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Experiments on the mean and integral characteristics of tidal turbine wake in the linear waves propagating with the current
Ocean Engineering 173 (2019) 1–11
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Experiments on the mean and integral characteristics of tidal turbine wake in the linear waves propagating with the current
T
Wei Zanga, Yuan Zhengb, Yuquan Zhangb,∗, Jisheng Zhangc, E. Fernandez-Rodriguezd a
College of Water Conservancy and Hydropower Engineering, Hohai University, Nanjing, 210098, China College of Energy and Electrical Engineering, Hohai University, Nanjing, 210098, China c College of Harbor, Coastal and Offshore Engineering, Hohai University, Nanjing, 210098, China d Technological Institute of Merida, Technological Avenue, Merida, 97118, Mexico b
A R T I C LE I N FO
A B S T R A C T
Keywords: Tidal-stream turbine Wave-current flow Wake recovery Turbulent intensity Integral time scale
The vast majority of tidal-stream sites have been described with turbulent flows coexisting with waves, but the wake of a tidal-stream turbine in such flows is not fully understood. A model tidal-stream turbine, of diameter 0.49 times the water depth, was tested under the influence of intermediate waves following the current, to analyze both of its mean and integral wake characteristics. An ambient intensity around 10% was established in the recirculating water flume. Acoustic doppler velocimeter (ADV) with Nortek Vectrino profiler probes were used to obtain the time-varying velocities, the turbulence intensities and the integral time scale. Analysis of velocity deficit indicated the mean wake and Gaussian distribution were consistent, with waves being of no real consequence on the wake recovery. The turbulence intensity was shown to be affected by the wave height for the upper region, and the influence of the wave period was greater for the integral time scale than for the wave height at the far-wake region. We believe these results offer significant insight into the turbine wake in a waveturbulence flow.
1. Introduction
turbine becomes vulnerable to current, turbulence and sea waves interactions. According to Lewis and Zheng et al. (Lewis et al., 2014), (Zheng et al., 2014), the waves or even undertow measured per meter wave height, reduce the net tidal resource by 10%. Therefore, it is crucial to investigate the influence of the waves on the wake of tidal stream units. To analyze the combined wave-current flow, research has mainly focused on the wave spectrum. Few studies, though, have considered the influence of waves on the mean and integral characteristics of the ambient flow. Experiments conducted by Kemp and Simons focused on the interactions between current and waves propagating along with (Kemp and Simons, 1982) and opposing the flow (Kemp and Simons, 1983). The opposing waves caused an increase of mean velocity in the upper profiles of water column, whereas the co-current-propagating waves reduced the mean velocity. Klopman and Thomas conducted experiments with different types of waves (e.g. regular, bi-chromatic (Klopman) and random waves (Thomas and Klopman, 1997)) and came to a similar conclusion. Much work on the potential, functioning and wake characteristics of tidal stream turbines have been put forward. Garrett et al. (Garrett and Cummins, 2005) were among the first to study the large theoretical
Following our current industrial scenario, within the next decades, the aftereffects of the fossil fuels burning and pollution on ecosystems will be critical to the survival of the human society (Kanemoto, 2010). In the search of a clean alternative to fossil fuels, the harnessing of tidal stream resources is attracting widespread interest due to the recent advancements of wind offshore technology and predictability of the tides and currents (Antonio, 2010). China, a country with a summary of 32,000 km shorelines, has abundant unexploited tidal stream resources; according to statistical studies, the nations theoretical generating capacity exceeds 13 GW (Liu et al., 2011). Current solutions to convert the kinetic energy of the tidal currents into electricity in an efficient manner (close to 50% of the available power) comprise mechanical apparatuses, called tidal stream turbines. There are a variety of tidal stream turbine concepts put into commercial operations in arrays; They are typically installed on an nearshore location close to the coast or wave front slope with a depth lesser than 40 m, about 1.5–3 times the size (diameter) of the deployed turbine (Lewis et al., 2015), (Zhang et al., 2017a). Because of the bathymetry, flow characteristics and depth range of turbine deployment, the functioning of a tidal stream
∗
Corresponding author. E-mail address: [email protected] (Y. Zhang).
https://doi.org/10.1016/j.oceaneng.2018.12.048 Received 3 July 2018; Received in revised form 18 December 2018; Accepted 20 December 2018 0029-8018/ © 2018 Elsevier Ltd. All rights reserved.
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Fig. 1. Schematic and photo of the wave-current recirculating water flume.
within far-wake are self-similar and follow a Gaussian distribution. The far-wake region and the length of wake recovery have been shown to depend strongly on the level of incident turbulence intensity (Myers (Myers and Bahaj, 2010), Maganga et al. (2010) and Mycek et al. (2014)). According to Bahaj et al. (2012) the vertical constraints, imposed by the free surface and the seabed, have significant effect on wake recovery behind a tidal turbine. The magnitude of turbulent kinetic energy near the blade tip, has been measured by Tedds et al. (2012), and Zhang et al. (2017b) studied the wake characteristics of rotors deployed at different submerged depths. On the other hand, the wake generated by the drag, owing to the support structure, was reported by Walker et al. (Walker and Cappietti, 2017). Despite more information is becoming available on the turbines performance and wake characteristics, yet there is still considerable ambiguity with regard to the wave-current interactions observed in tidal stream sites. A few laboratory studies have attempted to understand this unsteady behaviour. To this end, stallard et al. studied the interactions between the ambient flow and the waves (Stallard et al., 2013). In like manner, Alexander Olczak (2016) considered the mean and pulsation characteristic of the combined flow to quantify the influence of the waves on tidal turbine wake. As regards to the support structures force, Fernandez quantified the variation of extreme thrust (Fernandez-Rodriguez et al., 2014) and in his doctorate dissertation (Fernandez Rodriguez, 2015), he demonstrated the peak forces are in function of the measured wave heights. Moreover, T.A. de Jesus Henriques represented the performance characteristics of the turbine (de Jesus Henriques et al., 2014) and Sufian F. Sufian et al. (2017) developed a virtual blade model to simulate the
potential of tidal currents in a channel. Equally important, JI Whelan et al. (2009) studied the blockage effect, ratio of turbines swept area to channels cross-sectional area, on turbine performance. Such works offered encouraging insight of tidal stream potential, therefore, various experimental studies have been conducted to indicate the performance and wake structure of geometric tidal devices in a water flume or tank. The rotation induced by scale rotors of 0.2–0.8 m diameter has been studied; although smaller model rotors may also be employed if appropriate consideration is given to the low resulting blades Reynolds number (Whelan and Stallard, 2011). Alternatively, porous disks have been successfully employed by Bahaj et al. (2007) and Sun et al. (2008) to represent the momentum extraction of geometric scaled turbines. In terms of wake structure, the tidal stream turbines wake could be divided on the basis of downstream distance into two distinct regions: the near and far-wake (Myers and Bahaj (2009)). The near wake is distinguished by possessing a high swirl intensity, compared with the far wake, owing to its closeness to the torque-imparting rotor plane. Various studies have provided comprehensive knowledge of the wake properties. For instance, the anisotropy tensor bi j , defined by Choi and Lumley (2001), was used by Tedds et al. (2014) to investigate the anisotropy of wake turbulence but failed to present a contour profile on the wake-decay characteristics. Chen et al. (2017) calculated the Reynolds shear stress to simplify the wake analysis, but more clarification on the asymmetrical of free shear layer is still needed. Lam and Chen (2014) proposed a series of equations to predict the wake from a horizontal-axis tidal turbine with the Gaussian probability distribution; but it showed a lesser accuracy in the far wake region. Experiments conducted by Stallard et al. (2015) showed the wake velocity deficits 2
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(SNR) and correlation coefficient (COR) was measured to represent signal quality. The SNR of most samples (more than 90%) was greater than 15 dB, whereas the COR was greater than 80%. and Nortek states the probes accuracy is ± 0.5 % (refers to Vectrino Profiler User Guide (Nortek, 2012)).
effects on tidal stream turbines due to incoming waves. In addition to the mean wake structure of the turbine, the integral scale has been identified as another bulk parameter for the characterization of the scale of vortex, especially for the wave-current flow (Pope, 2001). To estimate this parameter, various models have been proposed (Von Karman, 1948), (Kaimal and Finnigan, 1994). Stallard et al. obtained the integral length scale of the ambient turbulence of a channel based on ref. (Stallard et al., 2015). But one of the major drawbacks adopting this approach is the lack of a detailed description of the ambient flow. Jin et al. (2016) suggests the growth rate of the integral length scale in a wind farm is linear at the far-wake region, although, more recent evidence suggests it may undergo a significant reduction near the turbine (Liu et al., 2018). This paper examines a three-bladed horizontal-axis tidal stream turbine, designed by the Blade Element Momentum theory (BEMT) (Batten et al., 2008a), (Bossanyi, 2009), in several wave-current conditions. The objective, is to present the distribution of mean wake structure and integral time scale in detail. In this context we try to characterize the turbine wake in terms of the wave parameters such as the wave height and frequency relationship.
