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Wind turbines functioning - 2
06/2006
| Part 1 | Part 3 | Part 4 |
Offshore
Offshore wind turbines are considered to be less obtrusive than turbines on land, as their apparent size and noise can be mitigated by distance. Because water has less surface roughness than land, the average wind speed is usually higher over open water. This allows offshore turbines to use shorter towers, making them less visible. In stormy areas with extended shallow continental shelves (such as Denmark), turbines are practical to install, and give good service — Denmark's wind generation provides about 25-30% of total electricity demand in the country, with many offshore windfarms. Denmark plans to increase wind energy's contribution to as much as half of its electrical supply.
The offshore environment is, however, more expensive. Offshore towers are generally taller than onshore towers once one includes the submerged height, and offshore foundations are generally more difficult to build and more expensive as well. Power transmission from offshore turbines is generally through undersea cable, which is more expensive to install than cables on land, and may use high voltage direct current operation if significant distance is to be covered — which then requires yet more equipment. The offshore environment is also corrosive and abrasive. Repairs and maintenance are much more difficult, and much more costly than on onshore turbines. Offshore wind turbines are outfitted with extensive corrosion protection measures like coatings and cathodic protection.
While there is a significant market for small land-based windmills, offshore wind turbines have recently been and will probably continue to be the largest wind turbines in operation, because larger turbines reduce the marginal cost of many of the difficulties of offshore operation.
There are some conceptual designs that might make use of the unique offshore environment. For example, a floating turbine might orient itself downwind of its anchor, and thus avoid the need for a yawing mechanism. One concept for offshore turbines has them generate rain, instead of electricity. The turbines would create a fine aerosol, which is envisioned to increase evaporation and induce rainfall, hopefully on land.
Aerial
It has been suggested that wind turbines could be flown in high speed winds at high altitude taking advantage of the steadier winds at high altitudes. No such systems currently exist in the marketplace. The idea of airborne wind turbines reappears in the industry every few years, and seldom (if ever) gets off the drawing board.
Turbine design and construction
Horizontal Axis Wind Turbine Aerodynamics
The aerodynamics of a horizontal axis wind turbine are not straight forward. The air flow at the blades is not the same as the airflow far away from the turbine. The very nature of the way in which energy is extracted from the air also causes air to be deflected by the turbine. In addition the aerodynamics of a wind turbine at the rotor surface exhibit phenomena that are rarely seen in other aerodynamic fields.
Axial Momentum and the Betz Limit
Energy in fluid is contained in four different forms: gravitational potential energy, thermodynamic pressure, kinetic energy from the velocity and finally thermal energy. Gravitational and thermal energy have a negligible effect on the energy extraction process. From a macroscopic point of view, the air flow about the wind turbine is at atmospheric pressure. If pressure is constant then only kinetic energy is extracted. However up close near the rotor itself the air velocity is constant as it passes through the rotor plane. This is because of conservation of mass. The air that passes through the rotor cannot slow down because it needs to stay out of the way of the air behind it. So at the rotor the energy is extracted by a pressure drop. The air directly behind the wind turbine is at sub-atmospheric pressure; the air in front is under greater than atmospheric pressure. It is this high pressure in front of the wind turbine that deflects some of the upstream air around the turbine.
Albert Betz was amongst the first to study this phenomenon. He notably determined the maximum limit to wind turbine performance. The limit is now referred to as the Betz Limit. This is derived by looking at the axial momentum of the air passing through the wind turbine. As stated above some of the air is deflected away from the turbine. This causes the air passing through the rotor plane to have a smaller velocity than the free stream velocity. The degree at which air at the turbine is less than the air far away from the turbine is called the axial induction factor. It is defined as below.
a = (U1-U2)/U1
a is the axial induction factor. U1 is the wind speed far away from the rotor. U2 is the wind speed at the rotor.
The first step to deriving the Betz limit is applying conservation of axial momentum. As stated above, far away from the turbine, the wind loses speed after the wind turbine. This would violate the conservation of momentum if the wind turbine was not applying a thrust force on the flow. This thrust force manifests itself through the pressure drop across the rotor. The front operates at high pressure while the back operates at low pressure. The pressure difference from the front to back causes the thrust force. The momentum lost in the turbine is balanced by the thrust force.
Axial momentum relates the wake flow to the pressure difference at the rotor. Another equation is needed to relate the pressure difference to the velocity of the flow near the turbine. Here the Bernoulli equation is used between for field flow and the flow near the wind turbine. There is one limitation to the Bernoulli equation. The equation cannot be applied to fluid passing through the wind turbine. Instead conservation of mass is used to relate the incoming air to the outlet air. Betz used these equations and managed to solve the velocities of the flow in the far wake and near the wind turbine in terms of the far field flow and the axial induction factor. The velocities are given below.
U2 = U1(1 - a)
U4 = U1(1 - 2a)
U4 is introduced here as the wind velocity in the far wake. This is important because the power extracted from the turbine is defined by the following equation. However the Betz limit is given in terms of the coefficient of power. The coefficient of power is similar to efficiency but not the same. The formula for the coefficient of power is given beneath the formula for power.
P = 0.5 . rho . A . U2 . (U1^2-U4^2)
C = P / (0.5 . rho . A . U1^3)
Betz was able to develop an expression for Cp in terms of the induction factors. This is done by the velocity relations being substituted into power and power is substituted into the coefficient of power definition. The relationship Betz developed is given below.
Cp = 4a(1 - a)2
The Betz limit is defined by the maximum value that can be given by the above formula. This is found by taking the derivative with respect to the axial induction factor, setting it to zero and solving for the axial induction factor. Betz was able to show that the optimum axial induction factor is one third. The optimum axial induction factor was then used to find the maximum coefficient of power. This maximum coefficient is the Betz limit. Betz was able to show that the maximum coefficient of power of a wind turbine is 16/27. Airflow operating at higher thrust will cause the axial induction factor to rise above the optimum value. Higher thrust cause more air to be deflected away from the turbine. When the axial induction factor falls below the optimum value the wind turbine is not extracting all the energy it can. This reduces pressure around the turbine and allows more air to pass through the turbine, but not enough to account for lack of energy being extracted.
The derivation of the Betz limit shows a simple analysis of wind turbine aerodynamics. In reality there is a lot more. A more rigorous analysis would include wake rotation, the effect of variable geometry. The effect of air foils on the flow is a major component of wind turbine aerodynamics. Within airfoils alone the wind turbine aerodynamicist has to consider the effect of surface roughness, dynamic stall tip losses, solidity, among other problems.
According to : Wikipedia