Wind turbines functioning - Part 3

Part 1

Part 2

Part 3

Part 4

Angular Momentum and Wake Rotation

The wind turbine described by Betz does not actually exist. It is merely an idealized wind turbine described as an actuator disk. Its a disk in space where fluid energy is simply extracted from the air. In the Betz turbine the energy extraction manifests itself through thrust. The equivalent turbine described by Betz would be a horizontal propeller type operating with infinite blades at infinite tip speed ratios and no losses. The tip speed ratio is ratio of the speed of the tip relative to the free stream flow. This turbine is not too far from actual wind turbines. Actual turbines are rotating blades. They typically operate at high tip speed ratios. At high tip speed ratios three blades are sufficient to interact with all the air passing through the rotor plane. Actual turbines still produce considerable thrust forces.

lambda = R . Omega / U1

One key difference between actual turbines and the actuator disk, is that the energy is extracted through torque. The wind imparts a torque on the wind turbine, thrust is a necessary by product of torque. Newtonian physics dictates that for every action there is an equal and opposite reaction. If the wind imparts a torque on the blades then the blades must be imparting a torque on the wind. This torque would then cause the flow to rotate. Thus the flow in the wake has two components, axial and tangential. This tangential flow is referred to as wake rotation.

Torque is necessary for energy extraction. However wake rotation is considered a loss. Accelerating the flow in the tangential direction increases the absolute velocity. This in turn increases the amount of kinetic energy in the near wake. This rotational energy is not dissipated in any form that would allow for a greater pressure drop (Energy extraction). Thus any rotational energy in the wake is energy that is lost and unavailable.

This loss is minimized by allowing the rotor to rotate very quickly. To the observer it may seem like the rotor is not moving fast, however it is common for the tips to be moving through the air at 6 times the speed of the free stream. Newtonian mechanics defines power as torque multiplied by the rotational speed. The same amount of power can be extracted by allowing the rotor to rotate faster and produce less torque. Less torque means that there is less wake rotation. Less wake rotation means there is more energy available to extract.

Tower height

The wind blows faster at higher altitudes because of the drag of the surface (sea or land) and the viscosity of the air. The variation in velocity with altitude, called wind shear, is most dramatic near the surface.

Typically, in daytime the variation follows the 1/7th power law, which predicts that wind speed rises proportionally to the seventh root of altitude. Doubling the altitude of a turbine, then, increases the expected wind speeds by 10% and the expected power by 34%. Doubling the tower height generally requires doubling the diameter as well, increasing the amount of material by a factor of eight.

In night time, or better: when the atmosphere becomes stable, wind speed close to the ground usually subsides whereas at turbine hub altitude it does not decrease that much or may even increase. As a result the wind speed is higher and a turbine will produce more power than expected from the 1/7th power law: doubling the altitude may increase wind speed by 20% to 60%. A stable atmosphere is caused by radiative cooling of the surface and is common in a temperate climate: it usually occurs when there is a (partly) clear sky at night. When the (high altitude) wind is strong (10 meter wind speed higher than approximately 6 to 7 m/s) the stable atmosphere is disrupted because of friction turbulence and the atmosphere will turn neutral. A daytime atmosphere is either neutral (no net radiation; usually with strong winds and/or heavy clouding) or unstable (rising air because of ground heating — by the sun). Here again the 1/7th power law applies or is at least a good approximation of the wind profile.

For HAWTs, tower heights approximately twice to triple the blade length have been found to balance material costs of the tower against better utilisation of the more expensive active components.

Blade count

Most wind turbines have three blades. Very small turbines may use two blades for ease of construction and installation. Vibration intensity decreases with larger numbers of blades. Noise and wear are generally lower, and efficiency higher, with three instead of two blades.

Turbines with larger numbers of smaller blades operate at a lower Reynolds number and so are less efficient. Small turbines with 4 or more blades suffer further losses as each blade operates partly in the wake of the other blades. Also, the cost of the turbine usually increases with the number of blades.

Rotation control

The ratio between the speed of the wind and the speed of the tips of the blades of a wind turbine. High efficiency 3-blade-turbines have tip speed/wind speed ratios of 6 to 7.

