Hydrodynamic implementation

Dear Jason,
I managed to solve the acceleration problem by extrapolating the mass matrix from the linearization of the system as you suggested (figure 1 on the left). Now, however, I have a problem with the displacement in the of surge and pitch directions.
In fact, as you can see from figure 1 on the right, the trend in my model is very similar to that of FAST, but the latter has a damping of the oscillations despite the absence of the DRAG. This is very strange to me because the speeds of the two models are also very similar to each other (figure 1 in the middle). In addition, I tried to integrate the output speed from FAST with my model and I also get the movements as FAST, so it is not a problem of the integration method used in my model.
Also I set the starting point coincident with the equilibrium point, therefore in static conditions the system is stable.

Is there any explanation that motivates the fact that although I have similar accelerations and speeds, there are these differences on displacements?
And in general why does the system dampen despite the wave forces continue to oscillate around the same values?

Thank you for your help, best regards.

Riccardo.

Dear Riccardo,

I’m not sure. Can you explain your simulation set up? What wind and wave conditions are you simulating and why aerodynamic and hydrodynamic options have you enabled?

Best regards,

Dear Jason,

Thanks for your valuable help. Analyzing the problem in more detail I found that the difference between the two models is given by the Radiation forces.
This is because for my model I used the state space model matrices obtained through FOAMM. These, unlike those used in FAST, generate very little damping.
I also tried to use WAMIT’s output matrices, but these generate instability in my model.
At this point I was wondering if there was a way to extract radiation force matrices through linearization. I tried to linearize by activating only the ElastoDyn and HydroDyn modules through OpenFAST, but I get this error:

"Error using Run_OpenLoop (line 30)
Error reported by S-function ‘FAST_SFunc’ in 'OpenLoop / FAST Nonlinear Wind
Turbine / S-Function ':
FAST_InitializeAll: FAST_Init: ValidateInputData: Linearization is not implemented
for the HydroDyn module. "

So my question is: how do I set up input files to get what I need?

Best regards,

Riccardo.

Dear Riccardo,

The capability to linearize an OpenFAST model with HydroDyn enabled was recently implemented and merged into the dev branch of OpenFAST–see: nrel.gov/docs/fy19osti/71865.pdf (the MATLAB-based preprocessor SS_Fitting was developed to support the fitting of a linear state-space model).

Best regards,

Dear Jason,

Thank you a lot for your help. As far as the damped behavior of FAST is concerned, I cannot understand the physical reason why the system has a damped movement until reaching the steady-state value equal to zero, although it continues to undergo the excitation force of the waves all the time .
As for the test settings, the HydroDyn input files and the ‘.fst’ file are shown below, while the wind has been set to zero.