2.3. Incident flow In order to represent a baseline of the undisturbed flow, velocity measurements were taken with an empty flume. The properties of x , y = 0 plane are illustrated in Fig. 3 (without the rotor). For the smooth flow, the sampling volume was located on mid plane ( y = 0 ). The heights ranged from z = 10 mm to z = 490 mm (z / h ≈ 0.1 to 0.9) with Δz = 40 mm. Three measurement points were distributed in each sampling volume. Multiple sets of tests were taken at different streamwise ( x = −1D to x = 15D ) and lateral (Mid plane and y = ± 1D ) sections to quantify the errors. Over these sections, the change in ambient velocity was lesser than 5%. To characterize the incident velocity, both log-law and power-law were applied in close-to-bed region (z / h < 0.2 ) as illustrated in Fig. 3 (a). The log-law approximation is expressed with Eq. (1) (Schlichting). As regards to this equation, ν = 1.006 × 10−6 m2 /s is the kinematic viscosity of water, κ = 0.41, the Von Kármán's constant, C = 5.0 , the constant for smooth flow and U * , the friction velocity; its value (U * = 0.0139 m/s) is estimated with the measured velocity (Ux ) and wall distance (z) within the close-to-bed region.
2. Experimental arrangement Laboratory experiments presented in this article were conducted in a wave-current recirculating water flume, constructed by the Tianjin University. The flume (see Fig. 1) has a width (w ) of 1.2 m, a length (lf ) of 57 m, a water depth of 0.55 m, a damping length og 5 m, a polished marble bed and flat Perspex walls. Flow enters through a porous weir to dissipate the large scale turbulent eddies. Wave paddles are utilized to generate regular waves following the direction of the current. A single rotor at mid-depth with a diameter D = 0.27 m is attached to a rigid support structure. Components of inflow velocity have been measured using acoustic doppler velocitimeter (ADV) probes, in pure-current and wave-current conditions. Measurements of the wave elevation are taken using a wave height probe situated behind the turbine.
Ux (z ) 1 zU * ⎞ + C , with C = 5.0 in undisturbed flow = ln ⎛ U* κ ⎝ ν ⎠ ⎜
⎟
(1)
If we now turn to the power law equation Eq. (2), the power order (α) and bed roughness coefficient (β) correlate with the observed measurements but are initially unknown (Soulsby and Humphery, 1990), (Soulsby et al., 1993). To solve this issue, we use an iterative process with a least-squares approach, assuming a 1/7th power order. As a result, a bed roughness coefficient of β = 0.43 is obtained. This exponential order assumption is in line with previous studies (See ref. (Batten et al., 2008b), (O'Doherty et al., 2010), (Robins et al., 2014) and (Lewis et al., 2017)) and correlates fairly well with the tidal measurements (Batten et al., 2008b). However, a well-known criticism of the power-law approach is its difficulty in predicting the ambient flow of the full-scale model, since solutions are dependent on the Reynolds number and the turbines are usually designed on a Froude-number similarity.
2.1. Flume setup All tests are taken with a depth averaged inlet velocity of U0 = 0.35 m/s. The origin of coordinate system is defined beneath the rotor centreline at the bed plane ( x − y plane with z = 0 ). The longitudinal, lateral and vertical axes are defined as x, y and z, as indicated in Fig. 2. The equipment is a traverse-moving device with increments of 1 mm. Velocities were measured at various vertical and lateral sections ( y − z planes), spanning from the water surface to the channel bed, in the longitudinal range of 1D upstream to 15D downstream (see Fig. 2 (a)). Twenty-three points were measured at each plane parallel to the rotor plane. The sampling sites are as shown in Fig. 2 (b).
1/ α
Ux (z ) z = ⎜⎛ ⎟⎞ U0 βh ⎝ ⎠
, with
α=7
for 1/7th order power − law
(2)
The upper depth profile of longitudinal velocity was recorded at rotor plane ( x = 0 ). As seen in Fig. 3 (b), both log-law and power-law fit agree well with measurements for depths of z / h < 0.2 . Interestingly, for values beyond this limit z / h = 0.2 , little correlation was observed between the models and the measurements. Eq. (3) describes another important parameter of the incident flow, named the turbulence intensity (TIiinc ), where Ui′ is the mean velocity fluctuations of three dimensions, and U ′, the total value. The components (TIiinc ) of and the total intensity (TI inc ) of the turbulence observed for the current-only case, are illustrated in Fig. 3 (c). The averagedturbulence intensity near the hub height (z / h = 0.49) in the longitudinal, lateral and vertical direction correspond to 7.0%, 5.1%, 4.4%, respectively; and they provide a total turbulence intensity of 9.8%, throughout different longitudinal sections. According to Fig. 3 (d), the averaged turbulence intensity for various wave forms corresponds to 12.1%, 15.0% and 16.7%, respectively.
2.2. Velocity measurement Two Nortek acoustic doppler velocimeter (ADV), with a 4-beam down-looking Vectrino profiler probe, were employed to record the velocity from 0 to 3.0 m/s. These devices have been widely adopted for both industrial and scientific applications and are known for its good accuracy and precision. They are able to calculate the three-dimensional velocity components using the phase shift of the acoustic signal caused by the reflection of the particles within the sampling volume. Throughout this paper, the time varying and mean velocity components are expressed as ui and Ui , where the suffix i = x , y, z means the direction of the flow component. The probe can profile the water over a 30 mm range for a cylindrical sampling of 40 mm with a measurement resolution of 1 mm. Velocities components were recorded with a sampling rate of 100 Hz. A sample duration of 100 s, large enough for a time-frequency analysis of the signal, was set for all tests. The signal to noise ratio
TIi =
3
(Ui′)2 U0
(3)
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Fig. 2. Velocity measurement positions.
current condition.
As regards to the longitudinal integral time scale of ambient turbulence, it is defined as Eq. (4), where τ is time lag and u x′ , r (τ ) , σx2 correspond to the velocity fluctuations, autocorrelation and variance of the stream-wise velocity, respectively. The integral is evaluated up to a small time lag τ = 0.01 s such that the correlation coefficient rτ is sufficiently small. Fig. 3 (e) shows the upper depth profile of longitudinal integral time scale (Txinc ) of the incoming flow. However, due to the limitation of sampling rate, such parameter may vary widely. Thus, a linear fit method is used to describe the mean value of normalized integral time scale Txinc U0/ D , and this is about 1.80 on the rotor plane.
Tx =
∫0
∞
rτ dτ , with rτ =
u x′ (t ), u x′ (t − τ ) σx2
2.5. Waveforms There are many wave theories available for predicting the characteristics of wave-current flows. Particularly, the linear wave theory is a commonly suitable approach for describing regular waves of a single frequency. Many experiments limit the applicability of the linear wave theory to long waves with small Ursell number (Ur ≪ 32π 2/3 ≈ 105). The Ursell number, Ur = Hλ2 / h3, where H represent the wave height and λ, the wavelength, is a normalized parameter put forward to indicate the non-linearity of waves; and it is used as a parametric indication of linear wave theorys suitability. The linear surface elevation is expressed as Eq. (6):
(4)
2.4. Model rotor
η=
The full-scaled commercial rotor operates with a mean incident flow velocity of 1.57 m/s at the depth of 11 m, and has a diameter of 5.4 m. On the grounds of the Froude scaling theory (Eq. (5)), we chose a 1:20 geometric scaling model with the corresponding flume conditions (U0 , TI , h, λ), where v, g and l are the mean incident flow velocity, local gravity acceleration and operating water depth, respectively. The suffix f and m represent the full and model scale rotor.
vf vm
=
(6)
and the dispersion equation is:
C=
λ = T
g tanh(kh) k
(7)
where g is the gravity acceleration, k = 2π / λ , the wave number. To obtain the wavelength in the experiments, these equations were fitted against the wave height measurements by using a least-squares approach. The experimental waveforms were generated by a piston type wave-maker, and measured by wave height recorders. The probes were installed at transverse positions ( y = −0.8, −0.4, 0,0.4, 0.8 m) and at every 20D longitudinal sections, starting from − 50D to 30D . The maximum error of wave height was less than 4%. The wave parameter obtained in our tests is in terms of the relative water depth, kh , a criterion of the class of waves: shallow, intermediate and deep. Table 2 illustrates this. In our test, the relative water depths kh correspond to intermediate wave region (π /10 < kh < π ).
gf lf gm lm
H cos(kx − ωt ) 2
(5)
The model rotor is made of stainless steel and each blade has a NACA 4412 airfoil profile with radial variation (r / R ), chord length (c / R ) and twist angle (θ) as indicated in Table 1: In our tests, the blockage rate is a = πR2 / wh ≈ 8.7%. The rotor was operated with a tip-speed ratio TSR = ωr R/ U0 ≈ 2.43 , where ωr represents the angle velocity and this is approximate 62.6 rpm in pure4
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Fig. 3. Vertical flow properties at x = 0 plane without turbine installed (a) Log-law and power-law fit method in close-to-bed region (z / h < 0.2 ); (b) Mean longitudinal velocity (Ux ) in upper profile (z / h > 0.2 ); (c) Turbulent intensiy (TIiinc , TI inc ) in upper profile (z / h > 0.2 ); (d) Total turbulent intensity (TI inc ) under wave conditions; (e) longitudinal integral time scale (Txinc U0/ D ) in upper profile (z / h > 0.2 ).
shown in Fig. 2 (b) from 1D upstream to 15D downstream. The threedimensional velocity variations provide insight into the wake structure and its development whereas the longitudinal and vertical plane measurements highlighted the influence of waves on the far-wake development. Wake velocity deficit ΔUx / U0 was calculated by the local deficit (ΔUx = U0 − Ux ), and the total turbulence intensity, by the components of the velocity (Eq. (3)).
