lift cofficient partial derivative about attack angle

Wind & Water Airfoils
1

Dear Prof. Jason,

I want to get the the lift cofficients partial derivatives about the attack angles.
Firstly I used the spline function to fit the lift cofficient and attack angle curve. Then the spline function was used to calculate the partial derivatives directly.
I compared my resuluts with an literature, but there has much differences between two partial derivative curves.
So I wonder the method I used for derivative calculation is reasonable?
The attachment is a interpolation result of NREL airfoil CL~α curve by using spline function.

Best regards!

Wenhua Wang
cl curve.pdf (52.7 KB)

2

Dear Wenhua,

Your approach sounds reasonable, so, I’m not sure why your results are not as you expect. The slope of the linear region of the lift curve (near zero degrees angle of attack) should be easy to estimate by hand; how does your solution compare with the results published in the literature in the linear region of the curve?

Best regards,

3

Dear Prof. Jonkman,

The attachment has the results of my interpolation and the literature. I wonder why the partial derivative curves so different?

Best regards!

Wenhua Wang
NREL-S818 Airfoil.rar (223 KB)

4

Dear Wenhua,

I’m not sure the source of your literature results, but they seem to be generic and not for the specific airfoil you’re comparing to.

Regardless, the biggest difference I see between the two results is related to units. The derivative, dCl/dalpha, in the literature plot is dimensionless (per radian), but the derivative in your results is per degree. If you multiply your result by 180/pi to convert from degrees to radians, your dCl/dalpha in the linear region of the lift curve is close the value of 6 found in the literature plot.

Best regards,

5

Dear Prof. Jonkman,

Thanks a lot for your help!

Best regards!

Wenhua Wang

6

Dear Prof. Jonkman,

I performed a coupled analysis of fixed botttom offshore wind turbine by using FAST V8, I have a question about the summary file of the SubDyn.
The SunDyn summary file involves the results of sub-structure eigenvalues, I wonder whether the eigenvalue results include the effects of water depth, marine growth and added mass.

Thanks a lot for you help!

Best regards!

Wenhua Wang

7

Dear Wenhua,

No. The eigensolution given in the SubDyn summary file is derived independent of the other FAST modules; the eigensolution does not depend on added mass, marine growth, etc. that may have been enabled via HydroDyn.

Best regards,

8

Dear Prof. Jonkman,

Thanks a lot for your reply!

I have some confusion about the coupled analysis results. I performed a Furior transformation of the member internal forces of the sub structure. I found two peaks in the frequency domain, one is 0.122Hz and the other is 0.365Hz. The former is the wave frequency and the last one I think it should be the integrated structure frequency, but it didn’t agree with my modal analysis results. I performed a modal analysis of the integrated structure by using other finite element software in the consideration of water depeth marine growth and so on. The modal analysis result is 0321Hz.

In order to vertify the results, I analyzed the integrated model separately.

(1) Blades + Hub + Nacelle + Tower(fixed)
1st fre result(Hz)
FAST V7, 0.378Hz;
FAST V8, 0.377Hz;
FE Software, 0.379Hz.

(2) Pentapod sub structure(fixed)
1st fre result(Hz)
FAST(Subdyn), 1.520Hz;
FE Software, 1.508Hz.

(3) Integrated structure
1st fre result(Hz)
FAST V8, 0.364Hz;
FE Software, 0.321Hz.

I enabled all the platform DOFs in the FAST, I can not think out why the FAST V8 result is higher than the FE result, whether the interface joint DOFs effect the result? The interface joint is fixed in the analysis according to the SubDyn User Manuel.

I also have some questions about the parameters of PtfmRIner PtfmPIner and PtfmYIner. I refered to the Test 20 of NREL 5MW OWT with tripod sub structure, in the test the mass center is also the platform reference point, the values of PtfmRIner and PtfmPIner are zero, the PtfmYIner’s value is 1.534E+06.
I choose the pentapod as the OWT subtructure. The pentapod sub structure is a symmetrical structure like the tripod sub structre, the only difference is the pentapod has five pile legs. Beacurse the pentapod and the tripod are symmetry, so the mass center is in the centerline of the structure. In my opinion, the PtfmRIner and PtfmPIner values are non zero, but the PtfmYIner should be zero.

Could you give me some instructions about these two questions?

Thanks a lot for your help!

Best regards,

Wenhua Wang

9

Dear Wenhua,

Was the FAST v8 result of 0.364 Hz from (3) found via Fourier analysis of a time series? What is the difference between that simulation and the one used to derive the 0.365 Hz mentioned in your first paragraph?

All six platform DOFs should be enabled in ElastoDyn when coupled to SubDyn, as described in Section 5.4 of the SubDyn User’s Guide and Theory Manual: wind.nrel.gov/nwtc/docs/SubDyn_Manual.pdf.

Also see Section 5.4 of the SubDyn User’s Guide and Theory Manual for an explanation why PtfmYIner is nonzero (“PtfmYIner” is incorrectly written as “PtfmYawIner” in this Section).

The integrated support structure frequencies are likely impacted by the tower mode shapes specified in ElastoDyn–did you derive these mode shapes for the coupled ElastoDyn+SubDyn model based on the approach outlined in Section 5.4 of the SubDyn User’s Guide and Theory Manual?

Best regards,