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Frequency analysis of the power output for a vertical axis marine turbine operating in the wake
Ocean Engineering 127 (2016) 325–334
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Frequency analysis of the power output for a vertical axis marine turbine operating in the wake ⁎
Amir Hossein Birjandi , Eric Louis Bibeau Department of Mechanical Engineering, University of Manitoba, Winnipeg, Canada R3T 0C4
A R T I C L E I N F O
A BS T RAC T
Keywords: Marine turbine Wake Turbulence Fatigue load Frequency analysis Power output
Flow condition in rivers is highly turbulent and unsteady due to upstream structures or geometry of the river. In a hydrokinetic farm downstream turbines are subjected to the wake of upstream turbines. Operating in the wake not only affects the average power output of the turbine but also influences the quality of the power by imposing fluctuations to the power. The current study presents the water tunnel testing results of a vertical axis turbine operating in the vortex shedding behind a cylinder with various sizes located at different distances upstream the turbine. The vortex shedding from a circular cylinder has similar patterns with vortex shedding from blades of a vertical turbine. Results show that for certain sizes of upstream cylinder the maximum negative effect occurs when the upstream cylinder is 1.5 turbine diameters away. At closer or farther distances the negative effect is limited. The frequency analysis of the power data shows that when the turbine operates in the wake, the frequency strength at the rotational frequency of the turbine and its multiples decreases. At the same time, new frequency peaks appear in the power spectrum as the result of the vortex shedding behind the cylinder.
1. Introduction In February 1977 Sheldahl and Blackwell (1977) tested a 5-m diameter Troposkein Darrieus turbine in the free air condition at the Sandia Laboratories Wind Turbine Site. Later when they repeated the test in late July and early August, they observed maximum power coefficient reduction from 0.28 to 0.24, as seen in Fig. 1. They investigated the source of this phenomenon by looking at the wind speed distribution and wind quality for these two tests. They found that the wind speed distribution for the February test, test a, is much smoother than the wind speed distribution for the August test, test b, Fig. 2. They attribute the high fluctuations in the wind speed for the power coefficient reduction in test b. Therefore it can be concluded that the power coefficient not only is a function of the average wind velocity but also is affected by the wind distribution pattern. Birjandi et al. conducted a series of field measurements upstream of a 5 and 25 kW vertical hydrokinetic turbines in the Winnipeg River at Pointe du Bois (Birjandi et al., 2012) and founded that the river flow carries large eddies with the order of magnitude of the turbine's diameter. Large eddies break into smaller size eddies as they approach the turbine. Small size eddies are still comparable with the chord length of the blade. These eddies are able to trigger temporal flow separation on the blade surface and cause dynamic stall to occur (Birjandi et al., 2012). Yokosi (1967) measurements in the Uji River and the Sosui
⁎
canal show that the depth and width of the river determine the order of magnitude of the largest eddies in the river. The large-scale eddies cascade energy from the mean flow velocity to the smaller eddies and they are created mainly in the wake zones or in regions with high velocity gradient. In rivers large-scale eddies are created in following circumstances:
• • • •
rapid changes in the profile of riverbeds or banks, presence of large boulders or ice floes, man-made obstructions like a bridge pier or upstream turbines, and rapid river level changes leading to hydraulic jumps.
In most cases the wake and eddies are smaller than the crosssection of the turbine; therefore, different parts of the turbine experience dissimilar inflow conditions due to different sizes of eddies and wake intensity. The large eddies and regional wakes create nonuniform inflow condition for the turbine that imposes higher power output fluctuations and higher fatigue loads on the structure of the turbine. There is little information available in the literature about regional wake and large-scale eddy interaction with hydrokinetic turbines. The National Renewable Energy Laboratory is currently doing a comprehensive investigation for better understanding the effects of unsteady inflow on horizontal wind turbines (Sutherland and Kelley, 1995; Hand et al., 2001; Kelley et al., 2002; Sheng et al.,
Corresponding author. E-mail address: [email protected] (A.H. Birjandi).
http://dx.doi.org/10.1016/j.oceaneng.2016.09.045 Received 12 August 2015; Received in revised form 16 July 2016; Accepted 29 September 2016 Available online 15 October 2016 0029-8018/ © 2016 Elsevier Ltd. All rights reserved.
Ocean Engineering 127 (2016) 325–334
A.H. Birjandi, E.L. Bibeau
1.1. Modeling the regional wake It is impossible to reconstruct or scale down actual river conditions for lab testing. In traditional water tunnel settings, an upstream screen increases the turbulence intensity of the flow by introducing small eddies to the flow; however, this technique is unable to simulate localized wakes, wakes smaller than the diameter of the turbine, and create large-scale eddies which are common phenomena in hydrokinetic turbine farms in rivers and oceans. Medici and Alfredsson (2006) measured the velocity field behind a two-bladed horizontal wind turbine model with 18 cm diameter in a wind tunnel. They measured all three velocity components using a two-component hot wire. In the frequency domain, they found that the velocity signal shows peaks at frequencies much lower than that of the rotational frequency of the turbine. The Strouhal number (St=fD/U) of these low frequency peaks decreases by increasing the tip speed ratio, and when the turbine exceeds a specific tip speed ratio, the frequency peaks level out. Here, f represents the frequency of the velocity peaks, D is the diameter of the turbine, and U is the free-stream velocity. This Strouhal number definition is similar to the Strouhal number of a solid disk with the same diameter of the turbine. Therefore, the vortex shedding behind the horizontal turbine has the same characteristics as the vortex shedding behind a bluff body. The operating condition for vertical turbines is different than horizontal turbines; therefore, they create different wake pattern behind them. Blades in vertical turbines are subjected to an oscillating angle of attack condition as the blade travels on the circumference of the turbine. Assuming no momentum loss when the flow passes through the actuating disk of the turbine, the angle of attack of the blade, α, can be defined as:
Fig. 1. Power coefficient data of the 5-m Troposkein turbine at 150 rpm for test a and test b (Sheldahl and Blackwell, 1977).
⎡ sin(θ ) ⎤ α = tan−1⎢ ⎥ − αp , ⎣ λ + cos(θ ) ⎦
(1)
where λ=ωr/U and is known as the blade speed ratio or tip speed ratio, θ is the azimuth angle of the blade, and αp is the preset pitch angle of the blade. Fujisawa and Shibuya (2001) showed that the vortex shedding behind the vertical axis turbine blade has the similar pattern as vortices in the Von Karman vortex street. The vortex shedding behind a two-dimensional circular cylinder is known as Von Karman vortex street. Consequently the vortex shedding behind a vertical axis turbine can be modeled by the vortex shedding behind a cylinder. In vertical axis turbine, two counter-rotating vortices are developed due to the flow separation from the leading edge and roll-up flow motion from the pressure side of the blade. The first pair of vortices forms between the azimuth angles of 45° and 90°. The second pair forms between the azimuth angles of 90° and 135°, as shown in Fig. 3. The flow visualization technique around the blade in a vertical turbine, depicted in Fig. 4, verifies the results obtained by Fujisawa and Shibuya (2001). Based on the results obtained from studies conducted by Medici and Alfredsson (2006) and Fujisawa and Shibuya (2001) and our team in the water tunnel, the wake behind a vertical turbine consists of two pairs of counter rotating vortices shed from the blade. This vortex shedding can be modeled by placing circular cylinders in the water tunnel. The size of the vortices and frequency of the vortex shedding can be controlled by the Reynolds number and the diameter of the cylinder. Cylinders with different diameters are placed upstream the scaled turbine to create vortex shedding. In this study, the upstream cylinder is aligned with the rotational center of the turbine with no lateral offset. The cylinder is placed at various longitudinal distances to assess the proximity effect. The torque, rotational speed and the azimuth angle of the turbine are recorded with high frequency sampling rate during the test. Then the average and instantaneous power output and of the turbine are calculated and plotted for different inflow conditions. The power output quality is investigated by analyzing the power data in the frequency domain.