------- OpenFAST example INPUT FILE ------------------------------------------- FAST Certification Test #24: NREL 5.0 MW Baseline Wind Turbine with OC3 Hywind Configuration, for use in offshore analysis ---------------------- SIMULATION CONTROL -------------------------------------- True Echo - Echo input data to <RootName>.ech (flag) "FATAL" AbortLevel - Error level when simulation should abort (string) {"WARNING", "SEVERE", "FATAL"} 1200 TMax - Total run time (s) 0.05 DT - Recommended module time step (s) 1 InterpOrder - Interpolation order for input/output time history (-) {1=linear, 2=quadratic} 0 NumCrctn - Number of correction iterations (-) {0=explicit calculation, i.e., no corrections} 1.5 DT_UJac - Time between calls to get Jacobians (s) 1E+06 UJacSclFact - Scaling factor used in Jacobians (-) ---------------------- FEATURE SWITCHES AND FLAGS ------------------------------ 1 CompElast - Compute structural dynamics (switch) {1=ElastoDyn; 2=ElastoDyn + BeamDyn for blades} 1 CompInflow - Compute inflow wind velocities (switch) {0=still air; 1=InflowWind; 2=external from OpenFOAM} 0 CompAero - Compute aerodynamic loads (switch) {0=None; 1=AeroDyn v14; 2=AeroDyn v15} 0 CompServo - Compute control and electrical-drive dynamics (switch) {0=None; 1=ServoDyn} 1 CompHydro - Compute hydrodynamic loads (switch) {0=None; 1=HydroDyn} 0 CompSub - Compute sub-structural dynamics (switch) {0=None; 1=SubDyn; 2=External Platform MCKF} 1 CompMooring - Compute mooring system (switch) {0=None; 1=MAP++; 2=FEAMooring; 3=MoorDyn; 4=OrcaFlex} 0 CompIce - Compute ice loads (switch) {0=None; 1=IceFloe; 2=IceDyn} ---------------------- INPUT FILES --------------------------------------------- "NRELOffshrBsline5MW_OC3Hywind_ElastoDyn.dat" EDFile - Name of file containing ElastoDyn input parameters (quoted string) "5MW_Baseline/NRELOffshrBsline5MW_BeamDyn.dat" BDBldFile(1) - Name of file containing BeamDyn input parameters for blade 1 (quoted string) "5MW_Baseline/NRELOffshrBsline5MW_BeamDyn.dat" BDBldFile(2) - Name of file containing BeamDyn input parameters for blade 2 (quoted string) "5MW_Baseline/NRELOffshrBsline5MW_BeamDyn.dat" BDBldFile(3) - Name of file containing BeamDyn input parameters for blade 3 (quoted string) "5MW_Baseline/NRELOffshrBsline5MW_InflowWind_12mps.dat" InflowFile - Name of file containing inflow wind input parameters (quoted string) "NRELOffshrBsline5MW_OC3Hywind_AeroDyn15.dat" AeroFile - Name of file containing aerodynamic input parameters (quoted string) "NRELOffshrBsline5MW_OC3Hywind_ServoDyn.dat" ServoFile - Name of file containing control and electrical-drive input parameters (quoted string) "NRELOffshrBsline5MW_OC3Hywind_HydroDyn.dat" HydroFile - Name of file containing hydrodynamic input parameters (quoted string) "unused" SubFile - Name of file containing sub-structural input parameters (quoted string) "NRELOffshrBsline5MW_OC3Hywind_MAP.dat" MooringFile - Name of file containing mooring system input parameters (quoted string) "unused" IceFile - Name of file containing ice input parameters (quoted string) ---------------------- OUTPUT -------------------------------------------------- True SumPrint - Print summary data to "<RootName>.sum" (flag) 1 SttsTime - Amount of time between screen status messages (s) 99999 ChkptTime - Amount of time between creating checkpoint files for potential restart (s) 0.05 DT_Out - Time step for tabular output (s) (or "default") 0 TStart - Time to begin tabular output (s) 2 OutFileFmt - Format for tabular (time-marching) output file (switch) {1: text file [<RootName>.out], 2: binary file [<RootName>.outb], 3: both} True TabDelim - Use tab delimiters in text tabular output file? (flag) {uses spaces if false} "ES10.3E2" OutFmt - Format used for text tabular output, excluding the time channel. Resulting field should be 10 characters. (quoted string) ---------------------- LINEARIZATION ------------------------------------------- False Linearize - Linearization analysis (flag) 2 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] [unused if Linearize=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] ---------------------- VISUALIZATION ------------------------------------------ 0 WrVTK - VTK visualization data output: (switch) {0=none; 1=initialization data only; 2=animation} 2 VTK_type - Type of VTK visualization data: (switch) {1=surfaces; 2=basic meshes (lines/points); 3=all meshes (debug)} [unused if WrVTK=0] false VTK_fields - Write mesh fields to VTK data files? (flag) {true/false} [unused if WrVTK=0] 15 VTK_fps - Frame rate for VTK output (frames per second){will use closest integer multiple of DT} [used only if WrVTK=2]

