Investigation of Hydrokinetic Tidal Energy Harvesting Using a Mangrove-Inspired Device

Abstract

There is a trend towards harvesting tidal energy in shallow water. This study examined how tidal energy can be harvested using a device of oscillating cylinders inspired by the roots of mangroves. A specific focus was placed on optimising the configuration of these devices, informed by the computational fluid dynamics (CFD) analysis of wake interference in the von Kármán vortex street of the cylinders. A maximum efficiency of 13.54% was achieved at a peak voltage of 16 mV, corresponding to an electrical power output of 0.0199 mW (13.5% of the hydrokinetic energy of the water) and a power density of 7.2 mW/m² for a flow velocity of 0.04 m/s ($Re=239$). The configuration of upstream cylinders proved to have a significant impact on the power generation capacity, corroborated further in CFD simulations. The effect of wake interference was non-trivial on the magnitude and quality of power, with tandem arrangements showing the largest impact followed by staggered arrangements. Though with comparatively low energy densities, the device’s efficiencies found in this study indicate a great potential to harvest tidal energy in shallow water, which provides a consistent baseload power to supplement intermittent renewables (e.g., solar and wind).

1. Introduction

Tidal energy exhibits significant potential for renewable energy generation, due to its predictability, dependability, and high energy density. Tidal currents often result in steady, periodic flows of water that are easily anticipated based on local site characteristics, where the kinetic energy can be converted into electrical power using suitable generation infrastructure [1]. The global tidal energy resource is currently estimated at 3 TW, with 1 TW available in shallow water [2]. The global installed capacity of tidal range and tidal stream technologies is 500 MW [3]. Extracting tidal energy in deep water can be costly and complicated, specifically when it comes to installation and maintenance. As tidal energy grows in the future, less complicated methods of extracting power in shallow water need to be developed and refined for specific sites of varying characteristics.

This research involves the investigation of these tidal flows and of how a mangrove-inspired device can be potentially utilised to harvest the hydrokinetic energy of water. This field of research materialised as a result of the global issue of coastal erosion, wherein mangroves help mitigate damage to coastlines by dissipating the kinetic energy of tidal flow [4,5].

The key source of energy for potential harvesting is through the oscillations of flexible cylinders submerged in shallow water, where the forces within the wake cause oscillatory movement (or vortex-induced vibrations) when fixed in one degree of freedom perpendicular to the water flow. This is a biomimetic application of the roots of mangroves and how they function in dissipating energy. This can potentially improve and complement existing tidal energy harvesting methods, which are not typically suited to shallow water conditions due to the depth and size requirements of current turbines [6]. The Rhizophora mangle (red mangrove) is the primary inspiration of this field of research, as it exhibits clusters of roots that interact with the tidal water flow [7], with their cylindrical and vertical structure seen in Figure 1.

The quantity of tidal electric energy that can be extracted in shallow water near the mangrove root depends on a series of factors such as the fluid dynamics and flow structure of water around flexible cylinders, cylinder structure (flexibility), porosity and spacing ratio, energy harvesting potential, and spatial arrangements. Gabbai and Benaroya [9] simulated a mangrove using an array of cylinders in a circular arrangement with the cylinders having an adjustable/varied flexibility. The array was tested in a water tunnel with 2D flow visualisation, where the results showed that a small turbulent region following the array formed the von Kármán vortex street—a wake structure due to vortex shedding, producing an oscillatory force on the cylinders perpendicular to the direction of the flow.

The von Kármán vortex street is the main cause of the oscillations on the cylinders (which can occur as one side is not fixed) that can be potentially harvested for energy [10]. Kazemi et al. [11], and Gómez et al. [12] confirmed that the generated energy is proportional to the amplitude of oscillation. The wake characteristics and velocity were found to be directly influenced by the porosity—the amount of free space—and flexibility of the roots [5]. Feliciano et al. [4] conducted a dimensional analysis to investigate and relate the physical parameters of a ‘patch’ of mangrove root-like cylinders—a patch is a group of mangroves and thus a cluster of cylindrical roots. They found the potential energy harvested from a patch increases as the porosity decreases [4]. The study by Kazemi et al. [7] indicated that the porosity significantly impacts the drag coefficient, wherein the coefficient increases as porosity decreases (and vice versa). In simple terms, more roots packed together increase drag, as it becomes more like a solid cylinder. Therefore, a less-porous patch with higher drag releases more energy [7].