Fig. 2. Wind frequency distribution for the test a and test b in Sheldahl and Blackwell (1977).
2010). In laboratory testing, the turbulence intensity of the flow is increased by employing a screen upstream the model. When flow passes through the screen, small vortices are shed off the screen wires and increase the turbulence intensity of the flow. The size of the generated vortices is in the order of magnitude of the screen wires’ diameter. This technique increases the turbulence intensity homogeneously in entire flow. Compared to the low turbulence intensity flow, a high turbulence intensity flow postpones the stall phenomenon to higher angle of attacks thus increases the maximum lift coefficient of the blade. Therefore, the performance of the turbine is enhanced in turbulent flows and results in higher power output. This statement is true as long as the vortices in the turbulent flow are much smaller than the chord length of the blade. Unlike water tunnels and towing tanks where flow is uniform and turbulence is low, in rivers, channels and oceans the flow is highly turbulent and non-uniform and contains large-scale structures exceeding the diameter of the turbine. This condition will be accentuated in hydrokinetic farm applications where some turbines operate in eddies shed by upstream turbines.
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Fig. 3. Schematic illustration of counter-rotating vortices from Fujisawa and Shibuya (2001).
bi-directional rotary torque and the rotational speed of the turbine. The accuracy of the torque transducer is ± 0.25% with a respond frequency of 100 Hz. The instrumentation setup is demonstrated in Fig. 7. During the test, the pitch angle of two blades is set to 2.5° toe out and the turbine rotates in the counterclockwise direction from the top view. Having 50 cm water depth in the test section of the water tunnel, the clearance coefficient of the turbine is 0.23. The clearance coefficient is the ratio of the water height above the turbine to the height of the blades described in Birjandi et al. (2013). The non-uniform inflow condition is simulated by four circular cylinders, 2.54 cm (1 in), 5.08 cm (2 in), 7.62 cm (3 in), and 10.16 cm (4 in) diameter size. The ratio of the cylinder diameter to the turbine diameter is a dimensionless number that describes the relative size of the cylinder to the turbine. This ratio is 0.08, 0.17, 0.25 and 0.34, respectively for cylinders with the diameter size of 2.54 cm, 5.08 cm, 7.06 cm, and 10.16 cm. The longitudinal distance of the cylinder is measured from the center of the turbine. Fig. 8(a) shows the picture of the turbine and the cylinder taken from the bottom of the water tunnel. In this picture, the separated flow behind the cylinder is clearly visible and both laminar and turbulent separation points are captured. The schematic top view of the turbine and cylinder is shown in Fig. 8(b) with positive directions demonstrated on it. Due to large number of test conditions a naming method is introduced to simplify referring to a test condition. In this naming method, the number following d represents the diameter of the upstream cylinder in inches, following x is the
2. Experimental apparatus The scaled model turbine sued in this study is a two-bladed squirrel-cage vertical axis turbine. Blades are machined from T6082T6 aluminum alloy with a computer numerical control machine at the University of Manitoba to an accuracy of 0.05 mm. Blades consist of NACA-0021 airfoil profile section, a symmetric profile, with no twist and no taper, Fig. 5. The turbine is 30 cm in diameter and 30 cm in height. Blades are attached to two solid disks at both ends to approximate two-dimensional flow condition for blades by eliminating tip vortexes and spanwise flow, Fig. 6. Experiments are performed in the closed-circuit water tunnel facility at the University of Manitoba. The dimensions of the test section are 61 cm wide, 60 cm deep and 183 cm long. The maximum flow speed in the section is 1 m/s when the water level is 60 cm, full water level condition. At lower water levels, the flow speed can reach higher values. During the test the water level in the test section is kept at 50 cm and the flow speed is set on 0.6 m/s. In this condition, the top of the turbine is 10 cm below the free surface and the bottom of the turbine is 10 cm above the water tunnel floor. The diameter of the turbine is half of the test section width; therefore, the operating condition of the turbine in the water tunnel approximates the condition of a turbine operating in an array of turbines with one turbine diameter lateral spacing. A Torqsense Rayleigh wave rotary torque transducer measures the
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Fig. 4. Vortex formation and convection from the leading edge of the blade at the position of (a) 35°, (b) 60°, (c) 85°, (d) 95°, and (e) 120°.
dimensionless number describing longitudinal distance between the turbine and upstream cylinder, x/D, following y is the dimensionless lateral distance of the cylinder from the center of the turbine, y/D, and following u is the free stream speed in m/s. For example, d4×1.5y0u0.6 represents a test in which the 4-in. diameter cylinder located at x/D =1.5 and y/D =0 upstream of the turbine and subjected to 0.6 m/s flow velocity. In this study the y/D is kept zero, no lateral offset. Fig. 5. The geometry of the blade (a) side view, and (b) profile section.
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quently reduces the angle of attack of the blade which results in smaller separation and therefore higher performance. However, at higher tip speed ratios the wake of the cylinder drops the blade angle of attack below the maximum lift angle of attack and decreases the power coefficient of the turbine. With no cylinder upstream of the turbine, the power diagram has a step between the tip speed ratio of 1.7 and 2.2. This step diminishes when the turbine operates in the wake of the cylinder. When the turbine is subjected to the wake of the d/D=0.08 cylinder, the power coefficient is above 90% of the power coefficient of the turbine with no cylinder upstream. In this case, the power coefficient increases slightly as the distance increases but is drops as the cylinder moves from x/D=3 to x/D=4. Larger cylinders have the most negative effect on the power coefficient of the turbine at x/D=1.5. At this distance, the maximum power coefficient is less than the power coefficient of the turbine when the upstream cylinder is at x/D=1. When the upstream cylinder is at x/D=1, the wake behind the cylinder interacts only with a small segment of the turbine, due to the limited distance for expansion before reaching the turbine. Therefore, it has a limited effect on the overall performance of the turbine. The strength of the wake diminishes as longitudinal distance increases, yet the wake envelope becomes wider. At x/D=1.5 the combination of wake strength and the width of the wake have the strongest adverse contribution on the power coefficient. After x/D=1.5 the power coefficient recovers as the longitudinal distance increases further. Among the cylinders, d/ D=0.25 has the fastest recovery rate. At x/D=4, the turbine behind the d/D=0.25 cylinder has 97% of the maximum power coefficient of the turbine operates with no cylinder upstream, Fig. 10.
Fig. 6. Two-bladed squirrel-cage vertical axis turbine.