Table 1 Key blade sections. Section
r /R
c /R
θ
Blade Bottom Widest Blade Tip
0.075 0.550 1.000
0.164 0.308 0.079
47. 9∘ 27. 8∘ 9. 5∘
Table 2 Wave conditions. Wave
1 2 3
Wave height
Period
Wavelength
Relative depth
Ursell number
(H)
(T)
(λ)
(kh )
(Hλ2/ h3 )
0.030 m 0.039 m 0.051 m
1.0 s 1.5 s 1.0 s
1.53 m 2.91 m 1.53 m
2.26 1.19 2.26
0.42 1.99 0.72
3.1.1. Longitudinal Variation A reduction in the velocity deficit was observed for each of the waveforms listed in Table 2. Fig. 4 shows the effect of wave variation on velocity deficit along the rotor centreline. The rate of the wake recovery was found to be similar near the rotor, and the deficit was slightly greater than the non-wave case in far-wake region. In the near-wake region ( x ≤ 3D ), the velocity deficit showed a rapid decrease and reached a mean value of 21% at 3D downstream. The maximum deficit occurred under the current-only condition close to the rotor (1D downstream) and on centreline ( y = 0, z = 0.27 m), with a value of ΔUx / U0 = 40.3%. The reduction in velocity deficit continued further downstream, however, given the small number of measurements in the far-wake ( x ≥ 5D ), caution of results must be applied. Beyond downstream distances of 10D, the variation of wake recovery was lesser than 20% and the mean deficit was about 7%. Fig. 5 depicts the distribution of the turbulence on the mid plane. In
3. Results and analysis 3.1. Mean and turbulent characteristics This section summarizes the wake deficit and turbulence intensity with different waves. Velocity was measured at the sampling points 5
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turbulence intensities of waves 1, 2, 3, and the no wave condition, were 12.9% , 15.2%, 17.6% and 8.6% respectively.
3.1.2. Vertical profile Fig. 6 contours the velocity deficit under a variety of test conditions and shows a highly similar wake recovery on the mid plane ( y = 0 ). Compared to the lateral development, the depth sections are asymmetrical and vary throughout the vertical position. The profiles of velocity deficit at x = 2D , 5D , 7D , 15D downstream are as shown in Fig. 7. Such cases demonstrate the significant effect of the support structures (nacelle and pile) on the wake, for the regions up to 2D downstream. Because of the high turbulence behind turbines support structure, the pile wake occurred at the upper depth region, close to the rotor (in agreement with ref. (Chen et al., 2017).). Further downstream ( x ≥ 5D ), the wake of the individual turbine rotor merged with the wake, caused by the circular cylinder support, to form a single, asymmetrical wake; and at x = 15D position, the stream-wise velocity in the wake core recovered to within 10% of the incident flow. The blockage effect of turbine stanchion decreased sharply over 1D to 3D downstream. The maximum deficit, however, was located at z = 305 mm position by 1D downstream, with a value of 45%. As illustrated in Fig. 7, with the development of wake, the centreline of velocity deficit tilted upward to the still water surface. The centre of the main wake was developed slowly from z / h = 0.62 ( x = 5D ) to 0.67 ( x = 7D ), and then became constant beyond distances of 10D . The wake recoveries, under current with and without waves, were almost identical. The significant effect of the wave-current flow on the wakes turbulence intensity is shown in Fig. 8. According to Paul Mycek et al. (2014), a high turbulence causes violent oscillation on the performance of the turbine. By comparing Fig. 8 (b) with (d), we observe a positive correlation between the downstream turbulence intensity and the wave height (wave 3). In addition, the apparent, faster attenuation of the turbulence at mid-plane can be attributed to longer wave periods (see Fig. 8 (c)). As illustrated in Fig. 9, the wakes turbulence is asymmetrical. In the pure-current test, the total turbulent intensity (TI ) approached a linear distribution, except at the 2D plane, due to the influence of turbine stanchion. The sub-figures in Fig. 9 outline the substantial effect of the wave-induced kinematic on the turbulent fluctuations. Therefore, under wave-current conditions, a high turbulence intensity in the upper half of the wake corresponded to a larger wave height. In far-wake region ( x ≥ 5D ) and close to water surface (z / h ≈ 0.855), the mean turbulence intensity of waves 1, 2, 3 was approximately 17.4%, 17.7% , 26.2% .
Fig. 4. Longitudinal Variation of stream-wise velocity deficit (ΔUx / U0 ) along the rotor centre ( y = 0 , z = 0.27 m).
Fig. 5. Longitudinal distribution of total turbulent intensity (TI ) along the rotor centreline ( y = 0 , z = 0.27 m).
the velocity measurements, the fluctuations due to turbulence and waves resulted difficult to separate, because of the proximity of the rotors and wave frequency. Waves affected the turbulence intensity and not the velocity deficit (same as ref. (Stallard et al., 2013).). In our experiments, the turbulence was more influenced by the waves rather than by the wingtip vortices. Because of the combined effect of the wave and the pile wake, the highest turbulence intensity was observed at 1D downstream along the top axis, with a value of 32.1%. Similarly, there was a sharp TI decrease at 1D ≤ x ≤ 3D due to the influence of support structures. Further downstream, the turbulence intensity was almost uniform; although the intermediate deep waves still affected the wake turbulence for x ≥ 5D . Over the range of 5D -15D downstream, the most important factor on turbulence intensity was wave height rather than wave period (see Fig. 5, e.g. wave 1 and 3). The averaged
Fig. 6. Contours of stream-wise velocity deficit (ΔUx / U0 ) on mid plane ( y = 0 ). 6
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Fig. 7. Vertical profiles of stream-wise velocity deficit at x = 2D , 5D , 7D , 15D on mid plane ( y = 0 ). Dash curves indicate the mean trend only.
Fig. 8. Contours of total turbulent intensity (TI ) on mid-plane ( y = 0 ).
Fig. 9. Vertical profiles of total turbulent intensity (TI ) at x = 2D , 5D , 7D , 15D on mid plane ( y = 0 ). Dash curves indicate the trend only.
For the lateral expansion of the wake profile, the rapid deficit of velocity occurred in the range of 1D to 5D downstream because of the high turbulence induced by rotor. Some of the wake profiles in lateral direction can be seen in Fig. 11. Because of the bypass flow effect, the
3.1.3. Lateral velocity deficit Fig. 10 contours the stream-wise velocity deficit across the rotor plane (z = 0.27 m), and shows a high similarity of wake recovery between the pure-current and wave-current conditions. 7
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Fig. 10. Contours of stream-wise velocity deficit (ΔUx / U0 ) on rotor plane (z = 0.27 m).
Fig. 11. Lateral profiles of stream-wise velocity deficit at x = 2D , 5D , 7D and 15D on rotor plane (z = 0.27 m ). Black curves indicate profile from Stallard et al. (2015) and Cyan curves indicate profile from Lam and Chen (2014). (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.).
Fig. 12. Experimental data and best-fit of normalized maximum deficit and half width at the rotor centreline ( y = 0, z = 0.27 m). Solid curves indicate the best-fit for Eqs. (10) and (11).
A self-similar traverse expansion wake was attained on the rotor plane ( y = 0 ). Now, referring to Stallard et al. (2015), the Gaussiandistributed wake profile is:
wake profiles of velocity deficit were axisymmetric in the near-wake region. As illustrated in Fig. 11 (b), (c) and (d), a slower recovery occurs for x 5D; the maximum deficit of the velocity is about 20%, 13% and 6% at 5D , 7D and 15D respectively. 8
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Fig. 13. Contours of normalized integral time scale (Tx / Txinc ) on mid plane ( y = 0 ). Table 3 Average value of normalized integral time Tx / Txinc at. x ≥ 5D Measurement axis Bottom tip Rotor centre Top tip
f (y ) =
(z = 0.135 m) (z = 0.270 m) (z = 0.405 m)
no wave
wave 1
wave 2
wave 3
0.969 0.395 0.845
0.135 0.118 0.132
0.160 0.172 0.196
0.109 0.117 0.133
U − Ux (y ) y2 ⎞ ΔUx ⎛ = 0 = exp ⎜−ln 2 2 ⎟ U0 − Ux (0) ΔUs y 1/2 ⎠ ⎝
(8)
where ΔUs is the maximum deficit, and Ux (y1/2 ) = 0.5ΔUs defined the half width ( y1/2 ) of the profile. As apparent from Fig. 11, the Gaussian profile can not be used to describe the lateral profiles at distances x ≤ 2D , but it is representative of the lateral expansion over x ≥ 5D downstream.
S≡
U0 dy1/2 ΔUs dx
(9)
In regards to Eq. (9), the self-similarity case requires a constant spreading parameter S (ref (Pope, 2001) P.148). According to the momentum theorem of the cylinder and wake (Batchelor, 2000), the parameter ΔUs y1/2 is independent of x. The constancy of S and ΔUs y1/2 means ΔUs and y1/2 vary to x −1/2 and x 1/2 , respectively. The spreading parameter of unbounded wakes correspond to the following: Splate = 0.073, Scylinder = 0.083 and Sairfoil = 0.103 for different generators (ref (Pope, 2001) P.149).
