CFD sail trim optimization

Discussion in 'Hydrodynamics and Aerodynamics' started by jlconger, Oct 23, 2014.

  1. daiquiri
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    daiquiri Engineering and Design

    Not so according to commonly accepted calculation method.

    The calculation of vertical wind gradient is based on the boundary layer theory. Together with an appropriate turbulence model (usually based on the mixing length), it yields a semi-empirical formula which relates the wind speeds at two different heights. The most often used formula for engineering calculations is the logarithmic relationship between two wind speeds:

    V1/V0 = log(h1/z0) / log (h0/z0)

    where h1 and h0 are the heights, z0 is the roughness height and V0 and V1 are the wind speeds. It is valid for a so-called "neutral atmosphere", which means stable and uniform wind flow over a flat rough surface.

    So, say that we know the wind speed (V1=8 m/s) at the top of the mast (h1=14 m) of a 10-meter sailboat, and need to know the wind speed at the level of the boom (h0=3 m). The roughness height is equal to the wave heigth, say z0=0.5 m.
    From the above relationship, the wind speed at the boom height is then V0=4.3 m/s

    So, if the boat is beam reaching (Beta=90°) at 7 kts (3.6 m/s), the vectorial speed analysis gives a difference in apparent wind angle of approximately 16° between the base and the top of the sail. That's a pretty significant value which can considerably change the results of the sail force and moment calculations, as well as the results of the optimization runs which Jlconger is trying to perform.

    A couple of very good readings on this subjects can be found here:
    http://www.wolfgang-neumann-gmm.de/upload/van_den_Berg_stat.pdf
    http://www.met.rdg.ac.uk/~swrhgnrj/teaching/MT36E/MT36E_BL_lecture_notes.pdf

    Cheers
     
  2. Alik
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    Alik Senior Member

    Old days, we had to read a lot of books before going into the subject. Starting from old ones such as Marchaj and papers by Herreshoff... to new ones from Larsson and Fossati. Now it seems like grabbing the software and left no time for study of physical basis... :D
     
  3. Nick_Sinev
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    Nick_Sinev Junior Member

    Actually, I was interested how does the "commonly accepted calculation method" ( i.e. "the logarithmic model") correspond to reality. According to data I found the "the logarithmic model" is not good at low heights.

    Have a look at the articles I've mentioned in the previous post.

    If you have another experimental data - please post it here. I'm really interested to discuss it.

    It should be mentioned, that I'm interested in the "raw" data.
    The meteorological articles without the "raw" data, where all the info is recalculated to the "logarithmic model", are useless for this discussion.
     
  4. Nick_Sinev
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    Nick_Sinev Junior Member

  5. daiquiri
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    daiquiri Engineering and Design

    See the attachment.
     

    Attached Files:

  6. Mikko Brummer
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    Mikko Brummer Senior Member

    We have plenty of real "raw data", measured at sea, as I mention in post 11. While we are interested in fairly low heights between 0,5 to 10 m (the size of the boats our research focuses on), the numbers measured at 2 m and 5 m heights correspond well to the logarithmic model.

    Sorry, cannot post the actual data, it's confidential. Besides the wind gradient, we are interested in turbulence, you'd be surprised how much there is turbulence at times in the natural wind.
     

    Attached Files:

  7. Nick_Sinev
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    Nick_Sinev Junior Member

    Thanks!

    The heights are not typical for small yachts.
    Yes, logarithmical model is good for the mast ~ 200m high

    Have a look at pic. #1. There is almost no difference in speed at 10m and 20m

    According to the data I've found it looks like the shape of the curve for low heights (2m ... 15m) doesn't resemble logarithm graph at all.
     
  8. daiquiri
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    daiquiri Engineering and Design

    I am looking at your reference data, and cannot find the non-validity of the logarithmic model which you are talking about.

    For example, in the first paper (http://www.dtic.mil/dtic/tr/fulltext/u2/734670.pdf) the authors clearly conlude the following:
    Vertical gradient - quote.jpg

    Cheers
     
  9. Nick_Sinev
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    Nick_Sinev Junior Member

    Thanks! That's interesting!
     