Varied porosity means that patches have a varying frontal area per unit volume (each cylinder in the patch contributes to this area), and thus a new scale of length called ‘effective diameter’ has been introduced [13]. The effective diameter describes the theoretical solid cylinder that would produce the same frequency of vortex shedding as a given patch [13]; increasing porosity means decreasing effective diameter [7], and can be interpreted as the obstruction or blockage seen by the water flow [14]. The effective patch diameter is calculated by measuring the stream velocity and vortex shedding frequency at a distance of two-patch diameter behind the patch, where the von Kármán vortex street begins [13]. This is a concept that may impact the optimal arrangement for energy harvesting [13]. The blockage parameter is another related non-dimensional parameter that describes the resistance to flow through the patch. Similar to the effective diameter, the blockage parameter increases with decreasing porosity. It was shown that the energy released in the wake always increases as the patch blockage increases, as the turbulent energy is most intense in the wake of denser patches, and that the blockage parameter versus the energy released per vortex has a linear relationship [13]. Experimentally, a larger amount of energy was released in the wake as the blockage parameter increased, as expected, which also means that a higher porosity leads to less energy being released [13] and, furthermore, decreasing with higher porosities.

Similar to porosity, the drag coefficient decreases by increasing the spacing ratio [7]. For the tested spacing ratios, the force exerted on the patch increases and the drag coefficient decreases as the free stream velocity increases in magnitude. This is due to the flow passing through individual cylinders more quickly, where ‘bleed’ flow from the patch increases and delays the formation of the von Kármán vortex street [7,14]. Furthermore, by increasing the flow velocity, it was determined that the net force on the patch increases quadratically (hence, the resistant force also increases). This was the same for the case of a singular cylinder [15]. A significant finding was that the roots closer to both the leading and trailing edge of the patch moved faster than the roots on the inner section [7,15], which is an important factor and observation in determining the optimal structure for harvesting electrical power from a patch.

Regarding flexibility, the drag coefficient increases with increasing the cylinder flexibility. This was found to be caused by the increased turbulence in the region behind the patch from oscillations, and an increased frontal area seen by the water flow as the flow velocity increases [7] (as oscillations are larger in magnitude—the cylinders can move more distance with more flexibility). Experimental and componential velocity measurements confirmed that higher flexibility results in a more scattered/turbulent wake structure [16]. As drag depends on flexibility, it suggests that the flexibility is a major factor in shallow, slower-moving water, e.g., in normal tidal flow conditions. In contrast, the flexibility of the cylinders was found to have less impact on flow resistance [16] for high water flow velocities.

It is evident that laudable efforts have been directed towards understanding the quantitative relationships between the harvested energy and the fluid dynamics of water flow through the device as a function of cylinder flexibility, porosity and spacing ratio. Less focus was placed on quantifying the effect of spatial arrangements of the cylinders, which, however, have been identified as playing a significant role in determining the water flow structure [9]. Moreover, most of previous studies pertaining to hydrokinetic energy harvesting from tidal flows were conducted in the context of coastal environmental applications, attempting to optimise parameters for mitigating coastal erosion and sediment erosion/deposition. A good understanding of tidal energy harvest in shallow water is largely lacking, particularly when it comes to the effect of spatial arrangements of the cylinders on the device’s power generation capacity.

The present study experimentally examines the harvest of hydrokinetic energy in shallow water using a device of oscillating cylinders that act as the roots of mangroves. Electricity generated using different patch configurations, arrangements, flow conditions, porosities, root ratios, and other relevant parameters has been measured and examined. CFD modellings of fluid flow dynamics when passing through the patch of cylinders have also been conducted to understand the underlying fundamental mechanisms. Systematic analysis of the maximum energy that could be harvested through the device was conducted with a view to unravelling the optimal operating conditions. The research outcomes achieved from these first prototypes are intended to inform the further development of this new technology. The broad objectives of this study will be achieved through a comprehensive experimental and numerical investigation.

