Hydrodynamic implementation

Discuss wave-energy device design and modeling

Moderator: Bonnie.Jonkman

Riccardo.Caradonna
Posts: 34
Joined: Mon May 04, 2020 3:31 am
Organization: Politecnico di Torino
Location: Italia

Hydrodynamic implementation

Postby Riccardo.Caradonna » Fri Jul 03, 2020 10:57 am

Dear Jason,
I'm trying to implement the hydrodynamics of the OC3 spar buoy on simulink.
To verify that my model is correct, I verified it by doing a test with the same input with FAST, but finding differences.
I therefore created a simulink in which I insert positions, speeds and accelerations detected in the Fast test, checking the forces exiting each block (figure 2). In this way I observed the following things:
- The radiation forces coming out of my model correspond to the outputs of Fast ('RdtnFxi', 'RdtnFyi', 'RdtnFzi', .'RdtnMxi ',.' RdtnMyi ',' RdtnMzi ')
- The hydrostatic forces exiting my model correspond to the Fast outputs ('HdrStcFxi', 'HdrStcFyi', .., 'HdrStcMzi')
- I used the wave forces of the Fast test 'WavesFxi', 'WavesFyi' ..., 'WavesMzi' as input to my model
- I checked the mooring forces, making sure that the tensions on the 6 lines of my model corresponded to those coming out of MAP (T [1], T [2], .. T [6]). However, the 3 forces and the 3 moments resulting in the global reference system are exiting the MOORING block.
- I applied gravity along z, using the mass indicated in the topic viewtopic.php? F = 3 & t = 748 as the mass
-I used the same topic to build the mass matrix M (see figure 1) which, multiplied by the accelerations of the test, should give the inertial loads.

The problem is that the resultant of these forces does not result in 0 (figure 3 on the left). Figure 3 on the right, shows the trend of the forces without the contribution of inertia (i.e. the only contribution that I have not been able to compare with the FAST outputs).
For now I would like to focus on the forces, since there is likely to be some translation problems of the reference systems along z (between Fmoor and Fhydro)
My question is whether I have forgotten any contributions.

In the follow is also the input file of Hydrodyn used to carry out the simulation in FAST:


------- 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)
250 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)
"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]
8029.21 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
(-) (-) (-) (-) (-) (-) (-) (-) (-) (-)
0.0 0.00 0.00 0.00 1.00 1.00 1.00 1.00 1.00 1.00
---------------------- 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!]
Attachments
fig3.jpeg
fig3.jpeg (139.88 KiB) Viewed 2201 times
fig2.jpeg
fig2.jpeg (92.67 KiB) Viewed 2201 times
fig1.jpeg
fig1.jpeg (28.97 KiB) Viewed 2201 times

Jason.Jonkman
Posts: 5763
Joined: Thu Nov 03, 2005 4:38 pm
Location: Boulder, CO
Contact:

Re: Hydrodynamic implementation

Postby Jason.Jonkman » Mon Jul 06, 2020 7:29 am

Dear Riccardo,

I'm not sure I understand what you are plotting to really comment.

I would suggest simplifying the model to debug, e.g., do you get the results you expect for a still-water simulation (WaveMod = 0)?

One thing I see missing in your block is the gravitational restoring from body weight, unless you've included that in your hydrostatic stiffness matrix (which is not where that term is accounted for in FAST). But this will effect the moments, not the forces.

Best regards,
Jason Jonkman, Ph.D.
Senior Engineer | National Wind Technology Center (NWTC)

National Renewable Energy Laboratory (NREL)
15013 Denver West Parkway | Golden, CO 80401
+1 (303) 384 – 7026 | Fax: +1 (303) 384 – 6901
nwtc.nrel.gov

Riccardo.Caradonna
Posts: 34
Joined: Mon May 04, 2020 3:31 am
Organization: Politecnico di Torino
Location: Italia

