Obtaining sensitivity of aerodynamic power to rotor-collective blade pitch

Hi,

I am trying to obtain aerodynamic power sensitivity to rotor-collective blade pitch. Reading through NREL 5MW paper I see that it is obtained through linearization process in OpenFAST. I cannot seem to find any output of it in linearization file. Is it obtained through another process after the linearization? If so where can I find how can do it?

Dear Deniz,

The AeroDyn output RtAeroPwr is the aerodynamic power, so, add this to AeroDyn’s OutList. Then ensure standard inputs are included in the linearization output files (LinInputs = 1 in the OpenFAST driver input file) and the OutList is included in the linearization output file (LinOutputs = 1). Then, the derivative of aerodynamic power (an output) with respect to the collective blade pitch angle (a standard input) will be included through the associated row and column of the “D” matrix output.

Best regards,

Dear Dr. Jason,

Thank you very much for your reply. I was able to obtain the “D” matrix. I was reading https://www.nrel.gov/docs/fy17osti/67015.pdf and at pg.12 I saw that for every 10 deg rotation a linearization is made and matrices are azimuth-averaged. Right now I can use fx_getMats.m file from matlab-toolbox to import and average one of the linearization outputs. How can I import every 10 deg linearization file or did I misunderstood how azimuth-averaging is done?

Best regards,
Deniz

Dear Deniz,

You can linearize at multiple azimuth steps by setting NLinTimes > 1, with LinTimes set such that the time between linearizations matches the azimuth step you want based on the rotor speed. Each linearization time will generate a separate linearization file. And the MATLAB script fx_getMats.m can be called with multiple OpenFAST linearization output files, e.g., with NLinTimes = 2:

FileNames = {'Test18.1.lin','Test18.2.lin'}

Best regards,

Dear Dr. Jason,

Thank you I was able to import multiple linearization files at the same time.

Best regards,
Deniz

Dear Jonkman,
I want to get aerodynamic power to rotor-collective blade pitch control in 12m/s wind. As you mentioned above, I set Lininputs and Linoutputs=1. Then, I opened the linearization files and looked at them, I found the associated row and column of the “D” matrix output is zero. This is why? Could you please help me check? I only switch on GenDof.

Best regards!!

For convenience, next is part of my file
FAST LINEARIZATION

---------------------- LINEARIZATION ------------------------------------------- true Linearize - Linearization analysis (flag) true CalcSteady - Calculate a steady-state periodic operating point before linearization? [unused if Linearize=False] (flag) 3 TrimCase - Controller parameter to be trimmed {1:yaw; 2:torque; 3:pitch} [used only if CalcSteady=True] (-) 0.0001 TrimTol - Tolerance for the rotational speed convergence [used only if CalcSteady=True] (-) 0.001 TrimGain - Proportional gain for the rotational speed error (>0) [used only if CalcSteady=True] (rad/(rad/s) for yaw or pitch; Nm/(rad/s) for torque) 0 Twr_Kdmp - Damping factor for the tower [used only if CalcSteady=True] (N/(m/s)) 0 Bld_Kdmp - Damping factor for the blades [used only if CalcSteady=True] (N/(m/s)) 36 NLinTimes - Number of times to linearize (-) [>=1] [unused if Linearize=False] 30, 60 LinTimes - List of times at which to linearize (s) [1 to NLinTimes] [used only when Linearize=True and CalcSteady=False] 1 LinInputs - Inputs included in linearization (switch) {0=none; 1=standard; 2=all module inputs (debug)} [unused if Linearize=False] 1 LinOutputs - Outputs included in linearization (switch) {0=none; 1=from OutList(s); 2=all module outputs (debug)} [unused if Linearize=False] False LinOutJac - Include full Jacobians in linearization output (for debug) (flag) [unused if Linearize=False; used only if LinInputs=LinOutputs=2] False LinOutMod - Write module-level linearization output files in addition to output for full system? (flag) [unused if Linearize=False]