ΔUs = 0.4792(x / D)−1/2 − 0.0525 U0
y1/2 D
= 0.0615(x / D)1/2 + 0.3149
(10) (11)
For a plates wake, the normalized maximum deficit (ΔUs / U0 ) and lateral half width ( y1/2 / D ) are plotted in Fig. 12. The empirically derived Eqs. (10) and (11) fitted well with the velocity deficit in far-wake region ( x ≥ 5D ). According to Eq. (9), the lateral spreading parameter is 0.064, a value smaller than the plates (Splate = 0.073). On the other hand, the lateral expansion of the turbine wake, proposed by Lam and Chen (2014), can be expressed as: Fig. 14. Log-log distributions of normalized integral time scale (Tx / Txinc ) along several axis on mid plane ( y = 0 ).
f (y ) =
U − Ux (y ) (|y| + Cx − (D /2))2 ⎞ ΔUx ⎟ = 0 = exp ⎛⎜− ΔUs U0 − Ux (0) 2(Cx )2 ⎠ ⎝
(12)
where C is defined as: C = σ / x 0 , σ denotes the standard deviation of velocity at traverse direction and x 0 is limitation to the end of the zone 9
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of flow establishment. According to Albertson (1948), the constant C is found to be 0.0806 when the zone of flow establishment occurs. The cyan curves shown in Fig. 11 represent the theoretical result by the proposed equation. The profile in Fig. 11 (a) indicates the compatibility of Eq. (12) with the velocity at the range of |y / D| = 0.34 − 1.0 ; but it fails in the high deficit core ( |y / D| ≤ 0.34 ; 2D ) due to the presence of the nacelle and the support. For given downstream, the following equation results more appropriate: X < 5D , Eq. (12); X ≥ 5D , Eq. (8). Although, we can not rule out the influence of the turbine in the far-wake regions results, thus these should be taken into consideration.
for the upper region (z / h ≥ 0.5) and by the wave period close to the bed surface (z / h ≤ 0.2 ). In the pure-current flow, a range of low turbulence intensities occurred. The Integral scale also highlighted some interesting but different result from the mean wake structure. Experimental wake inspection of the wave-current flow revealed a strong influence of waves on the integral time scale (Tx ). The integral was more influenced by the waveinduced small-scale vortices rather than by the wingtips vortices; and likewise, by the wave period rather than by the wave height at the farwake. This paper developeds a simple qualitative description of integral time scale, but further work with a series of waveforms is necessary to confirm these results.
3.2. Integral characteristic To represent the evolution of integral characteristic, stream-wise velocity fluctuations were measured on the mid plane at different vertical locations. The sample duration was 5 min, and the sampling rate was 100 Hz (30,000 samples in total). The normalized integral time scale was defined as Tx / Txinc , where Tx is the integral time scale calculated by the velocity fluctuations (see Eq. (4)) and Txinc is computed via the linear fit curve of Fig. 3 (d).
Acknowledgments The research was supported by the following funding programs: National Natural Science Foundation of China (51809083); Natural Science Foundation of Jiangsu Province (BK20180504); Fundamental Research Funds for the Central Universities (No.2019B15114) and Water Conservancy Science & Technology Project of Jiangsu Province (2018026).
3.2.1. Overview of the integral time scale Contours of normalized integral time scale on the mid-plane ( y = 0 ) are illustrated in Fig. 13. As shown in Fig. 13 (a), at 1D downstream, Tx is substantially reduced within the near-wake region and Tx / Txinc is ≈ 0.03 at the height of z = 0.305. As a result of the expansion of the internal wake, the large-scale vortices induced by the rotor affected the far-wake along the rotor centre ( y = 0, z = 0.27 m ), and produced a Tx / Txinc ≈ 0.4 . Because of the shear layer of flume bed and water surface, asymmetric distributions of Tx occurred along the bottom and top axis. Over the range of x ≥ 5D downstream, the Tx / Txinc along both the bottom and top axis, were approximately 0.97 and 0.85, respectively. Comparing Fig. 13 (b), with (c) and (d), the Tx results more influenced than the waves by the rate of blockage. Due to the small-scale vortices generated by the waves, Tx / Txinc along the rotor centreline is much lesser than the pure-current case. In the far-wake region, the integral time scale is substantially reduced to 0.118, 0.172 and 0.117 for the conditions corresponding to waves 1, 2 and 3 respectively.
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3.2.2. Longitudinal log-log distributions The representative log-log distributions of Tx / Txinc along several axis are illustrated in Fig. 14. In near-wake region (see Fig. 14 (b) and (c)), the normalized integral time scale Tx / Txinc developed a high-variation rate comparable (but higher) with a wind turbines wake (Jin et al., 2016); and it is doubtful whether tis wind finding is applicable to high turbulent flows. Another source of uncertainty was the effect of the large-scale vortices generated by the turbine stanchion. In contrast to the undisturbed flow, the integral scale Tx became lower in the wave-current flows. At the distance of x ≥ 5D , the wave with a longer period (wave 2) developed a larger Tx / Txinc along longitudinal direction and the integral scale did not vary greatly with the change of wave height. Table 3 indicates the average of Tx / Txinc for downstream distances of x ≥ 5D . 4. Conclusions This paper addressed the influence of the waves on tidal stream turbine wake. Mean and integral characteristic of the wake were analyzed for various wave-current conditions. Three-dimensional mean velocity and vertical turbulence intensity were presented to study the mean wake structure. In the near-wake region, the turbine stanchion had more influence on both wake recovery and turbulence. The waves had negligible effect on the wake recovery behind the turbine. Lateral expansion of the mean wake was consistent with the Gaussian profile. Under the wave-current conditions, the turbulence intensity was greatly affected by the wave height 10
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(1–3), 41–69. Stallard, T., Collings, R., Feng, T., Whelan, J., 2013. Interactions between tidal turbine wakes: experimental study of a group of three-bladed rotors. Phil. Trans. R. Soc. A 371 (1985), 20120159. Stallard, T., Feng, T., Stansby, P., 2015. Experimental study of the mean wake of a tidal stream rotor in a shallow turbulent flow. J. Fluid Struct. 54, 235–246. Sufian, S.F., Li, M., OConnor, B.A., 2017. 3d modelling of impacts from waves on tidal turbine wake characteristics and energy output. Renew. Energy 114, 308–322. Sun, X., Chick, J., Bryden, I., 2008. Laboratory-scale simulation of energy extraction from tidal currents. Renew. Energy 33 (6), 1267–1274. Tedds, S., Poole, R., Owen, I., 2012. Wake characteristics of horizontal axis tidal stream turbines in uniform and non-uniform steady flows. In: Proceedings of the 4th International Conference on Ocean Energy, Dublin, Ireland, pp. 17–19. Tedds, S., Owen, I., Poole, R., 2014. Near-wake characteristics of a model horizontal axis tidal stream turbine. Renew. Energy 63, 222–235. Thomas, G., Klopman, G., 1997. Wave-current interactions in the near shore region. Int. Series Adv. Fluid Mech. 10, 255–319. Von Karman, T., 1948. Progress in the statistical theory of turbulence. Proc. Natl. Acad. Sci. Unit. States Am. 34 (11), 530–539. Walker, S., Cappietti, L., 2017. Experimental studies of turbulent intensity around a tidal turbine support structure. Energies 10 (4), 497. Whelan, J., Stallard, T., 2011. Arguments for modifying the geometry of a scale model rotor. In: Proceedings of 9th European Wave and Tidal Energy Conference (EWTEC2011), (on–CD). Whelan, J., Graham, J., Peiro, J., 2009. A free-surface and blockage correction for tidal turbines. J. Fluid Mech. 624, 281–291. Zhang, C., Zhang, Q., Zheng, J., Zeki, D., 2017a. Parameterization of nearshore wave front slope. Coast Eng. 127, 80–87. Zhang, Y., Zhang, J., Zheng, Y., Yang, C., Zang, W., Fernandez-Rodriguez, E., 2017b. Experimental analysis and evaluation of the numerical prediction of wake characteristics of tidal stream turbine. Energies 10 (12), 2057. Zheng, J., Zhang, C., Zeki, D., Lin, L., 2014. Numerical study of sandbar migration under wave-undertow interaction. J. Waterw. Port, Coast. Ocean Eng. 140, 146–159.
