Alexei Sentchev
email: alexei.sentchev@univ-littoral.fr

Maxime Thiébaut

François G Schmitt

Impact of turbulence on power production by a free-stream tidal turbine in real sea conditions

Keywords: Tidal stream energy, Turbine performance, Turbulence, Velocity measurements

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Impact of turbulence on power production by a free-stream tidal turbine in real sea conditions

Introduction

Tidal stream energy is growing rapidly in interest as countries look for ways to generate electricity without relying on fossil fuels. In comparison to other sources of renewable energy, tidal stream energy is accurately predictable and the social acceptance level is higher due to a reduced visual impact.

Whilst the major characteristics of the mean tidal flow (speed, direction, current magnitude asymmetry, etc) are relatively simple to measure (e.g., [START_REF] Guerra | Turbulence measurements from five-beam acoustic Doppler current profilers[END_REF][START_REF] Thomson | Quantifying turbulence for tidal power applications[END_REF]Thiébaut andSentchev, 2016, 2017), much less is known about turbulence. This is indicative of the inherent technical difficulties (i.e., sensor movement, limited sampling rate) in acquiring measurements of turbulent motions in fast moving currents (e.g., [START_REF] Milne | Characteristics of the turbulence in the flow at a tidal stream power site[END_REF].

During the last decade, with increasing deployment of Tidal Energy Converters (TECs) prototypes in many countries, large effects of turbulence on turbine functioning and performance have been reported [START_REF] Macenri | Influence of tidal parameters on SeaGen flicker performance[END_REF][START_REF] Li | On natural frequency of tidal power systems-A discussion of sea testing[END_REF][START_REF] Verbeek | The near-wake of Horizontal Axis Tidal Turbines in a storm surge barrier[END_REF]. The design of TECs can be optimized in response to results revealed during trials. Until recently, the technology optimization, quality and reliability improvements of TECs were obtained by both experimental research in flume tanks (e.g., [START_REF] Bahaj | Power and thrust measurements of marine current turbines under various hydrodynamic flow conditions in a cavitation tunnel and a towing tank[END_REF][START_REF] Mycek | Experimental study of the turbulence intensity effects on marine current turbines behaviour. Part I: One single turbine[END_REF][START_REF] Chamorro | On the interaction between a turbulent open channel flow and an axial-flow turbine[END_REF] and modeling (e.g., Batten et al., 2008[START_REF] Batten | Accuracy of the actuator disc-RANS approach for predicting the performance and wake of tidal turbines[END_REF][START_REF] Pinon | Numerical simulation of the wake of marine current turbines with a particle method[END_REF]Li and Calisal, 2010;[START_REF] Churchfield | A large-eddy simulation study of wake propagation and power production in an array of tidal-current turbines[END_REF]. For example, the most sophisticated Large Eddy Simulations, performed by [START_REF] Churchfield | A large-eddy simulation study of wake propagation and power production in an array of tidal-current turbines[END_REF], yield a detailed time-dependent structure of the turbulent flow and showed that the way in which the turbulent flow is simulated greatly affects the predicted power production by the array of turbines.

As advances in numerical simulations support the increased confidence in prediction of turbine performance, the need remains to establish experimental verification of modeling results. Important results characterizing the functioning of a horizontal axis turbine and an array of turbines under a range of flow conditions have been obtained from device testing in flume tanks. These tests have provided valuable data at the small experimental scale and, in particular, provided indications on how current speed and current/wave interaction can affect the power production by the turbine (e.g., [START_REF] Tatum | Wave-current interaction effects on tidal stream turbine performance and loading characteristics[END_REF][START_REF] Pinon | Numerical simulation of the wake of marine current turbines with a particle method[END_REF]. Other experimental works highlighted the impact of turbulence on turbine performance (e.g. [START_REF] Bahaj | Shaping array design of marine current energy converters through scaled experimental analysis[END_REF][START_REF] Blackmore | Effects of turbulence on tidal turbines: Implications to performance, blade loads, and condition monitoring[END_REF][START_REF] Medina | Turbulence analysis and multiscale correlations between synchronized flow velocity and marine turbine power production[END_REF].

However, real life deployments of full-scale prototypes provide a great opportunity for detailed assessment of the tidal device performance. The number of scientific publications reporting the results of full-scale device trials is scarce. Experimental approach developed by [START_REF] Mcnaughton | Measuring and modelling the power curve of a commercial-scale tidal turbine[END_REF] allowed assessing the performance of Alstom 1 MW tidal turbine in real sea conditions at the European Marine Energy Centre in Orkney. The results showed a large sensitivity of the turbine performance to the shape of velocity profile and turbulence level in tidal flow. Assessment of the MCT SeaGen 1.2 MW tidal energy converter performed by [START_REF] Macenri | Influence of tidal parameters on SeaGen flicker performance[END_REF] came to similar conclusions. In particular, it revealed a large effect of turbulence strength, generated at high current speed, on the flicker level (i.e., the level of rapid fluctuations in the voltage of the power supply). [START_REF] Jeffcoate | Field measurements of a full scale tidal turbine[END_REF] investigated the performance of a 1/10 scale tidal turbine (1.5 m diameter) in both steady state and real sea flow conditions at the experimental site in Strangford Narrows (UK). A clear decrease and strong variations of the TEC performance in turbulent tidal flow were documented.

However turbulent properties of the flow at site were not estimated and a link with the power production was not established. A two-year experimental study of a full scale TEC prototype conducted at a demonstration site at Uldolmok (South Korea) demonstrated that the TEC's integrity is significantly affected by short-term inflow disturbances such as natural turbulence and vortex shedding. Moreover it was highlighted that turbulent instabilities in flow regime might ultimately contribute to a catastrophic failure through an excitation of the system resonance [START_REF] Li | On natural frequency of tidal power systems-A discussion of sea testing[END_REF].

