Sea Keeping, Scatter Table (Mediterranean Sea)

Discussion in 'Hydrodynamics and Aerodynamics' started by i.n.filippo, Jan 15, 2019.

  1. i.n.filippo
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    i.n.filippo New Member

    Hi there,
    I am in the process of evaluating the sea keeping performance of a hull I have designed (LOA 42 mt 15 kt - displacement and round bilge). I would like to test it using Strip Theory, however I would like to include the viscous effects in the roll damping factor. I am planning to perform a roll decay RANSE simulation in order to retrieve the appended damping factor (at zero speed since I don't have a very powerful computing workstation). I have two questions:

    1. Has anybody performed this before? And if yes are there any suggestions that you may share with me?

    2. Since the Vessel will be mainly cruising in the Med (mid and east), has anybody a suggestion on where I could retrieve a general scatter table of Hs vs. Ts?

    Thank you very much to anybody who could help out!

    Fil
     
  2. baeckmo
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    baeckmo Hydrodynamics

    On q2: try the oceanographic institutions in Italian universities; also the national meteorological organisation. Good luck and keep us informed, please!
     
  3. Dolfiman
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    Dolfiman Senior Member

  4. i.n.filippo
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    i.n.filippo New Member


    Thank you both, I am trying to retrieve some scatter table from an Italian University at the moment. I see Ventusky it's pretty comprehensive. I will try to look if they have a record of a certain amount of years. @ Dolfiman, have you ever done so? I mean extrapolated an statistic occurrence table? Do you know if it's possible?

    Thank you!

    /Fil
     
  5. Nick_D
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    Nick_D Junior Member

    Look up "Standardized Wave and Wind Environments for NATO Operational Environments" by Susan Bales et al. It contains a scatter table of the type you require for the Mediterranean Sea. (Available from dtic.mil)
     
  6. Heimfried
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    Heimfried Senior Member

    Remark: my download from "dtic.mil" contained only data of the North Atlantic (Appendix A), but with the same search string there is shown another source, which contains also Mediterranan Sea (Appendix B).
     
  7. i.n.filippo
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    i.n.filippo New Member

    Gentlemen!
    Thank you so much, I've found the scatter table and it was exactly what I was looking for!
    In the mean time I have been working on the roll damping factor:

    I have some updates here:

    I have performed the roll decay simulation at zero speed and with the appended hull. I have retrieved the damping factor which, as expected, is not linear since it's affected by the various components, including the viscous one.
    In simple words the ratio of amplitudes between the various Xi and Xi+1 is not constant. I would like now to use the value I retrieved in the strip theory calculation for sea keeping.
    Has anybody any idea on how to perform this? I mean how can I "linearise" the damping factor? Shall I use a weighted average? Shall I use the first cycle's damping ratio as sample for the damping factor? Any idea?

    Thank you to anybody who can help.


    /F
     
  8. Dolfiman
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    Dolfiman Senior Member

    I think the usual method is to linearised the real damping by assuming the equivalence of the dissipated energy dissipated with the one from a linearised damping source.
    Is your damping force a quadratic one type - Bq V^2 ? (V being the speed of the considered degree of freedom and Bq a coefficient of the type of Cd ½ Rho S …. or equivalent depending of this degree of freedom).
    In that case, you search the linearised damping coefficient B such as - B V = - Bq |V| V
    For monochromatic wave, where V = Vm cos((2*pi/T)*t), the solution resulting from the energy equivalence on one period T is B = Bq (8/3/pi) Vm , so leading to an iteration process :
    a first value Vm0 to initiate the process >> B = Bq (8/3/pi) Vm0 >> solution V = Vm1 cos(wt) from the linearised equation >> iteration with B=Bq (8/3/pi)Vm1 >>> etc …

    By hoping this can be helpful ...
     
  9. Dolfiman
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    Dolfiman Senior Member

    … and perhaps more clear with the full demonstration :

    *1* The mean power dissipated by a linear damping force during one period T :

    Damping force F = - B V >> Power P = F V = - B V^2 with V = Vm cos((2 pi /T) t)

    Mean Power Pm = 1/T Integrale(P dt) on 0, T = 1/T Integrale (- B Vm^2 cos^2((2 pi/T) t) dt)

    1/T Integrale (cos^2((2 pi/T) t) dt) being equal to 1 /2 , so we have : Pm = - ½ B Vm^2

    *2* The mean power dissipated by a quadratic damping force during one period T :

    Damping force F = - Bq V^2 >> Power P = F V^2 = - Bq V^3 with V = Vm cos((2 pi /T) t)

    Mean Power Pm = 1/T Integrale(P dt) on 0, T = 1/T Integrale (- Bq Vm^3 cos^3((2 pi/T) t) dt)

    1/T Integrale (cos^3((2 pi/T) t) dt) being equal to 4/3/pi, so we have : Pm = - 4/3/pi Bq Vm^3

    *3* Equivalence of the two mean powers :

    Pm = - ½ B Vm^2 = -4/3/pi Bq Vm^3 >>> B = Bq (8/3/pi) Vm
     
  10. Dolfiman
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    Dolfiman Senior Member

    … + here attached the illustration of this quadratic to linear law.
     