3. Test procedures
4.2. Frequency analysis
The longitudinal distance between the cylinder and the turbine affects the size and the strength of vortices interacting with the turbine and also changes the width of the wake. The upstream cylinder is placed at five longitudinal distances from the turbine, x/D =1, 1.5, 2, 3 and 4. During the tests, cylinders are aligned with the center of the turbine thus the wake is evenly distributed around the center of rotation if the turbine is not rotating. The rotation of the turbine creates asymmetric condition for the flow around the turbine; therefore the approaching wake and vortices have tendency to move toward the receding turbine blades. Tests are conducted at the flow speed of 0.6 m/s which is equivalent with the Reynolds number of 2.00×105, based on the diameter of the turbine. The torque, rotational speed of the turbine and the azimuth angle of the blades are recorded for 30 s for each test. The power coefficient diagram of the turbine is extracted based on the average power at each tip speed ratio. For each test condition, the maximum power coefficient of the turbine is obtained from the power coefficient diagram. The trend in the average power coefficient of the turbine is investigated base on the location and size of upstream cylinders. In the next phase, the power output data is investigated in the frequency domain to understand the effect of the wake on the power quality.
The average power is the main parameter to predict the output power of a hydrokinetic turbine farm. However, it contains no information about the quality of the output power and dynamic loads on the turbine. The power output with high fluctuations not only can complicate the power system components, but also can reduce the lifetime of the turbine due to higher fatigue loads. The harmonics in the power output of a turbine operating in a uniform inflow are the rotational frequency of the turbine and its multiples. The upstream cylinder changes the inflow pattern and causes local high-speed and low-speed areas on the turbine actuating disk. These local high and low velocity areas impose more fluctuations to the power output of the vertical turbine due to rapid changes in blade angle of attack. The maximum power coefficient of the turbine operating behind the d/D=0.34 occurs around the tip speed ratio of 2.7, Fig. 9d. Therefore, in this section, the frequency analysis is conducted on the power coefficient of the turbine at the tip speed ratio of 2.7. Fig. 11 shows the power coefficient variations of the turbine versus azimuth angle for several rotational cycles with and without the upstream cylinder. Measurements show that the power coefficient does not quite follow a quite pattern in different cycles, even in the absence of the upstream cylinder. Although in uniform inflow, the turbine theoretically generates an identical power outputs in every rotation in reality the power output fluctuates due to vortex shedding behind the upstream blades and their interaction with downstream blades. Power coefficient deviations deviation are much more limited for a turbine operating in an uniform inflow compare to the turbine operating behind a cylinder. Power coefficient fluctuations increase by the size of the upstream cylinder. For a better understanding of the effect of the upstream cylinder on the quality of the power output, the power coefficient of the turbine operating downstream of the d/D=0.34 cylinder at x/D=1.5 is investigated in the frequency domain.
4. Results and discussions 4.1. Average power results The upstream cylinder improves the performance of the turbine at tip speed ratios less than the tip speed ratio of the maximum power coefficient point (optimum tip speed ratio), Fig. 9. However, at tip speed ratios higher than optimum tip speed ratio it reduces the power coefficient. The wake of the upstream cylinder reduces the inflow velocity for the blade around the 90° azimuth angle, where the blade experiences the highest angle of attack. The lower inflow velocity means smaller angle of attack. At low tip speed ratios, blades experience flow separation due to high angle of attack near 90° azimuth angle. The upstream cylinder reduces the inflow velocity and conse-
4.2.1. Power spectral density analysis The power spectral density (PSD) function transfers the power output data of the turbine from the time domain to the frequency 329
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Fig. 7. Test setup for the water tunnel experiment.
Fig. 8. Turbine and cylinder arrangement, (a) down view of the arrangement in the water tunnel and (b) schematic top view of the setup.
method divides the signal into several overlapping segments and fits a specified window to each segment. A Hann window with 50% overlapping is applied to the power data.
domain and it presents the energy distribution of the signal in the frequency domain. In this study, the PSD function is obtained for the power output data using the Welch's method (Welch, 1967). Welch's 330
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Fig. 9. Average power coefficient of the turbine operating behind the cylinder at various longitudinal distances, (a) d/D=0.08, (b) d/D=0.16, (c) d/D=0.25, and (d) d/D=0.34.
The rotational frequency of the turbine is 1.72 Hz for the tip speed ratio of 2.7 and the flow velocity of 0.6 m/s. Since the turbine has two blades, the principal frequency of the power output is 1.72×2=3.44 Hz. Fig. 12 shows the energy distribution of the power output data for the turbine operating with no cylinder upstream. The highest energy belongs to the principal frequency, 3.44 Hz. The second highest energy peak in the PSD diagram belongs to a frequency which is twice the principle frequency. The PSD also shows other peaks in the power output data which are integer factors of the principal frequency. The frequencies that are integer factors of the principal frequency are called prime frequencies. Between the first and second prime frequencies, another energy peak occurs in the middle of those two frequencies. This pattern is repeated to the end of the frequency domain. At higher frequencies, the energy difference between these three peaks is reduced. Before the principal frequency, there is an energy peak at the frequency of 1.75 Hz, which represents the rotational frequency of the turbine. Although blades of the turbine are theoretically identical, in the manufacturing process it is impossible to have identical blades. Small differences, like surface roughness, could cause different hydrodynamic characteristics for each blade. Differences between two blades are magnified near the stall angle of attack at which the flow separates from the blade surface and the lift coefficient drops suddenly. A slight
Fig. 10. Maximum power coefficient of the turbine versus the longitudinal distance of the cylinder from the turbine.
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Fig. 11. Instantaneous power coefficient of the turbine versus azimuth angle at the tip speed ratio of 2.7 for (a) no cylinder test (b) 10.16 cm (4 in) diameter cylinder at x/D=1.5 upstream of the turbine.
difference in shape or property of the blade can accelerate or postpone the stall phenomenon considerably and significantly change the power output of the turbine. The upstream cylinder changes the inflow pattern on the turbine and creates local low and high velocity areas on the turbine. The local low and high velocity areas are the result of the wake and vortex shedding behind the cylinder and disrupt the smooth sinusoidal pattern of the blade angle of attack in one rotation. Fig. 13 compares the PSD of the power output data for the turbine operating in a uniform inflow and the turbine operating downstream the d/D=0.34 cylinder located at x/D=1.5. The upstream cylinder diminishes the power at the prime frequencies and it creates two peaks between two consequent prime frequencies instead of one. More investigations show that these two frequency peaks are related to the vortex shedding frequency behind the cylinder. The first one is the vortex shedding frequency of the cylinder and its multiple and the second peak is twice the vortex shedding frequency and its multiples. The power of the frequencies between two prime frequencies is higher for the turbine operating in the wake of the cylinder, Fig. 13b. In the PSD diagram, events that regularly occur in every rotation, like dynamic stall, contribute to the
Fig. 12. PSD of the power coefficient signal for the turbine operating in a uniform inflow with no cylinder in the upstream.
Fig. 13. Power signal PSD of the turbine operating behind the d/D=0.34 cylindr at x/D=1.5 (a) between the frequencies of 0.02 Hz and 100 Hz, and (b) between 2 Hz and 10 Hz.