------- HydroDyn v2.03.* Input File --------------------------------------------
NREL 5.0 MW offshore baseline floating platform HydroDyn input properties for the OC3 Hywind.
False            Echo           - Echo the input file data (flag)
---------------------- ENVIRONMENTAL CONDITIONS --------------------------------
          1025   WtrDens        - Water density (kg/m^3)
           320   WtrDpth        - Water depth (meters)
             0   MSL2SWL        - Offset between still-water level and mean sea level (meters) [positive upward; unused when WaveMod = 6; must be zero if PotMod=1 or 2]
---------------------- WAVES ---------------------------------------------------
             2   WaveMod        - Incident wave kinematics model {0: none=still water, 1: regular (periodic), 1P#: regular with user-specified phase, 2: JONSWAP/Pierson-Moskowitz spectrum (irregular), 3: White noise spectrum (irregular), 4: user-defined spectrum from routine UserWaveSpctrm (irregular), 5: Externally generated wave-elevation time series, 6: Externally generated full wave-kinematics time series [option 6 is invalid for PotMod/=0]} (switch)
             0   WaveStMod      - Model for stretching incident wave kinematics to instantaneous free surface {0: none=no stretching, 1: vertical stretching, 2: extrapolation stretching, 3: Wheeler stretching} (switch) [unused when WaveMod=0 or when PotMod/=0]
          3630   WaveTMax       - Analysis time for incident wave calculations (sec) [unused when WaveMod=0; determines WaveDOmega=2Pi/WaveTMax in the IFFT]
          0.25   WaveDT         - Time step for incident wave calculations     (sec) [unused when WaveMod=0; 0.1<=WaveDT<=1.0 recommended; determines WaveOmegaMax=Pi/WaveDT in the IFFT]
          1.25   WaveHs         - Significant wave height of incident waves (meters) [used only when WaveMod=1, 2, or 3]
           4.5   WaveTp         - Peak-spectral period of incident waves       (sec) [used only when WaveMod=1 or 2]
"DEFAULT"        WavePkShp      - Peak-shape parameter of incident wave spectrum (-) or DEFAULT (string) [used only when WaveMod=2; use 1.0 for Pierson-Moskowitz]
             0   WvLowCOff      - Low  cut-off frequency or lower frequency limit of the wave spectrum beyond which the wave spectrum is zeroed (rad/s) [unused when WaveMod=0, 1, or 6]
           500   WvHiCOff       - High cut-off frequency or upper frequency limit of the wave spectrum beyond which the wave spectrum is zeroed (rad/s) [unused when WaveMod=0, 1, or 6]
             0   WaveDir        - Incident wave propagation heading direction                         (degrees) [unused when WaveMod=0 or 6]
             0   WaveDirMod     - Directional spreading function {0: none, 1: COS2S}                  (-)       [only used when WaveMod=2,3, or 4]
             1   WaveDirSpread  - Wave direction spreading coefficient ( > 0 )                        (-)       [only used when WaveMod=2,3, or 4 and WaveDirMod=1]
             1   WaveNDir       - Number of wave directions                                           (-)       [only used when WaveMod=2,3, or 4 and WaveDirMod=1; odd number only]
            90   WaveDirRange   - Range of wave directions (full range: WaveDir +/- 1/2*WaveDirRange) (degrees) [only used when WaveMod=2,3,or 4 and WaveDirMod=1]
     123456789   WaveSeed(1)    - First  random seed of incident waves [-2147483648 to 2147483647]    (-)       [unused when WaveMod=0, 5, or 6]
    1011121314   WaveSeed(2)    - Second random seed of incident waves [-2147483648 to 2147483647]    (-)       [unused when WaveMod=0, 5, or 6]
TRUE             WaveNDAmp      - Flag for normally distributed amplitudes                            (flag)    [only used when WaveMod=2, 3, or 4]
""               WvKinFile      - Root name of externally generated wave data file(s)        (quoted string)    [used only when WaveMod=5 or 6]
             1   NWaveElev      - Number of points where the incident wave elevations can be computed (-)       [maximum of 9 output locations]
             0   WaveElevxi     - List of xi-coordinates for points where the incident wave elevations can be output (meters) [NWaveElev points, separated by commas or white space; usused if NWaveElev = 0]
             0   WaveElevyi     - List of yi-coordinates for points where the incident wave elevations can be output (meters) [NWaveElev points, separated by commas or white space; usused if NWaveElev = 0]
---------------------- 2ND-ORDER WAVES ----------------------------------------- [unused with WaveMod=0 or 6]
FALSE            WvDiffQTF      - Full difference-frequency 2nd-order wave kinematics (flag)
FALSE            WvSumQTF       - Full summation-frequency  2nd-order wave kinematics (flag)
             0   WvLowCOffD     - Low  frequency cutoff used in the difference-frequencies (rad/s) [Only used with a difference-frequency method]
           3.5   WvHiCOffD      - High frequency cutoff used in the difference-frequencies (rad/s) [Only used with a difference-frequency method]
           0.1   WvLowCOffS     - Low  frequency cutoff used in the summation-frequencies  (rad/s) [Only used with a summation-frequency  method]
           3.5   WvHiCOffS      - High frequency cutoff used in the summation-frequencies  (rad/s) [Only used with a summation-frequency  method]
---------------------- CURRENT ------------------------------------------------- [unused with WaveMod=6]
             0   CurrMod        - Current profile model {0: none=no current, 1: standard, 2: user-defined from routine UserCurrent} (switch)
             0   CurrSSV0       - Sub-surface current velocity at still water level  (m/s) [used only when CurrMod=1]
"DEFAULT"        CurrSSDir      - Sub-surface current heading direction (degrees) or DEFAULT (string) [used only when CurrMod=1]
