## Aerodynamic Performance Prediction

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The ratio of lift to drag for airfoils is around 100, so the two forces, which act at the quarter chord of the airfoil, are represented by a force that makes the blade rotate, tangential force, and a force trying to push the rotor over, perpendicular force. So if these lift and drag forces are calculated for a blade, then the tangential and perpendicular forces are calculated and the performance of the rotor can be predicted. If the angle between the blade path and the wind at the blade is O (see Figure 5.9), then the tangential and perpendicular forces are

F (per) = L cos O + D sin O Notice that the perpendicular force will be larger than the tangential force, and at 90° there is only drag.

Wind

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FIGURE 6.6 Diagram of blade element.

There are a number of computer programs for predicting aerodynamic performance of wind turbines [15]. These are based on momentum theory, also referred to as strip theory. The theory assumes that each element of the blade (Figure 6.6) can be analyzed independently from the others, and the two-dimensional data for lift and drag coefficients can be used at the center of the section. Performance predictions of power, torque, force, and power coefficient can be obtained for a blade (rotor) using a numerical technique. Values are calculated for sections of the blade and then summed to obtain the total performance.

Drag and lift coefficients versus angle of attack and Reynolds number are available for lots of airfoils. In general, the coefficients are given for attack angles from around zero to a few degrees past stall. Stall is where the lift decreases and drag increases steeply. So the problem, in the calculation for performance prediction, is to use the correct inflow angle to the blade, as the angle depends on the wind speed at the blade. So the relative wind speed has to be corrected for the actual speed at the blade, which uses the axial interference factor, a, and the rotational interference factor, a'. At each section of the blade, an iterative procedure is used to calculate the angle of the inflow to the airfoil. Because sections of the blade may operate at high angles of attack, for those attack angles, lift and drag data from a flap plate or other actual measured data from some airfoil are added to the tabular values. Tip losses and hub losses can be included along with wind shear and yaw (off-axis components). The main limitations with the programs are the treatment of unsteady aerodynamics in the region of dynamic stall and the use of 2-D data for lift and drag.

Rotors for vertical-axis wind turbines present another problem since the blades go through attack angles of 360° and the blades are curved for the Darrieus wind turbine. A number of performance models for the Darrieus rotor have been formulated [3, 16-18]. In general, symmetrical airfoils are used, so lift and drag data are needed from 0 to 180°. The operation of vertical-axis wind turbines also means at an attack angle of 90°, there is no lift, so the torque and power are negative, a cyclic variation on every revolution [19].

From observations of the flow field of a Savonius rotor, an analytical model was developed for the analysis of performance [3]. Two major discernable features of the flow field are: vortices are shed from the vane tips when the vane is approximately at right angles to the flow, and these vortices are counterrotating, and the vortices move rearward at approximately the free stream speed. The model was adequate in that it predicted a power coefficient around 0.30 at a tip speed ratio around 1, which is in line with field data and wind tunnel tests for Savonius rotors.

The dynamic stall vortex has been visualized and also noted by the analysis of time-varying surface pressure data from field tests and wind tunnel experiments [20]. Blades with pressure taps were used for the Unsteady Aerodynamics Experiment [21], which included a test of an extensively instrumented wind turbine in the giant NASA-Ames wind tunnel, 24.4 by 36.6 m. Results from computer models at high wind speeds under stall were significantly different, as power predictions range from 30% to 275% of the measured values. So the aerodynamic performance prediction programs are used as a design tool, not the final answer.