The purpose of this paper is twofold. First, the study aims to provide an estimated performance of a vertical axis (Darrieus type) tidal turbine. Insights into methodology and practice of tidal stream turbine testing in real turbulent flow are presented. The second objective aims to clarify how the turbulence in evolving tidal stream affects power production. The study attempts to identify the most relevant metrics of turbulence which help to better understand and quantify changes in turbulence regime in the real tidal flow as well as the relationship with power production.

Materials and methods

Tidal current turbine

The Darrieus type vertical axis tidal turbine (VATT) was designed and manufactured by the Dutch company Water2Energy B.V. (Ltd), based in Heusden (NL). The turbine rotor, equipped with four vertical blades (Fig. 1), employs a hydrodynamic lift principle that causes the blades to move proportionately faster than the surrounding water. A fairly low rotation speed, ranging from 5 to 45 rotations per minute (rpm), does not have a significant influence on the movement of fish and other marine biological species. A new generation turbine, tested in the Sea Scheldt in autumn 2014 and called Dragonfly II, was fitted with an improved pitch control of the foils.

The turbine was mounted on a floating frame, featuring two floaters and cross beams shown in Fig. 1. It was positioned in the 2-m thick uppermost surface layer in natural tidal flow. The elements rotating in the water (blades, arms) have the dimensions: 2 m rotor diameter and 1.5 m blade length, thus the area swept by the blades was 3 m 2 . The mechanical and electrical components of the turbine were located above the waterline, increasing the lifespan and enabling easy installation and maintenance. During the turbine test runs, the output power, rotation speed, and torque were continuously recorded at 100 Hz by the data acquisition unit mounted on the platform next to the turbine. The cut-in speed was about 0.5 m/s. The cut-off velocity was not specified by the manufacturer. The maximum power generation was expected to be about 5 kW. When the turbine is running, the electric power is used to charge the batteries and to supply any A/C loads attached. If the batteries are fully charged and the A/C load is lower than that produced by the turbine, the turbine slightly speeds down until the power output and loads are balanced. With the pitch control of the foils, the efficiency is expected to be high, of the order of 0.45 to 0.5.

Experimental site and tidal flow regime

The tidal turbine was tested in real sea conditions in a tidal estuary (the Sea Scheldt) at an experimental site located in Temse, west of Antwerp (Belgium). A floating pontoon (3m x 39 m), oriented in the streamwise direction, was installed in the middle of the Sea Scheldt between two piles, embedded in the river bed (Fig. 1 lower panel). The mean depth and the river width were approximately 10 m and 300 m. The turbine was installed alongside the pontoon during a six-week period from October 20, to December 11, 2014. More details on the trials conducted in the Sea Scheldt can be found in [START_REF] Goormans | In-situ scale testing of current energy converters in the Sea Scheldt, Flanders, Belgium[END_REF].

The flow regime in the estuary is essentially governed by tides of semi-diurnal period with a slight fortnight modulation. At site location, the water level varies between 7 and 13 m providing a mean tidal range of 6 m. The tidal wave propagates from roughly East to West along the main river axis (Fig. 2). During a tidal cycle, the current vector draws an ellipse (Fig. 3) whose semi-major axes match the flood (red dots) and ebb (blue dots) current direction. At rising tide, the mean flow direction in the surface layer 2-m thick is ~167° (with respect to East) and referred to as flood flow direction. At falling tide, the ebb flow direction is -7° revealing a slight misalignment with flood flow (Fig. 3). The current vector rotation is counter-clockwise due to bottom friction which affects the water movement at all depth levels.

The salinity at site is close to zero in the whole water column due to a strong mixing and large distance from the sea. The weather conditions were calm, during the targeted period, with low wind and insignificant wave height (< 0.2 m).

Velocity measurements

The tidal currents were measured by a downward-looking 1.2-MHz RDI Workhorse Sentinel acoustic Doppler current profiler (ADCP) and a velocimeter (ADV) Vector from Nortek. Both instruments were mounted on a steel beam extending out from the side of the pontoon and positioned upstream in front of the turbine (Fig. 1 lower panel). ADV was aligned with the middle line of the turbine whereas ADCP was out of line by approximately 1 m. Both ADV and ADCP were spaced from the tidal turbine by a distance of ~2D = 4 m, D being the turbine diameter.

The ADCP recorded current velocity during several tidal periods of turbine test runs. The instrument was set to operate at a pinging rate of 1 Hz recording velocity profiles every second. Each ping of velocity profiling was composed of three sub-pings averaged within 1-second interval providing velocity error of 0.04 m/s, according to manufacturer documentation and software.

Velocities were recorded in beam coordinates with 0.25 m vertical resolution (bin size), starting from 0.8 m below the surface (midpoint of the first bin). ADCP velocities were used for tidal flow characterization, evaluation of the kinetic power available in the flow and comparison with velocities measured by ADV. Three deployments were carried out at the test site using identical configuration.

The longest period of data acquisition lasted 11 tidal cycles (7-11 November 2014).

The ADV installed next to the ADCP, was recording 3 components of the flow velocity (east, north and vertical) at 16 Hz at ~1 m depth which corresponded to the second ADCP bin. The installation on the steel beam, tightly fixed to the pontoon, ensured a good stability of instruments. For the range of velocity variations encountered at site and under similar calm wave climate conditions, Richard et al. ( 2013) evaluated the Doppler noise of ADV measurements as 0.03-0.04 m/s. The Doppler noise in ADCP measurements was estimated following a technique proposed by [START_REF] Thomson | Measurements of turbulence at two tidal energy sites in Puget Sound,WA. Oceanic Engineering[END_REF]. The velocity standard deviations for ADCP and ADV were compared and the Doppler noise in ADCP data was found to be 0.06 m/s at flood and 0.05 m/s at ebb flow respectively. Before removing the Doppler noise, ADCP velocity standard deviations were almost 60% larger than that derived from ADV.