AeroDyn

------- AERODYN v15 for OpenFAST INPUT FILE ----------------------------------------------- NREL 5.0 MW offshore baseline aerodynamic input properties. ====== General Options ============================================================================ False Echo - Echo the input to "<rootname>.AD.ech"? (flag) "default" DTAero - Time interval for aerodynamic calculations {or "default"} (s) 1 WakeMod - Type of wake/induction model (switch) {0=none, 1=BEMT, 2=DBEMT, 3=OLAF} [WakeMod cannot be 2 or 3 when linearizing] 1 AFAeroMod - Type of blade airfoil aerodynamics model (switch) {1=steady model, 2=Beddoes-Leishman unsteady model} [AFAeroMod must be 1 when linearizing] 1 TwrPotent - Type tower influence on wind based on potential flow around the tower (switch) {0=none, 1=baseline potential flow, 2=potential flow with Bak correction} 1 TwrShadow - Calculate tower influence on wind based on downstream tower shadow (switch) {0=none, 1=Powles model, 2=Eames model} True TwrAero - Calculate tower aerodynamic loads? (flag) True FrozenWake - Assume frozen wake during linearization? (flag) [used only when WakeMod=1 and when linearizing] False CavitCheck - Perform cavitation check? (flag) [AFAeroMod must be 1 when CavitCheck=true] False CompAA - Flag to compute AeroAcoustics calculation [used only when WakeMod = 1 or 2] "unused" AA_InputFile - AeroAcoustics input file [used only when CompAA=true] ====== Environmental Conditions =================================================================== 1.225 AirDens - Air density (kg/m^3) 1.464E-05 KinVisc - Kinematic air viscosity (m^2/s) 335 SpdSound - Speed of sound (m/s) 103500 Patm - Atmospheric pressure (Pa) [used only when CavitCheck=True] 1700 Pvap - Vapour pressure of fluid (Pa) [used only when CavitCheck=True] 0.5 FluidDepth - Water depth above mid-hub height (m) [used only when CavitCheck=True] ====== Blade-Element/Momentum Theory Options ====================================================== [unused when WakeMod=0 or 3] 2 SkewMod - Type of skewed-wake correction model (switch) {1=uncoupled, 2=Pitt/Peters, 3=coupled} [unused when WakeMod=0 or 3] "default" SkewModFactor - Constant used in Pitt/Peters skewed wake model {or "default" is 15/32*pi} (-) [used only when SkewMod=2; unused when WakeMod=0 or 3] True TipLoss - Use the Prandtl tip-loss model? (flag) [unused when WakeMod=0 or 3] True HubLoss - Use the Prandtl hub-loss model? (flag) [unused when WakeMod=0 or 3] True TanInd - Include tangential induction in BEMT calculations? (flag) [unused when WakeMod=0 or 3] False AIDrag - Include the drag term in the axial-induction calculation? (flag) [unused when WakeMod=0 or 3] False TIDrag - Include the drag term in the tangential-induction calculation? (flag) [unused when WakeMod=0,3 or TanInd=FALSE] "Default" IndToler - Convergence tolerance for BEMT nonlinear solve residual equation {or "default"} (-) [unused when WakeMod=0 or 3] 100 MaxIter - Maximum number of iteration steps (-) [unused when WakeMod=0] ====== Dynamic Blade-Element/Momentum Theory Options ============================================== [used only when WakeMod=2] 2 DBEMT_Mod - Type of dynamic BEMT (DBEMT) model {1=constant tau1, 2=time-dependent tau1} (-) [used only when WakeMod=2] 4 tau1_const - Time constant for DBEMT (s) [used only when WakeMod=2 and DBEMT_Mod=1] ====== OLAF -- cOnvecting LAgrangian Filaments (Free Vortex Wake) Theory Options ================== [used only when WakeMod=3] "unused" OLAFInputFileName - Input file for OLAF [used only when WakeMod=3] ====== Beddoes-Leishman Unsteady Airfoil Aerodynamics Options ===================================== [used only when AFAeroMod=2] 3 UAMod - Unsteady Aero Model Switch (switch) {1=Baseline model (Original), 2=Gonzalez's variant (changes in Cn,Cc,Cm), 3=Minnema/Pierce variant (changes in Cc and Cm)} [used only when AFAeroMod=2] True FLookup - Flag to indicate whether a lookup for f' will be