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Fig. 14. Power signal PSD of the turbine operating behind the d/D=0.34 cylindr at various distances (a) between the frequencies of 0.02 Hz and 100 Hz, and (b) between 2 Hz and 10 Hz.
x/D=1, has the highest adverse effect on the total PSD power. This dataset is available for other researchers for more processing and investigation in Reference (Birjandi and Bibeau, 2013). Fig. 15 compares the spectrogram of the power coefficient of the turbine in the uniform flow and downstream the d/D=0.34 cylinder at x/D=2. The red color indicates high power frequencies and the blue color represents low power frequencies. Results show that the high power is mainly concentrated around the first and second prime frequencies when the turbine operates in the uniform inflow. Irregular events allocate insignificant power to themselves in this case. The upstream cylinder diminishes the power at prime frequencies and increases the power of irregular events. The level of the power between the two prime frequencies considerably increases. The smooth sinusoidal shape of the PSD is disrupted by the upstream cylinder.
Table 1 Energy distribution under the PSD diagram. Test
Between two first prime frequencies (dB/Hz)
Total frequency range (dB/Hz)
No cylinder test d1×1y0u0.6 d1×1.5y0u0.6 d1×2y0u0.6 d1×3y0u0.6 d1×4y0u0.6 d2×1y0u0.6 d2×1.5y0u0.6 d2×2y0u0.6 d2×3y0u0.6 d2×4y0u0.6 d3×1y0u0.6 d3×1.5y0u0.6 d3×2y0u0.6 d3×3y0u0.6 d3×4y0u0.6 d4×1y0u0.6 d4×1.5y0u0.6 d4×2y0u0.6 d4×3y0u0.6 d4×4y0u0.6
0.030 0.049 0.042 0.041 0.042 0.046 0.397 0.308 0.227 0.089 0.053 0.391 0.645 0.612 0.485 0.255 0.385 0.702 0.756 0.510 0.337
20.701 14.719 15.036 16.692 17.613 17.921 8.796 8.838 8.898 13.032 14.999 6.883 3.787 6.911 13.071 16.703 1.020 1.563 3.463 7.248 9.901
5. Conclusion Non-uniform inflow and regional wake were created by placing cylinders with different sizes upstream a vertical axis turbine. The effects of the size and longitudinal displacement of the upstream cylinder on the power output of the turbine were investigated. Results for the average power output show that the cylinder at the longitudinal distance of x/D=1.5 has the maximum adverse effect on the average power output of the turbine for most cylinder sizes except the smallest size, d/D=0.08. At x/D=1 despite the fact that the wake is stronger, the negative effect of the upstream cylinder is limited since the wake does not get enough time to expand and cover a large area of the vertical turbine. The power coefficient of the turbine recovers by increasing the distance between the cylinder and the turbine. The power coefficient recovery rate of the turbine can be described as a function of the dimensionless diameter of the cylinder with respect to the turbine diameter. This study shows that d/D=0.25 has the fastest recovery rate even faster than smaller cylinders like d/D=0.08 and d/D=0.16. The frequency analysis shows that the upstream cylinder not only affects the average power but also influences the quality of the power output. The upstream cylinder increases irregular fluctuations in the power output of the turbine. Theoretically the power output data has to repeat itself in every 360° azimuth angle but in reality imperfectness in manufacturing, assembly and inflow condition introduce disturbances in the power data. The upstream cylinder not only increases the power of frequencies between the two prim frequencies but also it increases the power of low frequencies, lower than the first prime frequency. The
energy of prim frequencies. Events that occur irregularly lie between the two consequent prime frequencies. Irregular events carry insignificant amount of energy, compare to regular events, Fig. 13; however, irregular events are important for power output quality and fatigue studies. Fig. 14 shows the PSD of the power output of the turbine operating behind the d/D =0.34 at various distances. Table 1 summarizes the power distributed under the PSD diagram for different test conditions. Results show that the turbine operating in a uniform inflow has the lowest power level between two prime frequencies. The power between two prime frequencies increases when the turbine operates downstream a cylinder. The larger and closer cylinder increases this energy more. For small cylinders, d/D=0.08 and d/D=0.16, the maximum power occurs when the cylinder is at the closest distance to the turbine, x/D=1. As the size of the cylinder increases, the maximum power occurs at farther distances, for d/ D=0.25, it occurs at x/D=1.5 and for d/D=0.34 it occurs at x/D=2. The total power of the PSD is highest when the turbine operates in uniform inflow. In general, upstream cylinder reduces the total PSD power. The largest cylinder, d/D=4, at nearest distances to the turbine, 333
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Fig. 15. Spectrogram of power coefficient signal for (a) no cylinder test and (b) test d4×2y0u0.6. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.) tunnel test configurations and available data campaigns unsteady aerodynamics experiment. NREL Technical Report, NREL/TP-500-29955. Kelley, N., Hand, M., Larwood, S., McKenna, E., January 2002. The NREL large-scale turbine inflow and response experiment: preliminary results. In: Proceedings of the Wind Energy Symposium, ASME, Reno, U.S. Medici, D., Alfredsson, P.H., 2006. Measurements on a wind turbine vortex shedding. Wind Energy 9, 219–236. Sheldahl, R.E., Blackwell, B.F., 1977. Free-air performance tests of a 5-metre diameter Darrieus turbine. Sandia National Laboratories, SAND77-1063. Sheng, W., Galbraith, R.A.M., Coton, F.N., 2010. Applications of low-speed dynamic-stall model to the NREL airfoils. J. Sol. Energy Eng. 132, 011006. Sutherland, H.J., Kelley, N.D., 1995. Fatigue damage estimate comparisons for Northern European and U.S. wind farm loading environments. In: Proceedings of the Wind Power, AWEA, Washington, DC., U.S. Welch, P.D., 1967. The use of fast Fourier transform for the estimation of power spectra: a method based on time averaging over short, modified periodograms. IEEE Trans. Audio Electroacoust. AU-15, 70–73. Yokosi, S., 1967. The structure of river turbulence. Bulletin of the Disaster Prevention Research Institute, Kyoto University, vol. 17, pp. 1–29.