A low eccentricity of the tidal current ellipse allowed taking into account only the streamwise velocity component for characterization of tidal motions in the estuary. Therefore horizontal velocity components recorded by ADCP were projected on along-and cross-stream axes (x and y) of the river (Fig. 2). The projection angle (13° clockwise) matches the orientation of the tidal current ellipse in the surface 2-m thick layer on flood tide (Fig. 3). Time series of the streamwise velocity, referred to as u component, and spanwise velocity (v component), derived from both ADCP and ADV, were thus generated for further analysis.

The streamwise velocities, recorded by ADCP during five flood flow intervals (Fig. 4), were used to estimate the turbine performance, whereas ADV data were used for assessing the turbulent properties of the tidal flow. We had a limited length of ADV velocity time series, a total of 24 hours during the trial period in November. Comparison of 10 min averaged velocities, derived from ADCP and ADV records, showed a good overall agreement (Fig. 8a) with relative error less than 6%.

Analysis techniques and metrics used for turbulence characterization

Standard statistical parameters were estimated using the velocity time series provided by ADCP: the time mean, the maximum and the standard deviation of velocity variations. Velocity values averaged over one-minute time intervals, were used to evaluate the turbine performance, whereas turbulent properties of the flow were quantified by using high frequency ADV measurements.

The turbulence intensity, often referred to as turbulence level, is defined as:

, U I σ =
where U is the mean velocity computed from the three mean velocity components U x , U y and U z as:

2 2 2 z y x U U U U + + ≡ , and
( )

2 2 2 3 1 z y x σ σ σ σ + + ≡
is the standard deviation of the mean velocity.

This metric has been shown to correlate with the extreme loads exerted on turbine blades and is assumed to be a source of fatigue.

The dissipation rate, 𝜀𝜀, of the turbulent kinetic energy is estimated from the power spectrum density (PSD) of velocity, E(k), assuming the Kolmogorov relationship of the local isotropic turbulence [START_REF] Frish | The legacy of A.N. Kolmogorov[END_REF][START_REF] Pope | Turbulent flows[END_REF]:

𝐸𝐸(𝑘𝑘) = 𝐶𝐶𝜀𝜀 2/3 𝑘𝑘 -5/3 ,
where C is the Kolmogorov's constant (C = 1.5) and k is the wavenumber. Using Taylor's assumption of frozen turbulence, the frequency f and wavenumber k can be related to the mean velocity U such as: k = 2πf /U. Thus, the dissipation rate can be estimated from the power spectrum as [START_REF] Thomson | Measurements of turbulence at two tidal energy sites in Puget Sound,WA. Oceanic Engineering[END_REF]:

𝜀𝜀 = � 𝐶𝐶 0 𝐶𝐶 � 3/2 � 2𝜋𝜋 𝑈𝑈 � 5/2
, where 𝐶𝐶 0 accounts for the height of the PSD slope which best fits the spectrum in the inertial subrange.

The value of 𝜀𝜀 is used to estimate three other important scaling properties: the integral lengthscale L, thought as the size of the most energetic turbulent eddies, the Kolmogorov dissipation scale 𝜂𝜂, and the Taylor lengthscale λ defined by [START_REF] Pope | Turbulent flows[END_REF]:

𝐿𝐿 = 𝜎𝜎 𝑢𝑢 3 𝜀𝜀 , 𝜂𝜂 = � 𝜈𝜈 3 𝜀𝜀 � 1/4
, and

𝜆𝜆 = � 15𝜈𝜈 𝜀𝜀 𝜎𝜎 𝑢𝑢 .
where 𝜈𝜈 is the kinematic viscosity of water (𝜈𝜈 = 1.5 × 10 -6 m 2 /s). Finally, two Reynolds numbers based on the Taylor lengthscale λ and on the water depth h were estimated according to:

𝑅𝑅𝑅𝑅 𝜆𝜆 = 𝜎𝜎 𝑢𝑢 𝜆𝜆 𝜈𝜈 Re = 𝑈𝑈 ℎ
𝜈𝜈 .

Results

Turbine performance assessment in real flow conditions

A typical cycle of tidal flow evolution is shown in Fig. 4a. On average, the streamwise velocity, u, exceeds the spanwise velocity, v, by an order of magnitude (Fig. 4a). The duration of the flood and ebb flow periods were found to be sensibly different -7 and 5.5 hours respectively. After the current reversal (CR) of low water (LW), the tidal current velocity evolves from 0.8 m/s to -0.8 m/s in less than 1 hour, revealing very short slack water duration.

The imbalance between flood and ebb flow, clearly identified in Fig. 3 and known as current magnitude asymmetry a, is defined as the ratio of the mean velocity during flood tide to the mean velocity during ebb tide: a = <u flood >/<u ebb >. This is a relevant metric allowing a more realistic estimate of tidal stream resource at site (e.g., [START_REF] Neill | The role of tidal asymmetry in characterizing the tidal energy resource of Orkney[END_REF][START_REF] Thiébaut | Asymmetry of tidal currents off the W. Brittany coast and assessment of tidal energy resource around the Ushant Island[END_REF].

On average, a was found to be 0.75 during the survey period. In the surface layer, the mean ebb tide velocity is above 1 m/s whereas during flood tide it is below 0.8 m/s. Such a difference is related to a particular shape of the velocity curve with a significant saddle point during the flood phase of the tide. The maximum velocities during the flood and ebb tide were observed at LW and HW respectively.

