Application of Vortex Induced Vibration Systems to Improve Vertical Mixing and Create Light/Dark Cycles for Enhanced Algal Biomass Productivity in Raceway Ponds

: Limited light availability due to insufﬁcient vertical mixing is one of the main drawbacks of raceway ponds (RWPs), the most common type of microalgae cultivation system. In this study, we have investigated the application of vortex induced vibration (VIV) systems to improve vertical mixing in order to enhance algal biomass productivity. The system consists of a cylinder submerged parallel to the bottom in the pond with two springs attached at its ends. The cylinder oscillates perpen-dicularly to the ﬂow direction at the pond to increase vertical mixing. A VIV system, which requires no additional energy input, was installed in a 0.3 m deep raceway pond and continuous cylinder oscillation was successfully achieved. Cylinder oscillation frequency of 1.24 s − 1 and amplitude of 6.5 cm have been obtained experimentally for 0.3 m s − 1 ﬂow velocity. Numerical simulations were carried out with experimental parameters using CFD code and were in good accordance with experimental results. Numerical analysis revealed that it is possible to create high frequency light/dark cycles; mean light/dark cycle frequencies were found to be 2.33 s − 1 , 5.28 s − 1 and 21.17 s − 1 , at lowermost, middle and uppermost cylinder positions, respectively. Enhanced velocity magnitude of 0.3 m s − 1 was achieved in the vertical direction; vertical motion of ﬂow resulting from cylinder oscillation covers about two thirds of pond depth. Effectiveness of the VIV system on biomass growth was also veriﬁed by comparative Chlorella vulgaris cultivation under outdoor conditions. It has been observed that the VIV system installed reactor enhanced biomass production capacity by over 20% compared to the control pond. These results indicate that the presented method possesses a potential for enhanced algal biomass production without signiﬁcant increase in installation and operating costs.


