O. DURAN MEDINA F.G. SCHMITT A. SENTCHEV T. LE KIEN M. THIEBAUT. Laboratory of Oceanology and Geosciences (LOG) November 2015

Transcription

1 Multiscale turbulence characterization of tidal currents in the Scheldt River and spectral analysis of two simultaneous time series: flow velocity and tidal turbine power production. O. DURAN MEDINA F.G. SCHMITT A. SENTCHEV T. LE KIEN M. THIEBAUT Laboratory of Oceanology and Geosciences (LOG) November 2015

2 1. Introduction. MULTISCALE ANALYSIS Two prototype tidal turbines were deployed in the Scheldt river, performance data were measured and collected with 2 surveys for each. The data analysis provides information about the performance of the in-stream tidal turbine and the relationship between the output power and the input flow velocity. The flow velocity reach a high Reynolds number, large values lead to huge intermittency of flow velocity fluctuations at all temporal or spatial scales, ranging from large-scale variations (years) to very small-scale variations (few minutes down to seconds). The understanding of such variations ranging from minutes to a few hours in our case, is necessary to provide efficient tools for management and control of tidal power generation. 2. Experimental setup. The measurements were performed at a site on the Scheldt river near Temsebridge. We focused on a four days data from 10:00 7 th November 2014 to 10 th November 2014 which correspond to the dates were the tidal turbine was in operation. There are 2 data sets measured simultaneously. One comes from Acoustic Doppler Current Profile and the other comes from a Darrieus type free stream turbine. The ADV was installed on 17 th of June 2015 and operated during almost 25 hours. Figure 1 ADV testing Figure 2 First turbine in water 3. Dataset. Flow velocity time series ADV measurement device was installed for this study. The 16 Hz ADV was installed at 1 meter depth from surface water and so samples will be collected at 1.2m below the surface (see figure 3). 1

3 On the other hand, the velocity profile was recorded by the ADCP system. At the testing site, ADCP was installed downward-looking to the bottom from the surface layer. The first sample (or the first bin) recorded at 0.5 m depth from the water surface. ADCP recorded data at 1Hz sample rate which means each second, one velocity profile will be recorded. The device was set with 44 bins as the deepest water depth possibly recorded. Each bin is 25 cm deep and the first bin is started at 0.5m from the water surface. ADCP was oriented in order to obtain the positive velocity values of U [m/s] during the ebb tide and negative values for flood tide. From the profiles we also can figure out that there is a big difference between surface velocity and bottom velocity. These collected profiles in time series are additionally valuable to estimate the available power. Fig.4 shows the differences between surface layer current velocity, bottom velocity and depth averaging of velocity during time which can help to say that there was a big changes along a water depth (roughly 0.7m/s). The tidal cycle can also be recognized from here by considering the minimum of velocity where the plot changes its tendency. Each flood and ebb tidal were marked as blue and red vertical line respectively. Current velocity varies along water depth and during time. At changing phase between flood and ebb, velocity is close to zero. Figure 3Current velocity recorded by an ADV at 16 Hz. Peak velocity (blue dash line), slack velocity (green cross). Figure 4 Time series of surface velocity (gray), depth averaging velocity (black dash line) and bottom velocity (pink) Power measurement 2

4 The power data have strong fluctuations about the mean value. These mainly came from turbulence superposed to several pikes. The pikes are all bad values (large absolute value) which are not related to current flow or any other natural factors. All these spikes can be treated by filtering the data. Figure 5 shows an example of power production where original signal is strongly fluctuating. The black solid line corresponds to the filter data without these periodic pikes that appears ina 0.5% of the unfiltered data. Figure5 Power of turbine recorded on 7th November second averaging data (red) and 1 minute averaging data (black) Figure 6 Power of turbine recorded on 8th November second averaging data (red) and 1 minute averaging data (black) Figure 7 Power of turbine recorded on 9th November second averaging data (red) and 1 minute averaging data (black) 4. Methodology 4.1 Kolmogorov s theory and spectral analysis We consider an homogeneous and isotropic turbulence. In this context, Kolmogorov and Obukhov (1941) assumedthat the power spectral density of the velocity will be a powerlaw of slope -5/3 in a certain frequencies range. This powerlaw behavior in a turbulent flow represents the multi-scale andinvariant kinetic energy transfer. The dissipation ϵ value iscalculated from the spectrum of the LDV velocity with a localisotropy hypothesis. 3

5 We have for a turbulent fluid: where E is power, C is a constant (C = 1,5) and k isthe wave number. V 0 being the average value of the currentvelocity, we rewrite the wave number k = 2π/l as a frequency function f = 1/T through the average velocity using Taylor shypothesis V 0 = 1/τ = l 0 f : This arrangement allows us to obtain the following dissipation estimation through a fit of the powerspectrum : where C 0 is a power law factor following the Kolmogorov sslope E(f) = C 0 f -5/3 This way the meandissipation ϵ can be estimated even if the dissipation scale is not resolved by the measurements.from this, we get access to the integral scale L (the biggesteddy size inside the measured flow): where is a standard deviation of velocity during flood tide (in this calculation we consider a part of velocity which is recorded simultaneously with the turbine and in this case it is flood tide). The Taylor length scale is: Kolmogorov s dissipation scale (the scale at witch the fluid isaffected by viscosity) is defined by: Where m 2 /s is water kinematic viscosity. The Taylor-based Reynolds number scale writes: Table 1 shows the principal results for these characters obtained from spectra and dissipation rate. All these value applied for a turbulent intensityaround. Dissipation rate (ε) [m 2 s -3 ] L [cm] η [mm] Re λ Table 1: Homogeneous turbulent properties 4