calculated (TRUE) or whether best-fit exponential equations will be used (FALSE); if FALSE S1-S4 must be provided in airfoil input files (flag) [used only when AFAeroMod=2] ====== Airfoil Information ========================================================================= 1 AFTabMod - Interpolation method for multiple airfoil tables {1=1D interpolation on AoA (first table only); 2=2D interpolation on AoA and Re; 3=2D interpolation on AoA and UserProp} (-) 1 InCol_Alfa - The column in the airfoil tables that contains the angle of attack (-) 2 InCol_Cl - The column in the airfoil tables that contains the lift coefficient (-) 3 InCol_Cd - The column in the airfoil tables that contains the drag coefficient (-) 4 InCol_Cm - The column in the airfoil tables that contains the pitching-moment coefficient; use zero if there is no Cm column (-) 0 InCol_Cpmin - The column in the airfoil tables that contains the Cpmin coefficient; use zero if there is no Cpmin column (-) 8 NumAFfiles - Number of airfoil files used (-) "../5MW_Baseline/Airfoils/Cylinder1.dat" AFNames - Airfoil file names (NumAFfiles lines) (quoted strings) "../5MW_Baseline/Airfoils/Cylinder2.dat" "../5MW_Baseline/Airfoils/DU40_A17.dat" "../5MW_Baseline/Airfoils/DU35_A17.dat" "../5MW_Baseline/Airfoils/DU30_A17.dat" "../5MW_Baseline/Airfoils/DU25_A17.dat" "../5MW_Baseline/Airfoils/DU21_A17.dat" "../5MW_Baseline/Airfoils/NACA64_A17.dat" ====== Rotor/Blade Properties ===================================================================== True UseBlCm - Include aerodynamic pitching moment in calculations? (flag) "../5MW_Baseline/NRELOffshrBsline5MW_AeroDyn_blade.dat" ADBlFile(1) - Name of file containing distributed aerodynamic properties for Blade #1 (-) "../5MW_Baseline/NRELOffshrBsline5MW_AeroDyn_blade.dat" ADBlFile(2) - Name of file containing distributed aerodynamic properties for Blade #2 (-) [unused if NumBl < 2] "../5MW_Baseline/NRELOffshrBsline5MW_AeroDyn_blade.dat" ADBlFile(3) - Name of file containing distributed aerodynamic properties for Blade #3 (-) [unused if NumBl < 3] ====== Tower Influence and Aerodynamics ============================================================= [used only when TwrPotent/=0, TwrShadow/=0, or TwrAero=True] 12 NumTwrNds - Number of tower nodes used in the analysis (-) [used only when TwrPotent/=0, TwrShadow/=0, or TwrAero=True] TwrElev TwrDiam TwrCd TwrTI (used only with TwrShadow=2) (m) (m) (-) (-) 0.0000000E+00 6.0000000E+00 1.0000000E+00 1.0000000E-01 8.5261000E+00 5.7870000E+00 1.0000000E+00 1.0000000E-01 1.7053000E+01 5.5740000E+00 1.0000000E+00 1.0000000E-01 2.5579000E+01 5.3610000E+00 1.0000000E+00 1.0000000E-01 3.4105000E+01 5.1480000E+00 1.0000000E+00 1.0000000E-01 4.2633000E+01 4.9350000E+00 1.0000000E+00 1.0000000E-01 5.1158000E+01 4.7220000E+00 1.0000000E+00 1.0000000E-01 5.9685000E+01 4.5090000E+00 1.0000000E+00 1.0000000E-01 6.8211000E+01 4.2960000E+00 1.0000000E+00 1.0000000E-01 7.6738000E+01 4.0830000E+00 1.0000000E+00 1.0000000E-01 8.5268000E+01 3.8700000E+00 1.0000000E+00 1.0000000E-01 8.7600000E+01 3.8700000E+00 1.0000000E+00 1.0000000E-01 ====== Outputs ==================================================================================== True SumPrint - Generate a summary file listing input options and interpolated properties to "<rootname>.AD.sum"? (flag) 0 NBlOuts - Number of blade node outputs [0 - 9] (-) 1, 9, 19 BlOutNd - Blade nodes whose values will be output (-) 0 NTwOuts - Number of tower node outputs [0 - 9] (-) 1, 2, 6 TwOutNd - Tower nodes whose values will be output (-) OutList - The next line(s) contains a list of output parameters. See OutListParameters.xlsx for a listing of available output channels, (-) "RtAeroFxh" -Total rotor aerodynamic load (force in x direction) END of input file (the word "END" must appear in the first 3 columns of this last OutList line) ---------------------------------------------------------------------------------------

