Spacing dependence on wind turbine array boundary layers

Transcription

1 Spacing dependence on wind turbine array boundary layers Raúl Bayoán Cal 1,*, Angelisse Ramos 2, Nicholas Hamilton 1, and Dan Houck 3 1 Department of Mechanical and Materials Engineering, Portland State University, Portland, Oregon, USA 2 Department of Mechanical Engineering, University of Puerto Rico-Mayaguez, Mayaguez, Puerto Rico, USA 3 Department of Mechanical Engineering, Cornell University, Ithaca, New York, USA * correspondent author: cal@me.pdx.edu Abstract Wind tunnel experiments of a 4 3 model wind turbine array are carried out to understand impact on the flow field and turbulence statistics due to the changes in turbine spacing. Stereo particle Image Velocimetry (SPIV) is used to obtain measurements in dual planes, fore and aft of wind turbine models in the centerline of the array. Variations in turbulence statistics are assessed by altering the streamwise and spanwise spacing. Spacing schemes tested include permutations of streamwise spacing, S x = [3D; 6D], and spanwise spacing, S z = [1.5D; 3D], where D is the rotor diameter. The kinetic energy flux, uv U and production of mean kinetic energy are also assessed. Furthermore, the mechanical power is measured for these turbines reflecting the influence of spatial variations. The analysis has consequences on land use versus power output. 1. Introduction Cost is a constant obstacle to the pursuit of wind energy as a viable alternative to fossil fuels. In the case of wind farms, the cost is considerable, requiring both land (including purchase or lease, grid connections, etc.) and the cost of the turbines themselves. As wind farms grow, the economic use of land on a generated power per area basis is an increasingly critical factor and measure of a wind farms efficiency. There are multiple factors affecting the costs and benefits of wind farms, and even smaller clusters of turbines, that can be directly affected by the spacing and overall layout of the turbines. In general, studies have addressed how wake mixing and wake recovery among multiple turbines, blade fatigue due to turbulence, and the effective roughness of large farms in regards to the atmospheric boundary layer (ABL) are affected by the spacing or density of turbines Gonzalez et al. (2012), Newman (1977). While most studies have not evaluated these effects as functions of different spacings specifically, those that have have all concluded that larger spacings are better in regards to wake recovery, effective roughness, overall cost, or similar metric, but there is no agreement on the optimal spacing. The Nysted and Horns Rev wind farms have been well studied. The Nysted farm is spaced 10.5 diameters downstream by 5.8 cross-stream. The Horns Rev farm is spaced seven diameters along the main directions and 9.4 or 10.4 along the diagonals. Barthelmie & Jensen (2010) quantified the impact of turbine spacing in the Nysted farm on wake losses and found that spacing is responsible for 68-76% of the variability in efficiency of the farm. It was further estimated that a 1.3% increase in normalized efficiency for every one diameter increase in turbine spacing for wind speeds under 15 m/s. At higher wind speeds, no relationship was found between the influence of wakes on farm efficiency. Hansen et al evaluated the effects of an effective spacing on the Horns Rev farm by looking at the power deficit as a function of downstream distance for different directions of mean wind flow. It was found that, approximately 10 diameters into the farm, the differences in power deficits for different spacings were almost negligible, though the initial deficits were larger for smaller spacings, and that the differences in power deficits for different spacings vanish with increasingly unstable conditions. Computer simulations and numerical optimizations tend to take one of two approaches to analyzing the effects of turbines on flow fields: models of wake interactions and their effects on wind velocity and thereby power extraction or evaluating the turbines as roughness elements and determine the effects of roughness on the - 1 -