            20   CurrNSRef      - Near-surface current reference depth            (meters) [used only when CurrMod=1]
             0   CurrNSV0       - Near-surface current velocity at still water level (m/s) [used only when CurrMod=1]
             0   CurrNSDir      - Near-surface current heading direction         (degrees) [used only when CurrMod=1]
             0   CurrDIV        - Depth-independent current velocity                 (m/s) [used only when CurrMod=1]
             0   CurrDIDir      - Depth-independent current heading direction    (degrees) [used only when CurrMod=1]
---------------------- FLOATING PLATFORM --------------------------------------- [unused with WaveMod=6]
             1   PotMod         - Potential-flow model {0: none=no potential flow, 1: frequency-to-time-domain transforms based on WAMIT output, 2: fluid-impulse theory (FIT)} (switch)
"5MW_Baseline/HydroData/Spar"    PotFile        - Root name of potential-flow model data; WAMIT output files containing the linear, nondimensionalized, hydrostatic restoring matrix (.hst), frequency-dependent hydrodynamic added mass matrix and damping matrix (.1), and frequency- and direction-dependent wave excitation force vector per unit wave amplitude (.3) (quoted string) [MAKE SURE THE FREQUENCIES INHERENT IN THESE WAMIT FILES SPAN THE PHYSICALLY-SIGNIFICANT RANGE OF FREQUENCIES FOR THE GIVEN PLATFORM; THEY MUST CONTAIN THE ZERO- AND INFINITE-FREQUENCY LIMITS!]
             1   WAMITULEN      - Characteristic body length scale used to redimensionalize WAMIT output (meters) [only used when PotMod=1]
       8078.4575   PtfmVol0       - Displaced volume of water when the platform is in its undisplaced position (m^3) [only used when PotMod=1; USE THE SAME VALUE COMPUTED BY WAMIT AS OUTPUT IN THE .OUT FILE!]
             0   PtfmCOBxt      - The xt offset of the center of buoyancy (COB) from the platform reference point (meters)  [only used when PotMod=1]
             0   PtfmCOByt      - The yt offset of the center of buoyancy (COB) from the platform reference point (meters)  [only used when PotMod=1]
             2   RdtnMod        - Radiation memory-effect model {0: no memory-effect calculation, 1: convolution, 2: state-space} (switch) [only used when PotMod=1; STATE-SPACE REQUIRES *.ss INPUT FILE]
            60   RdtnTMax       - Analysis time for wave radiation kernel calculations (sec) [only used when PotMod=1; determines RdtnDOmega=Pi/RdtnTMax in the cosine transform; MAKE SURE THIS IS LONG ENOUGH FOR THE RADIATION IMPULSE RESPONSE FUNCTIONS TO DECAY TO NEAR-ZERO FOR THE GIVEN PLATFORM!]
          0.05   RdtnDT         - Time step for wave radiation kernel calculations (sec) [only used when PotMod=1; DT<=RdtnDT<=0.1 recommended; determines RdtnOmegaMax=Pi/RdtnDT in the cosine transform]
---------------------- 2ND-ORDER FLOATING PLATFORM FORCES ---------------------- [unused with WaveMod=0 or 6, or PotMod=0 or 2]
             0   MnDrift        - Mean-drift 2nd-order forces computed                                       {0: None; [7, 8, 9, 10, 11, or 12]: WAMIT file to use} [Only one of MnDrift, NewmanApp, or DiffQTF can be non-zero]
             0   NewmanApp      - Mean- and slow-drift 2nd-order forces computed with Newman's approximation {0: None; [7, 8, 9, 10, 11, or 12]: WAMIT file to use} [Only one of MnDrift, NewmanApp, or DiffQTF can be non-zero. Used only when WaveDirMod=0]
             0   DiffQTF        - Full difference-frequency 2nd-order forces computed with full QTF          {0: None; [10, 11, or 12]: WAMIT file to use}          [Only one of MnDrift, NewmanApp, or DiffQTF can be non-zero]
             0   SumQTF         - Full summation -frequency 2nd-order forces computed with full QTF          {0: None; [10, 11, or 12]: WAMIT file to use}
---------------------- FLOATING PLATFORM FORCE FLAGS  -------------------------- [unused with WaveMod=6]
True             PtfmSgF        - Platform horizontal surge translation force (flag) or DEFAULT
True             PtfmSwF        - Platform horizontal sway translation force (flag) or DEFAULT
True             PtfmHvF        - Platform vertical heave translation force (flag) or DEFAULT
True             PtfmRF         - Platform roll tilt rotation force (flag) or DEFAULT
True             PtfmPF         - Platform pitch tilt rotation force (flag) or DEFAULT
True             PtfmYF         - Platform yaw rotation force (flag) or DEFAULT
---------------------- PLATFORM ADDITIONAL STIFFNESS AND DAMPING  --------------
             0             0             0             0             0             0   AddF0    - Additional preload (N, N-m)
             0             0             0             0             0             0   AddCLin  - Additional linear stiffness (N/m, N/rad, N-m/m, N-m/rad)
             0             0             0             0             0             0
             0             0             0             0             0             0
             0             0             0             0             0             0
             0             0             0             0             0             0
             0             0             0             0             0             0
             0             0             0             0             0             0   AddBLin  - Additional linear damping(N/(m/s), N/(rad/s), N-m/(m/s), N-m/(rad/s))
             0             0             0             0             0             0
             0             0             0             0             0             0
             0             0             0             0             0             0
             0             0             0             0             0             0
             0             0             0             0             0             0
             0             0             0             0             0             0   AddBQuad - Additional quadratic drag(N/(m/s)^2, N/(rad/s)^2, N-m(m/s)^2, N-m/(rad/s)^2)