diagram of the power output in one rotation is unrepeatable due to the variations in the inflow condition. The size of these fluctuations increases when the turbine operates downstream a cylinder. References Birjandi, A.H., Woods, J., Bibeau, E.L., 2012. Investigation of macro-turbulent flow structures interaction with a vertical hydrokinetic river turbine. Renew. Energy 48, 183–192. Birjandi, A.H., Bibeau, E.L., Chatoorgoon, V., Kumar, A., 2013. Power measurement of hydrokinetic turbines with free-surface and blockage effect. Ocean Eng. 69, 9–17. Birjandi, A.H., Bibeau, E.L., 2013. Performance of Marine Kinetic Turbine in the Wake. 〈http://dx.doi.org/10.5203/birjandi_1〉. Fujisawa, N., Shibuya, S., 2001. Observations of dynamic stall on Darrieus wind turbine blades. J. Wind Eng. Ind. Aerodyn. 89 (2), 201–214. Hand, M.M., Simms, D.A., Fingersh, L.J., Jager, D.W., Cotrell, J.R., Schreck, S., Larwood, S.M., December 2001. Unsteady aerodynamics experiment phase VI: wind
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Frequency analysis of the power output for a vertical axis marine turbine operating in the wake ⁎
Amir Hossein Birjandi , Eric Louis Bibeau Department of Mechanical Engineering, University of Manitoba, Winnipeg, Canada R3T 0C4
A R T I C L E I N F O
A BS T RAC T
Keywords: Marine turbine Wake Turbulence Fatigue load Frequency analysis Power output
Flow condition in rivers is highly turbulent and unsteady due to upstream structures or geometry of the river. In a hydrokinetic farm downstream turbines are subjected to the wake of upstream turbines. Operating in the wake not only affects the average power output of the turbine but also influences the quality of the power by imposing fluctuations to the power. The current study presents the water tunnel testing results of a vertical axis turbine operating in the vortex shedding behind a cylinder with various sizes located at different distances upstream the turbine. The vortex shedding from a circular cylinder has similar patterns with vortex shedding from blades of a vertical turbine. Results show that for certain sizes of upstream cylinder the maximum negative effect occurs when the upstream cylinder is 1.5 turbine diameters away. At closer or farther distances the negative effect is limited. The frequency analysis of the power data shows that when the turbine operates in the wake, the frequency strength at the rotational frequency of the turbine and its multiples decreases. At the same time, new frequency peaks appear in the power spectrum as the result of the vortex shedding behind the cylinder.
1. Introduction In February 1977 Sheldahl and Blackwell (1977) tested a 5-m diameter Troposkein Darrieus turbine in the free air condition at the Sandia Laboratories Wind Turbine Site. Later when they repeated the test in late July and early August, they observed maximum power coefficient reduction from 0.28 to 0.24, as seen in Fig. 1. They investigated the source of this phenomenon by looking at the wind speed distribution and wind quality for these two tests. They found that the wind speed distribution for the February test, test a, is much smoother than the wind speed distribution for the August test, test b, Fig. 2. They attribute the high fluctuations in the wind speed for the power coefficient reduction in test b. Therefore it can be concluded that the power coefficient not only is a function of the average wind velocity but also is affected by the wind distribution pattern. Birjandi et al. conducted a series of field measurements upstream of a 5 and 25 kW vertical hydrokinetic turbines in the Winnipeg River at Pointe du Bois (Birjandi et al., 2012) and founded that the river flow carries large eddies with the order of magnitude of the turbine's diameter. Large eddies break into smaller size eddies as they approach the turbine. Small size eddies are still comparable with the chord length of the blade. These eddies are able to trigger temporal flow separation on the blade surface and cause dynamic stall to occur (Birjandi et al., 2012). Yokosi (1967) measurements in the Uji River and the Sosui
⁎
canal show that the depth and width of the river determine the order of magnitude of the largest eddies in the river. The large-scale eddies cascade energy from the mean flow velocity to the smaller eddies and they are created mainly in the wake zones or in regions with high velocity gradient. In rivers large-scale eddies are created in following circumstances:
• • • •
rapid changes in the profile of riverbeds or banks, presence of large boulders or ice floes, man-made obstructions like a bridge pier or upstream turbines, and rapid river level changes leading to hydraulic jumps.
In most cases the wake and eddies are smaller than the crosssection of the turbine; therefore, different parts of the turbine experience dissimilar inflow conditions due to different sizes of eddies and wake intensity. The large eddies and regional wakes create nonuniform inflow condition for the turbine that imposes higher power output fluctuations and higher fatigue loads on the structure of the turbine. There is little information available in the literature about regional wake and large-scale eddy interaction with hydrokinetic turbines. The National Renewable Energy Laboratory is currently doing a comprehensive investigation for better understanding the effects of unsteady inflow on horizontal wind turbines (Sutherland and Kelley, 1995; Hand et al., 2001; Kelley et al., 2002; Sheng et al.,
Corresponding author. E-mail address: [email protected] (A.H. Birjandi).
http://dx.doi.org/10.1016/j.oceaneng.2016.09.045 Received 12 August 2015; Received in revised form 16 July 2016; Accepted 29 September 2016 Available online 15 October 2016 0029-8018/ © 2016 Elsevier Ltd. All rights reserved.
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1.1. Modeling the regional wake It is impossible to reconstruct or scale down actual river conditions for lab testing. In traditional water tunnel settings, an upstream screen increases the turbulence intensity of the flow by introducing small eddies to the flow; however, this technique is unable to simulate localized wakes, wakes smaller than the diameter of the turbine, and create large-scale eddies which are common phenomena in hydrokinetic turbine farms in rivers and oceans. Medici and Alfredsson (2006) measured the velocity field behind a two-bladed horizontal wind turbine model with 18 cm diameter in a wind tunnel. They measured all three velocity components using a two-component hot wire. In the frequency domain, they found that the velocity signal shows peaks at frequencies much lower than that of the rotational frequency of the turbine. The Strouhal number (St=fD/U) of these low frequency peaks decreases by increasing the tip speed ratio, and when the turbine exceeds a specific tip speed ratio, the frequency peaks level out. Here, f represents the frequency of the velocity peaks, D is the diameter of the turbine, and U is the free-stream velocity. This Strouhal number definition is similar to the Strouhal number of a solid disk with the same diameter of the turbine. Therefore, the vortex shedding behind the horizontal turbine has the same characteristics as the vortex shedding behind a bluff body. The operating condition for vertical turbines is different than horizontal turbines; therefore, they create different wake pattern behind them. Blades in vertical turbines are subjected to an oscillating angle of attack condition as the blade travels on the circumference of the turbine. Assuming no momentum loss when the flow passes through the actuating disk of the turbine, the angle of attack of the blade, α, can be defined as:
Fig. 1. Power coefficient data of the 5-m Troposkein turbine at 150 rpm for test a and test b (Sheldahl and Blackwell, 1977).
⎡ sin(θ ) ⎤ α = tan−1⎢ ⎥ − αp , ⎣ λ + cos(θ ) ⎦
(1)
where λ=ωr/U and is known as the blade speed ratio or tip speed ratio, θ is the azimuth angle of the blade, and αp is the preset pitch angle of the blade. Fujisawa and Shibuya (2001) showed that the vortex shedding behind the vertical axis turbine blade has the similar pattern as vortices in the Von Karman vortex street. The vortex shedding behind a two-dimensional circular cylinder is known as Von Karman vortex street. Consequently the vortex shedding behind a vertical axis turbine can be modeled by the vortex shedding behind a cylinder. In vertical axis turbine, two counter-rotating vortices are developed due to the flow separation from the leading edge and roll-up flow motion from the pressure side of the blade. The first pair of vortices forms between the azimuth angles of 45° and 90°. The second pair forms between the azimuth angles of 90° and 135°, as shown in Fig. 3. The flow visualization technique around the blade in a vertical turbine, depicted in Fig. 4, verifies the results obtained by Fujisawa and Shibuya (2001). Based on the results obtained from studies conducted by Medici and Alfredsson (2006) and Fujisawa and Shibuya (2001) and our team in the water tunnel, the wake behind a vertical turbine consists of two pairs of counter rotating vortices shed from the blade. This vortex shedding can be modeled by placing circular cylinders in the water tunnel. The size of the vortices and frequency of the vortex shedding can be controlled by the Reynolds number and the diameter of the cylinder. Cylinders with different diameters are placed upstream the scaled turbine to create vortex shedding. In this study, the upstream cylinder is aligned with the rotational center of the turbine with no lateral offset. The cylinder is placed at various longitudinal distances to assess the proximity effect. The torque, rotational speed and the azimuth angle of the turbine are recorded with high frequency sampling rate during the test. Then the average and instantaneous power output and of the turbine are calculated and plotted for different inflow conditions. The power output quality is investigated by analyzing the power data in the frequency domain.