2 atmospheric boundary layer (ABL) and thereby velocity and power extraction. Gonzalez et al. (2012) found in their wake model study that as spacing was increased in both directions (downstream and cross-stream) the wake coefficient (total power output with wake effect over total power output without wake effect) increased and that the effect was more pronounced in larger arrays. Furthermore, it was found that the direction of the incoming wind had a greater effect on the wake coefficient for more tightly spaced arrays. Kaminsky et al. (1987) analyzed the wake effects along a single line of turbines parallel to the wind direction to compare an optimized spacing to an equidistant one within a fixed distance, though they began with the assumption that all turbines were in the far wake region of the preceding turbine, which they calculated to be approximately 3.7 diameters. Broadly speaking, when optimizing spacing for 8, 9, 10, and 11 turbines in a row they found that the optimal spacing required larger spacings in the first few rows and smaller spacings in the last few rows, though not in any regular pattern. The optimal spacings were estimated to increase available power by 1-3% over equidistant spacings and a row of 10 turbines would produce more power than 8, 9, or 11. This study seeks to address a more specific question regarding spacing: What are the individual effects of downstream and cross-stream spacings in a finite array of aligned wind turbines? Particle image velocimetry data was collected for four cases: 6 x 3, 6 x 1.5, 3 x 3, and 3 x Experimental setup The 140 sq-m closed-circuit wind tunnel facility of Portland State University (PSU), which was built with sole purpose of analyzing and comprehending turbulent flows, was used for this experiment. The wind tunnel consist of a 5m long test section with operable clear glass doors which permits easy view for the researchers and for the measuring instruments. The test section has a passive grid at the inflow entrance,seen in figure 1, which consist of 7 horizontal and 6 vertical rods to introduce turbulence to the flow. They are placed at the beginning of the test section in order for the flow to reach an homogeneous state before hitting the first row. At 0.5m down of the test section nine vertical strakes are present after the passive grids to adjust the inflow and better simulate the atmospheric boundary layer (ABL).These strakes are made out of plexiglass with a thickness of about m and they have a spacing of 0.136m between them. Another thing used in the test section to mimic the ABL are small diameter chains in the floor with a 10.8cm spacing between them to introduce roughness to the system. Figure 1: Wind tunnel schematic for experimental setup. 2.1 Instrumentation Particle Image Velocimetry (PIV) method was used for the recollection data. The method which consist on taking 2000 PIV images in two windows,fore and aft of the wind turbines, at two locations in the wind farm. The first set of PIV planes were located in the centerline of the first and fourth row. The PIV equipment consist a double-pulsed laser (532nm,1200, 4ns pulse durations), 4 CCD cameras paired for the upstream and downstream of the wind farm and a seeding particle. It is important that the properties of the particle the flow and the flow are similar in order to track the flow successfully, that is why a buoyant fluid particles of diethylhexyl sebacate was used. The seeding particle was pumped into the wind tunnel at a constant rate to ensure homogeneous distribution throughout the tunnel

3 After collecting the 2000 PIV images for each case, the images where processed with a FFT correlation algorithm used to reduce the interrogation windows in order convert the data into vector fields. The obtained vector fields were then processed by a set of algorithms to identify and omit any erroneous measurements collected. 2.2 Wind Turbines The wind turbines used in this experiment were fabricated with the goal of simulating the structure and aerodynamic characteristic of full-scale win turbines. A laser was used to cut a m thick steel to make the rotor blades and using a 3D CAD software a 15 pitch from the rotor plane and a 5 twist from root to tip was specified for each of the blades. The nacelle of the turbines consisted of an electrical motor (Faulhaber GMBH Co series 1331T012SR) with a cylindrical shape which was mounted to a 0.01m hollow steel shaft. The motor had a diameter of m and a length of m, an operating voltage of 12V and it was aligned with the direction of the flow, shaft pointing upstream of the test section. The tower of the turbines were 0.12m at hub height and had a cylindrical shape with a hollow interior to remove from the flow the intrusion of electrical wiring of the motor and torque system. Four 1.14m 0.094m flat steel plates were used to mount three wind turbines per row making the adjustment for the test cases in the stream-wise direction easy. The steel plates had m circular perforation at 3D or 1.5D apart making the reduction in the span-wise direction possible. 2.3 Torque Sensor The torque sensing system consisted on mounting the dc motor described in the section below to a housing were it was held in place by two VXB ball bearings placed along the shaft at each side of the motor. At the rear side of the dc motor a pressing arm was implemented to press a bronze strip, m wide and m thick, to insure that the motor stayed in place.to the bronze strip 120 ½ strain gauges were included to measure the torque required in order for the motor to stay in place,which were calibrated according to the manufacturers specifications. An electrical circuit called Wheatstone bridge was done to measure the resistance by balancing the existing strain gauges with two more strain gauges of the same kind glued to the side of 0.1m cube made of aluminum. National Instruments Data Acquisition (DAQ) and measuring software (LabVIEW) where used at 10kHz to collect measurements. 2.4 Cases The cases consisted in variations in the stream-wise, S x, and span-wise, S z, spacing. The cases where categorized by letters, A through D. Case A is the base case with a standard spacing with a S x =6D and a S z =3D. The spacing was reduced to half in both direction, S x =3D and S z =1.5D for case C, while in case B S x was kept at 3D but S z was doubled to 3D. Compared to case A, S x =6D was kept for case D while the S z was reduced to half. The goal of the described arrangements its to analyze how the wake of the wind turbines behave when reduction in the specified direction are made and better understand how the land-use can be optimized when arranging multiple wind turbines in an array. Cases Sx Sz Area Case A 6D 3D 18D 2 Case B 3D 3D 9D 2 Case C 3D 1.5D 4.5D 2 Case D 6D 1.5D 9D 2 Table 1: Cases denoted by the changes in streamwise and spanwise spacing