2. Methodologies

2.1. Experimental Setup

The bench-scale experimental setup used in this study is shown in Figure 2. The experimental setup consisted of a water tank, a submersible pump, a water recirculating system, an oscillating cylinder with electrical current generation, and a control system. The recirculating water tank was built from 4.5 mm thick Perspex sheets (1 m × 0.25 m × 0.25 m), giving a total volume of 62.5 L. The cross-sectional area maintained was similar to the study carried out by Kazemi et al. [11], in order to gather comparable results and assess the validity of this experiment.

The tank included a 25 mm diameter inlet, and 50 mm diameter outlet, both with ball valves to control the water flow. The inlet valve was connected to a pump outlet using clear vinyl tubing and secured with hose clamps. The pump used was an Ozito submersible water pump rated at a maximum flowrate of 7000 L/h (i.e., 2 L/s). This was placed in a reservoir bucket (60 L), under the bench.

The water reservoir was filled from the tank outlet, which allowed water to be drained from the tank through a flexible PVC tubing. Clamps were used to prevent excess bowing toward the middle of the tank due to the outward pressure exerted by the water. The oscillating cylinder device was created using four individual 3D-printed parts that were assembled together (Figure 3). The oscillating cylinder device was fixed across the tank using a timber and Perspex mounting, which slotted over the sides of the tank. An Agilent U1252A handheld digital multi-metre was placed on the mount and connected to the device coil to measure the voltage produced.

To induce an electrical current from the device, copper wire (0.25 mm diameter) was wound (100 turns) on a hollow section attached to the cylinder, with 3 neodymium magnets (13 mm outer diameter × 4.5 mm inner diameter × 5 mm thickness). These each have a maximum pull force of 4 kg. A pine wood cylinder with a diameter of 6 mm was attached to the device, which was then submerged 23 cm into the flowing water. Thus, this part oscillates, with the pivot point being the flexible PVC sheet. The magnets supported by the fixed section of the device do not move. The movement perpendicular to the wiring of the coil induces the electrical voltage. Two timber supports were built to mount cylinders across the tank, allowing for the varying in configuration, to analyse the influence of the wakes on the oscillations of the main device. These cylinders were also submerged 23 cm in the water flow, with the supports slotting onto the sides of the tank. A flexible PVC stripe was used to connect the magnet segment to the wood and coil segment. The natural frequency of the device was approximately 3.26 Hz. This was determined using a high-speed camera at 240 fps, where the number of oscillations of the device (after being given an initial inertia) in the given time could be used to calculate the frequency.

The experimental work was initiated by filling both the Perspex tank and reservoir tub to approximately 75% capacity, with the inlet and outlet valves closed. The inlet valve was then opened, and the pump was switched on, followed by the opening of the outlet valve. The outlet flow rate was adjusted so that the water level stayed constant at 2 cm below the top of the tank. The multimeter was turned on and switched to the 500 mV range setting. With the multimeter leads connected to each end of the coil, perpendicular movements from the oscillations induced a voltage which was measurable on the digital display. The device mounting was placed 50 cm downstream of the inlet, with the cylinder submerged 23 cm. Once the inlet and outlet flows were balanced (constant flow velocity at 0.04 m/s), the peak voltage measured by the multimeter was recorded over a 30 s time-period, in which the peak voltage was recorded in the first 10 s block, followed by the peak in the next 10 s block, followed by the peak in the final 10 s block. The oscillation amplitude and frequency were measured for 21 different configuration, outlined in

Table 1. Cylinder configurations investigated experimentally.