Re: Hydrodynamic implementation

Postby Riccardo.Caradonna » Mon Jul 06, 2020 8:46 am

Dear Jason,

Thanks for your prompt reply. I will try to put wavemod = 0. My initial question can be summarized as follows: for hydrodynamics I use the following Cummins law, written using the FAST outputs with irregular waves and assuming no forces from the turbine:
M a = ((RdntFxi, RdntFyi, ... RdntMzi) + (HdrStcFxi, HdrStcFyi, ... HdrStcMzi) + (WavesFxi, WavesFyi, ... WavesMzi)) + Fmoor + Mg = (HydroFxi, HydroFyi, ... HydroMzi) + Fmoor + Mg

where a = acceleration in the 6 dof, M mass matrix.
I was also able to verify equality
(HydroFxi, HydroFyi, ... HydroMzi) = (RdntFxi, RdntFyi, ... RdntMzi) + (HdrStcFxi, HdrStcFyi, ... HdrStcMzi) + (WavesFxi, WavesFyi, ... WavesMzi)

What is missing besides the gravitational restoring from body weight (which as you said affects only the moments)?

Thank you for your help. Best regards,

Riccardo.

Jason.Jonkman
Posts: 5763
Joined: Thu Nov 03, 2005 4:38 pm
Location: Boulder, CO
Contact:

Re: Hydrodynamic implementation

Postby Jason.Jonkman » Mon Jul 06, 2020 9:08 am

Dear Riccardo,

I don't believe you are missing any terms. Are you using FAST to solve for the body acceleration? If so, then FAST intrinsically accounts for the body inertia forces and body gravitational forces, so, you shouldn't need to account for them in your Simulink model.

Best regards,
Jason Jonkman, Ph.D.
Senior Engineer | National Wind Technology Center (NWTC)

National Renewable Energy Laboratory (NREL)
15013 Denver West Parkway | Golden, CO 80401
+1 (303) 384 – 7026 | Fax: +1 (303) 384 – 6901
nwtc.nrel.gov

Riccardo.Caradonna
Posts: 34
Joined: Mon May 04, 2020 3:31 am
Organization: Politecnico di Torino
Location: Italia

Re: Hydrodynamic implementation

Postby Riccardo.Caradonna » Mon Jul 06, 2020 10:19 am

Dear Jason,

So, for example, you confirm that:
PtfmTAxi = (HydroFxi + Fmoorx) / m
where m = 8.0660481545E + 006 kg?
Because if so, my problem must be the transition from the tension T of the lines to the Fmoorx force.

Best regards,

Riccardo.

Jason.Jonkman
Posts: 5763
Joined: Thu Nov 03, 2005 4:38 pm
Location: Boulder, CO
Contact:

Re: Hydrodynamic implementation

Postby Jason.Jonkman » Mon Jul 06, 2020 10:29 am

Dear Riccardo,

Yes, I agree. That said, HydroFxi includes the added-mass effect, and so, its calculation assumes that you match the corresponding PtfmTAxi correctly.

Best regards,
Jason Jonkman, Ph.D.
Senior Engineer | National Wind Technology Center (NWTC)

National Renewable Energy Laboratory (NREL)
15013 Denver West Parkway | Golden, CO 80401
+1 (303) 384 – 7026 | Fax: +1 (303) 384 – 6901
nwtc.nrel.gov

Riccardo.Caradonna
Posts: 34
Joined: Mon May 04, 2020 3:31 am
Organization: Politecnico di Torino
Location: Italia

Re: Hydrodynamic implementation

Postby Riccardo.Caradonna » Tue Jul 07, 2020 3:05 am

Dear Jason,

I tried to check the equality:
m * 'PtfmTAxi' = 'HydroFxi' + ('Fx [1]' + 'Fx [2]' + 'Fx [3]' + 'Fx [4]' + 'Fx [5]' + 'Fx [6 ] '), with m = 8066048.15450000 kg and the trends of' PtfmTAxi ',' HydroFxi 'and' Fx [..] 'taken from the FAST test reported previously.
Equality doesn't match (as you can see in figure 1), I can't understand why.

Best regards,
Riccardo
Attachments
figure 1.png
figure 1.png (122.45 KiB) Viewed 2143 times

Jason.Jonkman
Posts: 5763
Joined: Thu Nov 03, 2005 4:38 pm
Location: Boulder, CO
Contact:

Re: Hydrodynamic implementation

Postby Jason.Jonkman » Tue Jul 07, 2020 7:12 am

Dear Riccardo,

What do you mean by Fx[i] in your equation? Which MAP++ output are you referring to?