If you have enough time, could you please help me check my results. Thank you!
There are my openfast files and linearization files.
5MW_Land_Linearization.rar (121 KB)

Best regards!

Dear Dezheng.Zhu,

Do you get zero for other wind speeds? What happens when you disable the generator DOF as well (GenDOF = False)?

Best regards,

Dear Jonkman,
I tried other wind speed at 13mps、14mps、15mps、16mps、17mps、18mps. Finally, I get zero rows. Also, I added other variables including RtAeroFxh、RtAeroCp、RtAeroFyh in AeroDyn OutList, and their rows are also zero.

There are my linearization files in wind speed 18mps.
5MW_Land_Linearization_18mps.rar (123 KB)

Then I set Gendof=false and linearized at 12mps, openfast did linearization at 0deg pitch. And it is still zero.
There are my linearization files with Gendof=false at wind speed
5MW_Land_ModeShapes_Gendof=false_12mps.rar|attachment (103 KB)

This is a LinFile.

Linearized model: Predictions were generated on 19-Jan-2022 at 10:09:29 using OpenFAST, compiled as a 64-bit application using single precision at commit Unversioned from 42a5a8196529ae0349eda6d797a79461c2c03ff0
 linked with  NWTC Subroutine Library; ElastoDyn; InflowWind; AeroDyn; ServoDyn

Description from the FAST input file: FAST Certification Test #18: NREL 5.0 MW Baseline Wind Turbine (Onshore)

Simulation information:
   Simulation time:                     4.9625 s
   Rotor Speed:                         1.2671 rad/s
   Azimuth:                             0.0048 rad
   Wind Speed:                         12.0000 m/s
   Number of continuous states:         0
   Number of discrete states:           0
   Number of constraint states:         0
   Number of inputs:                   66
   Number of outputs:                  42
   Jacobians included in this file?    No

