t mass flow rat t mass flow rat es at es at a water a water dept dept h of 5.6 h of 5.6 mm and mm and slope angles of slope angles of 1°, 2°, and 3°. 1°, 2°, and 3°. dierent mass flow rates at a water depth of 5.6 mm and slope angles of 1 , 2 , and 3 . Water depths, channel width, and the velocity of the suspension (i.e., Reynolds number) are the W Water depths, channel width, and the velocity of ater depths, channel width, and the velocity of the suspension (i.e the suspension (i.e., ., Re Reynolds ynolds n number) umber) ar are the e the very important parameters for analyzing the fluid pattern in the thin-layer cascade reactor. Velocity very very important important pa parameters rameters f for or a analyzing nalyzing the fl the fluid uid pa pattern ttern i in n the thi the thin-layer n-layer cascade rea cascade reactor ctor. . Vel Velocity ocity contours at constant mass flow rate with the variation in water depth and channel width are contours contours atatconstant constant ma mass ss f flowlow ratera with te wi the th the variation variat inion in w water depth ater depth and and channel width channel widt are presented h are presented in Figures 6 and 7. For better visualization, normalized velocity (U/Umax) has been plotted. in present Figur ees d in 6 and Figu 7res . For 6 and better 7. For b visualization, etter visual normalized ization, norm velocity alized v (Ue/locit U y) (U/ has Ubeen max) ha plotted. s been p U lotted. (m/s) max U (m/s) represents the fluid velocity, and Umax (m/s) is the maximum fluid velocity in the reactor. r U (m/ epresents s) repre thesent fluid s tvelocity he fluid veloc , and U ity, an (m d U /s) max is (m/s) the maximum is the mafluid ximum fluid velocity in the rea velocity in the reactor. ctor. max (a) (b) (a) (b) Figure 6. Cont. Appl. Sci. 2020, 10, 746 11 of 15 Appl. Sci. 2020, 10, 746 11 of 15 Appl. Sci. 2020, 10, 746 11 of 15 (c) (c) Figure 6. Velocity vector plots at a constant mass flow rate of 2.4 kg/s, slope angle of 1°, and various water depths: (a) 5.6 mm, (b) 7.5 mm, and (c) 10 mm. Figure 6. Figure 6. Velo Velocity city vevector ctor plots at plots a at constant a constant mass f mass low rate flow rate of 2.4 of 2.4 kg/s, slo kg/s, slop pe angle of e angle 1° of 1 , and various , and various water depths: ( water depths: a) 5. (a)6 mm, 5.6 mm, (b) ( b 7.5 mm, and ( ) 7.5 mm, and c)( 10 mm. c) 10 mm. (a) (b) (a) (b) (c) Figure 7. Figure 7. Velo Velocity city vevector ctor plots at plots a at constant a constant mass f mass low rate flow rate of 2.4 of kg/s, slo 2.4 kg/s, pe angle of slope angle 1°, of and various 1 , and various channel width/channel depth ratios: (a) channel width/channel depth = 180, (b) channel channel width/channel depth ratios: (a) channel width/channel depth = 180, (b) channel width/channel (c) width/channel depth = 260, and (c) channel width/channel depth = 340. depth = 260, and (c) channel width/channel depth = 340. Figure 7. Velocity vector plots at a constant mass flow rate of 2.4 kg/s, slope angle of 1°, and various With the increase in water depth and AR, a gradual decrement in velocity magnitude is evident. channel width/channel depth ratios: (a) channel width/channel depth = 180, (b) channel The increase in liquid volume with the increase in channel width and water depth causes a substantial width/channel depth = 260, and (c) channel width/channel depth = 340. Appl. Sci. 2020, 10, 746 12 of 15 Appl. Sci. 2020, 10, 746 12 of 15 With the increase in water depth and AR, a gradual decrement in velocity magnitude is evident. The increase in liquid volume with the increase in channel width and water depth causes a substantial reduction in the velocity magnitude. The TLC reactor with the smallest water depth and channel width reduction in the velocity magnitude. The TLC reactor with the smallest water depth and channel width represents the highest velocity magnitude for all the cases considered in this study. represents the highest velocity magnitude for all the cases considered in this study. The cascade is represented by a uniform velocity profile [8]. However, at the inlet section of the The cascade is represented by a uniform velocity profile [8]. However, at the inlet section of lower channel, an abrupt increase in velocity is observed. This increase in velocity magnitude is the lower channel, an abrupt increase in velocity is observed. This increase in velocity magnitude is attributed to the geometrical shape of the flow reversal module, which increases the velocity of fluid. attributed to the geometrical shape of the flow reversal module, which increases the velocity of fluid. The fast-moving fluid failed to follow the geometrical shapes; a recirculation zone is created on the The fast-moving fluid failed to follow the geometrical shapes; a recirculation zone is created on the lower channel. The velocity magnitude reaches its maximum value in this zone, as represented by lower channel. The velocity magnitude reaches its maximum value in this zone, as represented by the the arrow plots. arrow plots. From the algae cell productivity point of view, the TLC reactor is the better choice in comparison From the algae cell productivity point of view, the TLC reactor is the better choice in comparison to the conventional raceway ponds because of the smooth streamlined pattern, thus eliminating the to the conventional raceway ponds because of the smooth streamlined pattern, thus eliminating the need for flow deflectors to make the flow streamline. Moreover, the higher velocity magnitude or need for flow deflectors to make the flow streamline. Moreover, the higher velocity magnitude or turbulent flow in a thin-layer cascade reactor promotes the vigorous mixing of the cells in comparison turbulent flow in a thin-layer cascade reactor promotes the vigorous mixing of the cells in comparison to raceway ponds, where low liquid velocities results in high dead zone volume, thereby directly to raceway ponds, where low liquid velocities results in high dead zone volume, thereby directly affecting the algae cell productivity. aecting the algae cell productivity. 