Another, problem, which I missed yesterday, is that:

PtfmTAxi = (HydroFxi + Fmoorx) / m

is not correct. The equation a = F/m only works if the force (F) is applied at the center of mass and the acceleration (a) is the translational acceleration of the center of mass. In this case, the platform reference point (0,0,0) is not the center of mass of the full system. As such, the applied moments will also impact the translational acceleration of the platform reference point.

Best regards,
Jason Jonkman, Ph.D.
Senior Engineer | National Wind Technology Center (NWTC)

National Renewable Energy Laboratory (NREL)
15013 Denver West Parkway | Golden, CO 80401
+1 (303) 384 – 7026 | Fax: +1 (303) 384 – 6901
nwtc.nrel.gov

Riccardo.Caradonna
Posts: 34
Joined: Mon May 04, 2020 3:31 am
Organization: Politecnico di Torino
Location: Italia

Re: Hydrodynamic implementation

Postby Riccardo.Caradonna » Thu Jul 09, 2020 5:47 am

Dear Jason,

I modified my simulink model as you suggested, checking the equation at still water level (SWL) (0,0,0):
M_swl * qdd_swl = 'HydroFxi' + Fmoor + Restmom & gravity
where is it:
- 'HydroFxi' is the release of the FAST test in the 6 dof
- Fmoor is the contribution of the mooring in the 6 dof, where the forces are given by the sum of the 6 lines (example, 'Fx [1]' + 'Fx [2]' + 'Fx [3]' + 'Fx [4 ] '+' Fx [5] '+' Fx [6] '), the moments are obtained by multiplying force by arm.
- Restmom & gravity contains the contribution of gravity and restoring moment [0, 0, -mg, mg * COG * rx, mg * COG * ry, 0]
- qdd_swl is acceleration
- M_swl is the mass matrix shown in the figure in my previous post.

My problem is that qdd_swl thus obtained does not correspond to the corresponding outputs of FAST, in particular:
- 'PtfmRAxi' and 'PtfmRAyi' do not correspond to qdd_swl (rx) and qdd_swl (ry). This also causes problems with qdd_swl (x) and qdd_swl (y) reported at the CM (therefore 'PtfmTAxi' and 'PtfmTAyi'). The transport of the accelerations were made in this way: 'PtfmTAxi' = qdd_swl (x) + qdd_swl (ry) * 78 does not return, however I have verified that instead 'PtfmTAxi' = qdd_swl (x) + 'PtfmRAyi '* 78 matches.
- 'PtfmTAzi' = qdd_swl (z) matches.
These observations show that the problem is not in translations but in rotations as rxdd and rydd are wrong and therefore make xdd and ydd wrong. My suspicion is that I use the M matrix incorrectly, or that I am wrong in the frame of reference.
What do you think about it? Are all the loads used by me in the (SWL)?

In the figure is represented what i have explained: ok means that fast and my model matches, no is where the problems appear. As you can see, the problems are relative to rotations, so there are two alternatives:
- Moments of inertia in the M mass matrix are not correct
- All loads are not in the reference frame I supposed (0,0,0).

Best regards,

Riccardo.
Attachments
figure 1.jpg
figure 1.jpg (72.03 KiB) Viewed 2112 times

Jason.Jonkman
Posts: 5763
Joined: Thu Nov 03, 2005 4:38 pm
Location: Boulder, CO
Contact:

Re: Hydrodynamic implementation

Postby Jason.Jonkman » Thu Jul 09, 2020 1:47 pm

Dear Riccardo,

Sorry, but I'm not really following your nomenclature or logic. You seem to be writing an equation of motion about the SWL, but then you say
'PtfmTAxi' = qdd_swl (x) + qdd_swl (ry) * 78

which looks like your are assuming qdd_swl is about the center of mass (at 78-m below SWL for the OC3-Hywind spar). I also don't see the center of mass offsets in the mass matrix in the post above.

I should note that your equations of motion also miss the nonlinear inertial terms, e.g. omega x I dot omega, where I is the inertial dyadic, omega is the angular velocity, x is a cross product, and dot is the dot product (this term is included in ElastoDyn).

In the end, I'm not really sure I understand what you want to do to offer a suggested path forward.