Order of inputs:
     Column   Operating Point                     Rotating Frame? Derivative Order Description
   ---------- ---------------                     --------------- ---------------- -----------
          1    1.200E+01                                 F               0         IfW Extended input: horizontal wind speed (steady/uniform wind), m/s
          2    0.000E+00                                 F               0         IfW Extended input: vertical power-law shear exponent, -
          3    0.000E+00                                 F               0         IfW Extended input: propagation direction, rad
          4    0.000E+00                                 T               0         ED Blade 1 pitch command, rad
          5    0.000E+00                                 T               0         ED Blade 2 pitch command, rad
          6    0.000E+00                                 T               0         ED Blade 3 pitch command, rad
          7    0.000E+00                                 F               0         ED Yaw moment, Nm
          8    4.309E+04                                 F               0         ED Generator torque, Nm
          9    0.000E+00                                 F               0         ED Extended input: collective blade-pitch command, rad
         10    0.000E+00                                 T               0         AD User property on blade 1, node 1, -
         11    0.000E+00                                 T               0         AD User property on blade 1, node 2, -
         12    0.000E+00                                 T               0         AD User property on blade 1, node 3, -
         13    0.000E+00                                 T               0         AD User property on blade 1, node 4, -
         14    0.000E+00                                 T               0         AD User property on blade 1, node 5, -
         15    0.000E+00                                 T               0         AD User property on blade 1, node 6, -
         16    0.000E+00                                 T               0         AD User property on blade 1, node 7, -
         17    0.000E+00                                 T               0         AD User property on blade 1, node 8, -
         18    0.000E+00                                 T               0         AD User property on blade 1, node 9, -
         19    0.000E+00                                 T               0         AD User property on blade 1, node 10, -
         20    0.000E+00                                 T               0         AD User property on blade 1, node 11, -
         21    0.000E+00                                 T               0         AD User property on blade 1, node 12, -
         22    0.000E+00                                 T               0         AD User property on blade 1, node 13, -
         23    0.000E+00                                 T               0         AD User property on blade 1, node 14, -
         24    0.000E+00                                 T               0         AD User property on blade 1, node 15, -
         25    0.000E+00                                 T               0         AD User property on blade 1, node 16, -
         26    0.000E+00                                 T               0         AD User property on blade 1, node 17, -
         27    0.000E+00                                 T               0         AD User property on blade 1, node 18, -
         28    0.000E+00                                 T               0         AD User property on blade 1, node 19, -
         29    0.000E+00                                 T               0         AD User property on blade 2, node 1, -
         30    0.000E+00                                 T               0         AD User property on blade 2, node 2, -
         31    0.000E+00                                 T               0         AD User property on blade 2, node 3, -
         32    0.000E+00                                 T               0         AD User property on blade 2, node 4, -
         33    0.000E+00                                 T               0         AD User property on blade 2, node 5, -
         34    0.000E+00                                 T               0         AD User property on blade 2, node 6, -
         35    0.000E+00                                 T               0         AD User property on blade 2, node 7, -
         36    0.000E+00                                 T               0         AD User property on blade 2, node 8, -
         37    0.000E+00                                 T               0         AD User property on blade 2, node 9, -
         38    0.000E+00                                 T               0         AD User property on blade 2, node 10, -
         39    0.000E+00                                 T               0         AD User property on blade 2, node 11, -
         40    0.000E+00                                 T               0         AD User property on blade 2, node 12, -
         41    0.000E+00                                 T               0         AD User property on blade 2, node 13, -
         42    0.000E+00                                 T               0         AD User property on blade 2, node 14, -
         43    0.000E+00                                 T               0         AD User property on blade 2, node 15, -
         44    0.000E+00                                 T               0         AD User property on blade 2, node 16, -
         45    0.000E+00                                 T               0         AD User property on blade 2, node 17, -
         46    0.000E+00                                 T               0         AD User property on blade 2, node 18, -
         47    0.000E+00                                 T               0         AD User property on blade 2, node 19, -
         48    0.000E+00                                 T               0         AD User property on blade 3, node 1, -
         49    0.000E+00                                 T               0         AD User property on blade 3, node 2, -
         50    0.000E+00                                 T               0         AD User property on blade 3, node 3, -
         51    0.000E+00                                 T               0         AD User property on blade 3, node 4, -
         52    0.000E+00                                 T               0         AD User property on blade 3, node 5, -
         53    0.000E+00                                 T               0         AD User property on blade 3, node 6, -
         54    0.000E+00                                 T               0         AD User property on blade 3, node 7, -
         55    0.000E+00                                 T               0         AD User property on blade 3, node 8, -
         56    0.000E+00                                 T               0         AD User property on blade 3, node 9, -
         57    0.000E+00                                 T               0         AD User property on blade 3, node 10, -
         58    0.000E+00                                 T               0         AD User property on blade 3, node 11, -
         59    0.000E+00                                 T               0         AD User property on blade 3, node 12, -
         60    0.000E+00                                 T               0         AD User property on blade 3, node 13, -
         61    0.000E+00                                 T               0         AD User property on blade 3, node 14, -
         62    0.000E+00                                 T               0         AD User property on blade 3, node 15, -
         63    0.000E+00                                 T               0         AD User property on blade 3, node 16, -
         64    0.000E+00                                 T               0         AD User property on blade 3, node 17, -
         65    0.000E+00                                 T               0         AD User property on blade 3, node 18, -
         66    0.000E+00                                 T               0         AD User property on blade 3, node 19, -