Introduction
Microalgae have attained considerable attention in the last decades as a promising feedstock for biofuels, as well as for their high potential to produce pigments, food and feed supplements, pharmaceuticals and other high value chemicals [1][2][3].They also have applications in the field of environmental engineering for removal of pollutants from wastewater.
Raceway Ponds (RWPs) are the most common microalgae cultivation systems for commercial purposes as well as for wastewater treatment; over 90% of commercial scale microalgae production occurs in this type of system [4,5].The main advantages of raceway ponds over closed photobioreactor systems for microalgae production are their lower capital and operating costs, operating simplicity and scalability [5].However, their biomass production capacity is lower due to a number of reasons including vulnerability to environmental and climatic conditions, high risk of contamination and poor mixing.
Mixing is of particular importance among the factors that determine biomass productivity of RWPs since it influences gas to liquid mass transfer, cell-nutrient contact, frequent exposure of cells to sunlight, gas exchange, and it prevents thermal stratification [2,6,7].Light availability in RWPs, which is among the main parameters for microalgae growth, is directly linked to vertical mixing.Grobbelaar [8] reported that increase in biomass production due to enhanced vertical mixing is due to increasing cell-nutrient contact and nutrient uptake, along with increasing light availability.Light availability in RWPs should be increased for enhanced biomass productivity as algal cells should periodically be exposed to sunlight, which is hard to achieve in long channels of RWPs [9].It has been reported that very limited vertical mixing in the straight channel sections of RWPs is to be expected [5].While Murphy et al. [10] reported that around 90% of net O 2 production in raceway ponds is limited to the first 12-13 cm of the culture, Sutherland et al., (2015) reported that up to one third of water column in RWPs receive insufficient light to support net photosynthesis.Furthermore, Borowitzka et al. [11] stated that light availability further decreases in RWPs when used for wastewater treatment.Furthermore, channel length of RWPs can be increased by up to more than 1 km [12], which means that most of the biomass would reside in regions of ponds for a prolonged period where there is not enough light energy to photosynthesize.Thus, it is essential to cycle biomass between euphotic and non-euphotic parts of the pond in these long straight channels for improved biomass productivity.Therefore, vertical mixing in raceway ponds seems to be more important than axial mixing since it directly defines light availability for cells.Along with light availability, light utilization efficiency is also an important factor that effects biomass production capacity of RWPs [13].Creating vortex flow fields in ponds is known to create light/dark (L/D) cycles for cells to utilize so called the flashing light effect, as well as improving gas to liquid mass transfer [14][15][16].
There has been an ongoing effort to improve vertical mixing and L/D cycle frequencies (f L/D ) in RWPs.Increasing turbulence of the flow by increasing flow velocity is perhaps the most straightforward approach to improving vertical mixing; however, it is also energy intensive.Installing more bends or paddlewheels can increase vertical mixing but they also increase energy consumption since most of the head loss in RWPs arises from the bend sections [17].A number of researchers tried to improve light availability by creating vortices and directing flow upwards.The methods developed for this purpose are mainly the installation of static structures to flow field such as up-down chute baffles, foil wings or conic baffles.While it has been possible to improve biomass productivity considerably by the above mentioned methods, depth is very limited in these works, e.g., 6-10 cm [3,14,18,19], which would cause huge area demand and increased evaporation losses.Furthermore, paddlewheel speed in most of these studies was kept increasingly high, e.g., 30 to 50 rpm.
Vortex induced vibration is a form of flow induced motion whereby a body becomes excited, with vortices shed from its surface.It is notorious for its tremendous damage in engineering applications in many different fields, as it can devastate mega structures such as skyscrapers, bridges, offshore platforms, etc. Leonardo Da Vinci's Aeolian Tones is the first known application of VIV which dates back to the start of the 16th century [20].Ever since, engineers have been trying to suppress this destructive phenomenon.Imagine a stationary cylinder in a fluid.When the cylinder is exposed to a flow (in the +x direction in Figure 1), vortices shed.These vortices separate from the surface of the cylinder forming the famous Karman Vortex Street in the wake zone, which can be seen in Figure 1.
These vortices, when they shed and leave the surface, exert force on the cylinder.Directions of forces can be seen in Figure 2. When a vortex separates from the top part, the cylinder feels a downward force, pushing it in the −z direction (second image in Figure 2).When it separates from the bottom, the direction of the force is then upwards and pushes the cylinder to go in the +z direction (third image in Figure 2).However, the cylinder is forced to be stationary and does not move.
These vortices, when they shed and leave the surface, exert force on the cylinder.Directions of forces can be seen in Figure 2. When a vortex separates from the top part, the cylinder feels a downward force, pushing it in the -z direction (second image in Figure 2).When it separates from the bottom, the direction of the force is then upwards and pushes the cylinder to go in the +z direction (third image in Figure 2).However, the cylinder is forced to be stationary and does not move.When the cylinder is allowed to move in the direction perpendicular to the flow (z axis), the forces exerted on the cylinder by the vortices will actually make the cylinder move up and down.This is a periodic motion and will last forever as the fluid continues to flow.Vortex induced vibrations make use of the flow energy and convert this power of the fluid to oscillate the cylinder.In this study, we are trying to increase vertical mixing in the pond without applying any additional energy input into the system.A typical VIV setup consists of a cylinder connected to the main frame by two elastic springs.The cylinder is totally submerged in water and constrained to move only in the axis.An illustrative drawing is given in Figure 3. pushes the cylinder to go in the +z direction (third image in Figure 2).However, the cylinder is forced to be stationary and does not move.When the cylinder is allowed to move in the direction perpendicular to the flow (z axis), the forces exerted on the cylinder by the vortices will actually make the cylinder move up and down.This is a periodic motion and will last forever as the fluid continues to flow.Vortex induced vibrations make use of the flow energy and convert this power of the fluid to oscillate the cylinder.In this study, we are trying to increase vertical mixing in the pond without applying any additional energy input into the system.A typical VIV setup consists of a cylinder connected to the main frame by two elastic springs.The cylinder is totally submerged in water and constrained to move only in the axis.An illustrative drawing is given in Figure 3.When the cylinder is allowed to move in the direction perpendicular to the flow (z axis), the forces exerted on the cylinder by the vortices will actually make the cylinder move up and down.This is a periodic motion and will last forever as the fluid continues to flow.Vortex induced vibrations make use of the flow energy and convert this power of the fluid to oscillate the cylinder.In this study, we are trying to increase vertical mixing in the pond without applying any additional energy input into the system.
A typical VIV setup consists of a cylinder connected to the main frame by two elastic springs.The cylinder is totally submerged in water and constrained to move only in the axis.An illustrative drawing is given in Figure 3.  Springs are not required for vortex-induced vibrations to oscillate the cylinder bu they help in regulating its motion.This system can be mathematically defined by th widely known equation where mosc represents the total oscillating mass (all moving parts including one third o spring mass), c the mechanical damping, k the total spring stiffness and the Ffluid(t) forc applied on the cylinder by the fluid.Z(t) is the vertical displacement of the cylinder an its derivatives  ) and  ) are its velocity and acceleration, respectively. ),  )  ) and Ffluid(t) are functions of time, as the notations imply.As the fluid continues t flow, it generates Ffluid(t) on the cylinder which leads to continuous cylinder oscillation.Mass ratio, which is defined as ratio of oscillating mass/mass of oscillating parts o the system to displaced mass, is calculated with the following equation: Springs are not required for vortex-induced vibrations to oscillate the cylinder but they help in regulating its motion.This system can be mathematically defined by the widely known equation m osc ..
where m osc represents the total oscillating mass (all moving parts including one third of spring mass), c the mechanical damping, k the total spring stiffness and the F fluid (t) force applied on the cylinder by the fluid.Z(t) is the vertical displacement of the cylinder and its derivatives .z(t) and .. z(t) are its velocity and acceleration, respectively.z(t), . z(t), .. z(t) and F fluid (t) are functions of time, as the notations imply.As the fluid continues to flow, it generates F fluid (t) on the cylinder which leads to continuous cylinder oscillation.
Mass ratio, which is defined as ratio of oscillating mass/mass of oscillating parts of the system to displaced mass, is calculated with the following equation: Natural frequency of the cylinder/r in still water is calculated by: Here, m a represents the added mass and it is calculated by m a = C a m d where C a is the added mass coefficient and it is taken as C a = 1 in still water.Damping ratio ζ is given by the equation As stated previously, the cylinder should be oscillating with as large an amplitude as possible to ensure the highest vertical mixing.This happens when the cylinder's natural frequency is synchronized with the vortex shedding frequency, a range which is called "lock-in".In this special region, the cylinder is in the upper branch and the vortex shedding is in phase with the oscillation of the cylinder.The upper branch is generally in between 5 < U * < 10 ( Govardhan and Williamson, 2000).Here, U * is the reduced velocity, mathematically identified by the equation: The amplitude is non-dimensionalized by the cylinder diameter and mathematically given as This study aims to investigate possible implementation of vortex induced vibration (VIV) systems, which require no additional energy input and no obstructing fixed structures in the flow path, to improve vertical mixing for the enhancement of algal biomass productivity.