4 Figure 2: Schematic detailing turbine spacing 2.5 Power Production The power produced by the center turbine in the last row is measured and plotted against the angular velocity in figure 3. The maximum occurs for the largest spacing at 0.08 W. This is decreased when the spanwise spacing is decreased to 0.063W. The power is then severely affected when decreasing the streamwise spacing to three diameters downstream. The power decrease is about 40%. The peak power tends to shift slightly to greater angular velocities given that the larger spacings allow for faster moving fluid through the canopy of turbines. This then follows the particular order as the spacings are decreased, but the surprising quantities are the magnitudes. Figure 3: Power, P versus angular velocity, ω 2.6 Flow Field Looking at the contour of the mean velocity in the streamwise direction shown in figure 4, it can be seen that in cases A and D where the stream-wise spacing remained the same but the span-wise was reduced from 3D to 1.5D. Subsequently, the exit rows clearly show how the reduction in spacing effects the downstream flow. Comparing the velocities upstream of the exit row of case A with case D, it can be seen that the wake from case D does not recover sufficiently. At hub height, the velocity is about 2.7m/s where in case A the velocity is about 3.4m/s. It is also observed that in case D immediately behind the nacelle compared with case A, the wake has a greater region where the velocity tends to 0, meaning that the power output could be affected because of - 4 -

5 the reduction of spacing in the span-wise direction. Cases D and B share the similarities of having the same area of 9D 2, but the exit rows for each case the wake behind the nacelle behaves very differently for each of these cases. Case D shows a greater velocity deficit than in case B, suggesting that for case D which is causing a greater velocity deficit. Comparing the upstream of the exit rows for cases A and B, it can be seen that the wake coming from the upstream turbines remains rather constant suggesting that the wake could not recover given that the space between turbines was reduced half the diameter of case A in the stream-wise direction. When comparing the wake of the exit row turbines in cases A and B, the velocity deficit appears to be similar. This is an unexpected result because the wake from the third row turbine has not recovered and is present in the inflow for case B while the inflow for case A from third row turbines appears to have recovered. Similar to the upstream exit rows in cases A and B, case C compared with A shows a velocity deficit from the upstream wind turbines but in this case, it is more pronounced and this behavior is due to, unlike for case B, reducing the spacing in the span-wise direction. Figure 4: Contours of streamwise mean velocity. Case A (6D 3D), Case B (3 3), Case C (3D 1.5D) and Case D (6D 1.5D) For the contour of the mean velocity in the V direction (Figure 5), it can be said that for all cases the entrance row remain similar for both downstream and upstream direction. However for the exit rows there are some noticeable changes. Comparing case A with case B and C upstream of the exit rows, it is observed that the wake from upstream wind turbines still remains throughout the interrogation area for cases B and C and does not recover before arriving to the downstream wind turbine. Case C has a more pronounced behavior since the span-wise reduction is from 3D to 1.5D. Downstream of the exit rows, case B remains similar to case A but case C has a larger area where a fluid is moving in the positive wall normal direction from x/d = 1.0 to x/d=2.0. Looking at case D, the most noticeable behavior is occurring at downstream of the exit row. From y/d = 1.0 to 1.5, compared with the other cases the negative values of V extends further away from the rotor. An explanation for this behavior could be that the span-wise direction is very dense and the wake from upstream wind turbines pushes the wake from the downstream wind turbines in that direction. Furthermore, comparing case A with cases B and C in the upstream of the exit rows, the spanwise component of velocity shown in figure 6, shows there is still a great part of the upstream wind turbines wake trying to recover. Downstream of the exit rows, case C shows the smallest negative and positive wakes behind the wind turbine. Case B has a similar behavior to case C in the downstream exit rows. In case D, compared to A, there are still traces of the upstream wind turbine in upstream exit row, but the behavior remained similar in the downstream exit row with the difference that at y/d= 1.5, the wake coming in the positive direction is much smaller than in case A. The kinetic energy flux is, uv U, is shown in figure 8. When observing the back row, it is seen that in cases for which the streamwise spacing is greater, 6D, the magnitudes are lower by half when compared to the more aggressive spacings. Furthermore, the spanwise spacing variation is evident when comparing cases B and C as seen in the inflow and outflow of the last row, specifically below hub height. It is clear that the largest top - 5 -