             0             0             0             0             0             0
             0             0             0             0             0             0
             0             0             0             0             0             0
             0             0             0             0             0             0
             0             0             0             0             0             0
---------------------- AXIAL COEFFICIENTS --------------------------------------
             1   NAxCoef        - Number of axial coefficients (-)
AxCoefID  AxCd     AxCa     AxCp
   (-)    (-)      (-)      (-)
    1     0.00     0.00     1.00
---------------------- MEMBER JOINTS -------------------------------------------
             4   NJoints        - Number of joints (-)   [must be exactly 0 or at least 2]
JointID   Jointxi     Jointyi     Jointzi  JointAxID   JointOvrlp   [JointOvrlp= 0: do nothing at joint, 1: eliminate overlaps by calculating super member]
   (-)     (m)         (m)         (m)        (-)       (switch)
    1     0.00000     0.00000  -120.00000      1            0
    2     0.00000     0.00000   -12.00000      1            0
    3     0.00000     0.00000    -4.00000      1            0
    4     0.00000     0.00000    10.00000      1            0
---------------------- MEMBER CROSS-SECTION PROPERTIES -------------------------
             2   NPropSets      - Number of member property sets (-)
PropSetID    PropD         PropThck
   (-)        (m)            (m)
    1        9.40000        0.00010
    2        6.50000        0.00010
---------------------- SIMPLE HYDRODYNAMIC COEFFICIENTS (model 1) --------------
     SimplCd    SimplCdMG    SimplCa    SimplCaMG    SimplCp    SimplCpMG   SimplAxCa  SimplAxCaMG  SimplAxCp   SimplAxCpMG
       (-)         (-)         (-)         (-)         (-)         (-)         (-)         (-)         (-)         (-)
       0.00        0.00        0.00        0.00       0.00        0.00        0.00        0.00        0.00        0.00 
---------------------- DEPTH-BASED HYDRODYNAMIC COEFFICIENTS (model 2) ---------
             0   NCoefDpth       - Number of depth-dependent coefficients (-)
Dpth      DpthCd   DpthCdMG   DpthCa   DpthCaMG       DpthCp   DpthCpMG   DpthAxCa   DpthAxCaMG       DpthAxCp   DpthAxCpMG
(m)       (-)      (-)        (-)      (-)            (-)      (-)          (-)        (-)              (-)         (-)
---------------------- MEMBER-BASED HYDRODYNAMIC COEFFICIENTS (model 3) --------
             0   NCoefMembers       - Number of member-based coefficients (-)
MemberID    MemberCd1     MemberCd2    MemberCdMG1   MemberCdMG2    MemberCa1     MemberCa2    MemberCaMG1   MemberCaMG2    MemberCp1     MemberCp2    MemberCpMG1   MemberCpMG2   MemberAxCa1   MemberAxCa2  MemberAxCaMG1 MemberAxCaMG2  MemberAxCp1  MemberAxCp2   MemberAxCpMG1   MemberAxCpMG2
   (-)         (-)           (-)           (-)           (-)           (-)           (-)           (-)           (-)           (-)           (-)           (-)           (-)           (-)           (-)           (-)           (-)           (-)           (-)           (-)           (-)
-------------------- MEMBERS -------------------------------------------------
             3   NMembers       - Number of members (-)
MemberID  MJointID1  MJointID2  MPropSetID1  MPropSetID2  MDivSize   MCoefMod  PropPot   [MCoefMod=1: use simple coeff table, 2: use depth-based coeff table, 3: use member-based coeff table] [ PropPot/=0 if member is modeled with potential-flow theory]
  (-)        (-)        (-)         (-)          (-)        (m)      (switch)   (flag)
    1         1          2           1            1         0.5000      1        TRUE
    2         2          3           1            2         0.5000      1        TRUE
    3         3          4           2            2         0.5000      1        TRUE
---------------------- FILLED MEMBERS ------------------------------------------
             0   NFillGroups     - Number of filled member groups (-) [If FillDens = DEFAULT, then FillDens = WtrDens; FillFSLoc is related to MSL2SWL]
FillNumM FillMList             FillFSLoc     FillDens
(-)      (-)                   (m)           (kg/m^3)
---------------------- MARINE GROWTH -------------------------------------------
             0   NMGDepths      - Number of marine-growth depths specified (-)
MGDpth     MGThck       MGDens
(m)        (m)         (kg/m^3)
---------------------- MEMBER OUTPUT LIST --------------------------------------
             0   NMOutputs      - Number of member outputs (-) [must be < 10]
MemberID   NOutLoc    NodeLocs [NOutLoc < 10; node locations are normalized distance from the start of the member, and must be >=0 and <= 1] [unused if NMOutputs=0]
  (-)        (-)        (-)
---------------------- JOINT OUTPUT LIST ---------------------------------------
             0   NJOutputs      - Number of joint outputs [Must be < 10]
   0           JOutLst        - List of JointIDs which are to be output (-)[unused if NJOutputs=0]
---------------------- OUTPUT --------------------------------------------------
True             HDSum          - Output a summary file [flag]
False            OutAll         - Output all user-specified member and joint loads (only at each member end, not interior locations) [flag]
             2   OutSwtch       - Output requested channels to: [1=Hydrodyn.out, 2=GlueCode.out, 3=both files]
"ES11.4e2"       OutFmt         - Output format for numerical results (quoted string) [not checked for validity!]
"A11"            OutSFmt        - Output format for header strings (quoted string) [not checked for validity!]
---------------------- OUTPUT CHANNELS -----------------------------------------

