Discuss wave-energy device design and modeling

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Jason.Jonkman
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### Re: Hydrodynamic Drag loads formulation

Dear Lorenzo,

Your equations are correct, assuming that
• the platform is rigid,
• z < 0 for nodes below the water,
• the platform rotational velocities have the units of rad/s, and
• the platform has small displacements (in general, z will depend on pitch, and roll).
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

Lorenzo.Cottura
Posts: 56
Joined: Wed Jul 15, 2020 9:04 am
Organization: Politecnico di Torino
Location: Italy

### Re: Hydrodynamic Drag loads formulation

Dear Jason,
My calculations respect all the points in the list you indicated.
I also tried to make z_node variable as a function of z_plat, rx_plat and ry_plat, obtaining slightly different results (figure 1), with the formula:
vy_node = 'PtfmTVyi' - z_node * 'PtfmRVxi'
where
z_node = z_fix * (cos ('PtfmRoll') * cos ('PtfmPitch'))
for example, z_fix = -120;
I obtained the results in the figure for this node, with vy_node which in both cases differs quite a lot from the FAST 'M1N1STVyi' output.
Is there any other factor that could affect it?
Lorenzo.
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Jason.Jonkman
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Joined: Thu Nov 03, 2005 4:38 pm
Location: Boulder, CO
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### Re: Hydrodynamic Drag loads formulation

Dear Lorenzo,

Well, it would be better to write that rotation-induced translational velocity as

Code: Select all

`omega x r`

, where omega has all rotational components in global (PtfmRVxi, PtfmRVyi, PtfmRVzi, converted to rad/s), x is the cross product, and r is the displaced position vector in global (X,Y,Z). The direction cosine transformation matrix (DCM) from global to local coordinates is given in Eq. (2) in my 2009 Wind Energy Paper: https://onlinelibrary.wiley.com/doi/abs/10.1002/we.347. By taking the transpose (^T) of this DCM, r ( [ X,Y,Z ]^T) can be derived from z=-120 (with x=y=0) by:

Code: Select all

`r = DCM^T*[ 0, 0, -120 ]^T`

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

Lorenzo.Cottura
Posts: 56
Joined: Wed Jul 15, 2020 9:04 am
Organization: Politecnico di Torino
Location: Italy

### Re: Hydrodynamic Drag loads formulation

Dear Jason,
In the model I built I am trying to create simulations with different substructures (and therefore different positions of the nodes from simulation to simulation) independently from FAST.
MαNβVxi, MαNβVyi, MαNβVzi refer to specific output node β of output member α, and are therefore not very flexible to the work I want to do. For this reason I would need a spatial and temporal arrangement of the speed of the wave particles, similar to that coming out of Turbsim for the wind, where a spatial grid y-z is defined, from which we obtain a spectrum of U-wind speeds, V-wind, W-wind for each time instant.
Is there a similar procedure also for waves, defined Hs and Tp?
Thanks for collaboration,
Lorenzo.

Jason.Jonkman
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Joined: Thu Nov 03, 2005 4:38 pm
Location: Boulder, CO
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### Re: Hydrodynamic Drag loads formulation

Dear Lorenzo,

There is not currently a standard feature of FAST / OpenFAST that enables you to output the wave kinematics (velocity, acceleration, dynamic pressure) across a grid of points in the fluid domain. Of course, you could use the existing outputs (MαNβVxi, etc.) to output the wave kinematics at up to 9 nodes across 9 members (81 total per simulation), so, you could create a grid by setting up strip-theory members appropriately.

I'm sure it would possible to generate such an output by changing the source code. In fact, we have plans to do this in our ARPA-E ATLANTIS WEIS project, but not until 2021.

FYI, the HydroDyn driver already supports a feature to output the wave elevation on a grid of points at the free surface.

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

Lorenzo.Cottura
Posts: 56
Joined: Wed Jul 15, 2020 9:04 am
Organization: Politecnico di Torino
Location: Italy

### Re: Hydrodynamic Drag loads formulation

Dear Jason,

Jason.Jonkman wrote:you could use the existing outputs (MαNβVxi, etc.) to output the wave kinematics at up to 9 nodes across 9 members (81 total per simulation), so, you could create a grid by setting up strip-theory members appropriately.

In this way I can create a 2D grid of the speed of the waves on the structure: MαNβVxi, etc. are the velocities of the waves on the moving structure, and therefore depend on the displacement of the platform.
If I use another substructure or a simulation with different wind, I will have different displacements of the system and therefore also the speeds of the waves impacting the structure should be different.
From what I understand, MαNβVxi, etc. it is integral with the structure, moving with it and therefore changing according to its displacement. This is why it is different from U-wind V-wind W-wind output from Turbsim, which instead are placed on a fixed grid, not dependent on the movement of the system.
My need is to have a 3D wave speed grid that is independent of the platform position: depending on the platform positions I will go to the 3D grid to see the speeds at the knots.
Do you think it is possible, at present, to create the 3D grid?
Lorenzo.

Jason.Jonkman
Posts: 5771
Joined: Thu Nov 03, 2005 4:38 pm
Location: Boulder, CO
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### Re: Hydrodynamic Drag loads formulation

Dear Lorenzo,

Actually, MαNβVxi, etc. are the fluid velocities (not including structural or relative velocity) at the undisplaced position of the structure.

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

Lorenzo.Cottura
Posts: 56
Joined: Wed Jul 15, 2020 9:04 am
Organization: Politecnico di Torino
Location: Italy

### Re: Hydrodynamic Drag loads formulation

Dear Jason,
Ok, I get it, so the 2D grid (y-z) is the one found in the coordinates (0, y, z). But if for example during the simulation the platform is at a coordinate x = 10m, I have the grid at x = 0m, how can I know the speeds that act on the structure at that instant (when the structure is at 10m)?
Using the 2D grid for any x coordinate value means assuming that, at a given instant, at a node n = (y_n, z_n), the velocity of the wave particle Vx (x, y_n, z_n) = Vx (0, y_n, z_n) whatever x is.
Lorenzo.

Jason.Jonkman
Posts: 5771
Joined: Thu Nov 03, 2005 4:38 pm
Location: Boulder, CO
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### Re: Hydrodynamic Drag loads formulation

Dear Lorenzo,

The wave kinematics in the strip-theory solution of HydroDyn are currently computed at the undisplaced position of the structure. This follows the long wave-length approximation where we assume the structural motions are small relative to the wave length.

I mentioned our ARPA-E ATLANTIS WEIS project in a previous post. Included in that project is an effort to add a grid of points where wave kinematics will be solved, and use that together with the displaced position of the substructure to calculate the wave kinematics at the displaced position via interpolation. This will be a more accurate approach for large motion of the structure relative to the wave length.

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