Fig. 2. Wind frequency distribution for the test a and test b in Sheldahl and Blackwell (1977).
2010). In laboratory testing, the turbulence intensity of the flow is increased by employing a screen upstream the model. When flow passes through the screen, small vortices are shed off the screen wires and increase the turbulence intensity of the flow. The size of the generated vortices is in the order of magnitude of the screen wires’ diameter. This technique increases the turbulence intensity homogeneously in entire flow. Compared to the low turbulence intensity flow, a high turbulence intensity flow postpones the stall phenomenon to higher angle of attacks thus increases the maximum lift coefficient of the blade. Therefore, the performance of the turbine is enhanced in turbulent flows and results in higher power output. This statement is true as long as the vortices in the turbulent flow are much smaller than the chord length of the blade. Unlike water tunnels and towing tanks where flow is uniform and turbulence is low, in rivers, channels and oceans the flow is highly turbulent and non-uniform and contains large-scale structures exceeding the diameter of the turbine. This condition will be accentuated in hydrokinetic farm applications where some turbines operate in eddies shed by upstream turbines.
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Fig. 3. Schematic illustration of counter-rotating vortices from Fujisawa and Shibuya (2001).
bi-directional rotary torque and the rotational speed of the turbine. The accuracy of the torque transducer is ± 0.25% with a respond frequency of 100 Hz. The instrumentation setup is demonstrated in Fig. 7. During the test, the pitch angle of two blades is set to 2.5° toe out and the turbine rotates in the counterclockwise direction from the top view. Having 50 cm water depth in the test section of the water tunnel, the clearance coefficient of the turbine is 0.23. The clearance coefficient is the ratio of the water height above the turbine to the height of the blades described in Birjandi et al. (2013). The non-uniform inflow condition is simulated by four circular cylinders, 2.54 cm (1 in), 5.08 cm (2 in), 7.62 cm (3 in), and 10.16 cm (4 in) diameter size. The ratio of the cylinder diameter to the turbine diameter is a dimensionless number that describes the relative size of the cylinder to the turbine. This ratio is 0.08, 0.17, 0.25 and 0.34, respectively for cylinders with the diameter size of 2.54 cm, 5.08 cm, 7.06 cm, and 10.16 cm. The longitudinal distance of the cylinder is measured from the center of the turbine. Fig. 8(a) shows the picture of the turbine and the cylinder taken from the bottom of the water tunnel. In this picture, the separated flow behind the cylinder is clearly visible and both laminar and turbulent separation points are captured. The schematic top view of the turbine and cylinder is shown in Fig. 8(b) with positive directions demonstrated on it. Due to large number of test conditions a naming method is introduced to simplify referring to a test condition. In this naming method, the number following d represents the diameter of the upstream cylinder in inches, following x is the
2. Experimental apparatus The scaled model turbine sued in this study is a two-bladed squirrel-cage vertical axis turbine. Blades are machined from T6082T6 aluminum alloy with a computer numerical control machine at the University of Manitoba to an accuracy of 0.05 mm. Blades consist of NACA-0021 airfoil profile section, a symmetric profile, with no twist and no taper, Fig. 5. The turbine is 30 cm in diameter and 30 cm in height. Blades are attached to two solid disks at both ends to approximate two-dimensional flow condition for blades by eliminating tip vortexes and spanwise flow, Fig. 6. Experiments are performed in the closed-circuit water tunnel facility at the University of Manitoba. The dimensions of the test section are 61 cm wide, 60 cm deep and 183 cm long. The maximum flow speed in the section is 1 m/s when the water level is 60 cm, full water level condition. At lower water levels, the flow speed can reach higher values. During the test the water level in the test section is kept at 50 cm and the flow speed is set on 0.6 m/s. In this condition, the top of the turbine is 10 cm below the free surface and the bottom of the turbine is 10 cm above the water tunnel floor. The diameter of the turbine is half of the test section width; therefore, the operating condition of the turbine in the water tunnel approximates the condition of a turbine operating in an array of turbines with one turbine diameter lateral spacing. A Torqsense Rayleigh wave rotary torque transducer measures the
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Fig. 4. Vortex formation and convection from the leading edge of the blade at the position of (a) 35°, (b) 60°, (c) 85°, (d) 95°, and (e) 120°.
dimensionless number describing longitudinal distance between the turbine and upstream cylinder, x/D, following y is the dimensionless lateral distance of the cylinder from the center of the turbine, y/D, and following u is the free stream speed in m/s. For example, d4×1.5y0u0.6 represents a test in which the 4-in. diameter cylinder located at x/D =1.5 and y/D =0 upstream of the turbine and subjected to 0.6 m/s flow velocity. In this study the y/D is kept zero, no lateral offset. Fig. 5. The geometry of the blade (a) side view, and (b) profile section.
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quently reduces the angle of attack of the blade which results in smaller separation and therefore higher performance. However, at higher tip speed ratios the wake of the cylinder drops the blade angle of attack below the maximum lift angle of attack and decreases the power coefficient of the turbine. With no cylinder upstream of the turbine, the power diagram has a step between the tip speed ratio of 1.7 and 2.2. This step diminishes when the turbine operates in the wake of the cylinder. When the turbine is subjected to the wake of the d/D=0.08 cylinder, the power coefficient is above 90% of the power coefficient of the turbine with no cylinder upstream. In this case, the power coefficient increases slightly as the distance increases but is drops as the cylinder moves from x/D=3 to x/D=4. Larger cylinders have the most negative effect on the power coefficient of the turbine at x/D=1.5. At this distance, the maximum power coefficient is less than the power coefficient of the turbine when the upstream cylinder is at x/D=1. When the upstream cylinder is at x/D=1, the wake behind the cylinder interacts only with a small segment of the turbine, due to the limited distance for expansion before reaching the turbine. Therefore, it has a limited effect on the overall performance of the turbine. The strength of the wake diminishes as longitudinal distance increases, yet the wake envelope becomes wider. At x/D=1.5 the combination of wake strength and the width of the wake have the strongest adverse contribution on the power coefficient. After x/D=1.5 the power coefficient recovers as the longitudinal distance increases further. Among the cylinders, d/ D=0.25 has the fastest recovery rate. At x/D=4, the turbine behind the d/D=0.25 cylinder has 97% of the maximum power coefficient of the turbine operates with no cylinder upstream, Fig. 10.
Fig. 6. Two-bladed squirrel-cage vertical axis turbine.