Experimental Methods and Setup
In the context of the study, VIV setup was implemented to a raceway pond with 3 m channel length and 1 m total channel width as shown in Figure 4. VIV cylinder is positioned at 1.3 m downstream of the paddlewheel.VIV Setup consists of oscillator particulars, which were selected with respect to pond depth.Cylinder diameter should be around 1/5 of the water depth at maximum [2], so that it can move freely without any interference from the free water surface or the bottom wall.Thus, cylinder diameter (D) was set as 0.06 m as experiments were held in water level of 0.3 m and flow velocity of U = 0.3 m s −1 (12 rpm paddlewheel velocity) to reflect realistic conditions.A general illustration of the system and its details are shown in Figure 4. Oscillator particulars installed in the pond consist of a cylinder, reels, springs, reel beddings and a frame that beddings are mounted on, as shown in Figures 4 and 5.The cylinder is connected to reels via an aluminium lamellar, on which the reel is mounted.Same of the lammelars are in turn connected to springs.
from the free water surface or the bottom wall.Thus, cylinder diameter (D) was set as 0.06 m as experiments were held in water level of 0.3 m and flow velocity of U = 0.3 m s −1 (12 rpm paddlewheel velocity) to reflect realistic conditions.A general illustration of the system and its details are shown in Figure 4. Oscillator particulars installed in the pond consist of a cylinder, reels, springs, reel beddings and a frame that beddings are mounted on, as shown in Figures 4 and 5.The cylinder is connected to reels via an aluminium lamellar, on which the reel is mounted.Same of the lammelars are in turn connected to springs.With the flow, VIV motion starts and as illustrated in Figure 6 and shown in the video (Online Resource); the cylinder begins moving downwards from its initial (neutral) position perpendicular to flow direction, until reaching its extreme bottom (lowermost position).After this, it starts moving up until its extreme height (uppermost position) and eventually starts to go down back to its initial position to cover one oscillation.The cylinder is positioned as its center and will be 9 cm below water surface, where the oscillation with the highest amplitude was observed.
The VIV motion was captured by the open-source electronics platform, Arduino (https://www.arduino.ccaccessed at: 11 November 2022).Arduino boards have a number of facilities for communicating with computers, other boards, sensors, microcontrollers, etc.A functional code was developed to run with 16 MHz clock speed Arduino Mega 2560 board.A pair of compatible ultrasonic sensors were used to receive the reflecting sound waves over moving components of the VIV system.The sensor can store 40 data points a  Experiments were conducted in the raceway pond taking consideration of the VIV response of the circular cylinder.Govardhan and Williamson [21] described various branches associated with VIV and it is stated in their paper that the highest oscillation amplitude occurs in the region called the "upper branch".In our study, we tried to maximize the motion of the cylinder to increase the light availability for microalgae.Therefore, our experimental setup was fixed to a reduced velocity of U*=5 at which the upper branch is expected to be initiated.Parametric details of the VIV system installed on the RWP are presented in Table 1.With the flow, VIV motion starts and as illustrated in Figure 6 and shown in Supplementary Materials; the cylinder begins moving downwards from its initial (neutral) position perpendicular to flow direction, until reaching its extreme bottom (lowermost position).After this, it starts moving up until its extreme height (uppermost position) and eventually starts to go down back to its initial position to cover one oscillation.The cylinder is positioned as its center and will be 9 cm below water surface, where the oscillation with the highest amplitude was observed.Experiments were conducted in the raceway pond taking consideration of the VIV response of the circular cylinder.Govardhan and Williamson [21] described various branches associated with VIV and it is stated in their paper that the highest oscillation amplitude occurs in the region called the "upper branch".In our study, we tried to maximize the motion of the cylinder to increase the light availability for microalgae.Therefore, our experimental setup was fixed to a reduced velocity of U*=5 at which the upper branch is expected to be initiated.Parametric details of the VIV system installed on the RWP are presented in Table 1.
Here; ρ is the fluid density, u i is the flow velocity components, p is the pressure, µ is the dynamic viscosity and F i is the external (gravitational) force.The overbar ( ) represents the mean flow parameters in time.Equation (7) was solved together with the continuity equation and the last term at the right hand side is the turbulence term.This term is discretized with respect to the selected turbulence model.In this study, the k -ω SST model, which is the most suitable turbulence model for solving flow around bluffy bodies, was implemented.Details of the turbulence model can be found in [22] and its suitability of application to VIV problems in [23].

