Scale Effect at Low Reynolds Numbers

Discussion in 'Hydrodynamics and Aerodynamics' started by Earl Boebert, Nov 8, 2016.

  1. Earl Boebert
    Joined: Dec 2005
    Posts: 375
    Likes: 46, Points: 28, Legacy Rep: 302
    Location: Albuquerque NM USA

    Earl Boebert Senior Member

    I am looking for references that might help me gain insight into the following problem. I'm looking at two model yacht classes, one approximately half the size of the other. Both classes are development classes constrained by a box rule. Both classes are mature and have undergone type forming. (Marblehead and RG65 for the curious.)

    What I'm studying is whether and how the relationship between aerodynamic and hydrodynamic forces change as you scale down in this limited Reynolds Number domain. I have most of the standard references from Manfred Curry through Marchaj, AYRS pamphlets and other miscellany and have googled fairly intensely.

    I have a suspicion (or hope) that somewhere out there are obscure papers, probably student theses, that have touched on this problem. If anybody knows of any such I would deeply appreciate pointers to them.

    Cheers,

    Earl
     
  2. Doug Halsey
    Joined: Feb 2007
    Posts: 392
    Likes: 102, Points: 53, Legacy Rep: 160
    Location: California, USA

    Doug Halsey Senior Member

  3. Earl Boebert
    Joined: Dec 2005
    Posts: 375
    Likes: 46, Points: 28, Legacy Rep: 302
    Location: Albuquerque NM USA

    Earl Boebert Senior Member

    Thanks. I was unaware of this.

    Cheers,

    Earl
     
  4. Doug Halsey
    Joined: Feb 2007
    Posts: 392
    Likes: 102, Points: 53, Legacy Rep: 160
    Location: California, USA

    Doug Halsey Senior Member

  5. kilocharlie2
    Joined: Nov 2016
    Posts: 30
    Likes: 2, Points: 0, Legacy Rep: 35
    Location: Left Coast, North America

    kilocharlie2 Junior Member

    Earl -

    Do make a call to California Institute of Technology's bookstore. Many titles with chapters involving Reynold's numbers.

    -KC
     
  6. Doug Halsey
    Joined: Feb 2007
    Posts: 392
    Likes: 102, Points: 53, Legacy Rep: 160
    Location: California, USA

    Doug Halsey Senior Member

    The responses to the original post have, so far, been limited to finding sources for general information on Reynolds number effects, and haven't addressed how the relationships between the aero & hydro forces change.

    I would think that the hydro forces would be more strongly impacted than the aero forces. Both aero & hydro Reynolds numbers would be cut in half from scaling the model down, but the hydro Reynolds number would be reduced further because of the loss of boat speed. (The apparent wind speed would change too, but I'm assuming this would be by a smaller amount.)

    In addition, the hydro forces would increase further from wavemaking, as a result of reducing the Froude number.

    It would be an interesting exercise to try to scale the estimated forces & see what differences might result in some VPP code runs. As you say, this has probably been done in a student project somewhere. If nothing turns up, I'm tempted to dust off an old VPP code & have a go at it.
     
  7. Doug Lord
    Joined: May 2009
    Posts: 16,581
    Likes: 298, Points: 93, Legacy Rep: 1362
    Location: Cocoa, Florida

    Doug Lord Flight Ready

    Doug, that would be cool if you did that. This is an interesting topic and it would be great to learn more.
     
  8. Earl Boebert
    Joined: Dec 2005
    Posts: 375
    Likes: 46, Points: 28, Legacy Rep: 302
    Location: Albuquerque NM USA

    Earl Boebert Senior Member

    Thanks. That's pretty much my surmise from anecdotal evidence, but it would be great to see an analytic description.

    Cheers,

    Earl
     
  9. kilocharlie2
    Joined: Nov 2016
    Posts: 30
    Likes: 2, Points: 0, Legacy Rep: 35
    Location: Left Coast, North America

    kilocharlie2 Junior Member

    Gotta be careful at VERY LOW Reynold's numbers...and I do not know approximate RN's for yachts - I worked with that on model aircraft, so this may not apply at all, or perhaps only at near stand-still speeds with yachts.

    At very low RN's, turbulent boundary layers with attached flow gets pretty small - close to laminar drag forces. A turbulent bubble with re-attachment may appear, move back and forth differently as we rotate +/- through different angles of attack, may detach and create relative large drag, then re-attach at a slightly higher speed. Scaling things up will likely change how it behaves - we all know that lots of bad stuff goes away when our toys get bigger and/or faster.

    All I've ever really found is that long, slender hulls with lots of sail area usually go faster than short, beamy hulls with little sail area. You may find some advantages of changing shapes when a hull is turning, though.

    One area that does warrant some investigation is increasing or decreasing prismatic coefficient (how diamond-shaped vs. how cigar-shaped a hull is in top view and in elevation profile) on some of the better performing hulls. Surprisingly, increasing prismatic coefficient (making it more cigar-like and less diamond-shaped) will increase the hull speed of some designs - Some of the Down Easters (the Henry B. Hyde for one example) could run almost as fast as theeir clipper ship forerunners while carrying a whole bunch more cargo. An investigation on scale effect vs. prismatic coefficient at different AR's would be interesting...