	Case	Description	Flow Diagram (Not to Scale)
				5 cm	10 cm	15 cm	20 cm
Singular	1	Individual device	→•
Tandem	2	One cylinder 5 cm in front	→•	•
	3	One cylinder 10 cm in front	→•		•
	4	One cylinder 15 cm in front	→•			•
	5	One cylinder 20 cm in front	→•				•
	6	Two cylinders 5 cm and 10 cm in front	→•	•	•
	7	Two cylinders 10 cm and 15cm in front	→•		•	•
	8	One cylinder 5 cm in front, staggered 1.25 cm	→•	•
	9	One cylinder 10 cm in front, staggered 1.25 cm	→•		•
	10	One cylinder 15 cm in front, staggered 1.25 cm	→•			•
	11	One cylinder 20 cm in front, staggered 1.25 cm	→•				•
	12	One cylinder 5 cm in front, staggered 2.5 cm	→•	•
	13	One cylinder 10 cm in front, staggered 2.5 cm	→•		•
	14	One cylinder 15 cm in front, staggered 2.5 cm	→•			•
	15	One cylinder 20 cm in front, staggered 2.5 cm	→•				•
	16	Two cylinders 5 cm in front, staggered 1.25 cm each	→•
				•
				•
	17	Two cylinders 10 cm in front, staggered 1.25 cm each	→•
					•
					•
	18	Two cylinders 15 cm in front, staggered 1.25 cm each	→•
						•
						•
	19	Two cylinders 20 cm in front, staggered 1.25 cm each	→•
							•
							•
	20	Two cylinders staggered 2.5 cm on opposite sides, 5 and 10 cm in front	→•	•	•
				•	•
	21	Two cylinders staggered 2.5 on opposite sides, 10 and 20 cm in front	→•		•		•
					•		•

. In this table, the arrow indicates the direction of the flow, and the dots show the configuration arrangement and the number of cylinders for each set of experiments.

To measure the flow, the bucket (9 L) was filled from the outlet and timed, allowing for the overall flow rate to be calculated for the steady state flow. The average flow velocity was then calculated using Q = VA from the pump specification of 7000 L/h and tank cross section of 0.0625 m². The flow rate of 0.04 m/s corresponds to the lower end of the tidal flow Reynolds numbers, between 200 and 1500, calculated by

$$Re=\frac{Ud}{\upsilon }$$

(1)

where U is the flow velocity (m/s), d is the cylinder diameter (m), and $\upsilon$ is the kinematic viscosity of water at 20 °C (m²/s).

The measured peak voltages in each of the three 10 s blocks were averaged to give a more accurate representation of the power generated by the device under each configuration. The error of the Agilent U1252A Multimetre in the 500 mV range is rated at ±0.2 mV. The open circuit voltage recorded was then used to estimate the electrical power generated by the device by assuming that a load of equal resistance to the resistance of the copper wire was connected to the circuit. The efficiency was also estimated using the power of the water flow and the extracted energy in the form of electrical energy.

2.2. CFD Modelling

CFD modelling has become a promising approach to help understand the underlying mechanisms and explore more [17]. In the study, CFD simulations were conducted with a view to (i) providing support for interpreting the results measured/observed in experiments and (ii) unravelling more details of the flow dynamics, particularly local and transient flow structures, through the patch of cylinders. These data are pivotal to the understanding of underlying fundamental mechanisms, which, in turn, lend support to the design, optimisation, and further development of the device.

ANSYS Fluent 2020 R2 was used in a two-dimensional plane to visualise and analyse the fluid dynamics and wake structures around several cylinders. Using the geometry module, a sketch was created with the same dimensions as the tank used in the experiment (0.25 m width and 1 m length), with the main cylinder (6 mm diameter) centred in the tank. The mesh sizing was then adjusted to 0.00025 m around the cylinders and 0.005 m for the rest of the flow to reduce the computation time, whilst allowing for a more accurate simulation. The system walls, cylinders, outlet, and inlet were defined, as well as the flow (laminar at 0.04 m/s) and fluid medium (water with a density of 998.2 kg/m³ and dynamic viscosity of 0.001003 N × s/m²). The simulation was run at a timestep of 0.1 s and the total flow time was 22 s. This was ample time for the wake structure to become fully developed.

3. Results and Discussion

3.1. Experimental Results

3.1.1. Voltage

The voltage induced in each configuration is shown in Figure 4. In contrast to case 1, where the cylinder is operating without any obstruction, any configuration in which a cylinder or multiple cylinders is placed in the oncoming flow reduces the power generated in the device. It can therefore be deduced that this is a result of the cylinders reducing the kinetic energy available and disrupting the optimal flow conditions required for the device.

The highest voltages seen after case 1 occur with the cylinders placed furthest away (20 cm). The turbulence and reduction in kinetic energy in the wake of the cylinders has more time to settle and move back toward the average stream velocity, allowing for favourable power generation conditions. A consistent oscillation of the device in the individual case (case 1) was observed.