The performance of the W2E tidal turbine is characterized by estimating the power coefficient, C p , defined as a ratio of the output power P generated by the turbine to the kinetic energy in the approaching flow passing the area S swept by the blades:

𝐶𝐶 𝑝𝑝 = 𝑃𝑃 (1/2)𝜌𝜌𝜌𝜌𝑢𝑢 3
Here, ρ is the water density, and u is the streamwise velocity of incoming flow. Velocities recorded by ADCP 0.8 m below the surface, i.e. at the mid-depth of the operating turbine, are assumed to account for space averaged values. This assumption is realistic since the velocity profiles show a slight linear variation in the uppermost surface layer during the whole cycle of operation (Fig. 5).

The power coefficient C p was assessed using u velocity time series that were recorded during three flood tide periods (on November 7, 8, and 9) on a 1-minute average. The output power was also 1-minute averaged and synchronized with the velocity measurements. Only power time series recorded during flood flow, occurring in the afternoon of each date, were subsequently used in analysis as they provided better quality power data and larger record length (Fig. 4b). During two night trials, the power records showed abnormal variations which we cannot explain. These data were not used in the analysis. The resulting distribution of C p estimates is shown in Fig. 6a.

The optimum efficiency was achieved for a flow velocity close to 1.2 m/s, yielding 𝐶𝐶 𝑝𝑝 ~ 0.42. For lower current velocity values, 0.85 -1 m/s, the efficiency falls to 0.30. The spreading of the power coefficient throughout the tidal velocity range is caused by variations of the torque which, in turn, result from unsteady loading exerted on the blades by tidal flow instabilities.

By taking into account variations in turbine rotation speed it is possible to better understand the evolution of C p . Tidal flow velocity, evolving during the trials, changes the turbine rotation speed ω from 20 to 42 rpm. Lower and more stable rotation speed (~30 rpm) matches lower velocities, 0.8 -1.0 m/s, and lower C p . The increase of current velocity to 1.2 m/s leads to increase of rotation speed to 42 rpm (TSR ~3.6). This speed appears to be optimal for energy production because it allows the turbine's performance to reach its maximum value (0.42).

The power curve (Fig. 6b) shows a quasi-linear increase for velocity values ranging from 0.8 to 1.05 m/s. A considerable growth of power production is visible for higher velocities. The curve, obtained on the basis of 1-minute averaging, appears quite smooth and contains very few outliers.

Turbulent fluctuations of velocity and power production

Although the power coefficient achieves its optimal value for current velocities above 1.1 m/s, the power production appears unstable and largely intermittent. Fig. 7a clearly shows a higher level of power fluctuations during a longer period of approximately one-hour (14:50-15:50) on November 7.

Estimates of the standard deviation of power generated by the turbine, σ p , is a suitable way to quantify the magnitude of power variability. Fig. 7b shows that σ p increased more than twice (from 0.05 to 0.12 kW) during a short period of test on November 7. Very similar behavior of the output power was found for the other two turbine test runs: on November 8 and 9. Using the quantity σ p as a measure of the power production intermittency, two characteristic periods are identified in the time history of P: period I, with low σ p values, and period II when σ p values were doubled (Fig. 7b, Tab. 1).

To identify possible reasons behind such amplification of power fluctuations, ADV velocity time series were analyzed. The velocity evolution on flood flow is given in Fig 8a and compared with the power evolution for the same period (Fig. 7).

The level of ambient turbulence in a free tidal stream approaching the turbine, at high Reynolds numbers (Re ~10 6 ), is characterized by estimating two quantities: the standard deviation of the velocity, σ, and turbulence intensity, I, both derived from ADV measurements 1 m below the surface, close to the mid-depth of the turbine. 10-minute averaged time series of σ and I, together with two horizontal velocity components (raw data), are presented in Fig. 8. It was specified in section 3.1 that the flow in the Sea Scheldt is almost reversing with a largely dominating streamwise tidal component u. The vertical component of the velocity vector is very small given the low depth on site. On the other hand, v and w fluctuations are also important for turbulence characterization. The ratios of the standard deviations of the spanwise 𝜎𝜎 𝑣𝑣 and vertical component 𝜎𝜎 𝑤𝑤 to the streamwise velocity component 𝜎𝜎 𝑢𝑢 were found to be approximately 𝜎𝜎 𝑣𝑣 /𝜎𝜎 𝑢𝑢 ~0.90 and 𝜎𝜎 𝑤𝑤 / 𝜎𝜎 𝑢𝑢 ~0.63. The results appeared relatively stable for the whole length of velocity sample and revealed nearly homogeneous turbulence regime in the estuary (for given velocity range). These ratios are 15-20 % higher than that documented by [START_REF] Milne | Characteristics of the turbulence in the flow at a tidal stream power site[END_REF] in the highly energetic tidal flow at the Sound of Islay, UK.

The standard deviations σ of velocity, varied approximately in phase with U and with the standard deviation of power, 𝜎𝜎 𝑝𝑝 . The correlation between σ and 𝜎𝜎 𝑝𝑝 is high (0.92) but the relation between two quantities is like a power law function. For the second sub-period, values of σ revealed a large (~50%) increase of turbulent velocity pulsations (Tab. 1). This evolution highlights a significant quantitative change in the flow regime and the ambient turbulence level, in particular when the current velocity exceeds 1 m/s. At the same time, the turbulence intensity did not evolve much, tending towards a mean value I ~ 0.044 (Fig. 8b and Tab. 1). The correlation between I and 𝜎𝜎 𝑝𝑝 is low (0.44). This suggests that turbulence intensity is unlikely to be the most relevant metric for characterizing the turbulence variability in real tidal flow with continuous velocity evolution. This is the first finding we would like to put forward.

Turbulent properties of the tidal stream and relationship with the output power

A metric conventionally used for quantifying turbulence in a flow is the turbulent kinetic energy which is related to the standard deviation of the velocity as: TKE = 1/2σ 2 . Values of TKE, averaged over two successive sub-periods, show more than 100% increase in turbulent energy for sub-period II (Tab. 1). This highlights a relationship between the level of turbulence (TKE) and the magnitude of power fluctuations, which also doubled.