velocity profile at tidal-stream energy sites. Renew. Energy 114, 258–272. Liu, H.-w., Ma, S., Li, W., Gu, H.-g., Lin, Y.-g., Sun, X.-j., 2011. A review on the development of tidal current energy in China. Renew. Sustain. Energy Rev. 15 (2), 1141–1146. Liu, H., Hayat, I., Jin, Y., Chamorro, L.P., 2018. On the evolution of the integral time scale within wind farms. Energies 11 (1), 93. Maganga, F., Germain, G., King, J., Pinon, G., Rivoalen, E., 2010. Experimental characterisation of flow effects on marine current turbine behaviour and on its wake properties. IET Renew. Power Gener. 4 (6), 498–509. Mycek, P., Gaurier, B., Germain, G., Pinon, G., Rivoalen, E., 2014. Experimental study of the turbulence intensity effects on marine current turbines behaviour. part i: one single turbine. Renew. Energy 66, 729–746. Myers, L., Bahaj, A., 2009. Near wake properties of horizontal axis marine current turbines. In: Proceedings of the 8th European Wave and Tidal Energy Conference, Uppsala, Sweden, pp. 558–565. Myers, L., Bahaj, A., 2010. Experimental analysis of the flow field around horizontal axis tidal turbines by use of scale mesh disk rotor simulators. Ocean Eng. 37 (2–3), 218–227. Nortek, A., 2012. Vectrino Profiler User Guide. Tech. rep., Nortek AS, Vangkroken, Norway. Olczak, A., 2016. The Influence of Waves on Tidal Stream Turbine Arrays. Ph.D. thesis. University of Manchester. O'Doherty, T., Mason-Jones, A., O'Doherty, D.M., Evans, P.S., Wooldridge, C.F., Fryett, I.A., 2010. Considerations of a horizontal axis tidal turbine. Proc. ICE - Energy 163 (3), 119–130. Pope, S.B., 2001. Turbulent Flows. Robins, P.E., Neill, S.P., Lewis, M.J., 2014. Impact of tidal-stream arrays in relation to the natural variability of sedimentary processes. Renew. Energy 72, 311–321. H. Schlichting, Boundary-layer Theory, 7th. editon, McCraw-Hill Book Co., Ncw York. Soulsby, R., Humphery, J., 1990. Field observations of wave-current interaction at the sea bed. In: Water Wave Kinematics. Springer, pp. 413–428. Soulsby, R., Hamm, L., Klopman, G., Myrhaug, D., Simons, R., Thomas, G., 1993. Wavecurrent interaction within and outside the bottom boundary layer. Coast. Eng. 21
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Ocean Engineering journal homepage: www.elsevier.com/locate/oceaneng
Experiments on the mean and integral characteristics of tidal turbine wake in the linear waves propagating with the current
T
Wei Zanga, Yuan Zhengb, Yuquan Zhangb,∗, Jisheng Zhangc, E. Fernandez-Rodriguezd a
College of Water Conservancy and Hydropower Engineering, Hohai University, Nanjing, 210098, China College of Energy and Electrical Engineering, Hohai University, Nanjing, 210098, China c College of Harbor, Coastal and Offshore Engineering, Hohai University, Nanjing, 210098, China d Technological Institute of Merida, Technological Avenue, Merida, 97118, Mexico b
A R T I C LE I N FO
A B S T R A C T
Keywords: Tidal-stream turbine Wave-current flow Wake recovery Turbulent intensity Integral time scale
The vast majority of tidal-stream sites have been described with turbulent flows coexisting with waves, but the wake of a tidal-stream turbine in such flows is not fully understood. A model tidal-stream turbine, of diameter 0.49 times the water depth, was tested under the influence of intermediate waves following the current, to analyze both of its mean and integral wake characteristics. An ambient intensity around 10% was established in the recirculating water flume. Acoustic doppler velocimeter (ADV) with Nortek Vectrino profiler probes were used to obtain the time-varying velocities, the turbulence intensities and the integral time scale. Analysis of velocity deficit indicated the mean wake and Gaussian distribution were consistent, with waves being of no real consequence on the wake recovery. The turbulence intensity was shown to be affected by the wave height for the upper region, and the influence of the wave period was greater for the integral time scale than for the wave height at the far-wake region. We believe these results offer significant insight into the turbine wake in a waveturbulence flow.
1. Introduction
turbine becomes vulnerable to current, turbulence and sea waves interactions. According to Lewis and Zheng et al. (Lewis et al., 2014), (Zheng et al., 2014), the waves or even undertow measured per meter wave height, reduce the net tidal resource by 10%. Therefore, it is crucial to investigate the influence of the waves on the wake of tidal stream units. To analyze the combined wave-current flow, research has mainly focused on the wave spectrum. Few studies, though, have considered the influence of waves on the mean and integral characteristics of the ambient flow. Experiments conducted by Kemp and Simons focused on the interactions between current and waves propagating along with (Kemp and Simons, 1982) and opposing the flow (Kemp and Simons, 1983). The opposing waves caused an increase of mean velocity in the upper profiles of water column, whereas the co-current-propagating waves reduced the mean velocity. Klopman and Thomas conducted experiments with different types of waves (e.g. regular, bi-chromatic (Klopman) and random waves (Thomas and Klopman, 1997)) and came to a similar conclusion. Much work on the potential, functioning and wake characteristics of tidal stream turbines have been put forward. Garrett et al. (Garrett and Cummins, 2005) were among the first to study the large theoretical
Following our current industrial scenario, within the next decades, the aftereffects of the fossil fuels burning and pollution on ecosystems will be critical to the survival of the human society (Kanemoto, 2010). In the search of a clean alternative to fossil fuels, the harnessing of tidal stream resources is attracting widespread interest due to the recent advancements of wind offshore technology and predictability of the tides and currents (Antonio, 2010). China, a country with a summary of 32,000 km shorelines, has abundant unexploited tidal stream resources; according to statistical studies, the nations theoretical generating capacity exceeds 13 GW (Liu et al., 2011). Current solutions to convert the kinetic energy of the tidal currents into electricity in an efficient manner (close to 50% of the available power) comprise mechanical apparatuses, called tidal stream turbines. There are a variety of tidal stream turbine concepts put into commercial operations in arrays; They are typically installed on an nearshore location close to the coast or wave front slope with a depth lesser than 40 m, about 1.5–3 times the size (diameter) of the deployed turbine (Lewis et al., 2015), (Zhang et al., 2017a). Because of the bathymetry, flow characteristics and depth range of turbine deployment, the functioning of a tidal stream
∗
Corresponding author. E-mail address: [email protected] (Y. Zhang).
https://doi.org/10.1016/j.oceaneng.2018.12.048 Received 3 July 2018; Received in revised form 18 December 2018; Accepted 20 December 2018 0029-8018/ © 2018 Elsevier Ltd. All rights reserved.
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Fig. 1. Schematic and photo of the wave-current recirculating water flume.
within far-wake are self-similar and follow a Gaussian distribution. The far-wake region and the length of wake recovery have been shown to depend strongly on the level of incident turbulence intensity (Myers (Myers and Bahaj, 2010), Maganga et al. (2010) and Mycek et al. (2014)). According to Bahaj et al. (2012) the vertical constraints, imposed by the free surface and the seabed, have significant effect on wake recovery behind a tidal turbine. The magnitude of turbulent kinetic energy near the blade tip, has been measured by Tedds et al. (2012), and Zhang et al. (2017b) studied the wake characteristics of rotors deployed at different submerged depths. On the other hand, the wake generated by the drag, owing to the support structure, was reported by Walker et al. (Walker and Cappietti, 2017). Despite more information is becoming available on the turbines performance and wake characteristics, yet there is still considerable ambiguity with regard to the wave-current interactions observed in tidal stream sites. A few laboratory studies have attempted to understand this unsteady behaviour. To this end, stallard et al. studied the interactions between the ambient flow and the waves (Stallard et al., 2013). In like manner, Alexander Olczak (2016) considered the mean and pulsation characteristic of the combined flow to quantify the influence of the waves on tidal turbine wake. As regards to the support structures force, Fernandez quantified the variation of extreme thrust (Fernandez-Rodriguez et al., 2014) and in his doctorate dissertation (Fernandez Rodriguez, 2015), he demonstrated the peak forces are in function of the measured wave heights. Moreover, T.A. de Jesus Henriques represented the performance characteristics of the turbine (de Jesus Henriques et al., 2014) and Sufian F. Sufian et al. (2017) developed a virtual blade model to simulate the
potential of tidal currents in a channel. Equally important, JI Whelan et al. (2009) studied the blockage effect, ratio of turbines swept area to channels cross-sectional area, on turbine performance. Such works offered encouraging insight of tidal stream potential, therefore, various experimental studies have been conducted to indicate the performance and wake structure of geometric tidal devices in a water flume or tank. The rotation induced by scale rotors of 0.2–0.8 m diameter has been studied; although smaller model rotors may also be employed if appropriate consideration is given to the low resulting blades Reynolds number (Whelan and Stallard, 2011). Alternatively, porous disks have been successfully employed by Bahaj et al. (2007) and Sun et al. (2008) to represent the momentum extraction of geometric scaled turbines. In terms of wake structure, the tidal stream turbines wake could be divided on the basis of downstream distance into two distinct regions: the near and far-wake (Myers and Bahaj (2009)). The near wake is distinguished by possessing a high swirl intensity, compared with the far wake, owing to its closeness to the torque-imparting rotor plane. Various studies have provided comprehensive knowledge of the wake properties. For instance, the anisotropy tensor bi j , defined by Choi and Lumley (2001), was used by Tedds et al. (2014) to investigate the anisotropy of wake turbulence but failed to present a contour profile on the wake-decay characteristics. Chen et al. (2017) calculated the Reynolds shear stress to simplify the wake analysis, but more clarification on the asymmetrical of free shear layer is still needed. Lam and Chen (2014) proposed a series of equations to predict the wake from a horizontal-axis tidal turbine with the Gaussian probability distribution; but it showed a lesser accuracy in the far wake region. Experiments conducted by Stallard et al. (2015) showed the wake velocity deficits 2
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(SNR) and correlation coefficient (COR) was measured to represent signal quality. The SNR of most samples (more than 90%) was greater than 15 dB, whereas the COR was greater than 80%. and Nortek states the probes accuracy is ± 0.5 % (refers to Vectrino Profiler User Guide (Nortek, 2012)).
effects on tidal stream turbines due to incoming waves. In addition to the mean wake structure of the turbine, the integral scale has been identified as another bulk parameter for the characterization of the scale of vortex, especially for the wave-current flow (Pope, 2001). To estimate this parameter, various models have been proposed (Von Karman, 1948), (Kaimal and Finnigan, 1994). Stallard et al. obtained the integral length scale of the ambient turbulence of a channel based on ref. (Stallard et al., 2015). But one of the major drawbacks adopting this approach is the lack of a detailed description of the ambient flow. Jin et al. (2016) suggests the growth rate of the integral length scale in a wind farm is linear at the far-wake region, although, more recent evidence suggests it may undergo a significant reduction near the turbine (Liu et al., 2018). This paper examines a three-bladed horizontal-axis tidal stream turbine, designed by the Blade Element Momentum theory (BEMT) (Batten et al., 2008a), (Bossanyi, 2009), in several wave-current conditions. The objective, is to present the distribution of mean wake structure and integral time scale in detail. In this context we try to characterize the turbine wake in terms of the wave parameters such as the wave height and frequency relationship.