In cases 6 and 7, two cylinders are placed in tandem with the device. The voltage induced is lowest in case 6, where the cylinders are placed 5 cm and 10 cm in front of the device. There is a slight increase in voltage for case 7, where the cylinders are 10 cm and 20 cm in front (Figure 5b). Significant voltage spikes and inconsistent oscillations were observed, with oscillations also being irregular (slowing down and speeding up). These cases significantly impact the ideal power generation conditions for the device, as bringing multiple cylinders closer to the device (directly in front) distorts the incoming flow and impacts the formation and consistency of the von Kármán wake structure. Cases 20 and 21 follow similar characteristics. Cases 8–11 (Figure 5c) involved the staggered integration (offset at 1.25 cm) of one cylinder at the same distances from the device as seen in cases 2–5. The voltage reduces as the cylinder is brought closer to the device. These results suggest that the effect is similar to that in the tandem arrangement. This is expected, as the cylinder is only slightly staggered. Furthermore, significant voltage spikes were observed, as well as inconsistent irregular oscillations. Cases 12–15 (Figure 5d) involved the staggered integration (offset at 2.5 cm) of one cylinder at the same distances as the previous cases. Results were similar, with the voltage marginally higher than when the cylinder was staggered at 1.25 cm. The key difference/improvement in these cases was the more consistent oscillation, as opposed to the larger spikes seen previously. As the cylinder was moved further from the device, oscillation consistency was observed to improve significantly. These results suggest that the consideration of wake width and wake length are important factors in the optimisation of power generation by the device. Cases 16–19 (Figure 5e) involved a staggered configuration with the 1.25 cm offset, although with two cylinders on each side instead of one. This configuration had the largest impact on the induced voltage, reducing the amplitude and consistency of oscillation significantly. In comparison to case 1, where the cylinder was able to oscillate freely, the cylinder oscillation was confined to a reduced amplitude between the wakes of the staggered cylinders (Figure 6).

In cases 1–5, a second cylinder is placed in tandem with the device. Figure 5a illustrates the trend wherein the voltage produced by the device decreases as the cylinder is brought closer to the device, and the flow is increasingly disrupted. It was also observed during the experiment that the oscillations were inconsistent in comparison to case 1, which resulted in voltage spikes.

When these staggered cylinders were removed from the flow, the device almost immediately reverted to consistent oscillation with increased amplitude. These results suggest that the kinetic energy in the flow is further reduced by having multiple cylinders placed in front of the main device, and the resultant wakes obstruct the proper oscillation required for the generation of electricity. To compare the overall performance in each configuration, the induced voltage in staggered and tandem arrangements were averaged (see Figure 7). As shown, since the upstream cylinders are more staggered, more kinetic energy and more favourable flow conditions are seen by the device and allow it to generate more power. Conversely, the closer the upstream cylinders are to being arranged in tandem, the more the flow energy which is effectively blocked, resulting in higher degrees of wake interaction and less power produced.

Overall, compared to the work by Kazemi et al. [11], the induced voltage in this experiment has a lower magnitude, which is expected, as the coil contains a smaller number of turns. However, the results are in the same order of magnitude (maximum of 16 mV in this experiment) compared to the maximum of 26 mV in Kazemi et al. This provides a high level of confidence in the validity of the experiments in relation to the literature.

3.1.2. System Power and Efficiency

To obtain the estimated power generated by the device from the open-circuit voltage, it was assumed that the resistive load of the circuit is equal to the resistance of the copper wire used in the coil. This wire is 0.25 mm in diameter (33 AWG), which corresponds to a resistance of 692 Ω per 1000 m [18]. As the coil is wound on a 25 mm diameter coil holder with 100 turns, the length is 7.85 m. The resistance is then calculated as 5.432 Ω. The resistance of the multimeter leads can also be assumed to be 0.5 Ω each. Hence, the total resistance amounts to 6.432 Ω. Power can then be calculated by

$$P=\frac{{{(V}_{RMS})}^2}{R}$$

(2)

where P is electrical power (W), $V_{RMS}$ is root-mean-square voltage (V) and R is electrical resistance ($\mathsf{\Omega }$). The power generated from the device will therefore follow the same patterns as seen for voltage; however, the power is scaled by the square of this voltage. This means that optimising the configuration for power generation is crucial, as small changes in the voltage will have larger impacts on the electrical power produced (see Figure 8).

