Wind Energy Physics: Page 2 of 3

Intermediate

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Wind Energy Physics
Wind Energy Physics
The swept area of a turbine
The swept area of a turbine is its aperture window that captures the wind. The area is directly proportional to the amount of wind energy available to the turbine.
one-bladed turbines have the highest potential power coefficient
Believe it or not, one-bladed turbines have the highest potential power coefficient, but they are difficult to keep balanced. Two- and three-bladed turbines are the proven standard, balancing aerodynamic efficiency and stability during turbulent winds.
Ducts and shrouds are common attempted augmentations
Ducts and shrouds are common attempted augmentations to divert more wind into, or increase wind speed through, the turbine’s blades. However, the nature of fluid dynamics makes the wind adept at flowing around these obstructions rather than through them. Savvy turbine designers use larger swept area to increase power input instead of trying to trick the wind.
Multiple blades
Multiple blades only help in getting the turbine started in low-wind situations. After that, one blade’s wake quickly interferes with the blade following it.
“innovative” designs
Many “innovative” designs just complicate a system that would work better if simplified. Luckily, most kooky designs never leave the prototype stage.
Wind Energy Physics
The swept area of a turbine
one-bladed turbines have the highest potential power coefficient
Ducts and shrouds are common attempted augmentations
Multiple blades
“innovative” designs

The third (and most important for siting wind turbines) variable is wind speed. You can see that it’s cubed in the equation, meaning small changes in wind speed yield larger changes in available power. A 26% increase in wind speed (from 10 to 12.6 mph) doubles the available energy, while a 20% drop (from 10 to 8 mph) cuts it in half. This is why it is critical to put a wind turbine on a tall tower where it can intercept strong wind.

Wind Turbine Job Description

As a wind turbine extracts kinetic energy from the wind, it does not consume air mass (only nuclear reactions consume mass), so it must be “consuming” the wind speed. In other words, the wind approaches the turbine at one speed and leaves at a lesser speed. This is how any wind turbine extracts energy from the wind—by slowing it down. The difference between the wind speed before and after it passes through the turbine defines the energy the turbine has extracted from the wind. This is the fundamental function of the wind turbine, and some turbines do it better than others.

Wind Turbine Efficiency & Limits

It is not feasible to extract all of the power available in the wind—and no wind turbine can harness more energy than is available in the wind. Avoid any wind turbine that claims it can—no wind turbine can slow wind down to a speed of less than zero.

If a wind turbine were to extract all the available power in the wind—that is, slow the wind to a stop and capture all its power—we would say that turbine is 100% efficient. However, any wind turbine that did this would stop the wind, and then there would be no air movement from which to extract more power! An effective wind turbine must find a balance, slowing the wind enough to maximize power capture, yet still allow enough wind to pass through so it can keep capturing more. 

Efficiency is defined as the ratio between the output power and the input power. For wind turbines, aerodynamic efficiency is referred to as the power coefficient, Cp, so the governing equation for wind turbine power output is:

Poutput = 1/2 × air density × area × wind speed3 × Cp

We know Cp cannot be 100%, but what is the upper limit? In 1919, German scientist Albert Betz took the above governing equations for wind power, and used them to determine how much a theoretically “perfect” wind turbine could extract from the wind. His answer, which is referred to as Betz’ Law or the Betz limit, states that when the wind is slowed by two-thirds (wind speed out = 1/3 wind speed in), the wind turbine reaches its theoretical maximum possible efficiency, CP-max., of 59.3%.

It is critical to note that Betz’ Law is derived from the governing equations, and not from any assumptions about wind turbine type. Therefore, the Betz limit is not restricted to any particular type or style of wind turbine, as some people mistakenly believe. The Betz limit is a physical limit that applies to all wind turbines.

Wind Turbine Types

In the real world, no wind turbine can ever even reach—let alone exceed—the Betz limit. But which turbines do the best, and how well do they do?

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