CFD Solution and Boundary
Numerical simulations were used as a supplement to the experimental setup for two distinct purposes: for validation of the VIV response of the cylinder obtained at the raceway pond experimentally to visualize the flow in order to gain insight into the vorticity field and flow velocities in the fluid domain.
Vortex-induced vibration of a smooth circular cylinder was numerically solved by implementing the Reynolds-Averaged Navier-Stokes Equations (RANSE) based computational fluid dynamics method (CFD).Finite volume method was used to solve the viscous flow.The cylinder was only allowed to move perpendicular to the flow and motions in other axes are constrained.The flow was two dimensional (2D) and tip-flow effects are neglected.2D flows are ideal and assume that there are no cross-flows, cellular shedding or tip-flows, but this greatly reduces computational cost of numerical simulations and is widely used to understand the physics of VIV.Losses due to three-dimensionality of the flow were compensated by the approach described by Duranay and Kinaci [24].CFD software ANSYS Fluent 14.0 is used in this study.
The rectangular fluid domain around the cylinder rather large; this represents the cylinder diameter.The domain was divided into two regions: - The first domain is called the moving domain and surrounds the cylinder.The mesh is structured in this region and the elements are quadrilateral.The size of this inner rectangular domain is 17D × 6D.Number of elements in this region is around 7000. - The second domain is called the stationary domain and surrounds the moving domain.
The mesh is unstructured in this region and the elements are triangular.This is the outer domain and covers the rest of the fluid domain.Number of elements in this region is around 5000.
A total of 12,000 grids consisting of triangular and quadrilateral elements represent the fluid domain.The moving domain was allowed to move perpendicular to the flow inside the stationary domain.During the motion of the moving domain, elements in the stationary domain were remeshed at each time step.Therefore, elements in the stationary domain were deforming while elements in the moving domain were non-deforming.Figure 7 shows the general view of the computational domain.
k -ω SST was selected as the turbulence model to solve the turbulent flow around the bluff body, as mentioned in the previous section.Pressure and velocity were coupled by the SIMPLE algorithm.Momentum, turbulent kinetic energy and specific dissipation rate were first-order upwind.The time step size was selected according to the CFL condition and was 2.5 × 10 −3 s.For better resolution of the flow in the vicinity of the cylinder, residuals should be kept as low as possible.Therefore, inner iterations at each time step were selected as 50, while inlet velocity is set as 0.3 m s −1 , as in the experiments.Flow around cylinder was first solved with a steady approach and results from the steady state mode were used as initial conditions for transient calculations.The model was run for 10 s until dynamic equilibrium was reached.A functional code was developed to capture VIV motion, using equations described previously and implemented to the model as user defined function.Numerical output was processed by Fluent's post-processing tool.Details of the boundary conditions are given in Table 2.More details of numerical implementation can be found in [23,25]. -  was selected as the turbulence model to solve the turbulent flow around the bluff body, as mentioned in the previous section.Pressure and velocity were coupled by the SIMPLE algorithm.Momentum, turbulent kinetic energy and specific dissipation rate were first-order upwind.The time step size was selected according to the CFL condition and was 2.5 × 10 −3 s.For better resolution of the flow in the vicinity of the cylinder, residuals should be kept as low as possible.Therefore, inner iterations at each time step were selected as 50, while inlet velocity is set as 0.3 m s −1 , as in the experiments.Flow around cylinder was first solved with a steady approach and results from the steady state mode were used as initial conditions for transient calculations.The model was run for 10 s until dynamic equilibrium was reached.A functional code was developed to capture VIV motion, using equations described previously and implemented to the model as user defined function.Numerical output was processed by Fluent's post-processing tool.Details of the boundary conditions are given in Table 2.More details of numerical implementation can be found in [23] and [25].The center of the cylinder was located at X = 0 and Y = 0 in the beginning of the simulation.Only transverse motions are covered in this study; the cylinder will only move along the Y axis, while its X position will not change.

Evaluation of Vertical Mixing and L/D Cycles
Flow field and vortices created by VIV motion are important to understand vertical mixing and L/D cycles in the pilot scale RWP.While methods such as laser doppler anemometry (LDA) and particle image velocimetry (PIV) have been frequently used for flow visualization, CFD has been proved to be a reliable method for investigation of flow fields [26].Chiarini and Quadrio [27] assumed that algal cells followed flow streamlines when analyzing cell mixing and trajectories, while Xu et al. [9] treated cells as massless particles in their numerical studies.In this view, it would be safe to investigate the extent of vertical mixing and frequencies of L/D cycles based on vorticity data and flow streamlines.
As mentioned before, the cylinder moves in a perpendicular direction.With the start of VIV motion, vortex sheds at its near wake.Vortex area created by cylinder motion grows in both horizontal and vertical directions as the cylinder moves upwards and downwards.In the context of this study, it will be assumed that the extent of VIV-induced vertical mixing is dependent on the highest location of vortices and flow streamlines in a vertical direction.Angular velocity (Ω) is defined as the rotation rate of an object around a fixed location, which corresponds to the light to dark transition plane in our study.This is in turn equal to half of the vorticity magnitude (ω) (see [28], Section 7.7.1.) Thus, in the context of this study, L/D cycle frequencies were expressed as half of the vorticity magnitudes at the light to dark transition plane.In two-dimensional flows, L/D cycle frequency (s −1 ) is denoted by the expression; The critical point for light to dark transition is not constant for cultivation systems; it depends on biomass/solids concentration, color of media (for wastewater cases), as well as strain and species, and finally time of the day and season, due to varying solar irradiance.Luhtala and Tolvanen [29] assumed light depth where local intensity drops below 1% of incident intensity to be the dark region in reactors, while Moberg et al. [30] proposed light to dark volume ratio as 1:9 for closed photobioreactors.This approach was adopted to 30 cm deep RWP by Chen et al. [27], which was similar to our case.As the presented method is not suggested for certain species and/or operating conditions, we are in a position to make estimations accepted in the literature in order to assess the location of the L/D transition plane.Thus, the light to dark transition plane was assumed to be 3 cm below the culture surface in the present study.
For the investigation of L/D cycles, three equidistant positions of cylinder were considered; uppermost, neutral (middle) and lowermost positions (see Figure 6).Mean L/D cycle frequencies calculated in this study were for 10, 20, 30, 40, 50 and 60 cm downstream of the cylinder.