  10. Nick_Sinev
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    Nick_Sinev Junior Member

    The logarithmic model has several parameters. If we assume that the parameters are time-dependant, we can somehow comply the data with logarithm graph.

    What is more interesting.
    Have a look at the digits in table 1 page 26 pdf / 24 paper.
    E.g run number 149 (correlation coeff. 1.00)
    Height 11,4m Velocity 9.41 m/s
    Height 2.4m Velocity 8.07 m/s

    20 runs mentioned. The difference in wind speed at heights 11,4m and 2.4m is really small.


    Data from the second article I've mentioned.
    Broken line - wind speed
    Solid line - temperature (we are not interesed in it)

    [​IMG]

    The same situation. The difference in wind speed is small.
    We don't see a 2 times difference at the height of a boom and at the top of the mast for the typical mast heights.
     
  11. daiquiri
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    daiquiri Engineering and Design

    Nick, I think you are reading either those data or the Vlog relationship wrongly. ;)
    I have taken the data from the Run n.149 and analysed them with Excel. Result - the data are nearly coincident with the logarithmic curve. The maximum error is 1.6% . See the attached files.

    The logarithmic equation can be rewritten as V(H) = A log (H / B), where A and B are empirically determined coefficients.
    From the data measured in the run 149, the following values are found:
    A = 2.0116
    B = 0.0002394 (from a rough calculation based on two measured points, no attempts to do a regression analysis)
    The resulting plot of the logarithmic curve is visible in the attachments, along with the experimental values.

    In conclusion, the measured values conform extremely well with the logarithmic curve, as the authors of the paper have acknowledged too.

    I don't have time to address and analyse the other examples and graphs you have added while I was replying, but I am pretty sure the result of the comparison would be similar.

    Cheers
     

    Attached Files:

  12. Nick_Sinev
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    Nick_Sinev Junior Member

    Re: "I don't have time to address and analyse the other examples and graphs you have added while I was replying, but I am pretty sure the result of the comparison would be similar."


    The graphs from the second article look very strange - it's not logarithm at all. Just have a look - the shape is really amazing.

    Yes, you are correct - the data from the first article is perfectly approximated be the logarithmic model. Thanks for Exel file!
    I was wrong, the logarithmic model is correct.

    According to the data we are discussing (2 mine articles and 1 yours) the typical change of wind speed for the typical mast height is < 20%.
    We got one experiment with 30% difference http://www.publish.csiro.au/?act=view_file&file_id=PH560511.pdf page 15

    20% difference in wind speed, in my opinion, is small.

    Do we have any experiments, when somebody has seen >30% difference in wind speed for a typical mast?
     
  13. daiquiri
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    daiquiri Engineering and Design

    I think somebody should invite Tom Speer into this discussion. They must have done a whole lot of wind gradient measurements during the last AC72 campaign. The masts of AC72 cats were 40 meters high, so the wind gradient has played a strong role in the wing design and analysis.
     
  14. Mikko Brummer
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    Mikko Brummer Senior Member

    From post 11:
    , but we have measured on several occasions and locations the wind gradient on the water, with a mast with anemometers at 2 m and 5 m heights. The usual difference in wind speed there is 5-10%, the largest we have measured (in a light 5 kn wind) was 26%. It's true that most of the variation happens under 10 m of height, but there is a lot happening there, especially under 5 m.
     

  15. Joakim
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    Joakim Senior Member

    The wind gradient isn't that big. E.g. the formula in ORC VPP is TWS=TWSref * (Z/Zref)^0,109. My VPP has TWS*(0.621154+0.10857*log(Height/0.3048)), which is practically the same (reference at 10 m, height in meters and log is e based).

    With those formulas there is only 15% reduction from 14 to 3 m and 10% from 5 to 2 m. These fit in well with the measurements shown.

    Yes there are days when you don't feel the wind at the deck level and it is impossible to reach the targets. Then the reduction may be much bigger but 50% from 14 to 3 m does sound very unusual, especially at 8 m/s.
     
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