Wind Energy Physics: Page 3 of 3

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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

Harnessing wind power is an endeavor humans have been undertaking for thousands of years, so not surprisingly just about every type of machine design has been attempted. Some of the more common types are the Savonius, Darrieus, Dutch windmill, American multiblade (water-pumper), and modern propeller styles. The efficiencies of these machines has been determined by theory and confirmed by experience (see “Turbine Types & Typical Power Coefficients” table).

The propeller-style wind turbine achieves the best efficiency, so it is not surprising that this is the most commercially successful wind turbine type. Engineers use the superior efficiency of the propeller wind turbine, and combine it with a large rotor area—the other governing parameter that they have direct control over—to optimize performance of their designs.

“Breakthroughs” & “New” Concepts

There is a persistent myth that wind power is a new technology ripe for innovation. This thinking leads to wild claims of doubling (or more) the efficiency of “old” propeller designs. This, frankly, is impossible. At 45% aerodynamic efficiency, modern propeller designs are already achieving more than 75% of the theoretical Betz limit, leaving little room for “breakthroughs” in the aerodynamic efficiencies of wind turbines. Using our understanding of wind turbine fluid dynamics, we can expose some common wind turbine hype.

It can be counterintuitive that a propeller-style wind turbine rotor achieves the best efficiency. After all, those three (typically) thin blades let so much of the wind pass between them. Wouldn’t more blades help? That seems logical on the surface, and leads some designers to include an array of blades. This idea, however, ignores the laws of fluid dynamics. Remember, the wind turbine must strike a balance between slowing the wind and allowing it to pass. And it turns out that fewer, thinner blades spinning fast does this best. The American multiblade is effective at what it does—mechanically pumping water—but efficiency is not its goal.

“Augmenters” attempt to leverage the cubic function of wind speed in the energy equation by speeding up the wind into the rotor through ducts or shrouds. This method is akin to the nozzle on a hose that effectively turns a fat, trickle of water into a forceful, faster stream. The difference with wind is that it is not confined to a hose, so it does not  have to pass through the nozzle. And in fact, because the wind turbine at the end of the “nozzle” is trying to slow the wind (remember, that is its job), the wind simply sees the augmented turbine as an obstruction and passes around it rather than going through it—taking the path of least resistance.  Although a duct does serve to increase the capture area of a wind turbine, a more effective way to accomplish that goal is with longer blades.

One of the benefits touted for vertical-axis turbine designs, such as the Savonius and Darrieus rotors, is that they can take wind from any direction. While it is true that these designs can be simpler because they do not need moving parts to respond to changes in wind direction, the benefit stops there. Wind only blows in one direction at any given moment. Although wind does indeed change direction, sometimes abruptly, the flow through a vertical-axis turbine takes time to react to this changing flow—even if it is not as evident as with a propeller rotor reorienting itself. The claim that vertical-axis designs are better suited for the directional turbulence experienced on short towers is strictly a myth. With any wind turbine design, efficiency increases with steadier wind flow, which is another reason to place any wind turbine, regardless of type, on a tall tower. 

Physics Rule

Keep in mind the fundamentals of wind energy physics next time you are evaluating wind turbine claims. There are two points most worth remembering:

All wind turbines extract kinetic energy from the moving air by slowing it down, and those that find the best balance between slowing the wind and not disrupting its flow are the most efficient—up to the Betz limit of 59.3%.

The governing equations are dependent on two factors we have some control over—wind turbine swept area (bigger captures more energy) and wind speed (which is a huge factor because it is cubed in determining power). Use these factors to your advantage when choosing and siting a wind energy system.

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David Laino puts his aeronautical and mechanical engineering knowledge to use at work designing wind turbines for Endurance Wind Power, and for fun, sailing on the Chesapeake Bay in Maryland.

Comments (12)

mansberger's picture

Kenslow is actually correct. Betz totally ignores rotation in his calculations, and Glauert admits the calculations are wrong if rotation occurs. See page 194 of his most famous work "Airplane propellers", he proved nothing about wind turbines and was primarily focused on propeller design, only 17 out of 191 pages cover wind turbine design and they contain errors. Glauert died in 1934 before it was published and without proof reading it.

djlaino's picture

The differences between Betz' and Glauert's approaches explain the absence or inclusion of wake rotation in the calculations. Betz took the simplest approach of treating the entire turbine rotor as an ideal disc, often referred to as actuator disc theory (ADT). ADT considers the flow through the plane of the rotor as a whole. As such, it is both highly simplified and non-conservative since it treats the entire rotor area as having the same efficiency without considering real effects such as tip and hub losses, not to mention differences along the span of the blades.
Glauert uses the more realistic approach of dividing the blades into spanwise sections, often referred to as Blade Element Momentum (BEM) theory. This approach attempts to calculate the contribution of each spanwise position of each blade, omitting the hub (which has no airfoil) and including changes along the span due to different angular velocities.
Because ADT only considers flow through a plane, any rotational velocity would be irrelevant because the component of velocity that is not perpendicular to the plane would not pass through the plane. BEM can account for rotational velocity because the rotational component changes the inflow velocity and angle of attack for individual blade elements. BEM is certainly the more accurate method to determine propeller performance and is commonly used in wind turbine aero-elastic design codes today.
Having said all that, Betz' approach still represents an ideal case where all the flow through the disc (note that Betz' theorem is not limited to propellers, nor even circular discs or in fact even to air) is converted to useful power. If such an ideal disc could be created (it can't, but the propeller has proven to come closest), it could approach the Betz Limit for efficiency. A propeller may be influenced by rotational velocity components that Betz ignores, but any gains can never make up for the real-world losses of a real propeller (tip, hub and frictional losses), let alone exceed the ideal theoretical limit proven by Betz.
In summary, BEM is the more accurate approach for wind turbine design because it more accurately reflects reality. But reality does not solely incur benefits; the Betz limit still applies.