3. Test procedures
4.2. Frequency analysis
The longitudinal distance between the cylinder and the turbine affects the size and the strength of vortices interacting with the turbine and also changes the width of the wake. The upstream cylinder is placed at five longitudinal distances from the turbine, x/D =1, 1.5, 2, 3 and 4. During the tests, cylinders are aligned with the center of the turbine thus the wake is evenly distributed around the center of rotation if the turbine is not rotating. The rotation of the turbine creates asymmetric condition for the flow around the turbine; therefore the approaching wake and vortices have tendency to move toward the receding turbine blades. Tests are conducted at the flow speed of 0.6 m/s which is equivalent with the Reynolds number of 2.00×105, based on the diameter of the turbine. The torque, rotational speed of the turbine and the azimuth angle of the blades are recorded for 30 s for each test. The power coefficient diagram of the turbine is extracted based on the average power at each tip speed ratio. For each test condition, the maximum power coefficient of the turbine is obtained from the power coefficient diagram. The trend in the average power coefficient of the turbine is investigated base on the location and size of upstream cylinders. In the next phase, the power output data is investigated in the frequency domain to understand the effect of the wake on the power quality.
The average power is the main parameter to predict the output power of a hydrokinetic turbine farm. However, it contains no information about the quality of the output power and dynamic loads on the turbine. The power output with high fluctuations not only can complicate the power system components, but also can reduce the lifetime of the turbine due to higher fatigue loads. The harmonics in the power output of a turbine operating in a uniform inflow are the rotational frequency of the turbine and its multiples. The upstream cylinder changes the inflow pattern and causes local high-speed and low-speed areas on the turbine actuating disk. These local high and low velocity areas impose more fluctuations to the power output of the vertical turbine due to rapid changes in blade angle of attack. The maximum power coefficient of the turbine operating behind the d/D=0.34 occurs around the tip speed ratio of 2.7, Fig. 9d. Therefore, in this section, the frequency analysis is conducted on the power coefficient of the turbine at the tip speed ratio of 2.7. Fig. 11 shows the power coefficient variations of the turbine versus azimuth angle for several rotational cycles with and without the upstream cylinder. Measurements show that the power coefficient does not quite follow a quite pattern in different cycles, even in the absence of the upstream cylinder. Although in uniform inflow, the turbine theoretically generates an identical power outputs in every rotation in reality the power output fluctuates due to vortex shedding behind the upstream blades and their interaction with downstream blades. Power coefficient deviations deviation are much more limited for a turbine operating in an uniform inflow compare to the turbine operating behind a cylinder. Power coefficient fluctuations increase by the size of the upstream cylinder. For a better understanding of the effect of the upstream cylinder on the quality of the power output, the power coefficient of the turbine operating downstream of the d/D=0.34 cylinder at x/D=1.5 is investigated in the frequency domain.
4. Results and discussions 4.1. Average power results The upstream cylinder improves the performance of the turbine at tip speed ratios less than the tip speed ratio of the maximum power coefficient point (optimum tip speed ratio), Fig. 9. However, at tip speed ratios higher than optimum tip speed ratio it reduces the power coefficient. The wake of the upstream cylinder reduces the inflow velocity for the blade around the 90° azimuth angle, where the blade experiences the highest angle of attack. The lower inflow velocity means smaller angle of attack. At low tip speed ratios, blades experience flow separation due to high angle of attack near 90° azimuth angle. The upstream cylinder reduces the inflow velocity and conse-
4.2.1. Power spectral density analysis The power spectral density (PSD) function transfers the power output data of the turbine from the time domain to the frequency 329
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Fig. 7. Test setup for the water tunnel experiment.
Fig. 8. Turbine and cylinder arrangement, (a) down view of the arrangement in the water tunnel and (b) schematic top view of the setup.
method divides the signal into several overlapping segments and fits a specified window to each segment. A Hann window with 50% overlapping is applied to the power data.
domain and it presents the energy distribution of the signal in the frequency domain. In this study, the PSD function is obtained for the power output data using the Welch's method (Welch, 1967). Welch's 330
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Fig. 9. Average power coefficient of the turbine operating behind the cylinder at various longitudinal distances, (a) d/D=0.08, (b) d/D=0.16, (c) d/D=0.25, and (d) d/D=0.34.
The rotational frequency of the turbine is 1.72 Hz for the tip speed ratio of 2.7 and the flow velocity of 0.6 m/s. Since the turbine has two blades, the principal frequency of the power output is 1.72×2=3.44 Hz. Fig. 12 shows the energy distribution of the power output data for the turbine operating with no cylinder upstream. The highest energy belongs to the principal frequency, 3.44 Hz. The second highest energy peak in the PSD diagram belongs to a frequency which is twice the principle frequency. The PSD also shows other peaks in the power output data which are integer factors of the principal frequency. The frequencies that are integer factors of the principal frequency are called prime frequencies. Between the first and second prime frequencies, another energy peak occurs in the middle of those two frequencies. This pattern is repeated to the end of the frequency domain. At higher frequencies, the energy difference between these three peaks is reduced. Before the principal frequency, there is an energy peak at the frequency of 1.75 Hz, which represents the rotational frequency of the turbine. Although blades of the turbine are theoretically identical, in the manufacturing process it is impossible to have identical blades. Small differences, like surface roughness, could cause different hydrodynamic characteristics for each blade. Differences between two blades are magnified near the stall angle of attack at which the flow separates from the blade surface and the lift coefficient drops suddenly. A slight
Fig. 10. Maximum power coefficient of the turbine versus the longitudinal distance of the cylinder from the turbine.
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Fig. 11. Instantaneous power coefficient of the turbine versus azimuth angle at the tip speed ratio of 2.7 for (a) no cylinder test (b) 10.16 cm (4 in) diameter cylinder at x/D=1.5 upstream of the turbine.
difference in shape or property of the blade can accelerate or postpone the stall phenomenon considerably and significantly change the power output of the turbine. The upstream cylinder changes the inflow pattern on the turbine and creates local low and high velocity areas on the turbine. The local low and high velocity areas are the result of the wake and vortex shedding behind the cylinder and disrupt the smooth sinusoidal pattern of the blade angle of attack in one rotation. Fig. 13 compares the PSD of the power output data for the turbine operating in a uniform inflow and the turbine operating downstream the d/D=0.34 cylinder located at x/D=1.5. The upstream cylinder diminishes the power at the prime frequencies and it creates two peaks between two consequent prime frequencies instead of one. More investigations show that these two frequency peaks are related to the vortex shedding frequency behind the cylinder. The first one is the vortex shedding frequency of the cylinder and its multiple and the second peak is twice the vortex shedding frequency and its multiples. The power of the frequencies between two prime frequencies is higher for the turbine operating in the wake of the cylinder, Fig. 13b. In the PSD diagram, events that regularly occur in every rotation, like dynamic stall, contribute to the
Fig. 12. PSD of the power coefficient signal for the turbine operating in a uniform inflow with no cylinder in the upstream.
Fig. 13. Power signal PSD of the turbine operating behind the d/D=0.34 cylindr at x/D=1.5 (a) between the frequencies of 0.02 Hz and 100 Hz, and (b) between 2 Hz and 10 Hz.
