with consequent potential cost benefits. The hinge eliminates the transfer of out-of-plane aerodynamic moments from the rotor to the low-speed shaft, resulting in large reductions in the operational loadings on the shaft, nacelle and yaw drive. The dependence of these loads on rotational speed is also largely removed, with the result that the optimum rotational speed for a two-bladed machine in energy cost terms is increased, approaching the value giving maximum energy yield.

Although teetering provides scope for significant cost savings on the shaft, nacelle and yaw drive (which account for nearly 20 percent of the baseline machine cost), these savings are offset by the additional costs associated with the teeter hinge and teeter restraint system.

6.5.4 Effect of number of blades on loads

Moment loadings on the low speed shaft and nacelle structure from three-bladed and rigid-hub two-bladed machines were examined in Sections 5.10 and 5.11, and are compared in Table 6.6 below for machines of the same diameter and rotational speed. The stochastic loading comparison is based on a turbulence length scale to rotor diameter ratio of 1.84.

It is seen that loadings from a rigid-hub two-bladed rotor are significantly larger than from a three-bladed rotor. However, in most two-bladed machine designs, the rotor is allowed to teeter instead of being rigidly mounted, with the result that aerodynamic moments on the shaft and nacelle structure quoted in Table 6.6 are eliminated, and the blade out-of-plane root bending moments are reduced. The benefits and drawbacks of teetering the rotor are examined in Section 6.6.

The rotor thrust variations at blade passing frequency due to stochastic loading, which are a dominant factor in tower fatigue design, are very similar for two- and three-bladed machines rotating at the same speed. However, two-bladed machines usually rotate faster than three-bladed machines of the same diameter, so the cyclic rotor thrust variations are higher.

Table 6.6 Comparison of Loads on Shaft and Nacelle for Three-bladed and Rigid-hub Two-bladed Machines

Deterministic loading arising from wind Stochastic loading shear and/or yaw misalignment, in terms of blade root out-of-plane bending moment amplitude, Mo

Location of moment Three-bladed Rigid-hub two-bladed loading machine machine

Shaft bending 1.5 Mo moment amplitude

Nacelle nodding 1.5 Mo moment Nacelle yaw Zero moment

2 M0

% increase for rigid-hub two-bladed machine compared with three-bladed machine 22%

6.5.5 Noise constraint on rotational speed

As noted in Section 6.5.3, there may be significant cost benefits to be gained from a two-bladed design with increased rotational speeds, because, in addition to the blade saving, the cost of the whole of the drive train is reduced because of the reduced torque. However, as noted in Section 6.4.2, it is normal to restrict tip speed to about 65 m/s in order to limit aerodynamic noise emission. At 62.8 m/s, the tip speed of the baseline machine discussed in Section 6.5.3 is within this limit, but the tip speed of option (b) of 74 m/s would be less likely to be acceptable, except at remote sites or offshore. This subject is considered further in Section 6.9.

6.5.6 Visual appearance

Although the assessment of visual appearance is essentially subjective, there is an emerging consensus that three-bladed machines are more restful to look at than two-bladed ones. One possible reason for this is that the apparent 'bulk' of a three-bladed machine changes only slightly over time, whereas a two-bladed machine appears to contract down to a one-dimensional line element, when the rotor is vertical, twice per revolution. A secondary factor is that two-bladed machines generally rotate faster, which an observer can also find more disturbing.

6.5.7 Single-bladed turbines

Apart from the saving in rotor cost itself, the single-bladed turbine concept is an attractive one because of the reduction in drive train cost realizable through increased rotational speed (Section 6.5.2). An obvious disadvantage is the resulting increased noise emission resulting from the faster rotation, but this would not be an issue offshore. Another consideration is the reduced yield due to increased tip loss. For example, a 40 m diameter machine consisting of a TR blade rotating at 48 r.p.m., with twist distribution reoptimized to give maximum energy yield, will achieve the same maximum power output as the baseline design, but provide 12 percent less energy.

The single blade must be counterweighted to eliminate torque fluctuations and any whirling tendency due to centrifugal loads. Furthermore, as a rigid hub would expose the nacelle to very large nodding and yawing moments in comparison with two- or three-bladed machines, it is customary to mount the rotor on a teeter hinge, so that the unbalanced aerodynamic out-of-plane moment can be resisted by a centrifugal couple, thereby reducing the hub moment. However, the teeter motion of the blade is significantly greater than that of a two-bladed machine, so it is normal to mount the rotor downwind. Morgan (1994) reports that particular difficulties have been encountered in predicting teeter excursions after grid loss and emergency stops, leading to excessive risk of teeter stop impacts.

Solar Stirling Engine Basics Explained

Solar Stirling Engine Basics Explained

The solar Stirling engine is progressively becoming a viable alternative to solar panels for its higher efficiency. Stirling engines might be the best way to harvest the power provided by the sun. This is an easy-to-understand explanation of how Stirling engines work, the different types, and why they are more efficient than steam engines.

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