Modern wind turbines are designed to spin at varying speeds (a consequence of their generator design, see below). Use of aluminum and composites in their blades has contributed to low rotational inertia, which means that newer wind turbines can accelerate quickly if the winds pick up, keeping the tip speed ratio more nearly constant. Operating closer to their optimal tip speed ratio during energetic gusts of wind allows wind turbines to improve energy capture from sudden gusts that are typical in urban settings.

In contrast, older style wind turbines were designed with heavier steel blades, which have higher inertia, and rotated at speeds governed by the AC frequency of the power lines. The high inertia buffered the changes in rotation speed and thus made power output more stable.

The speed and torque at which a wind turbine rotates must be controlled for several reasons:
- To optimize the aerodynamic efficiency of the rotor in light winds.
- To keep the generator within its speed and torque limits.
- To keep the rotor and hub within their centripetal force limits. The centripetal force from the spinning rotors increases as the square of the rotation speed, which makes this structure sensitive to overspeed.
- To keep the rotor and tower within their strength limits. Because the power of the wind increases as the cube of the wind speed, turbines have to be built to survive much higher wind loads (such as gusts of wind) than those from which they can practically generate power. Since the blades generate more downwind force (and thus put far greater stress on the tower) when they are producing torque, most wind turbines have ways of reducing torque in high winds.
- To enable maintenance; because it is dangerous to have people working on a wind turbine while it is active, it is sometimes necessary to bring a turbine to a full stop.
- To reduce noise; As a rule of thumb, the noise from a wind turbine increases with the fifth power of the relative wind speed (as seen from the moving tip of the blades). In noise-sensitive environments, the tip speed can be limited to approximately 60 m/s.

Overspeed control is exerted in two main ways: aerodynamic stalling or furling, and mechanical braking. Furling is the preferred method of slowing wind turbines.

Stalling and furling

Stalling works by increasing the angle at which the relative wind strikes the blades (angle of attack), and it reduces the induced drag (drag associated with lift). Stalling is simple because it can be made to happen passively (it increases automatically when the winds speed up), but it increases the cross-section of the blade face-on to the wind, and thus the ordinary drag. A fully stalled turbine blade, when stopped, has the flat side of the blade facing directly into the wind.

Furling works by decreasing the angle of attack, which reduces the induced drag from the lift of the rotor, as well as the cross-section. One major problem in designing wind turbines is getting the blades to stall or furl quickly enough should a gust of wind cause sudden acceleration. A fully furled turbine blade, when stopped, has the edge of the blade facing into the wind.

A fixed-speed HAWT inherently increases its angle of attack at higher wind speed as the blades speed up. A natural strategy, then, is to allow the blade to stall when the wind speed increases. This technique was used on many early HAWTs, until it was realised that stalled blades generate a large amount of vibration (noise). Standard modern turbines all furl the blades in high winds. Since furling requires acting against the torque on the blade, it requires active pitch angle control which is only cost-effective on very large turbines. Many turbines use hydraulic systems. These systems are usually spring loaded, so that if hydraulic power fails, the blades automatically furl. Other turbines use an electric servomotor for every rotor blade. They have a small battery-reserve in case of an electric-grid breakdown.

The variable wind speed wind turbine uses furling as its main method of rotation control. The wind turbines have three modes of operation : below rated wind speed operation, around rated wind speed operation, above rated wind speed operation

At above rated wind speed the rotors furl at an angle to maintain the torque. This is also known as feathering.

Electromagnetic braking

Braking of a turbine can also be done by dumping energy from the generator into a resistor bank, converting the kinetic energy of the turbine rotation into heat. This method is useful if the kinetic load on the generator is suddenly reduced or is too small to keep the turbine speed within its allowed limit.

Cyclically braking causes the blades to slow down, which increases the stalling effect, reducing the efficiency of the blades. This way, the turbine's rotation can be kept at a safe speed in faster winds while maintaining (nominal) power output.

Mechanical braking

A mechanical drum brake or disk brake is used to hold the turbine at rest for maintenance. Such brakes are usually applied only after blade furling and electromagnetic braking have reduced the turbine speed, as the mechanical brakes would wear quickly if used to stop the turbine from full speed. There can also be a stick brake.

According to : Wikipedia