Progress on the Blackhawk Model Since October 2010

BlackHawk VAWT Simulation

Project Update

2 March 2011

Progress on the Blackhawk model since October 2010

Found and digitized lift and drag data for NACA 0015 airfoil
Developed a coordinate transformation system from the end of the blades to the rotor disc
Wrote a function to describe the torque on the rotor given any wind speed and orientation
Verified torque function using hand calculations and a lot of geometry
Developed a SimMechanics model of the non-tilting turbine using the coordinate transformations
Verified these results with a simulink model based on integration principles instead of the mechanics blocks
Met with Kurt Meyers in Idaho Falls and discussed the current status of the TR 10 in operation at INL and talked about possible instrumentation to be installed this summer.
Added induction factor to model to account for power extraction from wind.
Charted basic power curve of the turbine for a range of wind speeds
Researched ideal pitch function for the turbine

Features of current VAWT simulation

Vertical Axis, 3-bladed non-tilting turbine with no ‘cant’
Overall geometry comparable to TR-10
Simulation uses NACA 0015 data (NACA 0014 data not readily available)
Loading turbine with simple DC generator model
Pitch angle can follow a user-defined function of rotor angle
“SimMechanics” module in Matlab can easily accommodate forces and rotations in other planes (i.e. will accommodate tilting rotor)

Blackhawk Power Curve / L. Damon Woods / 2/25/2011
With Pitch Articulation / +/- 9°
Windspeed / Resistance / TSR / Omega / RPS / Torque / Cp / Power
m/s / mph / Ohms / rad/sec / rps / N-m / Watts
1 / 2.2 / 0.2 / 0.8 / 0.5 / 0.1 / 0.1 / 0.01 / 0.1
2 / 4.5 / 0.1 / 5.3 / 7.0 / 1.1 / 1.7 / 0.16 / 4.9
3 / 6.7 / 0.4 / 4.7 / 9.3 / 1.5 / 5.0 / 0.35 / 34.0
4 / 8.9 / 0.8 / 4.2 / 11.1 / 1.8 / 6.5 / 0.42 / 99.0
5 / 11.2 / 1.2 / 4.0 / 13.0 / 2.1 / 20.2 / 0.45 / 205.0
6 / 13.4 / 1.7 / 3.8 / 14.8 / 2.4 / 31.0 / 0.47 / 374.5
7 / 15.7 / 2.1 / 3.7 / 17.2 / 2.7 / 27.0 / 0.49 / 619.1
8 / 17.9 / 2.7 / 3.5 / 18.5 / 2.9 / 62.3 / 0.49 / 927.3
9 / 20.1 / 3.3 / 3.5 / 20.5 / 3.3 / 67.0 / 0.52 / 1360.0
10 / 22.4 / 4.0 / 3.3 / 21.5 / 3.4 / 87.0 / 0.50 / 1900.0
11 / 24.6 / 4.7 / 3.3 / 23.5 / 3.7 / 96.8 / 0.53 / 2560.0
12 / 26.8 / 5.3 / 3.2 / 24.8 / 3.9 / 135.0 / 0.51 / 3340.0
14 / 31.3 / 6.6 / 3.1 / 28.7 / 4.6 / 185.0 / 0.54 / 5350.0
16 / 35.8 / 8.0 / 3.0 / 31.3 / 5.0 / 250.0 / 0.52 / 8050.0
18 / 40.3 / 9.6 / 2.9 / 34.2 / 5.4 / 330.0 / 0.53 / 11500.0
20 / 44.7 / 11.2 / 2.8 / 37.0 / 5.9 / 420.0 / 0.52 / 15800.0