2.3. Incident flow In order to represent a baseline of the undisturbed flow, velocity measurements were taken with an empty flume. The properties of x , y = 0 plane are illustrated in Fig. 3 (without the rotor). For the smooth flow, the sampling volume was located on mid plane ( y = 0 ). The heights ranged from z = 10 mm to z = 490 mm (z / h ≈ 0.1 to 0.9) with Δz = 40 mm. Three measurement points were distributed in each sampling volume. Multiple sets of tests were taken at different streamwise ( x = −1D to x = 15D ) and lateral (Mid plane and y = ± 1D ) sections to quantify the errors. Over these sections, the change in ambient velocity was lesser than 5%. To characterize the incident velocity, both log-law and power-law were applied in close-to-bed region (z / h < 0.2 ) as illustrated in Fig. 3 (a). The log-law approximation is expressed with Eq. (1) (Schlichting). As regards to this equation, ν = 1.006 × 10−6 m2 /s is the kinematic viscosity of water, κ = 0.41, the Von Kármán's constant, C = 5.0 , the constant for smooth flow and U * , the friction velocity; its value (U * = 0.0139 m/s) is estimated with the measured velocity (Ux ) and wall distance (z) within the close-to-bed region.
2. Experimental arrangement Laboratory experiments presented in this article were conducted in a wave-current recirculating water flume, constructed by the Tianjin University. The flume (see Fig. 1) has a width (w ) of 1.2 m, a length (lf ) of 57 m, a water depth of 0.55 m, a damping length og 5 m, a polished marble bed and flat Perspex walls. Flow enters through a porous weir to dissipate the large scale turbulent eddies. Wave paddles are utilized to generate regular waves following the direction of the current. A single rotor at mid-depth with a diameter D = 0.27 m is attached to a rigid support structure. Components of inflow velocity have been measured using acoustic doppler velocitimeter (ADV) probes, in pure-current and wave-current conditions. Measurements of the wave elevation are taken using a wave height probe situated behind the turbine.
Ux (z ) 1 zU * ⎞ + C , with C = 5.0 in undisturbed flow = ln ⎛ U* κ ⎝ ν ⎠ ⎜
⎟
(1)
If we now turn to the power law equation Eq. (2), the power order (α) and bed roughness coefficient (β) correlate with the observed measurements but are initially unknown (Soulsby and Humphery, 1990), (Soulsby et al., 1993). To solve this issue, we use an iterative process with a least-squares approach, assuming a 1/7th power order. As a result, a bed roughness coefficient of β = 0.43 is obtained. This exponential order assumption is in line with previous studies (See ref. (Batten et al., 2008b), (O'Doherty et al., 2010), (Robins et al., 2014) and (Lewis et al., 2017)) and correlates fairly well with the tidal measurements (Batten et al., 2008b). However, a well-known criticism of the power-law approach is its difficulty in predicting the ambient flow of the full-scale model, since solutions are dependent on the Reynolds number and the turbines are usually designed on a Froude-number similarity.
2.1. Flume setup All tests are taken with a depth averaged inlet velocity of U0 = 0.35 m/s. The origin of coordinate system is defined beneath the rotor centreline at the bed plane ( x − y plane with z = 0 ). The longitudinal, lateral and vertical axes are defined as x, y and z, as indicated in Fig. 2. The equipment is a traverse-moving device with increments of 1 mm. Velocities were measured at various vertical and lateral sections ( y − z planes), spanning from the water surface to the channel bed, in the longitudinal range of 1D upstream to 15D downstream (see Fig. 2 (a)). Twenty-three points were measured at each plane parallel to the rotor plane. The sampling sites are as shown in Fig. 2 (b).
1/ α
Ux (z ) z = ⎜⎛ ⎟⎞ U0 βh ⎝ ⎠
, with
α=7
for 1/7th order power − law
(2)
The upper depth profile of longitudinal velocity was recorded at rotor plane ( x = 0 ). As seen in Fig. 3 (b), both log-law and power-law fit agree well with measurements for depths of z / h < 0.2 . Interestingly, for values beyond this limit z / h = 0.2 , little correlation was observed between the models and the measurements. Eq. (3) describes another important parameter of the incident flow, named the turbulence intensity (TIiinc ), where Ui′ is the mean velocity fluctuations of three dimensions, and U ′, the total value. The components (TIiinc ) of and the total intensity (TI inc ) of the turbulence observed for the current-only case, are illustrated in Fig. 3 (c). The averagedturbulence intensity near the hub height (z / h = 0.49) in the longitudinal, lateral and vertical direction correspond to 7.0%, 5.1%, 4.4%, respectively; and they provide a total turbulence intensity of 9.8%, throughout different longitudinal sections. According to Fig. 3 (d), the averaged turbulence intensity for various wave forms corresponds to 12.1%, 15.0% and 16.7%, respectively.
2.2. Velocity measurement Two Nortek acoustic doppler velocimeter (ADV), with a 4-beam down-looking Vectrino profiler probe, were employed to record the velocity from 0 to 3.0 m/s. These devices have been widely adopted for both industrial and scientific applications and are known for its good accuracy and precision. They are able to calculate the three-dimensional velocity components using the phase shift of the acoustic signal caused by the reflection of the particles within the sampling volume. Throughout this paper, the time varying and mean velocity components are expressed as ui and Ui , where the suffix i = x , y, z means the direction of the flow component. The probe can profile the water over a 30 mm range for a cylindrical sampling of 40 mm with a measurement resolution of 1 mm. Velocities components were recorded with a sampling rate of 100 Hz. A sample duration of 100 s, large enough for a time-frequency analysis of the signal, was set for all tests. The signal to noise ratio
TIi =
3
(Ui′)2 U0
(3)
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Fig. 2. Velocity measurement positions.
current condition.
As regards to the longitudinal integral time scale of ambient turbulence, it is defined as Eq. (4), where τ is time lag and u x′ , r (τ ) , σx2 correspond to the velocity fluctuations, autocorrelation and variance of the stream-wise velocity, respectively. The integral is evaluated up to a small time lag τ = 0.01 s such that the correlation coefficient rτ is sufficiently small. Fig. 3 (e) shows the upper depth profile of longitudinal integral time scale (Txinc ) of the incoming flow. However, due to the limitation of sampling rate, such parameter may vary widely. Thus, a linear fit method is used to describe the mean value of normalized integral time scale Txinc U0/ D , and this is about 1.80 on the rotor plane.
Tx =
∫0
∞
rτ dτ , with rτ =
u x′ (t ), u x′ (t − τ ) σx2
2.5. Waveforms There are many wave theories available for predicting the characteristics of wave-current flows. Particularly, the linear wave theory is a commonly suitable approach for describing regular waves of a single frequency. Many experiments limit the applicability of the linear wave theory to long waves with small Ursell number (Ur ≪ 32π 2/3 ≈ 105). The Ursell number, Ur = Hλ2 / h3, where H represent the wave height and λ, the wavelength, is a normalized parameter put forward to indicate the non-linearity of waves; and it is used as a parametric indication of linear wave theorys suitability. The linear surface elevation is expressed as Eq. (6):
(4)
2.4. Model rotor
η=
The full-scaled commercial rotor operates with a mean incident flow velocity of 1.57 m/s at the depth of 11 m, and has a diameter of 5.4 m. On the grounds of the Froude scaling theory (Eq. (5)), we chose a 1:20 geometric scaling model with the corresponding flume conditions (U0 , TI , h, λ), where v, g and l are the mean incident flow velocity, local gravity acceleration and operating water depth, respectively. The suffix f and m represent the full and model scale rotor.
vf vm
=
(6)
and the dispersion equation is:
C=
λ = T
g tanh(kh) k
(7)
where g is the gravity acceleration, k = 2π / λ , the wave number. To obtain the wavelength in the experiments, these equations were fitted against the wave height measurements by using a least-squares approach. The experimental waveforms were generated by a piston type wave-maker, and measured by wave height recorders. The probes were installed at transverse positions ( y = −0.8, −0.4, 0,0.4, 0.8 m) and at every 20D longitudinal sections, starting from − 50D to 30D . The maximum error of wave height was less than 4%. The wave parameter obtained in our tests is in terms of the relative water depth, kh , a criterion of the class of waves: shallow, intermediate and deep. Table 2 illustrates this. In our test, the relative water depths kh correspond to intermediate wave region (π /10 < kh < π ).
gf lf gm lm
H cos(kx − ωt ) 2
(5)
The model rotor is made of stainless steel and each blade has a NACA 4412 airfoil profile with radial variation (r / R ), chord length (c / R ) and twist angle (θ) as indicated in Table 1: In our tests, the blockage rate is a = πR2 / wh ≈ 8.7%. The rotor was operated with a tip-speed ratio TSR = ωr R/ U0 ≈ 2.43 , where ωr represents the angle velocity and this is approximate 62.6 rpm in pure4
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Fig. 3. Vertical flow properties at x = 0 plane without turbine installed (a) Log-law and power-law fit method in close-to-bed region (z / h < 0.2 ); (b) Mean longitudinal velocity (Ux ) in upper profile (z / h > 0.2 ); (c) Turbulent intensiy (TIiinc , TI inc ) in upper profile (z / h > 0.2 ); (d) Total turbulent intensity (TI inc ) under wave conditions; (e) longitudinal integral time scale (Txinc U0/ D ) in upper profile (z / h > 0.2 ).
shown in Fig. 2 (b) from 1D upstream to 15D downstream. The threedimensional velocity variations provide insight into the wake structure and its development whereas the longitudinal and vertical plane measurements highlighted the influence of waves on the far-wake development. Wake velocity deficit ΔUx / U0 was calculated by the local deficit (ΔUx = U0 − Ux ), and the total turbulence intensity, by the components of the velocity (Eq. (3)).