Aerodynamic performance prediction programs [3] are now available for personal computers with menu-driven interactive editing and graphical display to facilitate its use as a design

TABLE 6.1

Sample Output from PROP93

Propprint3

Blade element data for delta beta = 0.00, X = 6.11, yaw = 0.00

TABLE 6.1

Sample Output from PROP93

Propprint3

Blade element data for delta beta = 0.00, X = 6.11, yaw = 0.00

 Element 1 2 3 4 5 6 7 8 9 10 Theta 180 180 180 180 180 180 180 180 180 180 Vel 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 A 0.296 0.140 0.188 0.204 0.230 0.213 0.195 0.206 0.231 0.308 AP 0.073 0.021 0.016 0.012 0.010 0.008 0.006 0.006 0.006 0.007 CL 0.813 1.005 1.160 1.206 1.334 1.311 1.168 1.037 0.918 0.772 CD 0.014 0.098 0.053 0.043 0.020 0.019 x0.016 0.014 0.013 0.011 PHI 49.92 42.48 27.54 20.14 15.45 13.03 11.35 9.74 8.34 6.72 ANG 7.92 19.18 15.74 14.84 13.35 12.93 11.35 9.74 8.34 6.72 TC 0.384 0.526 0.622 0.656 0.707 0.665 0.609 0.610 0.609 0.572 QC 0.040 0.059 0.073 0.075 0.083 0.079 0.074 0.073 0.069 0.056 PC 0.243 0.363 0.443 0.459 0.508 0.485 0.453 0.443 0.421 0.344 TD, lb/ft 2.64 6.03 11.90 17.57 24.37 28.01 30.31 35.04 329.6 41.60 QD, ft-lb/ft 4.38 10.92 22.21 32.26 45.86 53.47 59.02 66.73 71.85 65.54 PD kW 0.024 0.298 0.606 0.880 1.251 1.458 1.610 1.820 1.959 1.788 Rey, *106 0.920 0.862 0.922 0.931 0.910 0.868 0.890 1.004 1.132 1.132 Rotor Pitch X TC QC PC V0 TD MD QD PD 2 blades m/s lb ft-lb ft-lb kW 0.0 6.1 0.614 0.070 0.427 10.0 752 3,984 1,372 23.3

Note: Output for one blade (Carter 25, 10 m diameter, pitch = 0°), divided into ten stations, and then the total is summarized at the bottom. Wind speed is 10 m/s and tip speed ratio, X = 6.11.

Note: Output for one blade (Carter 25, 10 m diameter, pitch = 0°), divided into ten stations, and then the total is summarized at the bottom. Wind speed is 10 m/s and tip speed ratio, X = 6.11.

FIGURE 6.7 Twist and planform for Carter 25 wind turbine blade. Blade is divided into ten sections for analysis, and the station is at the midpoint of the section.

tool: PROP93 [22]. The inputs to the program include the blade characteristics (number, length and hub cut-out, planform, twist at the section, and pitch), lift and drag coefficients of airfoils for different angles of attack, and operating characteristics, such as tip speed ratio, rpm, and wind speed. The tabular output, in metric or English units, of PROP93 can be directed to the screen, printer, or a data file. Notice for the selected input in the example (Table 6.1), the rotor is predicted to produce 23.3 kW at 10 m/s. Graphs of the standard output parameters can be displayed as functions of blade station, pitch, wind speed, or tip speed ratio. Calculated values can then be compared with experimental values. These programs, which are steady state, do not predict the high loads seen in the field due to gusts and in changing the pitch to feather in high winds (dynamic stall).

Graphs of the planform (Figure 6.7) lift and drag data can be produced. Sample output graphs (Figures 6.8 to 6.10) are for a Carter 25 wind turbine, NACA 2300 series airfoil. Smoother graphs

 r—t [] □ S 4 ♦ O IB i À A 1 A iL 1 1 1 o

4 5 6 7 8 9 10 Blade Station

4 5 6 7 8 9 10 Blade Station

FIGURE 6.8 PROP93: Prediction of power output for one blade by blade station for four wind speeds, tip speed ratio = 6.1.

