# On Blockage Effects for a Tidal Turbine in Free Surface Proximity

^{*}

## Abstract

**:**

## 1. Introduction

_{U}= h

_{U}/D (where h

_{U}represents water depth between turbine rotation disc and free surface and D represents turbine diameter). The turbine was subjected to various rotational speeds to achieve 1 ≤ TSR ≤ 8 at various depths of immersion 0.05 ≤ δh

_{U}≤ 0.55.

## 2. Materials and Methods

#### 2.1. Flow Channel Conditions and Turbine Assembly

^{3}/s. The propeller pump RPM and, hence, the test section flow velocity is controlled and regulated through a transistor inverter type, variable frequency controller (Toshiba Model VFAS1-2185PM-HN). Flow velocity can be varied from 0.03 m/s to 0.94 m/s and can be measured within an accuracy of ±2%. The flow quality is such that the turbulence intensity is maintained to a value of ~2% [25].

_{P}), the coefficient of thrust (C

_{T}), and tip speed ratio (TSR) defined as:

_{∞}is the area-averaged freestream velocity (m/s), ρ is the density of water (kg/m

^{3}), and A is the area of the rotor (m

^{2}). According to the manufacturer’s specifications, the torque/thrust sensor was accurate to within ±1% for the current measurement range, which was also confirmed by in-house calibration. A single sample uncertainty analysis for U, RPM, and torque, based on Kline and McClintock [27], showed a maximum uncertainty of 1% on the TSR and 3% on the C

_{P}calculations. The experimental data were corrected using a blockage correction methodology (based on the actuator disc theory coupled with free surface effects) developed by combining methods suggested by Bahaj et al. [10] and Whelan et al. [13] (see Appendix A for a summary of derivation).

_{U}= 0.55, which corresponded to the placement of the rotor hub at the center of the water channel test section. It was observed that beyond an inflow velocity of 0.7 m/s, the variation in the performance curve was negligible. Therefore, all experiments reported in this paper were performed at an inflow velocity of 0.8 m/s, that corresponded to a diameter-based Reynolds number, Re

_{D}of 2.24 × 105. However, we do not claim that our results are completely independent of Reynolds number effects. The C

_{P}and C

_{T}of the turbine evaluated at 0.8 m/s over a range of TSR’s is plotted in Figure 1c. A near bell-curve-like variation of C

_{P}with TSR is clearly observable in the figure; the maximum value of C

_{P}attained was 0.33 at a TSR of 4.6. As expected, the measured C

_{T}was observed to increase with TSR. The C

_{T}corresponding to peak performance was estimated to be 0.88, whereas peak C

_{T}observed at a TSR of 5.9 was found to be 0.9.

#### 2.2. Stereoscopic-Particle Imaging Velocimetry (PIV) System

^{2}interrogation region size. An effective overlap of 50% of the interrogation windows was employed in the PIV image processing. The 3D flow velocity vectors were then reconstructed using the mapping functions obtained by the in situ calibration procedure and the 2D displacements from each camera. The PIV measurements were carried out for a flow speed of 0.8 m/s and rotational speeds of 180 RPM (TSR = 3.29) and 270 RPM (TSR = 4.94). Free-run PIV measurements consisted of taking a series of 2000 images at a capture rate 72 Hz to determine the ensemble-averaged statistics of various flow quantities. In addition to free-run PIV, phase-locked PIV measurements were carried out in the near-wake region to study transient phenomena like wake development and propagation, tip and hub vortices formation and propagation, and to understand the dynamic interactions of wake with bypass flow regions.

_{tip}= 3 m/s that corresponds to U

_{∞}= 0.8 m/s and RPM = 180). The stereo-camera arrangement was such that the half stereo angle was approximately 12°, which led to an out-of-plane to in-plane RMS displacement error ratio of ~4.5. A convergence study was performed to understand the effect of number of realizations on averaged statistics. Time-averaged statistics showed less than 1% variation in averaged velocity beyond 1400 realizations. Hence, during the current study, time-averaging was performed over 2000 realizations that corresponded to 83 and 125 turbine rotations for TSR values of 3.29 and 4.94, respectively. On the other hand, for phase-averaged statistics, convergence was observed beyond 350 realizations. Hence, averaging was performed over 500 instantaneous images.

