Rotor Design: Part 4

The TSR (tip speed ratio) is a very important characteristic to consider when designing the rotor. For variable speed turbines, the rotor blade operates at an constant TSR over a specific range of wind speeds. The efficiency of the rotor blade drops when the TSR deviates from that optimum set point; therefore, it is important for the turbine to operate at the design TSR. If the operational TSR of the turbine is higher than the design TSR, the permanent magnet generator (PMG) is most likely undersized. This can lead to excess stress in the blades and increased wear on the PMG. Similarly, if the operational TSR is lower than the design TSR, the PMG is probably oversized. In this case, the blades will most likely stall during normal operation.

When a rotor blade passes through the air, it leaves turbulence in its wake. If the design TSR is too high, then the next blade will enter the region of turbulence created by the first blade, decreasing the efficiency of the turbine. At very high speeds the blades will appear as a solid wall to the wind, further reducing efficiency. If the design TSR is too low, then some wind will pass by the rotor plane with no energy extraction. The rule of thumb for designing two bladed turbines is to use a TSR of 6.28. However, this can be increased by about 25% with well designed blades that leave less turbulence in their wake. This would drive the TSR of the machine up to 7.85. The maximum potential power coefficient (Whirlpool Schmitz) at a TSR of 6.28 and 7.85 is 0.55 and 0.56 respectively.

For the same PMG, a lower design TSR will allow a constant speed turbine to operate at that TSR for a winder range of wind speeds before hitting the maximum rotational speed allowed by the PMG. A higher TSR will reach that limit much faster and will require more use of the braking system to prevent rotor runaway and burning out the generator. Generally, a higher TSR rotor has less torque, so the cut-in speed will be slightly higher than that of a lower TSR rotor. A higher design TSR also means that the alpha at startup (essentially when the rotational speed of the turbine is zero) will be greater than that of a turbine with a lower TSR, further raising the cut-in speed of the turbine.

The image below (generated with QBlade) is of a simulation for a rotor blade with a design TSR of 7. The L/D is maximized across the entirety of the blade length at a TSR of 7. As the TSR changes, the L/D ratio decreases. Furthermore, the alpha is at the optimum value across the length of the blade at the TSR of 7. As the TSR decreases, the values for alpha become increasingly large, resulting in the aforementioned lower L/D ratio. As the TSR increases, the values for alpha become smaller, though the difference is less extreme. However, any change in the TSR results in a decrease in the overall efficiency of the turbine.

Minvayu 400 TSR


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