FIGURE 6.9 PROP93: Prediction of rotor power output for different pitch angles at 10 m/s. The Carter 25 wind turbine is a fixed-pitch, constant-rpm machine.

would be obtained by using twenty data stations. These blades had large twist and larger chord toward the root, and then the same chord and twist from the midpoint, which produced an aerodynamic efficiency close to the theoretical limit. Notice the twist is to obtain the correct angle of attack due to the different inflow wind due to the contribution of the blade speed, which is slowest at the root. Also, twist on the inward part of the blade increases the torque for starting rotation. Note that for constant-pitch blades with little twist, there is not enough starting torque and the rotor needs to be motored for start-up. For variable-pitch blades, the blades are in the feather position, which produces enough torque for start-up. Notice that for constant tip speed ratio, the power continues to increase with wind speed (Figure 6.10).

Tangler and Kocurek [23] provided guidelines for input of post-stall airfoil data for the prediction of peak and post-peak rotor power for performance programs using blade element momentum theory. A steady-state data set from the rotor test in the Unsteady Aerodynamics Experiment was

Wind Speed, m/s

FIGURE 6.10 PROP93: Theoretical power curve for Carter 25 rotor, tip speed ratio = 6.1.

Wind Speed, m/s

FIGURE 6.10 PROP93: Theoretical power curve for Carter 25 rotor, tip speed ratio = 6.1.

used for the global post-stall method for the prediction of post-stall 3-D airfoil characteristics to be used with the 2-D airfoil data.

PROPID [24] is a program for personal computers for the rotor design and analysis of horizontal-axis wind turbines, and the executable program is available online [25]. The strength of the method is its inverse design capability. PROPID is based on the PROPSH blade element/momentum code, and it includes a 3-D post-stall airfoil performance synthesization method for better prediction of peak power at high wind speeds.

The blade fairness program determined the airfoils at ten sections from the three input airfoils (Figure 6.11). The templates were cut out on a numerical control milling machine and assembled

Root airfoil

Tip airfoil

FIGURE 6.11 Thin airfoil series for wind turbine blade, and their input placement for a 5 m blade.

Primary airfoil

Tip airfoil

FIGURE 6.11 Thin airfoil series for wind turbine blade, and their input placement for a 5 m blade.

FIGURE 6.12 Blade templates for Carter 25 wind turbine, fabricated by AEI. There are three different airfoils, and thus there are different shapes along with different chords and twists at the ten stations.

with the proper twist (Figure 6.12). Then the blade templates were used to construct a plug, from which two molds, top and bottom, were constructed. After fabrication of the blade skins, they were attached to a Carter 25 spar and hub and tested in the field in a side-by-side comparison with a production unit [29, 30]. Data were collected at low, medium, and high wind speeds for clean, medium, and heavy surface roughness conditions. The roughness conditions were simulated with the application of grit on 2.5 cm wide tape on the upper (0.02 chord) and the lower (0.05 chord) leading edge. Results of the tests showed little power difference at low wind speed, the reduced power from the outer part of the blade could not be tested since the teetering hub reduced high flap loads, and the new airfoils were much less sensitive to surface roughness for medium and high wind speeds.

Essentially the same amount of power can be obtained from one blade rotating fast or more blades rotating slower, or from the same number of blades with different chord lengths. From the performance prediction programs, as solidity increases for a given rotor area, the tip speed ratio that gives the maximum power coefficient becomes smaller. For a given size rotor operating at fixed rpm, different size generators (rated power) can be placed on the unit by increasing the rated wind speed. In the past a number of wind turbines were built with the same diameter, 10 m; however, they had the following rated powers: 8, 12, 15, 25, 40, and 90 kW. Today, most wind turbines have rated powers at wind speeds from 10 to 13 m/s.

Other parameters, for example, are the design point, wind speed for the rated power (which primarily determines rotor area), and tip speed ratio, which is determined by the solidity of the rotor. In general, the tip speed of the blades is limited to roughly 70 m/s, as the blade tips cause excessive acoustical noise at higher tip speeds. For offshore wind turbines, noise is not an important issue. Besides the rotor design then, there are the rest of the components: hub, which may include components for adjusting pitch of the blades; drive train and gearbox in most cases; generator; yaw control; tower; and the control system.