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 Ansys model tower - #4 by Jason.Jonkman. I converted the input files of the WT to the FASTv7-Format.
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.
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: OpenFast 2nd order Linearization - #2 by Jason.Jonkman.
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.
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?
The 6x6 rigid-body mass matrix generated through the linearization of FAST or OpenFAST should have the following form:
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.
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.
I have same problem as you, so I try to calculate the inertias translated to the tower tip-section by your data. In your mass matrix, M(1,1)=264119.859, this data should be the mass of RNA. M(4,2)=-26559750.65, this data should be -m*z_g. z_g is center of mass’s z coordinate relative to the platform reference point. So z_g value is 100.5595. But in your last result, cm_axial = 0.5595. It seems that you subtract 100 from z_g，I wonder know why you do this process.
The 6x6 mass matrix derived by @Xiaogang.Huang was relative to the platform reference at the base of the tower, so, while I didn’t check the math, I believe the tower height was subtracted from the z_g value.
Thank you for your reply. I believe 100 is the tower high too. But in my opinion, z_g is center of mass’s z coordinate relative to the platform reference point, and (I_11,I_12,…I_33) is inertias relative to the platform reference point, which located at the base of the tower. So we need to use parallel-shift theorem to calculate inertias of center of mass. So I don’t understand why tower height need to be substracted from z_g.
Xiaogang was interested in calculating the tower-top mass, center of mass, and inertia properties for input to BModes, in which the tower center of mass location is specified relative to the tower top.
