RNA Inertia FASTv7

Dear Dr. Jonkman,

I try to calculate the moments of inertia for the RNA of an onshore reference turbine (130-3.4MW, see nrel.gov/docs/fy19osti/73492.pdf). Therfore, I followed the steps described in post http://forums.nrel.gov/t/ansys-model-tower/1722/4. I converted the input files of the WT to the FASTv7-Format.

I created the following files:

130_lin.fst
130_AD.ipt
Blade_NoDamp.dat
Tower_NoDamp.dat
Platform.dat
Linear_130.dat (Control)

When I run the .fst-file I get an AeroDyn error:

I checked the AD.ipt-file but I cannot find the problem.

3.4 MW onshore reference turbine aerodynamic parameters.
SI                                     SysUnits - System of units for used for input and output [must be SI for FAST] (unquoted string)
STEADY                                 StallMod - Dynamic stall included [BEDDOES or STEADY] (unquoted string)
NO_CM                                  UseCm    - Use aerodynamic pitching moment model? [USE_CM or NO_CM] (unquoted string)
EQUIL                                  InfModel - Inflow model [DYNIN or EQUIL] (unquoted string)
SWIRL                                  IndModel - Induction-factor model [NONE or WAKE or SWIRL] (unquoted string)
   1.0E-6                              AToler   - Induction-factor tolerance (convergence criteria) (-)
PRANDtl                                TLModel  - Tip-loss model (EQUIL only) [PRANDtl, GTECH, or NONE] (unquoted string)
PRANDtl                                HLModel  - Hub-loss model (EQUIL only) [PRANdtl or NONE] (unquoted string)
"12ms.wnd"                             WindFile - Name of file containing wind data (quoted string)
  220.436                              HH       - Wind reference (hub) height [TowerHt+Twr2Shft+OverHang*SIN(ShftTilt)] (m)
   0.0                                 TwrShad  - Tower-shadow velocity deficit (-)
9999.9                                 ShadHWid - Tower-shadow half width (m)
9999.9                                 T_Shad_Refpt - Tower-shadow reference point (m)
   1.225                               AirDens  - Air density (kg/m^3)
   1.4639E-5                           KinVisc  - Kinematic air viscosity (m^2/sec)
   0.005                               DTAero   - Time interval for aerodynamic calculations (sec)
   30                                  NumFoil  - Number of airfoil files (-)
"Airfoils/Cylinder1.dat"    FoilNm   - Names of the airfoil files [NumFoil lines] (quoted strings)
"Airfoils/DU21_A17.dat"
"Airfoils/DU35_A17.dat"
"Airfoils/DU40_A17.dat"
  29                                   BldNodes - Number of blade nodes used for analysis (-)
RNodes    AeroTwst  DRNodes  Chord  NFoil  PrnElm
 0.63000  19.86     1.26000  2.600  1      NOPRINT
 2.52000  19.16     2.52000  2.740  2      NOPRINT
 5.04000  17.77     2.52000  3.090  2      NOPRINT
 7.47000  15.98     2.34000  3.490  2      NOPRINT
 9.81000  14.02     2.35000  3.880  2      NOPRINT
12.17000  12.02     2.35000  4.180  2      NOPRINT
14.47000  10.19     2.25000  4.290  2      NOPRINT
16.71000   8.54     2.25000  4.250  2      NOPRINT
18.96000   6.91     2.25000  4.150  2      NOPRINT
21.16000   5.36     2.15000  4.010  2      NOPRINT
23.31000   4.08     2.15000  3.860  2      NOPRINT
25.46000   3.15     2.15000  3.690  2      NOPRINT
27.61000   2.50     2.15000  3.460  2      NOPRINT
29.76000   1.98     2.15000  3.200  2      NOPRINT
31.91000   1.54     2.15000  2.940  3      NOPRINT
33.96000   1.18     1.95000  2.760  3      NOPRINT
35.91000   0.87     1.95000  2.590  3      NOPRINT
37.85000   0.61     1.95000  2.430  3      NOPRINT
39.80000   0.37     1.95000  2.290  3      NOPRINT
41.75000   0.15     1.95000  2.170  3      NOPRINT
43.68000  -0.07     1.92000  2.090  3      NOPRINT
45.60000  -0.28     1.92000  2.030  3      NOPRINT
47.52000  -0.46     1.92000  1.990  3      NOPRINT
49.44000  -0.64     1.92000  1.950  3      NOPRINT
51.42000  -0.86     2.03000  1.890  3      NOPRINT
53.45000  -1.17     2.03000  1.770  4      NOPRINT
55.48000  -1.62     2.03000  1.540  4      NOPRINT
57.86000  -2.40     2.73000  1.060  4      NOPRINT
61.11000  -3.77     3.78000  0.200  4      NOPRINT

Regarding the error message, I am not sure what is meant by “AeroDyn element table”. I assume it is the table at the end of the file? I hope my desription is sufficient to comprehend the problem.