Best regards,

Riccardo.

Dear Riccardo,

It looks like you’ve disabled aerodynamic loads, viscous drag, additional platform damping, and mooring damping in your model. So, the only remaining damping comes from wave radiation. It looks like you’ve selected RdtnMod = 2, i.e., the state-space-based radiation damping option. The damping in this model will depend on how you’ve set the linear state-space radiation model.

Best regards,

Dear Jason,

Thank you for the reply. To obtain the matrices A, B, C, D related to the linear state-space radiation model I used the “ss_fitting.m” function.
Is there any way to remove the damping effect from the state-space model settings?
The input file used is the following:

%%---- SS Fitting Options ----%%
HydroData/spar          % Rad.FileName:  Wamit Files name and Location
[1 1 1 1 1 1]           % gp.DoF:        Degree of Freedom enabled
[0.0 2.5]               % Rad.twr:       Typical local frequencies range (rad/s)
1                       % Rad.wwf:       Frequencies weighting factors
3                       % Rad.tfi:       Indentification Method: 1-Freq Ident; 2- FDI; 3- TD-Ls; 4-TD-Realization.
0.97                    % Rad.fit:       Fit required for the parametric model (max. recomended 0.99)
1                       % Rad.ppmf:      Plot the parametric model fit (0 or 1)
0                       % Rad.fmt:       Manual (1) or Automatic(0) order reduction (Only if method=4)

Best regards,
Riccardo.

Dear Ricardo,

Zeroing out the C matrix in the linear state-space wave-radiation model will eliminate the wave-radiation damping.

Best regards,

Dear Jason,
I’m having trouble switching between hydrodynamics alone in my model and the complete hydrodynamics + aerodynamics system. Starting from the fact that the results between my model and FAST in hydrodynamics alone are the same, and that the same applies to the study of aerodynamics alone. Once I try to join the two parts I get results regarding the accelerations at the base which are totally different, the equation I am using is the following:

[M_swl] [A_swl] = [Faero_swl] + [HydroF] - [Fmoor_swl] - [Gravity + restoring moment]
Where is it:
-M_swl: mass matrix in the swl refence frame;
-A_swl: acceleration in the swl refence frame;
-Faero_swl: Tower base forces purified of the tower’s inertia term and transported in the swl refence frame;
-HydroF: HydroDynamic forces
-Fmoor_swl: Mooring forces in the swl refence frame;
Each term of the equation is equal to the corresponding one in the FAST outputs, so it occurs to me that the equation is wrong or the mass matrix changes from the only hydrodynamics that does not consider the movement of the turbine.
As for the first hypothesis, I ran a test by activating only the DOFs relating to the 3 displacements (Surge, Sway, Heave), and the results return perfectly, so I think that the equation is right.
so my question is:
can I use the mass matrix of the hydrodynamics alone (Aerodyn = 0 in the glue code input file) also for the complete system?
If not, what changes do I need to make?

Thanks a lot for your help.
Best regards,
Riccardo

Dear Riccardo,

The body mass matrix does not change with the inclusion of aerodynamics.

