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### Viterna polar extrapolation method (alpha_s)

Posted: **Mon Dec 03, 2018 9:19 pm**

by **Alvaro.Olcoz**

Dear all,

I have original S822 airfoil data (Cl,Cd)] in an aoa range of [-25,25]º (XFOIL) and I have implemented a MATLAB script to make a 360º extrapolation following the Viterna method. The method is described in the original paper that Viterna wrote in 1982 (Theoretical and Experimental Power From Large HorizontaI Axis Wind Turbines) and also in AeroDyn Theory Manual.

In the original equations (Viterna,1982) the subscript s denotes the stall point, but in AeroDyn, it is said that subscript s could also mean the matching point.

As I have data beyond the stall point of the airfoil (until 25º), I wonder which point should I use as a match between original data and extrapolated data (stall point, around 15º or last data point, 25º). First option leads to a sharp curve near stall point, but it overestimates CL just beyond this point whereas second option shows a more abrupt stall condition.

Attached in this post you can see a figure that clarifies my concern.

Thank you in advance.

Best regards,

Alvaro Olcoz

### Re: Viterna polar extrapolation method (alpha_s)

Posted: **Tue Dec 04, 2018 6:56 am**

by **Jason.Jonkman**

Dear Alvaro,

I'm not an expert on this topic (so hopefully others can respond), but do you consider that your original airfoil data is accurate up to 25 degrees or is it only accurate up to the stall point? If it is accurate up to 25 degrees, there would be no point to applying the Viterna correction at lower angle of attack. However, if the accuracy of the original airfoil data is questionable beyond stall, the Viterna correction may be preferred above stall.

Best regards,

### Re: Viterna polar extrapolation method (alpha_s)

Posted: **Tue Dec 04, 2018 7:49 pm**

by **Alvaro.Olcoz**

Dear Jason,

Thank you for your rapid reply. Your help is more than welcome.

I have another doubt thay you may be able to answer:

I wanted to simulate in WT_Perf a rotor blade own design for which I want to apply Shen's 3D correction into the airfoil data lift coeffcients. As I have read in the forum, NREL codes implemet this kind of corrections out of the BEM code, so I think than this correction should be considered into the airfoil data files.

My problem is that I am aiming to do a multi Reynolds (12 values) study as Re numbers varies not only spanwise but also within a velocity range. I can solve this by making airfoil data files with several tables. But when it comes to Shen correction, c/r ratio will change in each section of the blade (22 elements), so, do I need to create 24 airfoil files in order to apply this correction, and asign each airfoil data table to each spanwise node? This method will lead to a 22 (nodes) x 12 (Tables in each data file) = 264 tables which makes this a bit unconfortable.

Thank you for your precious time.

Best regards,

Alvaro Olcoz

### Re: Viterna polar extrapolation method (alpha_s)

Posted: **Tue Dec 04, 2018 7:54 pm**

by **Jason.Jonkman**

Dear Alvaro,

Creating 264 tables would certainly be difficult via the AirfoilPrep spreadsheet, but there is a Python version also available, which could be more easily automated:

https://nwtc.nrel.gov/AirfoilPrepPy.

Best regards,

### Re: Viterna polar extrapolation method (alpha_s)

Posted: **Mon Jan 14, 2019 7:04 pm**

by **Alvaro.Olcoz**

Dear Jason,

Regarding the 3d correction for airfoil data I finally wrote an own MATLAB script in which I applied Snel et ali.'s correction model. Now I have also implemented an extrapolation to -180º +180º using the Viterna method and this has created me a doubt:

Initially I only applied the 3d correction model to positive angles of attack, when the 2 D data separated from the inviscid flow data. Now, I wonder if the same needs to be done for negative (left side of the graphs) values of angle of attack when inviscid flow data and 2D data start to differ.

I have tried to introduce my original 2D polars (which are between alpha=-25º and +25º) in AirfoilPrep worksheet to apply Du and Selig model but I can only obtain data corrections for angles of attack above -10º).

I am aware that my wind turbine will not work normally in high negative angles of attack, but as I want to use those polars in FAST v8 in the future, I would like to represent the airfoil characteristics between -180º and 180º in a quite accurate "physically correct" way.

Thank you in advance for your precious time ,

Alvaro Olcoz

### Re: Viterna polar extrapolation method (alpha_s)

Posted: **Wed Jan 16, 2019 2:12 pm**

by **Jason.Jonkman**

Dear Alvaro,

It is standard practice to only apply the rotational augmentation and Viterna extrapolation around stall at positive angle of attack, which is where these models were developed for and what a wind turbine would experience during operation. It is only under rare cases where an airfoil of a conventional wind turbine would reach stall at negative angles of attack. It is typically wise to extrapolate airfoil data to the full -180 to 180 degrees angle of attack range to ensure that the aerodynamic calculation does not fail under rare cases, but I'm not aware of good models or data that could be used to validate 3D corrections around stall at negative angles of attack. Thus, it is standard practice to simply use simple flat-plate extrapolation for these rare cases (which is what is done in AirfoilPrep).

Best regards,

### Re: Viterna polar extrapolation method (alpha_s)

Posted: **Fri Jan 18, 2019 2:01 pm**

by **Alvaro.Olcoz**

Dear Jason,

Thank you one more time for your response.

Best regards,

Alvaro Olcoz