The dissipation rate, ε, is another important indicator used for turbulence characterization. It is associated with turbulent eddies and velocity fluctuations that are not as readily accessible as the global estimation of turbulent kinetic energy. The dissipation rate is quantified through a spectral analysis of velocity time series in the inertial subrange.

The PSD of velocity time series recorded by ADV during two successive sub-periods of a tidal cycle is given in Fig. 9. The duration of velocity sample, shown in blue in Fig. 7a, is 1 hour 40 minutes and one hour for the two respective sub-periods. They were chosen to match two typical flow conditions: flood tide with current velocity less than 1 m/s (sub-period I) and more energetic flood flow with velocity ranging from 1 to 1.4 m/s (sub-period II).

For each sub-period, the PSD reveals three characteristic frequency subranges: the low frequency subrange (f < 0.3 Hz), the inertial subrange (0.3 Hz < f < 2 Hz), and high frequency subrange (f > 2 Hz), where the PSD curve is influenced by the noise in the data. Four fundamental properties of the turbulent flow were estimated for each sub-period: the dissipation rate, 𝜀𝜀, the integral lengthscale, 𝐿𝐿, the Kolmogorov scale, η, and the Taylor-based Reynolds number, Re λ . The PSD distribution showed good scaling in the inertial subrange for both sub-periods with spectral slope ranging from -1.5 to -1.6.

The results are summarized in Tab. 2. A significant difference in turbulent regime was found between periods I and II. The dissipation rate ε doubles when the tidal flow velocity exceeds 1 m/s. This velocity value represents a threshold highlighting a quantitative change in turbulence regime. Tidal stream with velocities larger than 1 m/s has much higher level of ambient turbulence. The PSD distribution (Fig. 9) and the standard deviation of the velocity (Fig. 8b) support this assumption.

Estimates of the integral lengthscale L also show large variations with respect to flow conditions.

During the flooding tide, the size of the largest (most energetic) eddies increases by a factor of 3.5: from 0.6 m to ~2.2 m (Tab. 2). In contrast, the Kolmogorov scale η appears relatively stable during the same period. The smallest eddy size was fond to be 0.3 -0.4 mm which is considered as typical for turbulent river flows or coastal waters.

Finally, the Taylor-based Reynolds number Re λ showed a significant increase, from 500 to 1000, while the mean tidal current speed rose only from 0.9 to 1.2 m/s. This also appears consistent with other estimates documented for different flow conditions in coastal regions (e.g., [START_REF] Luznik | Distribution of energy spectra, Reynolds stresses, turbulence production, and dissipation in a tidally driven bottom boundary layer[END_REF].

Re λ ~1000 characterizes highly turbulent flow.

Analysis of the scaling properties of velocity time series appears useful for understanding a possible coupling between the turbulence and instantaneous turbine response to velocity fluctuations. Fig. 9b shows the PSD of the power generated on November 7 on flood tide, estimated for each of two sub-periods. The spectra reveal a large difference (more than one decade) in the magnitude of power fluctuations between sub-periods I and II. They also show three characteristic frequency domains. At low frequency (0.03 < f < 0.3 Hz), power fluctuations seem to be related with velocity pulsations even if the scaling of the PSD for both quantities is not exactly the same.

In the inertial subrange (0.3 Hz < f < 2 Hz), scaling of the PSD distribution of the output power and flow velocity is similar (Fig. 9). Spectral slope is close to -5/3 for both quantities: -1.5 for velocity and -1.6 for power. This suggests that in this frequency band, the turbine power appears to be conditioned and probably coupled with the energy cascade in the flow. Fig. 9 also shows that, in this frequency domain, the shape of the power spectrum is largely distorted and reveals that the largest fluctuations of power occur at two frequencies f 0 and 4f 0 , where f 0 denotes the turbine frequency.

These frequencies are different for two flow regimes (Fig. 9b grey line). During sub-period I (velocity less than 1 m/s and low power production), the rotation speed of the rotor was found to vary in a range from 20 to 25 rpm, corresponding to f 0 range 0.33 -0.42 Hz. A large peak of the output power fluctuations occur in this frequency range (Fig. 9b). For sub-period II, characterized by a more energetic flow, the rotation speed of the rotor is close to 40 rpm, providing f 0 ~ 0.67 Hz. Strongest variations of power are observed at this frequency. The second harmonic, 4f 0 , corresponds to the blade pass frequency. It refers to the strike when the blade and central shaft are in line with the incident flow. Expression for 4f 0 , given in [START_REF] Li | On natural frequency of tidal power systems-A discussion of sea testing[END_REF], provides the value of ~2.7 Hz, for the mean velocity of 1.2 m/s. The PSD reveals a strong interaction of each of four turbine blades with the incoming flow at this frequency.

At high frequencies (f > 4 Hz), the output power fluctuations appear to be non-responsive to the dynamics of turbulence in the flow. The PSD for both quantities flattens (Fig. 9) making difficult any evaluation.

The fundamental turbulent properties of the flow, estimated from spectral representation of the velocity and summarized in Tab. II, appear to be closely related to the magnitude of power fluctuations. During sub-period II, values of ε, L, and Re λ are twice higher and correspond to the increase of σ p from 0.05 to 0.12 kW. However the link between σ p and the spatial structure of turbulence is not so straightforward. To further investigate a possible relationship between the power fluctuations during flow strengthening and how the turbulence is spatially organized, estimation of the integral lengthscale L was performed for multiple 10-min intervals within two successive sub-periods I and II (two hours in total). The results, shown in Fig. 10, reveal that, for lengthscales L < 1 m, the magnitude of the output power fluctuations was relatively low (σ p ~ 0.04 kW). As the flow speed increases and approaches the peak speed (~1.4 m/s), the size of energy containing eddies also increases (Tab. 2) and the magnitude of power fluctuations become, on average, three times larger (σ p ~0.13 kW). The relationship is linear thus evidencing that the size of energy containing eddies and the level of intermittency of power production are related. In particular, large size turbulent eddies generate large fluctuations of power.