Without Pitch Articulation / 0 pitch
Windspeed / Resistance / TSR / Omega / RPS / Torque / Cp / Power
m/s / mph / Ohms / rad/sec / rps / N-m / Watts
1 / 2.2 / 0.2 / 0.2 / 0.2 / 0.0 / 0.1 / 0.0014 / 0.0
2 / 4.5 / 0.1 / 0.3 / 0.4 / 0.1 / 0.1 / 0.0006 / 0.0
3 / 6.7 / 0.4 / 0.4 / 0.8 / 0.1 / 0.1 / 0.0029 / 0.3
4 / 8.9 / 0.8 / 0.3 / 0.7 / 0.1 / 0.4 / 0.0030 / 0.6
5 / 11.2 / 1.2 / 0.3 / 0.9 / 0.1 / 1.2 / 0.0047 / 1.3
6 / 13.4 / 1.7 / 0.3 / 1.0 / 0.2 / 2.0 / 0.0030 / 2.5
7 / 15.7 / 2.1 / 0.3 / 1.3 / 0.2 / 3.0 / 0.0037 / 4.0
8 / 17.9 / 2.7 / 0.3 / 1.3 / 0.2 / 5.0 / 0.0040 / 6.5
9 / 20.1 / 3.3 / 0.3 / 1.3 / 0.2 / 5.2 / 0.0040 / 9.0
10 / 22.4 / 4.0 / 0.3 / 1.4 / 0.2 / 6.0 / 0.0040 / 13.0
11 / 24.6 / 4.7 / 0.3 / 1.7 / 0.3 / 10.0 / 0.0041 / 18.0
12 / 26.8 / 5.3 / 0.3 / 1.8 / 0.3 / 12.5 / 0.0041 / 25.0
14 / 31.3 / 6.6 / 0.3 / 2.1 / 0.3 / 17.5 / 0.0043 / 42.5
16 / 35.8 / 8.0 / 0.2 / 2.2 / 0.4 / 24.0 / 0.0050 / 70.0
18 / 40.3 / 9.6 / 0.2 / 2.4 / 0.4 / 32.5 / 0.0055 / 115.0
20 / 44.7 / 11.2 / 0.2 / 2.8 / 0.4 / 42.5 / 0.0550 / 150.0

We also found that the turbine is very sensitive to how it is loaded. If the generator is too “aggressive” in harvesting energy, the power output falls dramatically. In the table and chart that follow, we use resistance values that are only slightly higher than optimal. This has very significant implications for generator and turbine design.

With Pitch Articulation and Overloaded
Windspeed / Resistance / TSR / Omega / RPS / Torque / Cp / Power
m/s / mph / Ohms / rad/sec / rps / N-m / Watts
1 / 2.2 / 0.2 / 0.8 / 0.5 / 0.1 / 0.1 / 0.01 / 0.1
2 / 4.5 / 0.1 / 1.6 / 2.2 / 0.4 / 0.7 / 0.03 / 0.7
3 / 6.7 / 0.5 / 1.4 / 2.7 / 0.4 / 1.0 / 0.04 / 3.8
4 / 8.9 / 0.9 / 1.3 / 3.4 / 0.5 / 3.2 / 0.04 / 10.4
5 / 11.2 / 1.3 / 1.4 / 4.8 / 0.8 / 3.5 / 0.07 / 30.0
6 / 13.4 / 1.8 / 1.3 / 5.3 / 0.8 / 5.6 / 0.06 / 50.0
7 / 15.7 / 2.3 / 1.1 / 5.1 / 0.8 / 22.3 / 0.05 / 59.0
8 / 17.9 / 2.9 / 1.0 / 5.4 / 0.9 / 23.9 / 0.05 / 84.4
9 / 20.1 / 3.5 / 1.1 / 6.7 / 1.1 / 27.0 / 0.06 / 157.5
10 / 22.4 / 4.1 / 1.1 / 7.0 / 1.1 / 40.0 / 0.06 / 203.7
11 / 24.6 / 4.8 / 1.1 / 7.7 / 1.2 / 41.0 / 0.06 / 350.0
12 / 26.8 / 5.4 / 1.1 / 8.5 / 1.4 / 45.0 / 0.06 / 425.0
14 / 31.3 / 6.7 / 1.0 / 9.4 / 1.5 / 52.0 / 0.06 / 590.0
16 / 35.8 / 8.1 / 1.0 / 11.1 / 1.8 / 80.0 / 0.07 / 1000.0
18 / 40.3 / 9.8 / 0.9 / 10.5 / 1.7 / 92.0 / 0.05 / 1082.0
20 / 44.7 / 11.3 / 1.0 / 13.4 / 2.1 / 121.0 / 0.07 / 1800.0

All three power curves are graphed on the same axes to show the remarkable difference in power outputs:

Why the difference? The answer lies in the transition of the turbine rotations to a particular tip speed ratio regime that keeps the blades experiencing small angles of attack and consequently high lift coefficients, as the graphs below demonstrate. The following graphs were generated from the SimMech model with a wind speed of 7 m/s (15 mph) and a resistance of 2 Ohms imparted by the generator.

Tip Speed Ratio increases to a value of 3.7 and then reaches equilibrium

The power output of the turbine follows the same curve as the tip speed ratio, eventually reaching a value of 600 Watts:

The graph below shows how the torque on the rotor will respond to a jump in the tip speed ratio:

The current MatLab model is shown below:

The wind speed can be changed by changing values in the yellow block

The resistance (simulating the generator) can be changed by changing the value in the orange block

The position of the blades is given by the theta (blue) block

The rotation of the turbine is given by the Omega (green) block

This model allows one to track the Power output (rightmost block), the Cp, the induction factor, the torques from each blade, and the tip speed ratio