Microalgae Growth Experiments with and without VIV System
Pure culture of Chlorella vulgaris was obtained from Cukurova University Faculty of Aquaculture (Adana, Turkey).Inoculum was grown in 10 L plastic bottles in Bold's Basal Medium (BBM) and the same medium was used for outdoor cultivation.There were three identical pilot scale RWPs on the roof of Istanbul Technical University Department of Environmental Engineering, with dimensions described under Section 2.1.As ponds were operated at 30 cm depth, the volume of each pond was 1335 L. VIV system was installed to the 1st pond and the 2nd pond was used as control.First, the culture grown in the laboratory was transferred to the 3rd pond and cultivated for one week to acclimate the diurnal cycle, as well as outdoor weather conditions.After this, inoculum was transferred to the 1st pond with VIV (V-RWP) and the 2nd pond (conventional RWP).To make sure identical ponds demonstrated the same biomass production performance, VIV system was removed from V-RWP and two ponds were operated under the same hydrodynamic conditions for one week.Then, the VIV system was installed to V-RWP and biomass production was monitored and compared with the conventional RWP.Cell growth was monitored by optical density (OD) measurements at 540, 680 and 750 nm wavelengths using BioRad SmartSpec spectrophotometer (Hercules, CA, USA).Outdoor experiments were held in October and November.

Experimental Pilot Scale VIV Cylinder Oscillation
Cylinder oscillation of A* = 0.54 was achieved experimentally, which means the cylinder covers 6.5 cm in the vertical direction through the pond depth, with a frequency of 1.24 s −1 .In Figure 8, y axis shows the amplitude response of VIV system obtained experimentally, while x axis shows data points captured by Arduino.Pan et al. [31] obtained similar A* responses at U* values near 5, while Khalak and Williamson [32] and Wanderley et al. [33] reached A* = 1 in same U*.On the other hand, Duranay and Kinaci [24] observed A* values higher than 1 at U* = 3.Furthermore, Kinaci [23] obtained A* > 1 at U* = 5.Different amplitude responses arise from flow characteristics, as well as difference in oscillator particulars such as cylinder diameter and oscillating mass.
in October and November.

Experimental Pilot scale VIV Cylinder Oscillation
Cylinder oscillation of A* = 0.54 was achieved experimentally, which means the cylinder covers 6.5 cm in the vertical direction through the pond depth, with a frequency of 1.24 s −1 .In Figure 8, y axis shows the amplitude response of VIV system obtained experimentally, while x axis shows data points captured by Arduino.Pan et al. [31] obtained similar A* responses at U* values near 5, while Khalak and Williamson [32] and Wanderley et al. [33] reached A*= 1 in same U*.On the other hand, Duranay and Kinaci [24] observed A* values higher than 1 at U* = 3.Furthermore, Kinaci [23] obtained A* > 1 at U* = 5.Different amplitude responses arise from flow characteristics, as well as difference in oscillator particulars such as cylinder diameter and oscillating mass.Relatively low amplitude response (A* < 1) in the experiments is thought to be due to irregular flow characteristics resulting from paddlewheel motion.Higher amplitudes may be achieved by increasing the aspect ratio of cylinder and introducing passive turbulence control, or PTC.PTC is a method to trigger galloping (a flow regime in which the cylinder oscillates at very high amplitudes and frequency) by introducing roughness to some selected parts of the cylinder [34].
For the greatest vertical mixing that can be achieved from VIVs, it is obvious that A* should be kept at a maximum.However, amplitude is not the only parameter that can enhance vertical mixing.Vertical mixing is actually associated with the power (P) available in the fluid, which can be defined by Equation (10); Flow velocities in real scale RWPs vary between 0.2 to 0.5 m s −1 (Mendoza et al., 2013 [5]).According to the above-mentioned equation, doubling the flow velocity in RWP will increase the power in the fluid by eightfold.Additionally, real scale RWPs have higher channel widths.An increase in the cylinder length will also enhance the vertical mixing process in the pond.