## 3. Results and Discussion

#### 3.1. Effect of Free Surface Proximity on Blockage

_{1}is the equivalent free stream velocity that will produce the same C

_{P}as measured in blockage environment, and U

_{∞}is the specified channel velocity. At low TSR values (1.66 2.76), when rotational speeds were low, the tip clearance ratio did not have any effect on the percentage increase in flow velocity. However, at larger TSR values (>3.86), %∆U started varying with the depth of immersion. The largest increment in the flow velocity was observed for $\delta {h}_{U}$ = 0.27 at the highest TSR plotted in Figure 2b. For the data in Figure 2b, it is interesting to note that the comparison of data points for a constant value of $\delta {h}_{U}$ demonstrated a wake blockage effect, while a comparison at a constant value of TSR demonstrated the effect of blockage due to the fact of free surface deformation. Lower TSR values led to smaller wake blockage while maximum free surface blockage was observed for $\delta {h}_{U}$ = 0.27. The actuator disc theory and the blockage correction methodology, applied during the current study, assume a stream tube (control volume) passing through the edge of the disc with uniform loading on the disc, steady-state flow, and no flow across the control surfaces [30,31]. During the present study, for a turbine operating in close proximity of the free surface, the deformation of the free surface was expected to change the shape of this stream tube behind the turbine rotation plane (this is illustrated in Section 3.2 from our flow visualization). However, this did not invalidate the use of the actuator disc model, as a deforming stream tube will modify both thrust and torque field on turbine blades. As the correction was based on measured thrust data (which reflects the deformation effects), it was expected to account for modifications in disc loading due to the variation of stream tube shape.

#### 3.2. Effect of Blockage and Free Surface Proximity on the Near-Wake Flow: Free-Run PIV

#### 3.2.1. Contours of Stream-Wise Velocity

_{∞}(where U represents local stream-wise velocity) for the rotational speed of 180 at $\delta {h}_{U}$ of 0.55, 0.27, and 0.05 respectively. Horizontal, dashed lines represent the position of the turbine tip, and vertical solid lines correspond to the turbine rotation plane. For depth of immersion $\delta {h}_{U}\text{}$= 0.55, free the surface is seen to have no effect on near-wake development behind the turbine resulting in more or less symmetric structures about the turbine rotation axis. At the blade root position, a circular localized low-velocity region (region I) was observed, the size of which was of the order of blade root diameter. For this low rotation speed (180 RPM), wake starts to develop behind the turbine rotation plane as a conical structure (regions II and III above and below the turbine axis, respectively) that expands downstream of the turbine as depicted in Figure 3(a-I). A localized high-velocity region developed right behind the blade root (region IV) due to the flow acceleration that occurred due to the presence of a smaller blockage near the blade root that had a diameter smaller than the blade chord. Region IV was followed by a region of comparatively lower velocity but still higher than the rest of the wake. It is interesting to note that in this region, the flow velocity was comparable to the free stream velocity upstream of the turbine (implying a faster wake core). For the case of $\delta {h}_{U}$ = 0.55, no significant differences were observed between the flow structures in the upper bypass and lower bypass regions. An increase in rotational speed to 270 RPM for $\delta {h}_{U}$ = 0.55 led to higher effective blockage developing recess-like structures in the upper and lower parts of the wake, as shown in Figure 3(b-I). This resulted in the formation of additional low-velocity structures in the upper and lower parts of the wake near the blade root and blade tip—regions IIa, IIIa, and IIb, IIIb. Regions IIa and IIIa started closer to the rotor plane compared to regions IIb and IIIb due to the fact of their smaller radius of rotation. In addition, regions IIa and IIIa were observed to expand faster than regions IIb and IIIb. With the increase in rotational speed, a localized high-velocity region (IV) was observed to elongate further and extend downstream of the turbine as can be seen in Figure 3(b-I).