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Fig. 14. Power signal PSD of the turbine operating behind the d/D=0.34 cylindr at various distances (a) between the frequencies of 0.02 Hz and 100 Hz, and (b) between 2 Hz and 10 Hz.
x/D=1, has the highest adverse effect on the total PSD power. This dataset is available for other researchers for more processing and investigation in Reference (Birjandi and Bibeau, 2013). Fig. 15 compares the spectrogram of the power coefficient of the turbine in the uniform flow and downstream the d/D=0.34 cylinder at x/D=2. The red color indicates high power frequencies and the blue color represents low power frequencies. Results show that the high power is mainly concentrated around the first and second prime frequencies when the turbine operates in the uniform inflow. Irregular events allocate insignificant power to themselves in this case. The upstream cylinder diminishes the power at prime frequencies and increases the power of irregular events. The level of the power between the two prime frequencies considerably increases. The smooth sinusoidal shape of the PSD is disrupted by the upstream cylinder.
Table 1 Energy distribution under the PSD diagram. Test
Between two first prime frequencies (dB/Hz)
Total frequency range (dB/Hz)
No cylinder test d1×1y0u0.6 d1×1.5y0u0.6 d1×2y0u0.6 d1×3y0u0.6 d1×4y0u0.6 d2×1y0u0.6 d2×1.5y0u0.6 d2×2y0u0.6 d2×3y0u0.6 d2×4y0u0.6 d3×1y0u0.6 d3×1.5y0u0.6 d3×2y0u0.6 d3×3y0u0.6 d3×4y0u0.6 d4×1y0u0.6 d4×1.5y0u0.6 d4×2y0u0.6 d4×3y0u0.6 d4×4y0u0.6
0.030 0.049 0.042 0.041 0.042 0.046 0.397 0.308 0.227 0.089 0.053 0.391 0.645 0.612 0.485 0.255 0.385 0.702 0.756 0.510 0.337
20.701 14.719 15.036 16.692 17.613 17.921 8.796 8.838 8.898 13.032 14.999 6.883 3.787 6.911 13.071 16.703 1.020 1.563 3.463 7.248 9.901
5. Conclusion Non-uniform inflow and regional wake were created by placing cylinders with different sizes upstream a vertical axis turbine. The effects of the size and longitudinal displacement of the upstream cylinder on the power output of the turbine were investigated. Results for the average power output show that the cylinder at the longitudinal distance of x/D=1.5 has the maximum adverse effect on the average power output of the turbine for most cylinder sizes except the smallest size, d/D=0.08. At x/D=1 despite the fact that the wake is stronger, the negative effect of the upstream cylinder is limited since the wake does not get enough time to expand and cover a large area of the vertical turbine. The power coefficient of the turbine recovers by increasing the distance between the cylinder and the turbine. The power coefficient recovery rate of the turbine can be described as a function of the dimensionless diameter of the cylinder with respect to the turbine diameter. This study shows that d/D=0.25 has the fastest recovery rate even faster than smaller cylinders like d/D=0.08 and d/D=0.16. The frequency analysis shows that the upstream cylinder not only affects the average power but also influences the quality of the power output. The upstream cylinder increases irregular fluctuations in the power output of the turbine. Theoretically the power output data has to repeat itself in every 360° azimuth angle but in reality imperfectness in manufacturing, assembly and inflow condition introduce disturbances in the power data. The upstream cylinder not only increases the power of frequencies between the two prim frequencies but also it increases the power of low frequencies, lower than the first prime frequency. The
energy of prim frequencies. Events that occur irregularly lie between the two consequent prime frequencies. Irregular events carry insignificant amount of energy, compare to regular events, Fig. 13; however, irregular events are important for power output quality and fatigue studies. Fig. 14 shows the PSD of the power output of the turbine operating behind the d/D =0.34 at various distances. Table 1 summarizes the power distributed under the PSD diagram for different test conditions. Results show that the turbine operating in a uniform inflow has the lowest power level between two prime frequencies. The power between two prime frequencies increases when the turbine operates downstream a cylinder. The larger and closer cylinder increases this energy more. For small cylinders, d/D=0.08 and d/D=0.16, the maximum power occurs when the cylinder is at the closest distance to the turbine, x/D=1. As the size of the cylinder increases, the maximum power occurs at farther distances, for d/ D=0.25, it occurs at x/D=1.5 and for d/D=0.34 it occurs at x/D=2. The total power of the PSD is highest when the turbine operates in uniform inflow. In general, upstream cylinder reduces the total PSD power. The largest cylinder, d/D=4, at nearest distances to the turbine, 333
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Fig. 15. Spectrogram of power coefficient signal for (a) no cylinder test and (b) test d4×2y0u0.6. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.) tunnel test configurations and available data campaigns unsteady aerodynamics experiment. NREL Technical Report, NREL/TP-500-29955. Kelley, N., Hand, M., Larwood, S., McKenna, E., January 2002. The NREL large-scale turbine inflow and response experiment: preliminary results. In: Proceedings of the Wind Energy Symposium, ASME, Reno, U.S. Medici, D., Alfredsson, P.H., 2006. Measurements on a wind turbine vortex shedding. Wind Energy 9, 219–236. Sheldahl, R.E., Blackwell, B.F., 1977. Free-air performance tests of a 5-metre diameter Darrieus turbine. Sandia National Laboratories, SAND77-1063. Sheng, W., Galbraith, R.A.M., Coton, F.N., 2010. Applications of low-speed dynamic-stall model to the NREL airfoils. J. Sol. Energy Eng. 132, 011006. Sutherland, H.J., Kelley, N.D., 1995. Fatigue damage estimate comparisons for Northern European and U.S. wind farm loading environments. In: Proceedings of the Wind Power, AWEA, Washington, DC., U.S. Welch, P.D., 1967. The use of fast Fourier transform for the estimation of power spectra: a method based on time averaging over short, modified periodograms. IEEE Trans. Audio Electroacoust. AU-15, 70–73. Yokosi, S., 1967. The structure of river turbulence. Bulletin of the Disaster Prevention Research Institute, Kyoto University, vol. 17, pp. 1–29.
diagram of the power output in one rotation is unrepeatable due to the variations in the inflow condition. The size of these fluctuations increases when the turbine operates downstream a cylinder. References Birjandi, A.H., Woods, J., Bibeau, E.L., 2012. Investigation of macro-turbulent flow structures interaction with a vertical hydrokinetic river turbine. Renew. Energy 48, 183–192. Birjandi, A.H., Bibeau, E.L., Chatoorgoon, V., Kumar, A., 2013. Power measurement of hydrokinetic turbines with free-surface and blockage effect. Ocean Eng. 69, 9–17. Birjandi, A.H., Bibeau, E.L., 2013. Performance of Marine Kinetic Turbine in the Wake. 〈http://dx.doi.org/10.5203/birjandi_1〉. Fujisawa, N., Shibuya, S., 2001. Observations of dynamic stall on Darrieus wind turbine blades. J. Wind Eng. Ind. Aerodyn. 89 (2), 201–214. Hand, M.M., Simms, D.A., Fingersh, L.J., Jager, D.W., Cotrell, J.R., Schreck, S., Larwood, S.M., December 2001. Unsteady aerodynamics experiment phase VI: wind
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