Furthermore, it is worth looking at the maximum power generated, which occurred when the device was operating individually, without the hydrodynamic integration of other cylinders. This was 16 mV peak voltage, hence $P_{device}=0.0199 \mathrm{m}\mathrm{W}$. The efficiency of the device can be expressed as a ratio of the output electrical power to the hydrokinetic power $P_f$ available in the flow of the water. This is dependent on the water density, the projected area of the oscillating cylinder (the area swept by the cylinder), and the water flow velocity, and reads

$$P_f=\frac{1}{2}\rho A_p{U}^3$$

(3)

where $\rho$ is the density of water (1000 kg/m³), $A_p$ is the projected area of the cylinder (m) and U is the water flow velocity (m/s). The power in the flow can then be calculated to be 0.147 mW.

Therefore, efficiency is expressed as

$$\eta =\frac{P_{out}}{P_{in}}=\frac{P_{device}}{P_f}$$

(4)

Thus, the maximum efficiency recorded in the experimental runs was 13.54%, which represents the overall efficiency of the device itself. This sits within a similar range as the device used by Kazemi et al. [11], wherein they found a maximum efficiency of 8%. In comparison to current tidal turbines, which are up to 90% efficient [19], these devices will require significant improvements in efficiency to compete with existing tidal technology.

3.1.3. Frequency and Amplitude

The oscillations of the device in case 1 reached a maximum of approximately 4 cm at the bottom tip of the cylinder. This is seen in Figure 9. This value was used in the calculations for the area swept by the cylinder (projected area).

The frequency in case 1 was analysed under high-speed camera footage, which was found to be 1.6 Hz, which corresponds to a flow velocity of 0.048 m/s according to Equation (5). The frequency in the rest of the cases was too inconsistent to give an accurate value. This can be compared to the theoretical frequency $f_s$ due to vortex shedding of the von Kármán effect [20]:

$$f_s=St·\frac{U}{d}$$

(5)

where U is the laminar free-stream velocity (m/s), d is the cylinder diameter (m), and St is the Strouhal number, which is 0.2 in this Reynolds number range [20]. Hence, $f_s=1.33 \mathrm{Hz}$. The measured frequency being higher than the theoretical frequency can also be a result of waves generated in the recirculating water tank, or changes in flow velocity due to changes in the pump speed.

3.2. Energy Density

Analysis of the CFD simulation in case 1 suggests that the minimum spacing between cylinders under these conditions is 3.25 cm perpendicular to the flow direction and 8 cm parallel to the flow direction, corresponding to 5.4 and 13.3 times the diameter of the cylinder. These are applicable to the flow at Re = 239, which is toward the lower end of tidal flow velocities. This can be used to create an arrangement that ensures that the wakes do not inhibit the production of power of other cylinders through their oscillations.

Hence, utilising an optimised configuration of the devices tested in this experiment results in a maximum of 360 devices per square metre (100/3.25 cm rounding down to 30 cylinders oriented perpendicular to the flow, and 100/8 cm rounding down to 12 cylinders oriented parallel to the flow). Assuming that each device is capable of producing a power equal to that in case 1, the total maximum power available at a Re of 239 would be 7.2 mW per square metre using 360 devices. This is the energy density per unit area of water surface required for the device.

The power density as seen by the flow of water can also be calculated using the power generated and swept area of the cylinder, which oscillated 4 cm. A power density of 4.3 mW per square metre, as seen by the flow of water, has therefore been generated from the estimated 32 mW of water-flow kinetic power per square metre (using Equation (3)). This reflects the efficiency of 13.54%.