#### 3.2.2. Contours of Vertical Velocity

_{∞}for the two rotational speeds: 180 RPM (row a), 270 RPM (row b), and three different tip clearance ratios ($\delta {h}_{U}$= 0.55, 0.27, and 0.05). For all cases, regions of high vertical velocity were observed at blade tip locations near the turbine rotation plane. The intensity of this high vertical velocity region increased with increasing rotational speed—compare the first row (180 RPM) to the second row (270 RPM). Additional regions of high velocity were observed behind the hub, indicating flow deflection as it passed over the hub. In general, the lower submersion depth ($\delta {h}_{U}$= 0.27, column II) resulted in lower vertical velocities compared to the case of the deeply submerged turbine ($\delta {h}_{U}$ = 0.55, column I). Moreover, for $\delta {h}_{U}$ = 0.27, a region of negative localized vertical velocity was observed behind the turbine rotation plane whose intensity increased with an increase in rotational speed (column II). This region of downward velocity is indicative of bulk downward motion of fluid due to the free surface deformation that occurred at approximately 0.3 R ≤ x ≤1.3 R downstream of the turbine. This is indicative of the earlier mentioned radial compression of the upper wake leading to an asymmetric wake and a faster upper bypass region. Higher free surface proximity ($\delta {h}_{U}$ = 0.05) resulted in even stronger bulk downward motion of fluid leading to wake penetration, as shown in Figure 4, column III. Similar to the case with $\delta {h}_{U}$ = 0.27, an increase in rotational speed resulted in higher downward velocity that spanned over a larger depth. In addition, in the case of ($\delta {h}_{U}$ = 0.05), the bulk downward motion in the near-wake region was followed by an upward-moving fluid, as elucidated in the upper right corner of Figure 4(a-III,b-III). This is indicative of free surface waves with small wavelengths and large amplitudes which were observed behind the turbine rotation plane during experimental runs.

#### 3.2.3. Proper Orthogonal Decomposition Analysis for Free-Run PIV Data

#### 3.3. Variation of Flow Velocities Along Wake Propagation Direction (Along Constant Y)

#### 3.3.1. Profiles of Streamwise and Vertical Velocity

_{∞}) at X/R ~0.8 downstream of the turbine rotation plane. This downward motion caused wake compression yielding higher stream-wise velocities for X/R = 1 in Figure 7. At Y/R = 1.3, even higher downward velocities (up to −8.2U

_{∞}) were observed at a similar downstream distance of X/R = 0.8. This downward flux from the upper bypass to wake region will result in faster wake recovery and is a very important consideration in designing a farm layout.

#### 3.3.2. Effect of Rotational Speed on Velocity Profiles

#### 3.3.3. Comparison of Flow in the Regions Above and Below the Turbine Axis

#### 3.4. Phase-Averaged Statistics for Bypass and Wake Regions

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A. Blockage Correction for Experimental Data

**Figure A1.**Blockage correction: Schematic of a tidal turbine in an open surface water channel environment.

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**Figure 1.**(

**a**) Blade profile (SG-6043) of the (1:20) model turbine rotor. (

**b**) Schematic of experimental set-up (Key: 1—Turbine, 2—Flexible Coupling, 3—Motor, 4—Thrust-Torque Sensor, 5—Support Structure, 6—To Motor Controller, 7—To Data Logging). (

**c**) C

_{P}and C

_{T}versus TSR curve for the turbine at an inflow velocity of 0.8 m/s.

**Figure 2.**Effect of tip clearance ratio on (

**a**) power coefficient and (

**b**) percent change in effective channel velocity as a function of TSR for U

_{∞}= 0.8 m/s.