Of course, as discussed above, the rotation-related terms result in a time-varying mass matrix; and there are also nonlinear rotation-related inertial terms that exist, but do not show up in your equation (which may explain why your solution only works when you disable the rotational DOFs).

Best regards

Dear Jason,
thanks for your prompt reply. as you suggested I made the changes you reported to me, in particular for the mass matrix that varies over time I used the same matrix of the previous places (therefore of the total system) to which I made the transformations indicated in the post of: May 04, 2020.
I also did a test using the FAST outputs in the equation of the previous post (I added the nonlinear rotation-related inertial terms), where for the tower forces I used: [TwrBsFxt, TwrBsFyt, TwrBsFzt, TwrBsMxt, TwrBsMyt, TwrBsMzt] reported in the swl reference frame.
But doing this does not return the results anyway. I doubt that in this way I consider the inertia of the turbine twice (once in the TwrBs and once in the mass matrix of the complete system). Is my assumption correct?

Thank you again for your valuable help. Best regards,

Riccardo.

Dear Riccardo,

Yes, the ElastoDyn tower-base load outputs (TwrBsFxt, etc.) include contributions from mass/inertia of the rotor, nacelle, and tower, so, you’d be double counting those terms. Instead, you’d want to express the aerodynamic applied loads relative to the platform reference point (0,0,0).

Best regards,

Dear Jason,

I was wondering if there are any output of FAST that express the aerodynamic applied loads relative to the platform reference point (0,0,0).

Thanks for your reply. Best regards,
Riccardo.

Dear Riccardo,

No, the aerodynamic applied loads are only output from AeroDyn v15 in the hub coordinate system (RtAeroFxh, etc.). You’d have to rotate these to the global coordinate system (accounting for deflection of the support structure and shaft tilt) and add the moment arm.

Best regards,

Dear Jason,
Starting from Test 24, I’m trying to verify the loads in the 6 DOFs in according to the formula:
M * a = Fhydro - Fmoor + Ftower - Fnonlinear - Frestoring

where is it:

M = variable mass matrix based on the position of the platform, obtained as indicated in the post reported here (11 July 2020)

a = [‘PtfmTAxi’, ‘PtfmTAyi’, ‘PtfmTAzi’, ‘PtfmRAxi’, ‘PtfmRAyi’, ‘PtfmRAzi’]

Fhydro = [‘HydroFxi’, ‘HydroFyi’, ‘HydroFzi’, ‘HydroMxi’, ‘HydroMyi’, ‘HydroMzi’]

Fmoor = [Fx [1] + Fx [2] + Fx [3] + Fx [4] + Fx [5] + Fx [6], Fy [1] + Fy [2] + Fy [3] + Fy [ 4] + Fy [5] + Fy [6], Fz [1] + Fz [2] + Fz [3] + Fz [4] + Fz [5] + Fz [6], Mx_moor, My_moor, Mz_moor]
with Mx_moor, My_moor, Mz_moor moments of transport of forces from Map ++ in (0,0,0)

Ftower forces and moments obtained starting at the rotor exits:
Fx_tow = ‘RtAeroFxh’
Fy_tow = ‘RtAeroFyh’ * cos (‘Azimuth’) - ‘RtAeroFzh’ * sin (‘Azimuth’)
Fz_tow = ‘RtAeroFzh’ * cos (‘Azimuth’) + ‘RtAeroFyh’ * sin (‘Azimuth’)
Mx_tow = ‘RotTorq’ * 1000
My_tow = ‘RtAeroMyh’ * cos (‘Azimuth’) - ‘RtAeroMzh’ * sin (‘Azimuth’)
Mz_tow = ‘RtAeroMzh’ * cos (‘Azimuth’) + ‘RtAeroMyh’ * sin (‘Azimuth’)
and were then rotated in the inertial reference system, with the addition of the transport moments and the weight of the turbine to have the forces at the base of the tower in (0,0,0)

Fnonlinear = given by omega x (omega x r_cm * mass) and omega x I dot omega, with
omega = [‘PtfmRVxi’, ‘PtfmRVyi’, ‘PtfmRVzi’],
r_cm * mass = [M (6,2), M (4,3), M (5,1)]
I = [M (4.4), M (4.5), M (4.6); M (5.4), M (5.5), M (5.6); M (6.4), M (6.5), M (6.6);]

Frestoring = where the weight of the platform and gravity restoring moments are considered [0, 0, M_plat, -M (5,1) * rx + M (6,2) * rz, -M (5,1) * ry + M (4.3) * rz] * g
with M = mass matrix variable according to the position

Comparing the sum of the loads in the 6 DOFs with the results in the 6 DOFs of the product M * a I obtain small differences, as shown in the figure.
(for example, I compared for the resultant in x:
M (1,1) * ‘PtfmTAxi’ + M (1,2) * ‘PtfmTAyi’ + M (1,3) * ‘PtfmTAzi’ + M (1,4) * ‘PtfmRAxi’ + M (1,5) * ‘PtfmRAyi’ + M (1,6) * ‘PtfmRAzi’
with
‘HydroFxi’ - Fmoor_x + Ftower_x - Fnonlinear_x - Frestoring_x)

Could you tell me what they are caused by?