Best regards,
Jason Jonkman, Ph.D.
Senior Engineer | National Wind Technology Center (NWTC)

National Renewable Energy Laboratory (NREL)
15013 Denver West Parkway | Golden, CO 80401
+1 (303) 384 – 7026 | Fax: +1 (303) 384 – 6901
nwtc.nrel.gov

Riccardo.Caradonna
Posts: 34
Joined: Mon May 04, 2020 3:31 am
Organization: Politecnico di Torino
Location: Italia

Re: Hydrodynamic implementation

Postby Riccardo.Caradonna » Fri Jul 10, 2020 7:37 am

Dear Jason,

My problem is simply to know the exact equation from which the accelerations are obtained. Figure 1 shows the equation I am using, according to the reference system (0,0,0) (which is supposed inertial). I remember you that I set CompAero=0 and wind speed=0 to don't take into account any loads dued to tower and turbine.
The mass matrix is shown in figure 2.
Also keep in mind that the MAP outputs were added for the mooring:
Fxm = 'Fx [1]' + 'Fx [2]' + 'Fx [3]' + 'Fx [4]' + 'Fx [5]' + 'Fx [6]',
Fym = 'Fy [1]' + 'Fy [2]' + 'Fy [3]' + 'Fy [4]' + 'Fy [5]' + 'Fy [6]'
FZM = 'Fz [1]' + 'Fz [2]' + 'Fz [3]' + 'Fz [4]' + 'Fz [5]' + 'Fz [6]'
and Mxm, Mym, Mzm are obtained by making the forces of each line for the arms.
At the moment I'm not getting the accelerations rxdd, rzdd and then ydd, while rydd, xdd and zdd are right (as you can see in figure 3).
What loads did I forget?

I hope the nomenclature is clearer this time, best regards.

Riccardo.
Attachments
figure3.jpeg
figure3.jpeg (255.53 KiB) Viewed 2070 times
Figure 2.jpeg
Figure 2.jpeg (30.66 KiB) Viewed 2070 times
Figure 1.jpg
Figure 1.jpg (75.13 KiB) Viewed 2070 times

Jason.Jonkman
Posts: 5763
Joined: Thu Nov 03, 2005 4:38 pm
Location: Boulder, CO
Contact:

Re: Hydrodynamic implementation

Postby Jason.Jonkman » Fri Jul 10, 2020 8:54 am

Dear Riccardo,

Your results appear to be much closer now. ydd, rxdd, and rzdd are very small in this basically 2D motion problem. xdd, zdd, and rydd are now quite close.

I still see a few terms missing from your equations of motion, but these may be small for this case:
  • There should be a small center of mass offset in the X direction due to the overhanging mass of the RNA.
  • Your equations of motion are missing a couple of the nonlinear inertial terms, i.e., omega x ( omega x r_cm*mass ) and omega x I dot omega (most of which are described in my prior post).
  • In general, the mass matrix in the ElastoDyn module depends on the displacement, e.g., the center of mass location and inertias will change in time as the system rotates.
Please also note that the equations of motion should be written as M*a rather then a*M (a typo in your Figure 1).

I hope that helps.

Best regards,
Jason Jonkman, Ph.D.
Senior Engineer | National Wind Technology Center (NWTC)

National Renewable Energy Laboratory (NREL)
15013 Denver West Parkway | Golden, CO 80401
+1 (303) 384 – 7026 | Fax: +1 (303) 384 – 6901
nwtc.nrel.gov

Riccardo.Caradonna
Posts: 34
Joined: Mon May 04, 2020 3:31 am
Organization: Politecnico di Torino
Location: Italia

Re: Hydrodynamic implementation

Postby Riccardo.Caradonna » Sat Jul 11, 2020 7:13 am

Dear Jason,

Thanks for the reply.
I tried to make the changes you suggested, however these have not yet solved the problem.
Nonlinear inertial terms (Figure 1), i.e., omega x (omega x r_cm * mass) and omega x I dot omega have little effect (around 5 N or 5Nm for each force / moment except Fz where there are peaks of 800N). Can you confirm that omega = [rxd, ryd, rzd]?
I tried to multiply the accelerations obtained by FAST by the mass matrix M, obtaining the resulting forces acting in the 6dof (Figure 2): as you can see it takes moments on Mx and Mz of order 10 ^ 4, I can't understand how they are caused since non-linear terms have such a low incidence.
I modified the mass matrix, translating it for each timestep in relation to the movements of the platform:

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 "https://wind.nrel.gov/forum/wind/viewtopic.php?f=4&t=1257&hilit=mass+matrix+spar" 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.