    Attached Files:

  11. i.n.filippo
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    i.n.filippo New Member

    Thank you Dolfiman for your super help, however I think I am a bit lost here due to the fact that I do not have the Bq coefficient. The only data that I have at the moment is the time dependent motion signal of the evolution of the roll amplitude.
    As far as I know the [​IMG] equation for example where B1 is the linear damping coeff B2 the quadratic DC and B3 is the cubic one, is solved using the P-Q diagram but then in the formulation where B1/c=PT0/2Pi^2, B2/c=3QT0/32Pi^2 and B3/c=RT0^3/6Pi^4. Where c is the restoring term of the vessel (in function of GM). My problem arises when I need to retrieve T0 (the natural rolling period)...because it is again another approximation and I would prefer not to use it.

    So making the long story short I would like from the signal retrieved (see attached graph) to calculate the damping factor to use for my strip theory calculation. A standard value I was give long ago for a 43 mt vessel with BK and @T=3mt and BOA=10 mt is 0.076.
    I apologize if I may have misunderstood any of your explanation so far.


    upload_2019-1-25_13-17-19.png

    My peaks are [deg]:

    MAX
    X0 30.00
    X1 21.92 @7.7 sec
    X2 16.82 @ 14.25 sec
    X3 14.67 @ 20.75 sec
    X4 13.72 @ 27.2 sec
    X5 12.86 @ 33.65 sec
    X6 12.18 40.05 sec


    min
    X-1 -26.35 @ 4.3 sec
    X-2 -18.84 @ 11 sec
    X-3 -15.59 @ 17.55 sec
    X-4 -14.15 @ 24 sec
    X-5 -13.29 @ 30.4 sec
    X-6 -12.56 @ 36.85 sec

    Thank you again!

    /F
     

    Attached Files:

  12. Dolfiman
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    Dolfiman Senior Member

    I think you have your answers in this document : "Dynamic of Marine Vehicles" by R. Bhattacharya, chapter 10.3 Non linear damping
    (pages 214-215) dealing with a rolling motion with a damping type : b1 phi + b2 phi abs(phi), where b1 and b2 can be evaluated from a declining angle curve (of which method is itself described page 80). So then, if you want to deal with full linear equation, I think you have just to replace b2 by the equivalent b1 as described above.
    Bhattacharya Dynamics of Marine Vehicles - PDF Free Download https://edoc.site/bhattacharya-dynamics-of-marine-vehicles-pdf-free.html
     
  13. tspeer
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    tspeer Senior Member

    Here's something that's never mentioned in seakeeping analyses: phase variation. When you look at a seaway, the wave amplitudes and frequencies are obvious, but the phase variation is not. A Fourier approximation is based on sine waves of various frequencies that have an initial phase angle, and their relative phases never change. If you do an FFT of wave buoy data, you'll see that the the spectrum has a shape to it, but is otherwise nearly white. You can do a pretty good approximation of the frequency and amplitude with a few wave components, but it takes an infinite number of wave components to capture the phase.

    A simulated response based on summing a finite number of sine waves may look similar to a simulated response based on passing recorded wave data through the transfer functions for the boat. But the two responses are actually quite different. For example, if you try to predict what the motion will be in the future, you can do a good job with the simulated response based on the sum of sine waves. But when you apply the same predictor to actual wave data, you'll find that predicting much more than about 10 seconds into the future is garbage.

    If you really want to do a good job of simulating the dynamic response to a seaway, you should add random phase variation to the sine waves you're using to drive the simulation.

    With regard to obtaining the damping factor, can't you use a least-squares estimator? You can set this up easily in Excel. Calculate the response for the points in your graph using an assumed value for the damping. Take the differences between the calculated response and the graph and square them, then sum those to get the total squared error. Use Excel's Solver add-in to vary the value of the damping factor so as to minimize the sum of the errors. You can also estimate other parameters at the same time. FWIW, I think you'll find you get better estimates by using many points in the first period or two, than using the same number of points spread out over many periods.
     

  14. Nick_D
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    Nick_D Junior Member

    30 degrees roll? Your GZ curve will be non linear.
    At your smaller angles (the last few oscillations) it is starting to stabilise...
     
    Last edited: Feb 2, 2019
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