## Power law exponent problem

Discuss the effects of turbulence on wind turbines and its simulation.

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Mostafa.Haggag
Posts: 34
Joined: Tue Jun 26, 2018 7:50 am
Organization: self
Location: Egypt

### Power law exponent problem

Hello
I hope everybody is fine
I have a wind field from a large eddy simulation (LES) that I want to make something similar to it in Turb sim. I was advised to use the power law exponent to calculate the wind speed profile but I am not sure what exactly should I do to choose the best power-law exponent that gives me results similar to the one I have in the LES.
I can export wind field data from the LES to post process it to calculate the best power exponent.my problem is that i am not sure how to post-process the data to get the most fitting component
What do I have in mind?
I thought if I know the average velocity at a certain height in the LES and the average velocity at hub height I can calculate the power exponent.
The idea is I can output the average velocity for many different heights so then I will be getting many power law exponent. How to pick the best one that fits? I am not sure what to do?
Also, I was wondering what wind field should I be using from the LES simulation? Should I output the 3d wind velocities hitting the rotor and average it? Do I output the wind fields positioned before my turbine how many rotor diameters before the turbine ?? What should I do? should I only care for wind speed hitting the rotor of my turbine in the les simulation?

Jason.Jonkman
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### Re: Power law exponent problem

Dear Mostafa,

I would suggest time-averaging the wind speed at multiple heights from your LES output and fitting a power lower through a least-squares regression.

If you are not familiar, you may want to consider using the TIMESR feature of TurbSim v2, whereby the wind time series derived from TurbSim can match to some prescribed time series (from LES) at specific points (but not all points) in space; other points in the field will be based on the spectra of the prescribed time series and standard coherence functions. See the TurbSim v2 archive for more information: https://nwtc.nrel.gov/alphas.

Another option if you want to use your LES field within FAST, is to save your LES data in e.g. TurbSim format.

Best regards,
Jason Jonkman, Ph.D.
Senior Engineer | National Wind Technology Center (NWTC)

National Renewable Energy Laboratory (NREL)
15013 Denver West Parkway | Golden, CO 80401
+1 (303) 384 – 7026 | Fax: +1 (303) 384 – 6901
nwtc.nrel.gov

Mostafa.Haggag
Posts: 34
Joined: Tue Jun 26, 2018 7:50 am
Organization: self
Location: Egypt

### Re: Power law exponent problem

so I read about the regression method and I wanted to ask you if I am implementing it correctly
I cannot save my les files in turbsim format and someone using the Les implemented a Matlab script to output the velocities out of a saved data in the les but there is something making it unable to work properly
Please correct me if I am wrong in the following concerning the regression method. I will output time series of different heights for the velocity U at position (x,y)(2D before the first wind turbine, the position of the centre of the rotor) (as my les is in a 3d simulation)I average the time series of the U component at different heights to get an average U velocity at every height.I output the average Uhub speed also. THen I use least square regression to calculate the best power coefficient that fits the different points. I have attached picture of the law I will be using . I wanted to know should i pick a different x y positions other than the ones i chose or what exactly?
Also,I wanted to ask how should i pick the turbulence intensity for the turb sim .
Can I calculate the turbulence intensity at a specific point in my les simulation and use it for the turbsim simulation? I know that the turbulence intensity is the standard deviation /mean value of a time series of U component at a specific point. My question is where should I pick to calculate the turbulence intensity?I mean i have many positions to calculate the turbulence intensity which should I choose? I was thinking of calculating the average turbulence intensity and inputting it to turb sim but I am not sure how to calculate the average turbulence intensity. I was thinking about the following method to calculate it but I am not sure. this is the method i was thinking about :
I have a 3d grid in the x y z with u components for different positions in the x y z. I was going to pick all u components that are situated inside of my rotor disk in the yz plane and cube each velocity component then sum them about the rotor plane then divided by the area of my rotor then cubic root the answer to getting an average rotor speed about the rotor at a certain x position. Keep repeating the previous thing for different x positions, then calculate the mean value of different x positions. So now I have one velocity value at a certain time instant for an average velocity U about the rotor disk for different X positions.I repeat the following for different time instances to have a time series of the average velocity about the rotor disk for different X positions and use this time series to calculate the average Turbulence intensity .Am i doing it correctly ?
Attachments toomarc.png (17.57 KiB) Viewed 5090 times

Jason.Jonkman
Posts: 4858
Joined: Thu Nov 03, 2005 4:38 pm
Location: Boulder, CO
Contact:

### Re: Power law exponent problem

Dear Mostafa,

Yes, I agree with your least-squares regression approach.

So, does your LES simulation include a wind turbine or does the LES simulation only consider the atmospheric boundary layer? If a wind turbine is modeled within your LES, I agree picking points in the ambient wind say 2D upstream of the rotor makes sense. If the wind turbine is not modeled within the LES, then I would pick points at the rotor plane.

Are you cubing the wind speed in your spatial averaging to derive some sort of power-equivalent average wind speed? I agree that there are many points that you could derive the turbulence intensity from and I'm not sure whether there is a best practice on the approach taken. I would first judge how different the turbulence intensity is across the domain. If you want to limit the number of points considered, I would use points at the hub height.

Best regards,
Jason Jonkman, Ph.D.
Senior Engineer | National Wind Technology Center (NWTC)

National Renewable Energy Laboratory (NREL)
15013 Denver West Parkway | Golden, CO 80401
+1 (303) 384 – 7026 | Fax: +1 (303) 384 – 6901
nwtc.nrel.gov

Mostafa.Haggag
Posts: 34
Joined: Tue Jun 26, 2018 7:50 am
Organization: self
Location: Egypt

### Re: Power law exponent problem

Jason.Jonkman wrote:Dear Mostafa,

Yes, I agree with your least-squares regression approach.

So, does your LES simulation include a wind turbine or does the LES simulation only consider the atmospheric boundary layer? If a wind turbine is modeled within your LES, I agree picking points in the ambient wind say 2D upstream of the rotor makes sense. If the wind turbine is not modeled within the LES, then I would pick points at the rotor plane.

Are you cubing the wind speed in your spatial averaging to derive some sort of power-equivalent average wind speed? I agree that there are many points that you could derive the turbulence intensity from and I'm not sure whether there is a best practice on the approach taken. I would first judge how different the turbulence intensity is across the domain. If you want to limit the number of points considered, I would use points at the hub height.

Best regards,

thank you so so so much
my wind turbine is modelled in my les . I am using palm if you heard about it .
I am cubing the wind speed to derive some sort of power equivalent average wind speed as it helps in what I am doing.I wil judge according how different the turbulance intensity at hub height.

I am having some hard time as my supervisor is on vacation and everybody in the research centre I am working in are very busy to help. I am very thankful for your kind help.