6 to bottom differences occur for cases A and D. Coincidentally, these cases generate the highest values of power production. In addition, this is also supported by the results of mean streamwise velocity. These changes are not as evident in the first row but certainly the effects are compounded due to the park effect or also viewed as the wake-to-wake interactions. The production of mean kinetic energy is presented in figure 9. Once again the trends follow closely those of the kinetic energy flux. The most important differences occur at the top and bottom tip after the fourth turbine. At the top tip, the quantities of production is the largest for case A with a spacing of 6 and 3D in the streamwise and spanwise directions, respectively. Followed by case D, where the magnitudes are increased and the shapes persist over longer longitudinal ranges. On the incoming flow, production is visibly affecting the turbine for cases B and C at the top tip height. The bottom tips also possess the greatest magnitudes in cases A and D. This is also not surprising given that the in-plane stress is large as well as the gradients of mean velocity. Both quantities composing the production term. 3. Conclusions Measurements of power and the flow field have been performed in a wind tunnel experiment to observe the effects of spacing. Flow measurements are obtained via PIV. There is a clear effect of the wake into the preceding turbines from the previous when the spacing is decreased. This corresponds to a decrease in power. The wakes are not fully recovered by three diameters downstream thus this has a profound effects on the power extracted by the turbine. These effects are also found in the kinetic energy flux and production terms, where the largest magnitudes of these quantities occur for cases A and D containing the largest streamwise spacing. It is also found that the spanwise spacing plays a role in affecting all the analyzed quantities but not with the same severity as the streamwise spacing. This analysis allows to observe the direct impact on power production and how this relates to quantities contained in the equations of mean momentum and kinetic energy. Figure 5: Contours of wall-normal mean velocity. Case A (6D 3D), Case B (3 3), Case C (3D 1.5D) and Case D (6D 1.5D) - 6 -

7 Figure 6: Contours of W. Case A (6D 3D), Case B (3 3), Case C (3D 1.5D) and Case D (6D 1.5D) Figure 7: In-plane Reynolds shear stress. Case A (6D 3D), Case B (3 3), Case C (3D 1.5D) and Case D (6D 1.5D) Figure 8: Flux of kinetic energy - 7 -

8 Figure 9: Production of mean kinetic energy - 8 -

9 References Gonzalez-Longatt, F., Wall, P. & V. Terzija 2012 Wake effect in wind farm performance: Steady-state and dynamic behavior Renewable Energy, 39, 1, Newman, B. G The spacing of wind turbines in large arrays Energy Conversion, 16, 4, Barthelmie, R. J. and Jensen, L. E Evaluation of wind farm efficiency and wind turbine wakes at the Nysted offshore wind farm Wind Energy, 13, 6, Kaminsky, F. C., Kirchhoff, R.H. & Sheu, L.-J Optimal spacing of wind turbines in a wind energy power plant Solar Energy, 39, 6, Calaf, M., Meneveau, C. & Meyers, J Large eddy simulation study of fully developed wind-turbine array boundary layers Phys. Fluids, 22,