Wind farm aerodynamics

Dr. Neil Canter, Contributing Editor | TLT Tech Beat May 2011

A new model determines the positioning of wind turbines to achieve more cost-effective power generation.

KEY CONCEPTS
• A new model shows how wind turbines should be placed in a farm to achieve more cost-effective power generation.
• The turbulent mixing of the air above the wind turbine farm is critical to obtaining the entrained kinetic energy needed to more efficiently turn wind turbines.
• Optimizing the performance of wind turbines should help reduce the stress placed on gearboxes and improve their durability.

Much attention has been directed to figuring out ways in improving the gearbox problems plaguing wind turbines. A recent TLT article details the challenges facing the lubricant industry (1).

The gearbox must convert low-speed wind energy captured by the rotation of the rotor blades into high-speed energy that can be used to run an electricity-producing generator. A substantial amount of torque is produced in this process, which places major stress on the gearbox. For example, a 3.2-megawatt wind turbine creates a torque of 2.5 million newton-meters.

The result has been premature gearbox failures that have not enabled the wind turbine industry to achieve original operating life goals of 20 years. Most turbines undergo significant repairs and even complete overhauls after five to seven years of operation. One additional problem is that wind turbines are situated in geographical regions that are hard to reach such as mountain tops and offshore.

Gearbox replacement is also quite expensive and is estimated to account for 38% of the total cost of a wind turbine. For a 1.5-megawatt wind turbine, the replacement cost is $250,000.

One factor that may provide assistance to reducing the stress on wind turbines is aerodynamics. Dr. Charles Meneveau, Louis Sardella Professor of mechanical engineering at Johns Hopkins University in Baltimore, Md., says, “Wind turbines placed in close proximity of each other become involved in complex interactions that can reduce their ability to extract kinetic energy from the wind flow. Other factors that must be considered are the geographical terrain where the wind farm is situated and the atmospheric boundary layer.” 

Research that can establish how wind turbines should be positioned to optimize performance also may indirectly benefit the stress placed on the gearbox, if the optimal spacing is found to be larger than currently practiced. Such work has now been conducted.

WIND TURBINE SPACING
Meneveau, in collaboration with his colleague Johan Meyers, has developed a new model that determines the optimal positioning for how wind turbines should be placed in a farm to achieve more cost-effective power generation. He says, “We have based our findings on extensive computer simulations and the use of a wind tunnel.”

Past work focused on determining how individual wind turbines interact with each other. Meneveau explains that each turbine generates a wake, so the thinking was to superimpose the wakes for multiple units to determine the total aerodynamic effect. In contrast, the researchers determined that for very large wind farms, it is the turbulent mixing of the air above the wind turbine farm that is the key to obtaining entrained kinetic energy, which can be used to more efficiently turn the wind turbines.

Meneveau indicates that if one wind turbine is placed too close in front of a second one, the kinetic energy flux difference is too small. “Imagine placement of a lid on a wind farm with dimensions of 10 kilometers-by-10 kilometers—this will pretty much shut down the turbines,” he says.

The researchers found that the atmospheric boundary layer plays an important role. This is the lowest part of the atmosphere near the earth’s surface.

Meneveau says, “The atmospheric boundary layer is typically 1 to 1.5 kilometers above the earth’s surface. This means that if a wind farm has a stretch of 10 to 15 kilometers in length, the entire wind farm is in equilibrium with the entire height of the atmospheric boundary layer.” 

Typical wind turbine farms place individual units approximately 7. 5 rotor diameters apart. Based on their new model, Meneveau and Meyers are recommending that the distance between individual units be doubled to 15 rotor diameters. He says, “Not much is gained in performance by placing wind turbines too close to each other. A significant fraction of energy to turn rotors is coming from kinetic energy that is above the wind farm.” their recommendation is valid for the very large wind farms of the future and for typical costs of land and wind turbines but may vary due to local conditions and other costs.

The important aspect is that turbulent mixing of the air above the wind farm provides the energy needed to drive the wind turbines. Meneveau indicates that finding the optimization curve for rotor diameter vs. efficiency is pretty shallow. He says, “When we find that 15 rotor diameters is the ideal distance between wind turbines, reducing the distance to 10 rotors drops the expected power extraction by 10%.” 

As is well known, staggering the wind turbines in the farm also can provide some benefit by reducing the number of units in the wake of another one. The typical benefit is about a 5% to 8% improvement in efficiency, according to Meneveau.

Figure 1 shows the wind tunnel and the little model wind turbines used by the researchers. Meneveau says, “The little model wind turbines are 12 centimeters high and have a rotor diameter of 12 centimeters. A DC motor is used to generate electricity as wind is blown over the model units. The model wind turbines are 1/800 the size of actual devices.” 


Figure 1. The horizontal air flow moving through a wind farm was simulated in a wind tunnel through the use of model wind turbines. (Courtesy of John Hopkins University)

The wind tunnel provides the researchers with a three-dimensional view so that they can measure the horizontal air flow moving through the 3d field under very well-controlled conditions. As part of this work, the researchers also determined how to measure the torque generated by the wind turbines and have developed a sensor to measure the mechanical power extracted (2).

Future work will involve learning more about the structure of the air flow in the atmospheric boundary layer, taking into account temperature effects. Meneveau says, “Our modeling has been done using a neutral atmosphere, but we know that a daily cycle exists where the atmosphere moves from a more stable condition during night time to a more turbulent state as it warms during the day.” 

Meneveau is not stating that optimizing the placement of wind turbines will remove all of the stress placed on gearboxes. But he indicates that determining how to optimize the performance of wind turbines should help to improve their durability and that durability considerations should also play a role in optimization.

Additional information can be found in an article (3) recently accepted for publication and by contacting Meneveau at meneveau@jhu.edu. 

REFERENCES
1. Rensselar, J. (2010), “The Elephant in the Wind Turbine,” TLT, 66 (6), pp. 38–48.
2. Kang, H. and Meneveau, C. (2010), “Direct Mechanical Torque Sensor For Model Wind Turbines,” Measurement Science and Technology, 21 (10), doi: 10.1088/0957-0233/21/10/105206.
3. Meyers, J. and Meneveau, C. (2011), “Optimal Turbine Spacing in Fully Developed Wind-Farm Boundary Layers,” Wind Energy, accepted for publication.


Neil Canter heads his own consulting company, Chemical Solutions, in Willow Grove, Pa. Ideas for Tech Beat items can be sent to him at neilcanter@comcast.net.