All the rotations are expressed in Radiants.

Thank you a lot. Best regards,

Riccardo.


Dear Riccardo,

Indeed, your results are quite close, with only some small differences. I don’t see any obvious errors in your approach, but I do have a few questions:

  • Why are you using RotTorq rather than RtAeroMxh?
  • In Frestoring, you haven’t stated what M_plat is (zero?) and the value of M should not change with displacement in this linearized equation, even though that is implied. That said, ElastoDyn does include some amount of nonlinearity in this equation, i.e. using the displaced center of mass using the transformation matrix given in Eq. (2) in my 2009 Wind Energy paper: onlinelibrary.wiley.com/doi/abs/10.1002/we.347.
  • I can’t check all of the details because they are not in your post (e.g., how the mass matrix changes with displacement, how Ftower is transformed to global coordinates, how MX_moor, etc. are calculated).
  • Could the problem simply be that of numerical round-off in the variables you are comparing?

Best regards,

Dear Jason,

Thanks for your prompt reply.

  • I used RotTrq to consider also the inertia of the rotor (I noted that in an Onshore Test the TwrBsMx= RotTrq+transport moments);
  • M_plat is the mass platform (M_plat=7466330 kg) since I consider the turbine weight in Fz_tower;
  • Mooring moments are obtained by multiply C_rot x F where:

-C_rot= X/Y/Z coordinates of the fairlead respect (0,0,0) in each time step.

-I obtained the mass matrix relative to the center of mass through the following inverse transformation: Mcg = (TransMat^T)^-1 * M_swl * TransMat^-1
(where TransMat is the one indicated in this topic "http://forums.nrel.gov/t/oc3-hywind-raos/1085/1 where the
inputs of the rotation matrix are those in still water). Then the mass matrix (in 0 0 0) relative to the position of the system is obtained by applying the
direct transformation M_swl = TransMat^T * Mcg * TransMat, using the current positions of Cg as the input of TransMat.

-We consider [Fx_tow Fy_tow Fz_tow Mx_tow My_tow Mz_tow] applied in (0,0,Rotor height) because I set: OverHang=ShftGagL=NacCMxn=NcIMUxn=0 so
I transported forces and moments in the system frame (0,0,0) integral to the structure then considering the platform rotation.

by setting the parameters OverHang=ShftGagL=NacCMxn=NcIMUxn=0, is it possible that the mass matrix changes?

Best regards,
Riccardo.

Dear Riccardo,

Just a few comments:

  • I would use RtAeroMxh instead of RotTorq so as to not double count any inertial terms.
  • M_plat makes sense; thanks for clarifying.
  • I follow your calculation of M_swl, but this assumes linearity of the structural model. Again, ElastoDyn includes some nonlinearity in the platform rotations as I indicated in my prior post, which may result in some small differences to what you are calculating.
  • For Ftower, presumably you also consider the shaft tilt, unless this has also been zeroed.
  • I’m not sure I understand your last question about the mass matrix changes.

Best regards,

Dear Jason,
Thanks for the reply and for your help. First of all I forgot to clarify that in the Test I considered the rigid body, so for this reason I don’t have considered any nonlinearities. If there are non-linearities also for the rigid body case, how can I take them into account?
As for the mass matrix, I started from the one indicated in the post previously reported. However, I suspect that considering Overhang & Co. to be null, the moments of inertia and therefore the total mass matrix M_cg, as well as the position of the center of mass, can change.

Best regards,
Riccardo.

Dear Riccardo,

Even the rigid body contains many nonlinear terms; that is, each term in Fhydro, Fmoor, Ftower, Fnonlinear, and Frestoring includes nonlinearities. Some of the nonlinearities are included in HydroDyn, MAP++, AeroDyn, etc. whose outputs you are using.

One of the nonlinearities I gather you are missing in your equations is how the rotation/orientation of the rigid body is handled in ElastoDyn, i.e. per Eq. (2) in the Wind Energy paper I referenced. This will impact, e.g., how aerodynamic loads are transferred to global in Ftower, how the CG is determined in Fnonlinear and Frestoring.

Best regards,