Numerical Investigation of Vertical Mixing and L/D Cycles
Table 3 shows the comparison of experimental and numerical simulation results using similar input parameters.
Contours in Figure 9 were captured when the cylinder is at its neutral position (see Figure 6), moving up (below contour) and down (above contour).Center of the cylinder is at Y = 21 cm for a 30 cm deep RWP.As can be observed from Table 3, similar input parameters, amplitude and oscillation frequencies obtained with numerical simulation and experiments were in good accordance.Thus, it is believed that numerical simulations can be used to visualize the flow to gain insight into the physical aspects associated with vertical mixing.As the cylinder moves, its center reached Y = 17.75 cm at lowermost and Y = 24 at uppermost positions.Bottom of the cylinder will be at Y ~ 15 cm and top of the cy will be at Y ~ 27 cm at these positions, respectively, if the greatest extent of vertical m is to be considered.As seen in Figure 9, vertical motion of flow covered about two of pond depth.Light availability, which depends on vertical mixing, is regarded most important factor effecting biomass productivity in RWPs and is essential for su able algal biomass production [35].Light limited growth, when light availability only factor to effect overall biomass productivity can be achieved in dilute cultures light can penetrate into culture sufficiently to support net photosynthesis.Howev erating RWPs with low biomass concentration results in lower biomass productivit thermore, harvesting costs will very much increase in this case, as water to be rem per dry matter will substantially increase.For RWPs, tubular and flat panel photo actors, Norsker et al. [36] estimated biomass production costs per kg biomass as 4.16 € and 5.96 €, respectively, as closed systems can be operated with much high mass concentrations.On the other hand, mixing costs were estimated as 0.08 €, 1.27 3.10 € per kg biomass for these three systems.Thus, operating RWPs with increase mass concentration would significantly improve the economics of algae based pro However, for RWPs with dense cultures, not all the cells can receive sufficient amo light for photosynthesis as light intensity through the depth of RWPs declines sharp mentioned above, it has been reported that around 90% of net O2 production in RW limited to first 12-13 cm of the culture [10] while non -euphotic portion of RWPs up to one third of water column [13].To overcome this, biomass in the long straigh nels of RWPs should be periodically cycled between euphotic and non-euphotic p Above contour is captured when cylinder is moving down, below contour is captured when cylinder is moving up.
As the cylinder moves, its center reached Y = 17.75 cm at lowermost and Y = 24.25 cm at uppermost positions.Bottom of the cylinder will be at Y ~15 cm and top of the cylinder will be at Y ~27 cm at these positions, respectively, if the greatest extent of vertical motion is to be considered.As seen in Figure 9, vertical motion of flow covered about two thirds of pond depth.Light availability, which depends on vertical mixing, is regarded as the most important factor effecting biomass productivity in RWPs and is essential for sustainable algal biomass production [35].Light limited growth, when light availability is the only factor to effect overall biomass productivity can be achieved in dilute cultures, when light can penetrate into culture sufficiently to support net photosynthesis.However, operating RWPs with low biomass concentration results in lower biomass productivity.Furthermore, harvesting costs will very much increase in this case, as water to be removed per dry matter will substantially increase.For RWPs, tubular and flat panel photobioreactors, Norsker et al. [36] estimated biomass production costs per kg biomass as 4.95 €, 4.16 € and 5.96 €, respectively, as closed systems can be operated with much higher biomass concentrations.On the other hand, mixing costs were estimated as 0.08 €, 1.27 € and 3.10 € per kg biomass for these three systems.Thus, operating RWPs with increased biomass concentration would significantly improve the economics of algae based products.However, for RWPs with dense cultures, not all the cells can receive sufficient amount of light for photosynthesis as light intensity through the depth of RWPs declines sharply.As mentioned above, it has been reported that around 90% of net O 2 production in RWPs is limited to first 12-13 cm of the culture [10] while non-euphotic portion of RWPs can be up to one third of water column [13].To overcome this, biomass in the long straight channels of RWPs should be periodically cycled between euphotic and non-euphotic parts of the pond depth.
Streamlines in Figure 9 indicate VIV-induced vertical motion of fluid covered pond depth from about Y = 8 cm to about Y = 30 in one oscillation period and directed cells near surface parts of the pond.With continuous cylinder oscillation, cells were directed to uppermost parts of the pond with a vertical velocity of 0.3 m s −1 when cylinder is moving down, which is the highest reported magnitude in RWPs, to the authors' knowledge, without increasing operating costs.It is noteworthy that vertical velocity achieved in the wake of the cylinder was as high as horizontal velocity.This was due to relatively high cylinder oscillation frequency.As the cylinder moves downwards, cells were directed to more photobiologically favored zones of the pond, with varying vertical velocity magnitudes.When the cylinder moves up, it creates downward flow in its downstream.As cylinder oscillates continuously, cells were either directed to euphotic or non-euphotic parts of the channel.Thus, keeping in mind that light intensity decreases exponentially in RWPs, VIV motion effectively cycled cells between euphotic and non-euphotic parts through the pond depth, which would substantially increase overall light availability for cells, most of which otherwise would be residing in the zones where there is not enough light energy for net photosynthesis.
Flow velocities in real scale RWPs vary between 0.2 to 0.5 m s −1 [5].According to Equation (10), doubling the flow velocity in RWP will increase the power in the fluid by eightfold.Additionally, real scale RWPs have higher channel widths.An increase in the cylinder diameter will also enhance the vertical mixing process in the pond.
Compared to the studies in the literature, we could achieve significantly higher L/D frequencies with our novel VIV system for 0.3 m depth and 0.3 m s −1 horizontal flow velocity, which are common for full scale RWPs.
As Figures 10 and 11 denote, VIV motion created vortices, a process which is directly linked to both light utilization efficiency and gas to liquid mass transfer, with magnitudes significantly higher than those reported in the literature.Contour in Figure 12 is captured when the cylinder was at its lowermost position, which indicates that effective shedding of vortices through the pond surface was not limited to certain positions of cylinder.On the other hand, as seen in Figure 11, when the cylinder is moving up, vortex shedding direction is through the pond bottom.Mean L/D cycle frequencies for first 10, 20, 30, 40, 50 and 60 cm after the cylinder at light to dark transition plane, for uppermost, neutral and lowermost cylinder positions, are shown in Table 4.
down, which is the highest reported magnitude in RWPs, to the authors' knowledge, without increasing operating costs.It is noteworthy that vertical velocity achieved in the wake of the cylinder was as high as horizontal velocity.This was due to relatively high cylinder oscillation frequency.As the cylinder moves downwards, cells were directed to more photobiologically favored zones of the pond, with varying vertical velocity magnitudes.When the cylinder moves up, it creates downward flow in its downstream.As cylinder oscillates continuously, cells were either directed to euphotic or non-euphotic parts of the channel.Thus, keeping in mind that light intensity decreases exponentially in RWPs, VIV motion effectively cycled cells between euphotic and non-euphotic parts through the pond depth, which would substantially increase overall light availability for cells, most of which otherwise would be residing in the zones where there is not enough light energy for net photosynthesis.
Flow velocities in real scale RWPs vary between 0.2 to 0.5 m s −1 [5].According to Equation (10), doubling the flow velocity in RWP will increase the power in the fluid by eightfold.Additionally, real scale RWPs have higher channel widths.An increase in the cylinder diameter will also enhance the vertical mixing process in the pond.
Compared to the studies in the literature, we could achieve significantly higher L/D frequencies with our novel VIV system for 0.3 m depth and 0.3 m s −1 horizontal flow velocity, which are common for full scale RWPs.
As Figures 10 and 11 denote, VIV motion created vortices, a process which is directly linked to both light utilization efficiency and gas to liquid mass transfer, with magnitudes significantly higher than those reported in the literature.Contour in Figure 12 is captured when the cylinder was at its lowermost position, which indicates that effective shedding of vortices through the pond surface was not limited to certain positions of cylinder.On the other hand, as seen in Figure 11, when the cylinder is moving up, vortex shedding direction is through the pond bottom.Mean L/D cycle frequencies for first 10, 20, 30, 40, 50 and 60 cm after the cylinder at light to dark transition plane, for uppermost, neutral and lowermost cylinder positions, are shown in Table 4.As explained previously, the critical point of transition from light to dark zone is considered at 3 cm below pond surface.At this transition plane, cylinder oscillation created vorticities with varying magnitudes.While L/D cycle frequencies could reach up to 60 s −1 in certain locations of flow field for certain cylinder positions, mean L/D cycle frequencies for the first 10 cm downstream of cylinder were found to be 21.17 s −1 , 5.28 s −1 and 2.33 s −1 for uppermost, neutral and lowermost cylinder positions, respectively.For the first 60 cm downstream of cylinder, mean L/D cycle frequencies range from 4.43 s −1 to 21.17 s −1 for uppermost cylinder position.As oscillation frequency is 1.24 s −1 , the cylinder will be in this uppermost position every 0.8 s, where L/D cycles with highest frequencies are achieved.
In the view of the reported results, continuous cylinder oscillation created high frequency L/D cycles for cells to utilize the flashing light effect for increased biomass productivity.Creating L/D cycles, in which cells move between light and dark zones of the pond with an appropriate frequency, is known to promote algal growth [27,37,38].It has been stated that high yields of photosynthesis require L/D cycle frequencies in the range of 10-50 s −1 [39], which could not yet be continuously achieved at RWPs.Furthermore, studies have reported increased biomass productivity by creating vortices and improving vertical velocity are for a limited depth (6-10 cm), which strongly reduces their applicability in full scale facilities (Table 5).* For works that reported vorticity, L/D cycle frequency is given as half of vorticity magnitude, as described previously.
Grobbelaar et al. [41] reported that, for L/D cycle frequencies higher than 1 s −1 , photosynthetic rates increase exponentially, which implies a possibly much higher impact of VIV on biomass productivity at the near wake of the cylinder.Considering the magnitude of L/D cycle frequencies achieved in the present study, it can be presumed that a much higher enhancement of biomass productivity in RWPs can be achieved with the presented method in real scale RWPs than that reported in the literature.