This work suggests that higher porosities are more suited for power generation, and hence lower root ratios. The root ratio (R) of the optimised patch is calculated as the ratio of cylinder to fluid, using the cross-sectional area of the cylinder multiplied by the number of devices (360), and dividing by the leftover space per unit area. For a cylinder with a radius of 0.03 m, the root ratio is 1.02%. Accordingly, the porosity ($\phi$) can then simply be calculated as $\phi =1-R=98.98\%$. This high porosity allows for wakes to flow between the cylinders without interacting with the incoming flow of subsequent cylinders. This increases the effectiveness of the downstream cylinders toward the rear of a patch. This mitigates the behaviour found in the literature, where the cylinders downstream in a patch tended to oscillate more frequently and erratically due to the interference of upstream cylinders [7,21]. It is further apparent that the circular patches analysed in the literature may not be optimal for power generation where their structure is formed by a central cylinder surrounded by rings of cylinders at a specific spacing ratio. This results in a higher probability of wake interference, as each of the cylinders is insufficiently spaced for the von Kármán vortex street to pass other cylinders without causing fluctuations in frequency or oscillation amplitude. Figure 10 illustrates the existing patches in the literature in comparison to the newly suggested patch arrangements that may be more suited to power generation.

Overall, whilst the efficiency of the device is promising, the energy density of the device is significantly lower than other renewable energy technologies. For example, wind is approximately 20 W/m² [22] and solar is up to 120 W/m² [23] on average. However, we should put the scale of the present device into perspective for the comparison. We also wish to note that the aim of the present study is not to fully evaluate the efficiency of the method at a commercialised, industrial scale, but rather examine the effectiveness and feasibility of this new renewable energy technology, which is very much in its infancy. These first prototypes have numerous potential improvements that will improve the efficiency and power generation potential moving into the future.

3.3. Wake Structure

The wake structure for the flow conditions with Re = 239 in experiments were further investigated using the CFD model.

The oscillations in case 1 (Figure 11a) were steady and the vortex shedding frequency was 1.3 Hz, matching the theoretical frequency. The wake width peaks 4 cm downstream of the cylinder, at a width of 3.25 cm, or 5.4 times the width of the cylinder. The length of the von Kármán vortex street structure within the wake is 8 cm (13.3 times the cylinder diameter), before reverting to a more streamlined, laminar flow. The region directly behind the cylinder contains significantly reduced kinetic energy (as flow velocity is decreased, denoted by blue), whereas the wake further downstream recovers most of the kinetic energy. Downstream kinetic energy, however, is still reduced, as part of the initial kinetic energy is converted from the flow to the oscillation of the cylinder and is released in the immediate wake. The oscillations for the upstream cylinder in case 2 (Figure 11b) match the oscillations in case 1. Under video analysis, the downstream cylinder experiences reduced oscillation amplitude as well as less energy released in the wake. The oscillations were impacted by the wake of the first cylinder, being more inconsistent and fluctuating in frequency. However, the frequency was typically higher than the first cylinder, agreeing with results found by Castillo et al. [21]. The reduced kinetic energy released in the wake of the second cylinder agrees with the experimental results, where the induced voltage decreased with an upstream tandem cylinder.

The staggered arrangement in case 8 (Figure 11c) resulted in a greater amount of kinetic energy reaching the downstream cylinder. This can be attributed to the slight offset of the upstream cylinder blocking less of the water flow. The maximum oscillation amplitude appeared to be equal to the amplitude of the upstream cylinder, although the frequency was irregular and was impacted by the first wake. This is reflected in the experimental results where staggered arrangements performed more favourably than tandem regarding the voltage generated—higher voltage was produced in case 8 compared to case 2. Case 16 exhibited (Figure 11d) significant reduction in the cylinder’s oscillation amplitude and frequency in the wake, as the interactions of the wake of the upstream cylinders effectively cancelled out the von Kármán street structure. This supports the experimental result, where this configuration reduced the voltage induced to the greatest extent. It also provides an explanation for the reduced oscillation amplitude (between the two cylinders, Figure 11), as the wake of the device’s cylinder is confined between the wakes of the upstream cylinders. Furthermore, having another cylinder in the upstream region ultimately dissipates larger amounts of kinetic energy. As in each of the other cases, the wake experiences a prolonged reduction in kinetic energy.