Thank you very much in advance!

Dear Friedrich,

I think the error is that you’ve specified that there are 30 airfoil files (NumFoil = 30), but you’ve only identified 4 of them. Perhaps you want to set NumFoil = 4?

That said, you shouldn’t need to convert a model into FAST v7 format in order to get calculate the moments of inertia of the RNA. You can use the linearization functionality in newer versions of FAST/OpenFAST for that. The FAST v8 and OpenFAST linearizations do not show the mass matrix directly, but this matrix can often be inferred from other matrices generated through the linearization process. A similar question was asked and answered in the following forum topic: http://forums.nrel.gov/t/openfast-2nd-order-linearization/2249/2.

Best regards,

Dear Jason,

Sorry for answering so late. Thank you for your helpful hints! I was able to derive the RNA inertia in FASTv7. When I find the time I will also try to reproduce the solution with openfast.

Best regards,

Dear Jason,

Following the suggestions about how to calculate the moments of inertia of the RNA, I can obtain a 6*6 matrix for the active platform DOF using the OpenFAST linearizations. However, I found there is some difficulty to convert the matrix to the tower top. For example, the matrix of the 130-3.4MW, see nrel.gov/docs/fy19osti/73492.pdf I obtained is as follows,
264119.859717403 -0.0961056939879476 -0.00188459775307208 9.77156286514160 26559707.1525140 0.187247189813421
-0.0961056724257763 264120.284155140 0.000612350721314040 -26559750.1692261 -9.72554892063563 -396528.273289655
-0.00584761070365937 0.000612354531870813 264119.764671429 -0.101134028872518 396526.773596832 0.000838292282230785
9.77156087516821 -26559750.6576134 -0.101133645208790 2700783004.54588 988.719158188322 38543670.0089392
26559701.8061558 -9.72554913888835 396527.638234930 988.719159851760 2688227909.92568 18.9240064327141
0.187247159938998 -396528.280225096 0.000838298631633757 38543669.9731381 18.9240072243189 18724753.0955109
The matrix values corresponding to positions 4-4, and 5-5 are significantly larger than the matrix value corresponding to 6-6 mainly because of the existence of the tower height. My question is how I can exactly change them to the moments of inertia of the RNA? I have tried to use the parallel axis theorem, but a minor change in the relative distance can cause a large variation in the result. Hence, how I can determine the exact vertical distance between the platform center and the RNA center?

Thank you very much in advance!

Dear @Xiaogang.Huang,

The 6x6 rigid-body mass matrix generated through the linearization of FAST or OpenFAST should have the following form:

MassMatrix

where
m = mass
(x_g,y_g,z_g) = center of mass relative to the platform reference point
(I_11,I_12,…I_33) = inertias relative to the platform reference point.

So, you can calculate the center of mass relative to the platform reference point from the off diagonal entries. Based on knowledge of the center of mass, you can shift the inertias to a different reference point using the parallel axis theorem.

Best regards,

Dear Jason,

Thank you for your response!

I have checked my mass matrix and found its form is similar to that you gave. Then I think I still have difficulty to calculate the moments of inertia of the RNA using the parallel axis theorem because I do not know the position of the center of RNA mass.

Best regards,
Xiaogang

Dear @Xiaogang.Huang,

The position of the RNA center of mass (x_g,y_g,z_g) can be calculated using off-diagional entries of the 6x6 mass matrix, as I explained above.

Best regards,

Dear Jason,

Thank you for your help!

Here are the inertias translated to the tower tip-section:
tip_mass = 2.641198597174030e+05 kg
cm_axial = 0.559460716173334 m
cm_loc = -1.501317010614793 m
ixx_tip = 3.003147019722959e+07 kg-m** 2
iyy_tip = 1.747637557703009e+07 kg-m** 2
izz_tip = 1.872475309551086e+07 kg-m** 2
izx_tip = -1.109093850354899e+06 kg-m** 2

Best regards,
Xiaogang