**Figure 3.**Time-averaged contours of normalized stream-wise velocity (U* = U/U

_{∞}) for $\delta {h}_{U}$ = 0.55 (column

**I**), 0.27 (column

**II**), and 0.05 (column

**III**) at rotational speeds of 180 RPM (row

**a**) and 270 RPM (row

**b**). The center line represents the turbine axis location while the dotted lines represent blade tip location.

**Figure 4.**Time-averaged contours of normalized vertical velocity (V* = V/U

_{∞}) for rotational speeds of 180 RPM (row

**a**) and 270 RPM (row

**b**) for $\delta {h}_{U}$ 0.55 (column

**I**), 0.27 (column

**II**), and 0.05 (column

**III**).

**Figure 5.**Proper orthogonal decomposition (POD) analysis for time-averaged data: Vorticity contours showing (

**I**) first mode (22% of total energy), (

**II**) second mode, and (

**III**) third POD modes for different tip clearance ratios ($\delta {h}_{U}$ = 0.55, row

**a**, and $\delta {h}_{U}$ = 0.27, row

**b**).

**Figure 6.**(POD) analysis for time-averaged data: Vorticity contours reconstructed using (

**I**) first 5 POD modes (50% of total energy), (

**II**) first 50 POD modes (75% of total energy), and (

**III**) all 2000 POD modes for different tip clearance ratios ($\delta {h}_{U}$ = 0.55, row

**a**, and $\delta {h}_{U}$ = 0.27, row

**b**).

**Figure 7.**Variation of normalized stream-wise velocities of the upper-wake bypass region for a rotational velocity of 180 RPM and tip clearance ratios of 0.55 and 0.27 on horizontal lines at depths of (

**a**) Y/R = 0, (

**b**) Y/R = 0.5, (

**c**) Y/R = 1, and (

**d**) Y/R = 1.3.

**Figure 8.**Variations of normalized vertical velocities in the upper-wake bypass region for the rotational velocity of 180 RPM and tip clearance ratios of 0.55 and 0.27 on horizontal lines at depths of (

**a**) Y/R = 0, (

**b**) Y/R = 0.5, (

**c**) Y/R = 1, and (

**d**) Y/R = 1.3.

**Figure 9.**Variation of normalized stream-wise velocities in the upper-wake bypass region for rotational velocity of 270 RPM and tip clearance ratios of 0.55 and 0.27 on horizontal lines at various depths: (

**a**) Y/R = 0, (

**b**) Y/R = 0.5, (

**c**) Y/R = 1, and (

**d**) Y/R = 1.3.

**Figure 10.**Variation of normalized vertical velocities in the upper-wake bypass region for the rotational velocity of 270 RPM and tip clearance ratios of 0.55 and 0.27 on horizontal lines at various depths: (

**a**) Y/R = 0, (

**b**) Y/R = 0.5, (

**c**) Y/R = 1, and (

**d**) Y/R = 1.3.

**Figure 11.**Variation of normalized stream-wise velocities in the lower bypass region for rotational velocity of 180 (row

**a**) and 270 RPM (row

**b**) and tip clearance ratios of 0.55 and 0.27 on horizontal lines at various depths: Y/R = −0.5 (column

**I**), Y/R = −1 (column

**II**), and Y/R = −1.3 (column

**III**).

**Figure 12.**Variation of normalized vertical velocities in the lower bypass region for the rotational velocity of 180 (row

**a**) and 270 RPM (row

**b**) and tip clearance ratios of 0.55 and 0.27 on horizontal lines at various depths: Y/R = −0.5 (column

**I**), Y/R = −1 (column

**II**), and Y/R = −1.3 (column

**III**).

**Figure 13.**Contour plot of normalized stream-wise velocity (U* = U/U

_{∞}) for $\delta {h}_{U}$ of 0.55 (column

**I**), 0.27 (column

**II**), and 0.05 (column

**III**) at different rotational velocities (180 RPM, row

**a**; 270 rpm, row

**b**).

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**MDPI and ACS Style**

Kolekar, N.; Vinod, A.; Banerjee, A.
On Blockage Effects for a Tidal Turbine in Free Surface Proximity. *Energies* **2019**, *12*, 3325.
https://doi.org/10.3390/en12173325

**AMA Style**

Kolekar N, Vinod A, Banerjee A.
On Blockage Effects for a Tidal Turbine in Free Surface Proximity. *Energies*. 2019; 12(17):3325.
https://doi.org/10.3390/en12173325

**Chicago/Turabian Style**

Kolekar, Nitin, Ashwin Vinod, and Arindam Banerjee.
2019. "On Blockage Effects for a Tidal Turbine in Free Surface Proximity" *Energies* 12, no. 17: 3325.
https://doi.org/10.3390/en12173325