Order of outputs:
        Row   Operating Point                     Rotating Frame? Derivative Order Description
   ---------- ---------------                     --------------- ---------------- -----------
          1    1.200E+01                                 F               0         IfW Wind1VelX, (m/s)
          2    0.000E+00                                 F               0         IfW Wind1VelY, (m/s)
          3    0.000E+00                                 F               0         IfW Wind1VelZ, (m/s)
          4    5.000E+03                                 F               0         SrvD GenPwr, (kW)
          5    4.309E+01                                 F               0         SrvD GenTq, (kN-m)
          6    0.000E+00                                 T               0         ED OoPDefl1, (m)
          7    0.000E+00                                 T               0         ED IPDefl1, (m)
          8    0.000E+00                                 T               0         ED TwstDefl1, (deg)
          9    0.000E+00                                 T               0         ED BldPitch1, (deg)
         10    2.775E-01                                 F               0         ED Azimuth, (deg)
         11    1.210E+01                                 F               0         ED RotSpeed, (rpm)
         12    1.174E+03                                 F               0         ED GenSpeed, (rpm)
         13    0.000E+00                                 F               0         ED TTDspFA, (m)
         14    0.000E+00                                 F               0         ED TTDspSS, (m)
         15    0.000E+00                                 F               0         ED TTDspTwst, (deg)
         16   -2.504E+01                                 T               0         ED Spn2MLxb1, (kN-m)
         17    3.351E+03                                 T               0         ED Spn2MLyb1, (kN-m)
         18    2.949E+02                                 T               0         ED RootFxb1, (kN)
         19   -4.425E+01                                 T               0         ED RootFyb1, (kN)
         20    4.507E+02                                 T               0         ED RootFzb1, (kN)
         21    1.530E+03                                 T               0         ED RootMxb1, (kN-m)
         22    1.152E+04                                 T               0         ED RootMyb1, (kN-m)
         23    8.621E+00                                 T               0         ED RootMzb1, (kN-m)
         24    4.882E+03                                 F               0         ED RotTorq, (kN-m)
         25   -2.775E+03                                 F               0         ED LSSGagMya, (kN-m)
         26    2.734E+02                                 F               0         ED LSSGagMza, (kN-m)
         27    7.880E+02                                 F               0         ED YawBrFxp, (kN)
         28    1.633E+00                                 F               0         ED YawBrFyp, (kN)
         29   -3.494E+03                                 F               0         ED YawBrFzp, (kN)
         30    4.882E+03                                 F               0         ED YawBrMxp, (kN-m)
         31   -7.599E+01                                 F               0         ED YawBrMyp, (kN-m)
         32   -1.716E+02                                 F               0         ED YawBrMzp, (kN-m)
         33    8.236E+02                                 F               0         ED TwrBsFxt, (kN)
         34    1.633E+00                                 F               0         ED TwrBsFyt, (kN)
         35   -6.902E+03                                 F               0         ED TwrBsFzt, (kN)
         36    4.739E+03                                 F               0         ED TwrBsMxt, (kN-m)
         37    7.048E+04                                 F               0         ED TwrBsMyt, (kN-m)
         38   -1.716E+02                                 F               0         ED TwrBsMzt, (kN-m)
         39    7.908E+05                                 F               0         AD RtAeroFxh, (N)
         40    4.741E-01                                 F               0         AD RtAeroCp, (-)
         41    1.507E+03                                 F               0         AD RtAeroFyh, (N)
         42    6.188E+06                                 F               0         AD RtAeroPwr, (W)


Linearized state matrices:

D: 42 x 66
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    0.000E+00  0.000E+00 -1.200E+01  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00
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Best regards!

Dear Dezheng.Zhu,

I was able to reproduce the issue you are reporting and see it in OpenFAST v3.0 and the current dev branch. The aerodynamic derivatives are computed properly in OpenFAST v2.6 and earlier. I’ve now raised this as an issue on the OpenFAST github site: github.com/OpenFAST/openfast/issues/972. Until this bug is fixed, you can revert to OpenFAST v2.6.

Best regards,

Dear Jonkman,
Thank you very much!!!
Best regards!