Enhanced Biomass Production in V-RWP
Results of comparative cultivation of Chlorella vulgaris in pilot scale ponds is shown in Figure 12.It can be seen that, after one week of cultivation in V-RWP, optical density of culture medium increased over 20 % compared to conventional RWP.Optical densities measured at 540, 680 and 750 nm increased by 22.7%, 30.9% and 20.45%, respectively.Preliminary observations of cell growth indicate that application of VIVs could considerably increase biomass production in RWPs, due to enhanced vertical mixing created by the VIV system.

Concluding Remarks and Future Directions
In this study, a novel vortex induced vibration (VIV) method to improve vertical mixing and therefore light and dark cycles in raceway ponds (RWP) was developed.
The VIV system was installed to a paddlewheel driven pilot scale RWP and continuous cylinder oscillation was successfully achieved.The VIV cylinder covered 6.5 cm in the vertical direction which corresponds to reduced amplitude of A* = 0.54 with an oscillation frequency of 1.24 s −1 .Numerical simulations, which were in good accordance with experimental results, revealed that VIV motion directed cells to near-surface parts of the pond and vertical flow covered about two thirds of pond depth with a magnitude of 0.3 m s −1 .VIV cylinder motion also created high frequency light-dark cycles with mean magnitudes ranging from 21.17 to 1.05 s −1 which is suitable for high photosynthetic yields.
The effect of improved vertical mixing with VIV system on biomass growth was also verified by comparative Chlorella vulgaris cultivation under outdoor conditions.It was observed that the VIV system installed reactor enhanced biomass production capacity by over 20% compared to control pond.
In the view of present results, it can be concluded that cycling biomass between upper and lower parts of the pond depth and creating high frequency light/dark cycles in long channel sections with the VIV could considerably increase biomass production capacity without significant installation costs and additional energy requirement.VIVs can be installed in both existing and new raceway ponds, due to their simplicity and the absence of fixed structures in the flow zone.Costs will also be minimal since no complex and expensive equipment is needed.
Our future studies will cover a further understanding of the impact created by vortex induced vibrations on the hydrodynamic environment of raceway ponds and on enhancement of algal biomass growth with different growth mediums having varying light penetration characteristics.Furthermore, distance between two consecutive VIV cylinders, possibility of deeper ponds and coupling VIV system with static structures in the flow field will be investigated.

Figure 1 .
Figure 1.A simple illustration of Karman Vortex Street.

Figure 2 .
Figure 2. Direction of the exerted force when vortices shed from the cylinder.

Figure 1 .
Figure 1.A simple illustration of Karman Vortex Street.

Figure 1 .
Figure 1.A simple illustration of Karman Vortex Street.

Figure 2 .
Figure 2. Direction of the exerted force when vortices shed from the cylinder.

Figure 2 .
Figure 2. Direction of the exerted force when vortices shed from the cylinder.