Table 1 Key blade sections. Section
r /R
c /R
θ
Blade Bottom Widest Blade Tip
0.075 0.550 1.000
0.164 0.308 0.079
47. 9∘ 27. 8∘ 9. 5∘
Table 2 Wave conditions. Wave
1 2 3
Wave height
Period
Wavelength
Relative depth
Ursell number
(H)
(T)
(λ)
(kh )
(Hλ2/ h3 )
0.030 m 0.039 m 0.051 m
1.0 s 1.5 s 1.0 s
1.53 m 2.91 m 1.53 m
2.26 1.19 2.26
0.42 1.99 0.72
3.1.1. Longitudinal Variation A reduction in the velocity deficit was observed for each of the waveforms listed in Table 2. Fig. 4 shows the effect of wave variation on velocity deficit along the rotor centreline. The rate of the wake recovery was found to be similar near the rotor, and the deficit was slightly greater than the non-wave case in far-wake region. In the near-wake region ( x ≤ 3D ), the velocity deficit showed a rapid decrease and reached a mean value of 21% at 3D downstream. The maximum deficit occurred under the current-only condition close to the rotor (1D downstream) and on centreline ( y = 0, z = 0.27 m), with a value of ΔUx / U0 = 40.3%. The reduction in velocity deficit continued further downstream, however, given the small number of measurements in the far-wake ( x ≥ 5D ), caution of results must be applied. Beyond downstream distances of 10D, the variation of wake recovery was lesser than 20% and the mean deficit was about 7%. Fig. 5 depicts the distribution of the turbulence on the mid plane. In
3. Results and analysis 3.1. Mean and turbulent characteristics This section summarizes the wake deficit and turbulence intensity with different waves. Velocity was measured at the sampling points 5
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turbulence intensities of waves 1, 2, 3, and the no wave condition, were 12.9% , 15.2%, 17.6% and 8.6% respectively.
3.1.2. Vertical profile Fig. 6 contours the velocity deficit under a variety of test conditions and shows a highly similar wake recovery on the mid plane ( y = 0 ). Compared to the lateral development, the depth sections are asymmetrical and vary throughout the vertical position. The profiles of velocity deficit at x = 2D , 5D , 7D , 15D downstream are as shown in Fig. 7. Such cases demonstrate the significant effect of the support structures (nacelle and pile) on the wake, for the regions up to 2D downstream. Because of the high turbulence behind turbines support structure, the pile wake occurred at the upper depth region, close to the rotor (in agreement with ref. (Chen et al., 2017).). Further downstream ( x ≥ 5D ), the wake of the individual turbine rotor merged with the wake, caused by the circular cylinder support, to form a single, asymmetrical wake; and at x = 15D position, the stream-wise velocity in the wake core recovered to within 10% of the incident flow. The blockage effect of turbine stanchion decreased sharply over 1D to 3D downstream. The maximum deficit, however, was located at z = 305 mm position by 1D downstream, with a value of 45%. As illustrated in Fig. 7, with the development of wake, the centreline of velocity deficit tilted upward to the still water surface. The centre of the main wake was developed slowly from z / h = 0.62 ( x = 5D ) to 0.67 ( x = 7D ), and then became constant beyond distances of 10D . The wake recoveries, under current with and without waves, were almost identical. The significant effect of the wave-current flow on the wakes turbulence intensity is shown in Fig. 8. According to Paul Mycek et al. (2014), a high turbulence causes violent oscillation on the performance of the turbine. By comparing Fig. 8 (b) with (d), we observe a positive correlation between the downstream turbulence intensity and the wave height (wave 3). In addition, the apparent, faster attenuation of the turbulence at mid-plane can be attributed to longer wave periods (see Fig. 8 (c)). As illustrated in Fig. 9, the wakes turbulence is asymmetrical. In the pure-current test, the total turbulent intensity (TI ) approached a linear distribution, except at the 2D plane, due to the influence of turbine stanchion. The sub-figures in Fig. 9 outline the substantial effect of the wave-induced kinematic on the turbulent fluctuations. Therefore, under wave-current conditions, a high turbulence intensity in the upper half of the wake corresponded to a larger wave height. In far-wake region ( x ≥ 5D ) and close to water surface (z / h ≈ 0.855), the mean turbulence intensity of waves 1, 2, 3 was approximately 17.4%, 17.7% , 26.2% .
Fig. 4. Longitudinal Variation of stream-wise velocity deficit (ΔUx / U0 ) along the rotor centre ( y = 0 , z = 0.27 m).
Fig. 5. Longitudinal distribution of total turbulent intensity (TI ) along the rotor centreline ( y = 0 , z = 0.27 m).
the velocity measurements, the fluctuations due to turbulence and waves resulted difficult to separate, because of the proximity of the rotors and wave frequency. Waves affected the turbulence intensity and not the velocity deficit (same as ref. (Stallard et al., 2013).). In our experiments, the turbulence was more influenced by the waves rather than by the wingtip vortices. Because of the combined effect of the wave and the pile wake, the highest turbulence intensity was observed at 1D downstream along the top axis, with a value of 32.1%. Similarly, there was a sharp TI decrease at 1D ≤ x ≤ 3D due to the influence of support structures. Further downstream, the turbulence intensity was almost uniform; although the intermediate deep waves still affected the wake turbulence for x ≥ 5D . Over the range of 5D -15D downstream, the most important factor on turbulence intensity was wave height rather than wave period (see Fig. 5, e.g. wave 1 and 3). The averaged
Fig. 6. Contours of stream-wise velocity deficit (ΔUx / U0 ) on mid plane ( y = 0 ). 6
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Fig. 7. Vertical profiles of stream-wise velocity deficit at x = 2D , 5D , 7D , 15D on mid plane ( y = 0 ). Dash curves indicate the mean trend only.
Fig. 8. Contours of total turbulent intensity (TI ) on mid-plane ( y = 0 ).
Fig. 9. Vertical profiles of total turbulent intensity (TI ) at x = 2D , 5D , 7D , 15D on mid plane ( y = 0 ). Dash curves indicate the trend only.
For the lateral expansion of the wake profile, the rapid deficit of velocity occurred in the range of 1D to 5D downstream because of the high turbulence induced by rotor. Some of the wake profiles in lateral direction can be seen in Fig. 11. Because of the bypass flow effect, the
3.1.3. Lateral velocity deficit Fig. 10 contours the stream-wise velocity deficit across the rotor plane (z = 0.27 m), and shows a high similarity of wake recovery between the pure-current and wave-current conditions. 7
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Fig. 10. Contours of stream-wise velocity deficit (ΔUx / U0 ) on rotor plane (z = 0.27 m).
Fig. 11. Lateral profiles of stream-wise velocity deficit at x = 2D , 5D , 7D and 15D on rotor plane (z = 0.27 m ). Black curves indicate profile from Stallard et al. (2015) and Cyan curves indicate profile from Lam and Chen (2014). (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.).
Fig. 12. Experimental data and best-fit of normalized maximum deficit and half width at the rotor centreline ( y = 0, z = 0.27 m). Solid curves indicate the best-fit for Eqs. (10) and (11).
A self-similar traverse expansion wake was attained on the rotor plane ( y = 0 ). Now, referring to Stallard et al. (2015), the Gaussiandistributed wake profile is:
wake profiles of velocity deficit were axisymmetric in the near-wake region. As illustrated in Fig. 11 (b), (c) and (d), a slower recovery occurs for x 5D; the maximum deficit of the velocity is about 20%, 13% and 6% at 5D , 7D and 15D respectively. 8
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Fig. 13. Contours of normalized integral time scale (Tx / Txinc ) on mid plane ( y = 0 ). Table 3 Average value of normalized integral time Tx / Txinc at. x ≥ 5D Measurement axis Bottom tip Rotor centre Top tip
f (y ) =
(z = 0.135 m) (z = 0.270 m) (z = 0.405 m)
no wave
wave 1
wave 2
wave 3
0.969 0.395 0.845
0.135 0.118 0.132
0.160 0.172 0.196
0.109 0.117 0.133
U − Ux (y ) y2 ⎞ ΔUx ⎛ = 0 = exp ⎜−ln 2 2 ⎟ U0 − Ux (0) ΔUs y 1/2 ⎠ ⎝
(8)
where ΔUs is the maximum deficit, and Ux (y1/2 ) = 0.5ΔUs defined the half width ( y1/2 ) of the profile. As apparent from Fig. 11, the Gaussian profile can not be used to describe the lateral profiles at distances x ≤ 2D , but it is representative of the lateral expansion over x ≥ 5D downstream.