Ben Root's picture
Awesome! Do you want to write a BPB "Back Page Basics" for HP (and for our non aero-physist readership) about theoretical max power from the wind. We don't need to nit-pick over a few percentage points...that's for the engineers. But we'd love for the typical reader to understand the limits, and recognize BS in the new-design investment scams.
djlaino's picture

I'd be happy to write more on this topic Ben, though it sounds like you are asking for a summary of this very article. Please clarify if there is something more or different that you feel was not covered and maybe HP will consider it.

mansberger's picture

Yes, more precisely, Betz, Glauert, and modern Blade Element Momentum Theory all rely on the flawed 19th century Froude's actuator disc theory. This is part of the problem, Froude's ADT equations are in fact invalid and diverge from that of real airflow as axial induction factors approach 0.5. Also most all methods including Glauert's are based on simplifying assumptions which either remove or improperly account for rotational terms within the energy equation. That said, my only point is to emphasize that these are strictly very outdated theorems, not laws nor physical limits, and to accept otherwise serves only to stifle innovation.

djlaino's picture

It is important to remember that the theorems are just models, varying in complexity, and must be viewed as such. All engineering uses models to some extent, with the critical aspect being that the assumptions on which the model is based are applicable to the real situation being modeled. Therefore I would not categorize the ADT as "flawed" or even "outdated." It is a very good tool for a generalized performance model of energy extraction from a fluid flow. It is not so good for wind turbine blade design. I also would not blame the theorems for stifling innovation. If one chooses to use use the wrong tools for design, it is not the tools fault.
Finally, the ADT is in fact quite valid for what it is intended as it is based on fundamental fluid physics. As the article states, the Betz proof is technology agnostic and simply defines the amount that a fluid must be slowed (by 2/3rds) to maximize power extracted from the flow. It is quite valid for this purpose and is applicable to wind turbines regardless of any other - better - tools used to design them.

mansberger's picture

From your refernced source, Martin Hansen's Aerodynamics of Wind Turbines, 2nd ed. page 41 "It is possible to exceed the Betz limit by placing the wind turbine in a diffuser."

djlaino's picture

Hansen makes the mistake (in my view) of ignoring the area intercepted by the diffuser. By ignoring the diffuser area one can claim that the turbine could exceed the Betz limit, but this is technically incorrect, and - as Hansen notes - the diffuser has to be accounted for both structurally and economically (so why not aerodynamically?). Furthermore, as Hansen also notes, this concept of an augmented rotor "beating Betz" by (erroneously) ignoring the diffuser area has never been demonstrated on a full-size turbine despite many attempts costing many millions of dollars.

Michael Kenslow_2's picture

Betz limit is not a true limit. It doesn't take rotational velocities into account. That's why it was immediately discounted by the engineering community when it was claimed.

djlaino's picture

Michael,

I am not aware of Betz' theory being discounted by the engineering community when it was proposed in 1919, so please share any evidence you have in that regard. As for it not being a "true limit" you are correct in so far as it is only a theoretical limit and can never be truly achieved with a real wind turbine.
I am unsure of what you refer to as "rotational velocities," but the effect of wake rotation has been considered in regards to wind turbine rotor efficiency. In 1935, British aerodynamicist Hermann Glauert investigated the effect of wake rotation on theoretical rotor efficiency. His conclusion reinforced Betz' result, proving that the theoretical efficiency approaches 16/27 as the tip speed ratio of the rotor approaches infinity. [ref: Hansen M. O. L. (2015). Aerodynamics of Wind Turbines]

Michael Welch's picture
Not sure what your point is. Are you saying that the Betz limit might be higher if you consider rotational velocities? Or lower?
djlaino's picture

I don't think your question was directed to me Michael, but you raise an interesting point. A propeller rotor induces a rotational velocity as well as an axial velocity on the inflow. In general this provides no benefit but rather a loss because that induced rotation is energy imparted by the rotor into the flow (assuming no rotation originally exists in the inflow). There is potential that inflow with rotation could provide benefit to a rotor that induces opposite rotation, but that would require a specific condition that is unlikely in reality, and the benefit would not be great since the rotational induced velocity is a much smaller effect than axial induced velocity from which the vast majority of power is extracted from the flow. And in the end, ideal rotational velocity on a real rotor cannot provide enough benefit to exceed the ideal condition described by Betz in the theoretical world prescribed by the laws of physics.

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