6 Figure 7 Power spectral density of flood velocity data (ADV) f0 4*f0 Figure 8 Power spectral density of Turbine power 8 November 2014 for 2 running cycles f0 4*f0 Figure 9: Power spectral density of Turbine power 9 November 2014 for 2 running cycles In this case, the turbine possess 4 blades and this would create 4 times the rotor frequency f 0. Meanwhile the first peak probably comes from a dissymmetry on the turbine structure. 5

7 As can be seen from spectra, there is the frequency zone that exist the initial subrange or the frequency range where energy was transformed without any losses theoretically (Kolmogorov) and it is highlighted by a dash blue line with a -5/3 slope. 4.2 Coherence function To have a better understanding of the relationship between the 2 spectra figures of velocity and power, we performed the coherency spectrum H xy as the fig.10 below. The co-spectrum is the Fourier transform of the covariance function, and the coherency spectrum is defined as the ratio of the modulus of the co-spectrum E xy by the square root of the product of both spectra: where x, y are two time series and E x (f), E y (f) their respective power density spectra. The value of H xy varies from 1 down to 0 stands for the correlativity between x (velocity) and y (power) is good or not. For the uncorrelated case, the co-spectrum goes to 0 and vice versa, if one data set proportionate with the other then the value of H xy is 1.To do this, these 2 data sets must be recorded at the same rate. The power data need to be averaged from 100 Hz to 16 Hz (ADV sample rate) firstly. In the fig.10, the coherency spectrum is about 1 for large scale (Duran Medina, 2015) (f < ), time scale larger than 30 minutes). It means that for these scale, the power is proportional to the current velocity. For lower scales, H xy decreases until it maintains its value about 0.8 from 0.1 Hz up to 2Hz. Figure 10 Coherency spectrum of Turbine power (PSD) and flood velocity (PSD).Globally, there is a high correlation between 2 spectrums (H xy > 0.8) 5. Conclusion In this work, we were interested in the connections between the input and the output of a marine current turbine in a natural environment.we have analyzed in a multiscale way, the non-linear characteristics of two simultaneoustime series: an upstream flow velocity and the power generated by a tidal turbine. 6

8 A spectral analysis through Fast Fourier Transform allowed us to realize a comparison with the theor 5/3 power law in the flow velocity spectrum corresponding to the Richardson-Kolmogorov energy cascade. First, we focus on inertial scales of turbulence (see 4.1) where the -5/3 power law is not clearly shown throw the power spectral density of the flood velocity data. The obtained slope could be a result of the measurement device and the way this devise calculate an estimation of the income velocity. In other studies concerning renewable energies, it was shown that wind power spectra follows the observed 5/3 power law in the wind spectrum (R. Calif et al. 2014) and we expected to find this behavior on tidal energy.for the lower frequencies (f<10-2 ), there exists a chaotic spectrum with a slope close to zero that represent a noise spectrum, after this frequency we observe a zone with invariant kinetic energy transfer between 10-2 <f<10 0 and finally for f>10 0 the obtained slope that tends to zero. Besides, this spectral approach allow to estimate the dissipation through the flood velocity spectrum and to characterize the turbulent flow and its properties. The length scales obtained in this natural environment are small if we compare with previous studies realized in a laboratory flume tank (Duran Medina et al., EWTEC 2015). In this study, we obtained a perfect -5/3 power law that allow us to get access to a more precise estimation of the C 0 coefficient and then, a better estimation of the dissipation and the corresponding length scales. In this case, natural conditions of the river, the device and other uncontrolled conditions modify the flood velocity spectrum and then the turbulence scaling flow properties. The current value of the Reynolds number based on Taylor number found in natural conditions turns around 400, here we obtainedaround 100. It shows the difficulty to well estimate the dissipation. On the other hand, the turbine power spectra present on both case (flood and ebb tidal) two peaks that correspond to the rotor frequency (f 0 ~ Hz) and the blades passing frequency(f~2 Hz). Indeed, this last increase correspond to the blades passing frequency, four times the rotor frequency f0 (Fig.8 and 9). Under f~10-2 we observe as well a noise spectrum in a small frequency range compared to the flow spectrum. These energy peaks (f 0 and 4f 0 ) have been observed in previous works (E. Fernandez- Rodriguez, 2014) with high correlations with the energy cascade over low frequencies in the case of shallow turbulent flow. Finally, concerning the coherency spectra, we find a high correlation for lower frequencies scales for f<3.10-4, H xy coefficient is close to one). We observe then a loss of correlation until reach to a value around 0.8. It means that both time series are globally correlated. 7