4.2.2. Power Consumption 4.2.2. Power Consumption The hydraulic mixing power consumed by the TLC reactors is the product of flow velocity, The hydraulic mixing power consumed by the TLC reactors is the product of flow velocity, surface surface inclination, and water depth. With the increase in mass flow rate and slope angle, flow inclination, and water depth. With the increase in mass flow rate and slope angle, flow velocity increases velocity increases such that the reactor consumes more power to move the liquid along the reactor such that the reactor consumes more power to move the liquid along the reactor (Figure 8a,c). The (Figure 8a,c). The hydraulic power consumption increases by more than twofold for the slope angle hydraulic power consumption increases by more than twofold for the slope angle of 3 in comparison of 3° in comparison with the reactor inclined at 1°. Higher velocities require considerably more with the reactor inclined at 1 . Higher velocities require considerably more energy. High cell densities energy. High cell densities can be achieved by faster flow rates, but the energy cost to achieve this is can be achieved by faster flow rates, but the energy cost to achieve this is very high [14]. very high [14]. (a) (b) (c) Figure Figure 8. 8. Hydraulic Hydraupower lic power co consumption nsumption ( (a)afor ) for different mass flow rate dierent mass flow ratess a att a water depth of 5.6 mm a water depth of 5.6 mm and slope angle of 1°, (b) for various water depths at a mass flow rate of 2.4 kg/s and slope angle of and slope angle of 1 , (b) for various water depths at a mass flow rate of 2.4 kg/s and slope angle of 1 , 1°, and (c) for the complete reactor with the variation in mass flow rate and slope angle. and (c) for the complete reactor with the variation in mass flow rate and slope angle. Moreover, an increase in water depth resulted in the slow movement of fluid, which indicates that the reactor with increased water depth requires more power to move the liquid along the reactor (Figure 8b). In other words, greater reactor dimensions require greater power. The hydraulic power Appl. Sci. 2020, 10, 746 13 of 15 required by each compartment of the reactor is presented in Figure 8a. The power required by the lower channel of the reactor is greater than that required by the upper channel because of the flow reversal module. The flow reversal module directs the fluid at the lower channel by increasing the flow velocity in the lower channel. The high velocity results in increased power consumption in the lower channel. 5. Conclusions A three-dimensional CFD model was developed to evaluate the algae cell mixing features and hydrodynamic performance of a TLC reactor. Numerical simulations were performed considering the dierent geometrical variations (water depth, slope angle, and channel width) of the reactor. A comparison in terms of the average velocity was made with the reference experimental data of Apel et al. [11]. The reactor dimensions significantly aected the algae cell mixing and hydrodynamic performance of the TLC reactor. The subsequent conclusion can be derived from the numerical calculation of present study. The mixing process is more eective when the reactor has narrow geometry and operates at high mass flow rates. The residence time of algae cells increases with the increase in water depth and aspect ratio. The increases in liquid volume with the increase in channel width and water depth causes a substantial reduction in the velocity magnitude. The hydraulic power consumption required to move the liquid along the channel increases with the increase in mass flow rate, slope angle, and water depth. In order to achieve high mass densities of microalgae in the TLC reactor, an optimal inclination of the surface must be adopted to reduce the power consumption without decreasing the productivity of algae due to a low liquid velocity, causing lower turbulence. Therefore, a detailed design optimization study of the TLC reactor is recommended to overcome this compromised situation. Author Contributions: All the authors were involved in the conception and design of the study. All the simulations, analysis, and interpretation of data have been done by S.A. and supported by H.A. and C.W.P. The manuscript was written by S.A. and H.A. The work was supervised and supported for improvement with critical questions by C.W.P. The paper review and edit was done by C.W.P. All authors have read and agreed to the published version of the manuscript. Acknowledgments: This study was supported by a grant from the National Research Foundation of Korea grant funded by the Korea government (No. 2017R1A2B2005515). Conflicts of Interest: The authors declare no conflict of interest. Nomenclature A cross sectional area, m I inclination of surface (-) D hydraulic diameter, m AR aspect ratio, (-) Re Reynolds number, (-) Q volumetric flow rate, m /s u velocity vector, m/s St Stokes number (-) I identity matrix E hydraulic power, W/m U time-averaged velocity, m/s Greek symbols L length, m water density, kg/m m mass flow rate, kg/s water viscosity, Pa. s W channel width, m turbulent viscosity, Pas M mixing length, m algae cell density, kg/m R residence time, s ! turbulent dissipation rate, 1/s F drag force, N u chlorella cell velocity, m/s d algae cell diameter, m relaxation time, s p p d channel depth, m Prandtl number for dissipation rate 2 2 k turbulent kinetic energy, m /s Prandtl number for kinetic energy k Appl. Sci. 2020, 10, 746 14 of 15 References 1. Mata, T.M.; Martins, A.A.; Caetano, N.S. Microalgae for Biodiesel Production and Other Applications: A Review. Renew. Sustain. Energy Rev. 2010, 14, 217–232. [CrossRef] 2. 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