S≡
U0 dy1/2 ΔUs dx
(9)
In regards to Eq. (9), the self-similarity case requires a constant spreading parameter S (ref (Pope, 2001) P.148). According to the momentum theorem of the cylinder and wake (Batchelor, 2000), the parameter ΔUs y1/2 is independent of x. The constancy of S and ΔUs y1/2 means ΔUs and y1/2 vary to x −1/2 and x 1/2 , respectively. The spreading parameter of unbounded wakes correspond to the following: Splate = 0.073, Scylinder = 0.083 and Sairfoil = 0.103 for different generators (ref (Pope, 2001) P.149).
ΔUs = 0.4792(x / D)−1/2 − 0.0525 U0
y1/2 D
= 0.0615(x / D)1/2 + 0.3149
(10) (11)
For a plates wake, the normalized maximum deficit (ΔUs / U0 ) and lateral half width ( y1/2 / D ) are plotted in Fig. 12. The empirically derived Eqs. (10) and (11) fitted well with the velocity deficit in far-wake region ( x ≥ 5D ). According to Eq. (9), the lateral spreading parameter is 0.064, a value smaller than the plates (Splate = 0.073). On the other hand, the lateral expansion of the turbine wake, proposed by Lam and Chen (2014), can be expressed as: Fig. 14. Log-log distributions of normalized integral time scale (Tx / Txinc ) along several axis on mid plane ( y = 0 ).
f (y ) =
U − Ux (y ) (|y| + Cx − (D /2))2 ⎞ ΔUx ⎟ = 0 = exp ⎛⎜− ΔUs U0 − Ux (0) 2(Cx )2 ⎠ ⎝
(12)
where C is defined as: C = σ / x 0 , σ denotes the standard deviation of velocity at traverse direction and x 0 is limitation to the end of the zone 9
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of flow establishment. According to Albertson (1948), the constant C is found to be 0.0806 when the zone of flow establishment occurs. The cyan curves shown in Fig. 11 represent the theoretical result by the proposed equation. The profile in Fig. 11 (a) indicates the compatibility of Eq. (12) with the velocity at the range of |y / D| = 0.34 − 1.0 ; but it fails in the high deficit core ( |y / D| ≤ 0.34 ; 2D ) due to the presence of the nacelle and the support. For given downstream, the following equation results more appropriate: X < 5D , Eq. (12); X ≥ 5D , Eq. (8). Although, we can not rule out the influence of the turbine in the far-wake regions results, thus these should be taken into consideration.
for the upper region (z / h ≥ 0.5) and by the wave period close to the bed surface (z / h ≤ 0.2 ). In the pure-current flow, a range of low turbulence intensities occurred. The Integral scale also highlighted some interesting but different result from the mean wake structure. Experimental wake inspection of the wave-current flow revealed a strong influence of waves on the integral time scale (Tx ). The integral was more influenced by the waveinduced small-scale vortices rather than by the wingtips vortices; and likewise, by the wave period rather than by the wave height at the farwake. This paper developeds a simple qualitative description of integral time scale, but further work with a series of waveforms is necessary to confirm these results.
3.2. Integral characteristic To represent the evolution of integral characteristic, stream-wise velocity fluctuations were measured on the mid plane at different vertical locations. The sample duration was 5 min, and the sampling rate was 100 Hz (30,000 samples in total). The normalized integral time scale was defined as Tx / Txinc , where Tx is the integral time scale calculated by the velocity fluctuations (see Eq. (4)) and Txinc is computed via the linear fit curve of Fig. 3 (d).
Acknowledgments The research was supported by the following funding programs: National Natural Science Foundation of China (51809083); Natural Science Foundation of Jiangsu Province (BK20180504); Fundamental Research Funds for the Central Universities (No.2019B15114) and Water Conservancy Science & Technology Project of Jiangsu Province (2018026).
3.2.1. Overview of the integral time scale Contours of normalized integral time scale on the mid-plane ( y = 0 ) are illustrated in Fig. 13. As shown in Fig. 13 (a), at 1D downstream, Tx is substantially reduced within the near-wake region and Tx / Txinc is ≈ 0.03 at the height of z = 0.305. As a result of the expansion of the internal wake, the large-scale vortices induced by the rotor affected the far-wake along the rotor centre ( y = 0, z = 0.27 m ), and produced a Tx / Txinc ≈ 0.4 . Because of the shear layer of flume bed and water surface, asymmetric distributions of Tx occurred along the bottom and top axis. Over the range of x ≥ 5D downstream, the Tx / Txinc along both the bottom and top axis, were approximately 0.97 and 0.85, respectively. Comparing Fig. 13 (b), with (c) and (d), the Tx results more influenced than the waves by the rate of blockage. Due to the small-scale vortices generated by the waves, Tx / Txinc along the rotor centreline is much lesser than the pure-current case. In the far-wake region, the integral time scale is substantially reduced to 0.118, 0.172 and 0.117 for the conditions corresponding to waves 1, 2 and 3 respectively.
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3.2.2. Longitudinal log-log distributions The representative log-log distributions of Tx / Txinc along several axis are illustrated in Fig. 14. In near-wake region (see Fig. 14 (b) and (c)), the normalized integral time scale Tx / Txinc developed a high-variation rate comparable (but higher) with a wind turbines wake (Jin et al., 2016); and it is doubtful whether tis wind finding is applicable to high turbulent flows. Another source of uncertainty was the effect of the large-scale vortices generated by the turbine stanchion. In contrast to the undisturbed flow, the integral scale Tx became lower in the wave-current flows. At the distance of x ≥ 5D , the wave with a longer period (wave 2) developed a larger Tx / Txinc along longitudinal direction and the integral scale did not vary greatly with the change of wave height. Table 3 indicates the average of Tx / Txinc for downstream distances of x ≥ 5D . 4. Conclusions This paper addressed the influence of the waves on tidal stream turbine wake. Mean and integral characteristic of the wake were analyzed for various wave-current conditions. Three-dimensional mean velocity and vertical turbulence intensity were presented to study the mean wake structure. In the near-wake region, the turbine stanchion had more influence on both wake recovery and turbulence. The waves had negligible effect on the wake recovery behind the turbine. Lateral expansion of the mean wake was consistent with the Gaussian profile. Under the wave-current conditions, the turbulence intensity was greatly affected by the wave height 10
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velocity profile at tidal-stream energy sites. Renew. Energy 114, 258–272. Liu, H.-w., Ma, S., Li, W., Gu, H.-g., Lin, Y.-g., Sun, X.-j., 2011. A review on the development of tidal current energy in China. Renew. Sustain. Energy Rev. 15 (2), 1141–1146. Liu, H., Hayat, I., Jin, Y., Chamorro, L.P., 2018. On the evolution of the integral time scale within wind farms. Energies 11 (1), 93. Maganga, F., Germain, G., King, J., Pinon, G., Rivoalen, E., 2010. Experimental characterisation of flow effects on marine current turbine behaviour and on its wake properties. IET Renew. Power Gener. 4 (6), 498–509. Mycek, P., Gaurier, B., Germain, G., Pinon, G., Rivoalen, E., 2014. Experimental study of the turbulence intensity effects on marine current turbines behaviour. part i: one single turbine. Renew. Energy 66, 729–746. Myers, L., Bahaj, A., 2009. Near wake properties of horizontal axis marine current turbines. In: Proceedings of the 8th European Wave and Tidal Energy Conference, Uppsala, Sweden, pp. 558–565. Myers, L., Bahaj, A., 2010. Experimental analysis of the flow field around horizontal axis tidal turbines by use of scale mesh disk rotor simulators. Ocean Eng. 37 (2–3), 218–227. Nortek, A., 2012. Vectrino Profiler User Guide. Tech. rep., Nortek AS, Vangkroken, Norway. Olczak, A., 2016. The Influence of Waves on Tidal Stream Turbine Arrays. Ph.D. thesis. University of Manchester. O'Doherty, T., Mason-Jones, A., O'Doherty, D.M., Evans, P.S., Wooldridge, C.F., Fryett, I.A., 2010. Considerations of a horizontal axis tidal turbine. Proc. ICE - Energy 163 (3), 119–130. Pope, S.B., 2001. Turbulent Flows. Robins, P.E., Neill, S.P., Lewis, M.J., 2014. Impact of tidal-stream arrays in relation to the natural variability of sedimentary processes. Renew. Energy 72, 311–321. H. Schlichting, Boundary-layer Theory, 7th. editon, McCraw-Hill Book Co., Ncw York. Soulsby, R., Humphery, J., 1990. Field observations of wave-current interaction at the sea bed. In: Water Wave Kinematics. Springer, pp. 413–428. Soulsby, R., Hamm, L., Klopman, G., Myrhaug, D., Simons, R., Thomas, G., 1993. Wavecurrent interaction within and outside the bottom boundary layer. Coast. Eng. 21
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