# Wake Interaction

Hello, I have a simple question on wake interaction if any one would like to explain.
Below is the image of a simple two-dimensional linear wake interaction.
It is easy to understand that wake behind the turbine expands increasing in the area downstream of the turbine. And hence the ratio of the overlapping areas are used to calculate the wake interaction between the turbines.

My question is this expansion seems to be dependent on the angle (w) in the image. What are some factors that determine this angle? Is there any range that is generally seen for such an angle? What determines the angle? Is there any equation that can help me calculate it? Please provide some link I can read more in this.

Thank you.

Dear Anurag,

Some versions of NREL’s FLORIS wind-farm control design tool use the simple wake expansion model that you reference in your post. I would review some of the papers on FLORIS by Pieter Gebraad et al to see how the wake-expansion factor “k” has been set.

Best regards,

Thanks Jason for the reply. I went through a few versions of FLORIS models. They are great to implement the yaw misalignment but the relations are based on the wake radius which I feel is confusing and contradictory since this radius is the result of the wake angle at certain distance from the turbine. It would rather be more accurate if I can model them from any other source such as rotor rotation or tip-speed working through axial induction factor. What’s your take on this? Any leads would be great. Thanks again.

Dear Anurag,

I’m sorry, but I’m not sure I understand what you are asking.

Best regards,

My intention is to derive the angle (w). Considering the wind is perpendicular to the blade rotational axis. How would the wake angle be calculated? I understand that it would depend on the blade geometry to some extent.

Improving the FLORIS Wind Plant Model for Compatibility with Gardient-based Optimization- Pieter M.O. Gebraad et al. and
Application of a LES technique to characterize the wake deflection of a wind turbine in yaw- Angle Jimenez et al. both among others calculate this angle from the wake radius.

Since wake radius is a result of the wake expansion given by the angle (w) at a certain distance from the turbine, I feel it should be modeled from some other parameters. “It’s like the wind hits the rotating blade and gets diverted at an angle (w) loosing its speed and gaining turbulence.” So the properties of the angle must depend on the blade face, wind speed, rotational speed of the rotor, the angle of attack and air density.

Please tell me if this makes sense. Also if you can suggest something that wold be great.

Dear Anurag,

I would think the wake radius would naturally depend e.g. on the ambient wind speed, rotor radius, the thrust distribution across the disk, the ambient turbulence intensity/length scales etc. But I am not an expert on these simple wake models so I don’t think I can suggest more than reviewing the papers on FLORIS and associated references.

Best regards,

Okay, thanks for replying. Tell me how would Fast.Farm model it. Are any documentation available?

Also, can you suggest anything on considering the terrain slope on my calculations? I am aware that depending on a slope the wind speed can increase or decrease but am not sure how it determines the speed-up or slow down?

Dear Anurag,

FAST.Farm does not model the wake as a uniform deficit with a linear wake expansion. Instead, FAST.Farm–as with most DWM formulations–models the wake-deficit evolution via the thin shear-layer approximation of the Reynolds-averaged Navier-Stokes equations under quasi-steady-state conditions in axisymmetric coordinates, with turbulence closure captured by using an eddy-viscosity formulation. More information is provided in our AIAA SciTech 2017 paper: nrel.gov/docs/fy17osti/67528.pdf (although we’ve made some modifications to this since, which will be documented along with the release.

In FAST.Farm the background ambient flow is solved in a CFD-based precursor (without wind turbines/wakes). I’m not sure how terrain slope would be treated in a simpler wake model.

Best regards,