Discussion

The present work addressed several issues. First, an estimation of the performance of the Dutch VATT "W2E" was done in continuously evolving tidal flow. During the trials, the optimal conditions for power production were reached when flow speed was approaching 1.2 m/s, providing the highest performance: C p ~ 0.4. However, the power produced in these flow conditions experienced large fluctuations, much larger than for velocity ~1 m/s, for example. This kind of intermittency of power production was revealed earlier during device testing in real sea conditions.

A number of experimental studies focusing on assessment of the performance of scaled horizontal axis tidal turbines (HATTs) were conducted recently in the Strangford Lough (Northern Ireland) (e.g., [START_REF] Macenri | Influence of tidal parameters on SeaGen flicker performance[END_REF][START_REF] Jeffcoate | Field measurements of a full scale tidal turbine[END_REF][START_REF] Frost | The Effect of Control Strategy on Tidal Stream Turbine Performance in Laboratory and Field Experiments[END_REF]. [START_REF] Frost | The Effect of Control Strategy on Tidal Stream Turbine Performance in Laboratory and Field Experiments[END_REF] assessed the performance of a 1.5 m diameter HATT (designed by SCHOTTEL Hydro Ltd) in a real tidal flow and in a towing tank. The laboratory results showed a peak C p = 0.44 in uniform flow, whilst peak performance in the real tidal flow featured a C p = 0.38. The 13% drop in peak power performance between the laboratory and field results was attributed (i) to the Doppler noise, biasing the velocity data recorded by ADCP, and (ii) to the turbulence modifying the flow regime and producing the flow instability. Similar effect was documented by [START_REF] Jeffcoate | Field measurements of a full scale tidal turbine[END_REF] during a 1/10 scale Eppler type turbine tests mounted on a moored pontoon in a tidal flow. It was inferred that the performance of the tested turbine was affected by turbulence. At the same time, the results revealed that higher velocity fluctuations in the approaching tidal flow caused higher variations in the rotation speed, torque and power generated by the turbine.

The present study aimed to clarify how the turbulence in a tidal flow affects the power production. This raises some specific questions: what is the range of velocity when there are strong interactions with the turbine, what is the dominant response frequency, how large is the response amplitude? We also sought to highlight a relation between a time-dependent structure of the turbulent flow and the magnitude of power fluctuations. Spectral analysis of velocities and the output power fluctuations were used to identify a region in which the turbine power appears to be conditioned by and strongly coupled with the energy cascade in the flow. Such a region corresponds to the inertial subrange (0.3 -2 Hz) where the PSD distribution follows the Oboukhov-Kolmogorov k -5/3 law. This is not a coincidence but a particular indication that there is a relationship between fluctuations of the output power generated by the tidal turbine and turbulence in the flow.

Our results showed that in a tidal flow with velocities ranging from 0.8 to 1.4 m/s, the turbulent kinetic energy is cascading from larger eddies of size L ~ 0.6 -2 m to smaller eddies of size less than one mm (η ~ 0.4 mm) and then dissipates into heat. Values of dissipation ε corresponding to these integral lengthscales are 1.2 × 10 -4 m 2 s -3 and 2.4 × 10 -4 m 2 s -3 respectively (Tab. 1). The larger the flow speed, the larger the level of velocity pulsations, the turbulent kinetic energy production and dissipation [START_REF] Pope | Turbulent flows[END_REF].

The impact of the level of ambient turbulence on turbine performance in the real flow conditions, is not easy to quantify because all quantities change continuously. Low flow velocities (~ 0.8-1.0 m/s) observed during sub-period I correspond to lower turbulence level (ε ~1.2 × 10 -4 m 2 s -3 ) and lower C p values (~ 0.3). Larger velocities, recorded during the peak flood flow (1.1 -1.4 m/s), generate more turbulence (ε ~2.4 × 10 -4 m 2 s -3 ) but do not decrease the turbine performance. Another important point is that turbulent properties in natural flow are site dependent and influenced by the flow configuration, bathymetry, nature of the seabed, presence of built infrastructure such as bridges, piers, etc. Therefore, the impact of turbulence on turbine performance will be also site dependent. This makes turbine test results difficult to interpret. In this sense, a comparative study of the turbine performance in a turbulent tidal flow and in calm water using towed platforms (e.g. [START_REF] Jeffcoate | Field measurements of a full scale tidal turbine[END_REF] would be valuable and complementary to experiments in flume tanks where the ratio of lengthscales of turbulent motions, in relation with the size of tested devices, is limited. [START_REF] Macenri | Influence of tidal parameters on SeaGen flicker performance[END_REF] was the first who performed a comprehensive analysis of the SeaGen performance and demonstrated that standard deviation of the velocity, assumed to be a measure of the turbulence strength, is likely to be one of the significant factors that contributes to flicker level. Large fluctuations of the output power were found at frequency ~ 0.5 Hz which is fundamental (turbine) frequency. Similar results were documented by [START_REF] Frost | The Effect of Control Strategy on Tidal Stream Turbine Performance in Laboratory and Field Experiments[END_REF] for a scaled turbine, tested in the Strangford Lough. Power fluctuations were related to turbulence effect. To the best of our knowledge, results of field experiments published and available for the community to date are far and few. Our experimental results demonstrated a considerable increase in output power fluctuations occurring when velocity exceeds 1 m/s and when the flow regime becomes more turbulent. The frequency f 0 of the largest fluctuations of power changes continuously with respect to the flow speed.