In contrary to case 16, the upstream cylinders in case 19 are placed far enough to allow the wakes to settle back to streamlined flow (Figure 11e). This resulted in a consistent oscillation and frequency in the von Kármán vortex street, with a reduced amplitude compared to the upstream wakes. This reduction in amplitude is again a result of the upstream cylinders dissipating kinetic energy and hence reducing flow velocity in the stream. Experimentally, the physical movement of the cylinders will also widen the wake structure. This arrangement is essentially three cylinders operating separately (Figure 11f), displaying the same characteristics as in case 1. This suggests that the wake interactions do not influence the wake structure when configured with enough distance (larger spacing ratio). This arrangement displays four cylinders essentially operating separately (Figure 11g), with the wake of the furthest upstream cylinder settling enough for the downstream cylinder to experience a perfect von Kármán street wake (with slightly less magnitude).

Overall, the CFD simulations showed that the reduction in velocity following the cylinders is consistent in each case, with more cylinders reducing the velocity by a greater magnitude as they dissipate more kinetic energy in the flow of the water. This aligns with the experimental results, where having more upstream cylinders tended to cause the device to yield less power. The changes in frequency seen experimentally have also been seen in the CFD, where it was observed that the wakes of upstream cylinders influenced the formation of a steady von Kármán vortex street following the device cylinder. This also impacted the magnitude of the wake oscillations, which aligns to the inconsistency in amplitude in the experimental conditions. Furthermore, in each of the CFD cases with multiple cylinders, increasing the spacing ratio both lengthwise and widthways relative to the wake resulted in more consistent oscillations in the wake. The closer the cylinders were configured to each other, the higher the degree of wake interference observed both experimentally and in the CFD simulation.

This resulted in the irregular frequency seen for both tandem and staggered arrangements in the cases where there was not enough time for the upstream cylinders’ wakes to return to laminar flow. Wake interference was the primary characteristic observed in each case, with a small of degree proximity interference seen in the staggered arrangements—proximity interference can occur with cylinders directly side by side, or staggered. Proximity interference can also result in a combined, singular vortex street when cylinders are close enough together and flow in the gap is very low [24]. In case 1, and in cases where the upstream cylinder was more than 8 cm in front of the device cylinder, the wake was able to form a predictable von Kármán vortex street (seen in the CFD), which translates directly to a predictable frequency and amplitude for the device generating power.

4. Conclusions

To conclude, the review of the relevant literature has allowed for the identification of an area of investigation into optimising power generation in mangrove-inspired hydrokinetic energy harvesting using an oscillating device. The experimental aspect of this study involved the construction of a recirculating water tank, and a 3D-printed oscillating device with a cylinder (which forms a von Kármán vortex street, thereby producing an oscillatory force), copper wire coil, and neodymium magnets to induce a voltage. Using this apparatus, a maximum efficiency of 13.54%, maximum voltage of 16 mV, and power densities of 4.3 mW/m² (from the area swept by the cylinder oscillation) and 7.2 mW/m² (devices per unit surface area) were recorded for a flow velocity of 0.04 m/s and $Re=239$.

The configuration of upstream cylinders was shown to have significant impact on the power generated by the device, which was validated using CFD simulations to model the fluid dynamics of the von Kármán vortex street wake. It has been determined that the wake interference between cylinders significantly impacts the potential for power generation with respect to the magnitude of power and the quality of power, due to the effect on frequency and consistency of oscillation. Tandem arrangements were shown to have the largest impact, followed by staggered arrangements. Within the staggered arrangements, the higher the offset of the upstream cylinder (more staggered), the less impact the wake had on the device. It was further shown that cylinders spaced sufficiently, so that wake interference was minimised, allowed the device to operate effectively. In relation to the literature, which has primarily focused on mitigating coastal erosion, this research suggests that the applications of these devices in coastal protection and power generation may involve different optimised configurations. Despite the comparatively low energy densities with respect to other renewables, the efficiencies found in this experiment exhibit significant potential in the development of shallow-water tidal energy generation, which contains an estimated 1 TW of currently untapped energy. Being a novel area of research with only initial prototypes of oscillating devices, there are numerous ways in which the effectiveness and efficiency of such devices can be improved. Thus, the technology remains a potentially feasible option for renewable energy generation, particularly with tidal energy being reliable, predictable, and able to provide a steady baseline of power compared to intermittent renewables such as solar and wind.