Even with this change there are no improvements, Mx and Mz of my model still remain too low.

Best regards,

Riccardo
Attachments
Figure 1.jpg
Figure 1.jpg (63.22 KiB) Viewed 2052 times
Figure 2.jpeg
Figure 2.jpeg (254.45 KiB) Viewed 2052 times

Jason.Jonkman
Posts: 5763
Joined: Thu Nov 03, 2005 4:38 pm
Location: Boulder, CO
Contact:

Re: Hydrodynamic implementation

Postby Jason.Jonkman » Mon Jul 13, 2020 7:25 am

Dear Riccardo,

Yes, I meant that omega = [ rxd, ryd, rzd ]^T.

You haven't stated what values you are using for r_cmM or I, so, I can't confirm them; of course, these are time-dependent in FAST, dependent on the rotation of the platform.

I'm not really sure I can comment more.

Best regards,
Jason Jonkman, Ph.D.
Senior Engineer | National Wind Technology Center (NWTC)

National Renewable Energy Laboratory (NREL)
15013 Denver West Parkway | Golden, CO 80401
+1 (303) 384 – 7026 | Fax: +1 (303) 384 – 6901
nwtc.nrel.gov

Riccardo.Caradonna
Posts: 34
Joined: Mon May 04, 2020 3:31 am
Organization: Politecnico di Torino
Location: Italia

Re: Hydrodynamic implementation

Postby Riccardo.Caradonna » Mon Jul 13, 2020 8:52 am

Dear Jason,

Thanks for your reply. The value of r_cmM is:
-par.hull.FDA.hydrostatic.r_cmM=[0 0 par.hull.FDA.hydrostatic.M(1,5)]=[0,0,-78*8.0660481545E+006];
While I is a matrix that contain only the values of inertia of the mass matrix (3X3 matrix from index (4,4) to (6,6)).
However I tried to implement a 'new' mass matrix similar to the previous one, but with only diagonal inertia values (figure 1). In this case my results are very similar to those FAST (figure 2). But as you can see from figure 2, there is an offset especially in xdd and rydd, which I think is due to an offset of 1.5e^6 N*m in the mean value of the moment along y axis "My(Total)" from zero (Figure3).

I chose to remove the off-diagonal terms in M, seeing that 'My' mainly influenced rx and rz, creating values ​​with too large amplitudes. Is it a coincidence that by doing this you get forms very close to the results of FAST? Or is it connected to the fact that we have inexplicably a very large offset of My which therefore does not oscillate around 0 and affects more on rx and rz?
I continue to suspect that there is something wrong with my equations for moments, in particular the moment you turn around y for me is given by:
My (TOTAL) = HydroMyi + My_restoring + My_moor + My_nonlinear
where, looking at figure 3, it is evident that My_moor and My_nonlinear has little effect, while mean (HydroMyi) = -3.7 * 10 ^ 6 and mean (My_restoring) = 5.2 * 10 ^ 6.
The offset is therefore about the difference of the offsets between My_restoring and HydroMyi (1.5 * 10 ^ 6).
To have accelerations that oscillate around 0 I expect My (TOTAL) to oscillate around 0, or have a much smaller offset.
So I wonder if there is another contribution to My or if
My_restoring = mass * g * COG * ry is right (where mass = 8.066 * 10 ^ 6 kg, COG = 89.9155 m).

Thank you a lot for your help. best regards.

Riccardo.
Attachments
figure3.jpeg
figure3.jpeg (53.71 KiB) Viewed 2019 times
Figure 2.jpeg
Figure 2.jpeg (226.3 KiB) Viewed 2019 times
figure1.jpeg
figure1.jpeg (27.35 KiB) Viewed 2019 times


Return to “Wave Energy”

Who is online

Users browsing this forum: No registered users and 1 guest