A linear relationship between the turbulence lengthscale L and the magnitude of power fluctuation σ P was established. The correlation was found high (0.96). The use of L allowed to demonstrate how the turbulence is spatially organized and to compare the turbulence lengthscale with the turbine dimensions. In particular, as the size of turbulent eddies matches the turbine size, σ P exhibits a considerable increase. A quantitative change in interaction between the operating turbine and turbulence is observed at scale L ~ 1.0 -1.5 m (Fig. 10). Large size turbulent eddies exert large loads on the blades, strongly affecting torque and causing large power pulsations. The significance of the effect of turbulence on rotor loads and turbine performance was demonstrated recently by [START_REF] Blackmore | Effects of turbulence on tidal turbines: Implications to performance, blade loads, and condition monitoring[END_REF] and [START_REF] Chamorro | On the interaction between a turbulent open channel flow and an axial-flow turbine[END_REF], based on extensive tests of a scaled turbine in a flume tank. Our results confirm their findings and provide further explanation of the interaction between a turbulent flow and a tidal turbine.

Conclusion

The performance of a Darrieus type tidal turbine of the Dutch company "W2E" was assessed in real sea conditions in the Sea Scheldt. Based on simultaneous output power and velocity measurements, the turbine performance (C p ) was evaluated at different flow regimes, providing the peak value of 0.42 for velocity range 1.15-1.2 m/s. It was shown that turbulent fluctuations of velocity in a tidal flow is the major factor responsible for the intermittency of power production by the turbine.

Turbulence intensity 𝐼𝐼, commonly used by engineers to quantify the level of ambient turbulence, is a metric that in general does not alone capture quantitative changes in the turbulent regime during the tidal flow transition from lower to higher velocities. Other quantities, such as dissipation rate, 𝜀𝜀, the integral lengthscale, 𝐿𝐿, and the standard deviation of the velocity appear more appropriate for turbulence characterization. The magnitude of power fluctuations was found to be proportional to L and the strongest impact of turbulence on power generation was detected when the size of highest energy eddies attains and exceeds the turbine size. Our results highlighted that the magnitude of power fluctuations is related to the spatial structure of the turbulence. This finding has important practical implications since it suggests that the design of hydrokinetic turbines needs to take into account the spectral content of turbulence in the approaching flow which could vary significantly from site to site.

Our recommendation to the community of engineers involved in tidal energy conversion projects is hence the following: because turbulence is site dependent, ADV measurements should be performed at tidal energy sites prior to turbine testing. High quality data recorded by ADV can help to optimize the design and size of turbines in order to minimize an extra load on the blades which are clearly identified as the prime source of fatigue. Table 1. Parameters of the flow regime approaching the turbine for two sub-periods of flood tide: mean horizontal velocity components, standard deviation (s.t.d.) of the current velocity, turbulent kinetic energy and turbulent intensity. Sub-periods I and II are identified in Fig. 7.

Tables

Sub

Figure captions Fig. 1 .

 captions1 Figure captionsFig. 1. Upper panel: Darrieus type tidal turbine of the Dutch company Water2Energy mounted on a surface floating platform for trials in the Sea Scheldt, in autumn 2014.Lower panel: Experimental pontoon installed in the tidal estuary (the Sea Scheldt) for tidal turbine tests in real sea conditions. Velocity measurements were performed by ADCP and ADV installed on a steel beam extending out from the side of the pontoon and positioned upstream in front of the turbine (inset in lower panel).

Fig. 2 .Fig. 3 .

 23 Fig. 2. Arian view of the test site location in the Sea Scheldt. The pontoon and turbine locations are shown in white within the red circle close to the bridge (Temse bridge). Flood flow direction is given in white and the orthogonal frame, used for projection of current velocity components, is given in black.Fig. 3. Tidal current ellipse on site derived from ADCP velocity measurements averaged in the surface layer 2-m thick. Red and blue points indicate 1-min averaged current velocities during flood and ebb tide respectively. Black crosses show the mean flood and ebb flow velocity values.

Fig. 4 .

 4 Fig. 4. (a) Ten minutes averaged velocity time series measured by ADCP at 0.8 m depth in November 2014 during the trials. Flood and ebb tide velocities are shown in red and blue respectively. Solid and dashed lines show the streamwise (u) and spanwise (v) velocity components. (b) Power generated by the turbine on flood flow during the same period. Power records shown by shading were used for turbine performance assessment.

Fig. 5 .

 5 Fig. 5. Current velocity profiles (1-minute averaged) derived from ADCP measurements during twohour period on November 7, 2014 14:00 -16:00 (UTC). Color matches the depth-average velocity.

Fig. 6 .

 6 Fig. 6. Performance coefficient C p as a function of flow velocity (a) and the power curve of the tidal turbine "W2E" (b). The output power and velocity are one-minute averaged (grey dots). Standard deviations (red dashed lines) are estimated within the velocity intervals of 0.05 m/s.

Fig. 7 .

 7 Fig. 7. (a) Power generated by the "W2E" tidal turbine during the test run on November 7, 2014. One second averaged time series of the power recorded at 100 Hz is given in black. One minute averaged power is given in grey. (b) Standard deviation of power fluctuations estimated within 10-min intervals. Periods of moderate and high fluctuations of the output power, denoted by I and II, are shown in light and dark blue respectively.

Fig. 8 .

 8 Fig. 8. (a) Current velocity time series (raw data) recorded by ADV at 16 Hz during flood tide on November 7, 2014. Streamwise velocity component u is shown in blue, spanwise component v in grey. Light grey line shows the mean (low-pass filtered) velocity. Black dots represent the ADCP velocities at 0.8 m depth and averaged within 10-min intervals. (b) Evolution of the turbulence intensity (𝐼𝐼) and the standard deviation of current velocity (σ) during the same period. Light and dark blue match subperiods of lower and larger velocity variations and numbered I and II in (a).

