Works and Days

What's Going Around Wind Turbines: Turbulent Vortices

A wind turbine.

I am researching how wind flows behind wind turbines by analyzing experimental and numerical data. The experimental data has been collected around the turbine that is pictured at right, and the numerical model is based on this turbine.

I’m specifically analyzing the structure and evolution of the vortices that are created at the blade tips. The vortices are caused by areas of low pressure around the turbine. Turbines’ blades rotate because the aerodynamic shape of the blades guides incoming wind into creating a pressure difference that, in turn, drives the blades. Another difference in pressure is due to the fact that the blades block wind, so behind the blade there are fewer air molecules and thus, there is a lower pressure. Objects feel forced to move to lower pressures. Both the blades and the wind are forced into the lower pressure. Some wind wraps around the blades in order to get to the low pressure area.

A vortex forms where the wind curls because the low pressure applies a centripetal force — like how a hurricane is a vortex where wind wraps around the hurricane’s low-pressure eye. Vorticity quantifies how much the fluid rotates around a region. In math terms, the vorticity is the curl of the wind velocity. Strong vortices are created at the blade tips because here the wind can radially bypass the blade, which provides the path of least resistance in the pursuit of lower pressure. This vortex is then pushed downstream by the wind, away from the blades’ low pressure region; the wind continues to curl due to a law of angular momentum conservation. The tip vortices are major sources of turbulence that damage downstream turbines. Consequentially, tip vortex research can lead to improvements in the longevity of turbines in wind farms.

I have made most of my current research progress by using a colleague's numerical simulation that estimates wind velocity around a wind turbine. I am examining how tip vortices change across time and space. One specific investigation concerns the merging of two adjacent vortices. Since corotational vortices attract each other, the tip vortices sometimes merge together. To quantify this process, I am measuring the distances between adjacent vortices and the areas of those vortices. I hypothesize that by graphing the ratio of their distance to their area as they move downstream, I will find distinct phases in the merging process. I believe that when this ratio of distance to area decreases below a certain level, they will accelerate towards each other much more quickly.

A two dimensional slice of a numerical simulation is depicted below. The color shows the vorticity magnitude; the downstream direction is right, and the ground is located about 100 m below the x axis. The top of the turbine blades would be located on the lower left; here you can see distinct circular tip vortices in red. Farther downstream, the vortices appear to interact, as the vorticity in between the vortices is higher than it is upstream.

A graph showing vorticity.

The image below depicts how these vortices merge into a vortex sheet. This vortex sheet does not always develop, for it depends on the amount of incoming turbulence and on the ratio of the wind speed to the turbine’s rotational velocity. The color scheme has been changed since the last image to emphasize the merging process.

False color image of vortices merging into a vortex sheet.

While I work in Minneapolis, MN, I live in St. Paul. I am staying with five Macalester College students. The rent is great: $200/month for the best room in the house (it has great big windows). This is my first time living in a college house, and I like it, as there are usually people around to talk to. I enjoy the camaraderie of the house. The Twin Cities have been very nice. Minneapolis’s culture is a lot like Portland’s. Everyday, I take 6 miles of fabulous biking trails to work. This is a tiring, yet rewarding ride. When it rains, I use the city's good public transportation system. I have gone to fun, free events, including a museum, a jazz festival, a hip-hop/spoken word festival, a bike race, a play, fireworks, and a swimming lake. I have been thinking about living here in the future, but the cold winters and the mosquito-infested summers might keep me away. I have, however, successfully fought off the mosquitoes and I am thoroughly enjoying my time.

Tags: PSF, wind power, turbines