Figure 3 .
Figure 3.A cylinder is totally submerged in water with two springs attached at both ends.

Figure 3 .
Figure 3.A cylinder is totally submerged in water with two springs attached at both ends.

Figure 4 .
Figure 4. General view of VIV system implemented to RWP channel (left).Details of VIV system components (right).

Figure 4 .
Figure 4. General view of VIV system implemented to RWP channel (left).Details of VIV system components (right).

J
. Mar. Sci.Eng.2023, 11, x FOR PEER REVIEW 6 of 19 second.Stored data was processed and denoised by the help of the Wavelets tool of MATLAB software.

Figure 5 .
Figure 5.A view of experimental RWP with VIV system: General view of RWP with VIV system (right), Detailed view of VIV system (left).Figure 5.A view of experimental RWP with VIV system: General view of RWP with VIV system (right), Detailed view of VIV system (left).

Figure 5 .
Figure 5.A view of experimental RWP with VIV system: General view of RWP with VIV system (right), Detailed view of VIV system (left).Figure 5.A view of experimental RWP with VIV system: General view of RWP with VIV system (right), Detailed view of VIV system (left).

Figure 5 .
Figure 5.A view of experimental RWP with VIV system: General view of RWP with VIV system (right), Detailed view of VIV system (left).

Figure 6 .
Figure 6.Positions of cylinder during one oscillation (not to scale).

Figure 6 .
Figure 6.Positions of cylinder during one oscillation (not to scale).The VIV motion was captured by the open-source electronics platform, Arduino (https://www.arduino.cc,accessed on 11 November 2022).Arduino boards have a number of facilities for communicating with computers, other boards, sensors, microcontrollers, etc.A functional code was developed to run with 16 MHz clock speed Arduino Mega 2560 board.A pair of compatible ultrasonic sensors were used to receive the reflecting sound waves over moving components of the VIV system.The sensor can store 40 data points a second.Stored data was processed and denoised by the help of the Wavelets tool of MATLAB software.Experiments were conducted in the raceway pond taking consideration of the VIV response of the circular cylinder.Govardhan and Williamson[21] described various branches associated with VIV and it is stated in their paper that the highest oscillation amplitude occurs in the region called the "upper branch".In our study, we tried to maximize the motion of the cylinder to increase the light availability for microalgae.Therefore, our experimental setup was fixed to a reduced velocity of U*=5 at which the upper branch is expected to be initiated.Parametric details of the VIV system installed on the RWP are presented in Table1.
is the outer domain and covers the rest of the fluid domain.Number of elements in this region is around 5000.A total of 12,000 grids consisting of triangular and quadrilateral elements represent the fluid domain.The moving domain was allowed to move perpendicular to the flow inside the stationary domain.During the motion of the moving domain, elements in the stationary domain were remeshed at each time step.Therefore, elements in the stationary domain were deforming while elements in the moving domain were non-deforming.Figure7shows the general view of the computational domain.

Figure 7 .
Figure 7. Details of the computational domain and the boundary conditions.In this figure, region 1 is the moving domain while region 2 is the stationary domain.

Figure 7 .
Figure 7. Details of the computational domain and the boundary conditions.In this figure, region 1 is the moving domain while region 2 is the stationary domain.

Figure 9 .
Figure 9. Vertical velocity created by cylinder oscillation when cylinder is at neutral (middle) position.Above contour is captured when cylinder is moving down, below contour is captured when cylinder is moving up.

Figure 10 .
Figure 10.Vorticity field created by cylinder oscillation when cylinder is at neutral (middle) position.Above contour is captured when cylinder is moving down, below contour is captured when cylinder is moving up.

Figure 10 .
Figure10.Vorticity field created by cylinder oscillation when cylinder is at neutral (middle) position.Above contour is captured when cylinder is moving down, below contour is captured when cylinder is moving up.

Figure 11 .
Figure 11.Vorticity field created by cylinder oscillation when cylinder is at its lowermost position.Figure 11.Vorticity field created by cylinder oscillation when cylinder is at its lowermost position.

Figure 11 . 19 Figure 12 .
Figure 11.Vorticity field created by cylinder oscillation when cylinder is at its lowermost position.Figure 11.Vorticity field created by cylinder oscillation when cylinder is at its lowermost position.J. Mar.Sci.Eng.2023, 11, x FOR PEER REVIEW 15 of 19

Figure 12 .
Figure 12.Growth of Chlorella vulgaris in V-RWP and conventional RWP monitored at three wavelengths; 540 nm, 680 nm and 750 nm.

Table 1 .
Parametric details of the experiments.
In this study, numerical simulations were solved using the finite volume method implementing Reynolds-Averaged Navier Stokes (RANS) Equations.In tensoral notation, RANS Equations are, in short, given as follows:

Table 2 .
A summary of boundary conditions and computational domain details.

Table 3 .
Comparison of Experimental and Numerical Simulation Results.
J. Mar.Sci.Eng.2023, 11, x FOR PEER REVIEW 1 Figure 9. Vertical velocity created by cylinder oscillation when cylinder is at neutral (middl tion.Above contour is captured when cylinder is moving down, below contour is captured cylinder is moving up.

Table 4 .
Mean L/D cycle frequencies (s −1 ) obtained for the uppermost, neutral and lowermost cylinder positions.

Table 4 .
Mean L/D cycle frequencies (s −1 ) obtained for the uppermost, neutral and lowermost cylinder positions.

Table 5 .
Comparison of studies conducted to create L/D cycles to improve biomass productivity in RWPs.