Fig. 9 .

 9 Fig. 9. (a) Power Spectral Density (PSD) of the current velocity recorded by ADV (streamwise component) in the approaching flow during two specific sub-periods I and II on flood tide, identified in Fig. 7a. Red dashed line shows the spectral slope 𝑓𝑓 -5/3 . Grey dashed lines show the best fit of the spectral slope in the inertial subrange. (b) PSD of the output power generated by the turbine on November 7, 2014, during sub-periods I and II on flood flow. Red line shows the spectral slope 𝑓𝑓 -5/3 . The mean frequency of turbine rotation isshown by f 0 for each sub-period. The second harmonic, 4f 0 , matches the blade pass frequency.

Fig. 10 .

 10 Fig. 10. The standard deviation of output power fluctuations σ P versus the integral lengthscale L, both estimated over six successive 10-minute intervals of sub-periods I and II.

FiguresFig. 1 .

 1 Figures

Fig. 2 .

 2 Fig. 2. Arian view of the test site location in the Sea Scheldt. The pontoon and turbine locations are shown in white within the red circle close to the bridge (Temse bridge). Flood flow direction is given in white and the orthogonal frame, used for projection of current velocity components, is given in black.

Fig. 3 .

 3 Fig. 3. Tidal current ellipse on site derived from ADCP velocity measurements averaged in the surface layer 2-m thick. Red and blue points indicate 1-min averaged current velocities during flood and ebb tide respectively. Black crosses show the mean flood and ebb flow velocity values.

Fig. 4 .

 4 Fig. 4. (a) Ten minutes averaged velocity time series measured by ADCP at 0.8 m depth in November 2014 during the trials. Flood and ebb tide velocities are shown in red and blue respectively. Solid and dashed lines show the streamwise (u) and spanwise (v) velocity components. (b) Power generated by the turbine on flood flow during the same period. Power records shown by shading were used for turbine performance assessment.

Fig. 5 .

 5 Fig. 5. Current velocity profiles (1-minute averaged) derived from ADCP measurements during twohour period on November 7, 2014 14:00 -16:00 (UTC). Color matches the depth-average velocity.

Fig. 6 .

 6 Fig. 6. Performance coefficient C p as a function of flow velocity (a) and the power curve of the tidal turbine "W2E" (b). The output power and velocity are one-minute averaged (grey dots). Standard deviations (red dashed lines) are estimated within the velocity intervals of 0.05 m/s.

Fig. 7 .

 7 Fig. 7. (a) Power generated by the "W2E" tidal turbine during the test run on November 7, 2014. One second averaged time series of the power recorded at 100 Hz is given in black. One minute averaged power is given in grey. (b) Standard deviation of power fluctuations estimated within 10-min intervals. Periods of moderate and high fluctuations of the output power, denoted by I and II, are shown in light and dark blue respectively.

Fig. 8 .

 8 Fig. 8. (a) Current velocity time series (raw data) recorded by ADV at 16 Hz during flood tide on November 7, 2014. Streamwise velocity component u is shown in blue, spanwise component v in grey. Light grey line shows the mean (low-pass filtered) velocity. Black dots represent the ADCP velocities at 0.8 m depth and averaged within 10-min intervals. (b) Evolution of the turbulence intensity (𝐼𝐼) and the standard deviation of current velocity (σ) during the same period. Light and dark blue match subperiods of lower and larger velocity variations and numbered I and II in (a).

Fig. 9 .

 9 Fig. 9. (a) Power Spectral Density (PSD) of the current velocity recorded by ADV (streamwise component) in the approaching flow during two specific sub-periods I and II on flood tide, identified in Fig. 7a. Red dashed line shows the spectral slope 𝑓𝑓 -5/3 . Grey dashed lines show the best fit of the spectral slope in the inertial subrange. (b) PSD of the output power generated by the turbine on November 7, 2014, during sub-periods I and II on flood flow. Red line shows the spectral slope 𝑓𝑓 -5/3 . The mean frequency of turbine rotation is shown by f 0 for each sub-period. The second harmonic, 4f 0 , matches the blade pass frequency.

Fig. 10 .

 10 Fig. 10. The standard deviation of output power fluctuations σ P versus the integral lengthscale L, both estimated over six successive 10-minute intervals of sub-periods I and II.

Table 2 .

 2 Turbulent properties of the tidal flow approaching the turbine for two characteristic subperiods (I and II) of flood tide: dissipation rate ε of the turbulent kinetic energy, integral lengthscale L, Kolmogorov scale 𝜂𝜂, Taylor based Reynolds number Re λ , and spectral slope s.

	-period	Mean velocity (m/s)	s.t.d. of the velocity (m/s) and TKE (m 2 /s 2 )	Turb. intensity
		< u >	< v >	σ		TKE	𝐼𝐼
	I	0.9	0.1	0.065		0.002	0.041
	II	1.25	0.15	0.102		0.005	0.047
	Turbulent properties	𝜀𝜀(m 2 s -3 )	𝐿𝐿(m)	𝜂𝜂(mm)	Re λ	s
	Sub-period I	1.2 × 10 -4	0.6	0.4	492	-1.6
	Sub-period II	2.3 × 10 -4	2.2	0.3	1073	-1.5

Acknowledgments

The authors acknowledge the support of the Interreg IVB (NW Europe) «Pro-Tide» Program. The output power data were kindly provided by Reiner Rijke (Water2Energy). Technical support of

Roeland Notele (Seakanal) and experience of Eric Lecuyer (LOG) during the surveys are also acknowledged. The authors wish to thank two anonymous reviewers whose comments on an earlier draft of this manuscript helped in improving the final accepted version.