    My apology for diverging from the subject matter if I missed the RN window of this discussion, which I likely did. I just throw out this in hope that these considerations may help.

    Oh, yes, one more reference for aerodynamics: Herk Stokely's Soartech Journal #8 - Airfoils at Low Speed, by Michael Selig. This is the source of the Selig & Donovan airfoils, it deals with aerodynamics from RN's of 40,000 to less than 1,000,000.
     
  10. markdrela
    Joined: Jun 2004
    Posts: 306
    Likes: 28, Points: 28, Legacy Rep: 324
    Location: MIT Aero & Astro

    markdrela Senior Member

    In general, for a given geometric shape, the aero force coefficients depend on the aero Reynolds number, and the hydro force coefficients depend on the hydro Reynolds and Froude numbers. Both sets of numbers depend on boat size and speed via their usual definitions. Given this, it's not obvious what you mean by "relationship between aerodynamic and hydrodynamic forces". Can you be more specific about what you're after?
     
  11. Earl Boebert
    Joined: Dec 2005
    Posts: 375
    Likes: 46, Points: 28, Legacy Rep: 302
    Location: Albuquerque NM USA

    Earl Boebert Senior Member

    To give an example: let's say that for the larger class, anecdotal evidence is that an increase in measured sail area of X% has Y% effect on performance. Anecdotal evidence in the smaller class is that an increase in measured sail area of X% results in much less than Y% increase in performance.

    My question then would be, does the relationship between thrust-producing aero forces to drag-producing hydro forces change as you scale down in this limited Reynolds Number domain, or are we being misled by the anecdotal evidence?

    Cheers,

    Earl
     
  12. markdrela
    Joined: Jun 2004
    Posts: 306
    Likes: 28, Points: 28, Legacy Rep: 324
    Location: MIT Aero & Astro

    markdrela Senior Member

    It's not necessarily a Reynolds number effect. If your larger-class rig is underpowered, and your smaller-class is overpowered, then this alone could be the cause of what you're describing.

    In general, there's no way to know if redesign info like you described will apply to another boat. This is especially true if one boat is not a scale copy of another, because geometry (e.g. sail/keel area ratios) also matter, not just Re and Fr.

    A more systematic approach would be to estimate the sail and keel lift coefficients on each boat, at one or more speeds. Then compare the CLs for each surface, and also see how they compare to the appropriate CL for that Reynolds number. If the CL is too high or too low, then the surface's area wants to be increased or decreased, respectively.
     
  13. HJS
    Joined: Nov 2008
    Posts: 335
    Likes: 44, Points: 28, Legacy Rep: 288
    Location: 59 45 51 N 019 02 15 E

    HJS Member

    At low Reynolds numbers profiles behave in a completely different way than you might expect. This is an often overlooked phenomenon. See accompanying illustrations.

    Good luck

    JS
     

    Attached Files:

  14. markdrela
    Joined: Jun 2004
    Posts: 306
    Likes: 28, Points: 28, Legacy Rep: 324
    Location: MIT Aero & Astro

    markdrela Senior Member

    Yes, but only if you insist on still using airfoils intended for high Reynolds numbers.

    As long as the chosen operating CL range and the airfoil is appropriately chosen or designed for the intended application, the airfoil behavior will be more or less "normal" down to insect-sized Reynolds numbers. Specifically, CL(alpha) will be nearly linear up to stall, and the CD(CL) polar will be reasonably well behaved. So the whole "low Reynolds number" thing is largely a non-issue with proper design practice.
     

  15. kilocharlie2
    Joined: Nov 2016
    Posts: 30
    Likes: 2, Points: 0, Legacy Rep: 35
    Location: Left Coast, North America

    kilocharlie2 Junior Member

    Just curious, Earle, how fast do the Marblehead 50/800 model yachts go? I see the masts on most of them are 85 inches, how long are the booms? From that, I could take a stab at approximate Rn ranges for the sail rigs.

    You may ask Mr. Drela to walk you through the Froude number / Reynolds number design routine on the 50 inch hulls.

    From what I gather the RG65 class is about half the scale of the Marblehead class, and seems to encourage many hull designs, some of which are indeed scaled-down, 50% M-class hulls. I could not find design parameter rules, though.
     
Loading...
Similar Threads
  1. vignesh
    Replies:
    4
    Views:
    1,768
  2. Senrab
    Replies:
    12
    Views:
    3,550
  3. Daniella Driver
    Replies:
    4
    Views:
    1,747
  4. dpaws
    Replies:
    21
    Views:
    3,526
  5. jesdreamer
    Replies:
    49
    Views:
    7,099
  6. Will Fraser
    Replies:
    150
    Views:
    21,694
  7. hump101
    Replies:
    18
    Views:
    4,035
  8. Autodafe
    Replies:
    29
    Views:
    5,555
  9. Southern Cross
    Replies:
    3
    Views:
    1,391
  10. Anum
    Replies:
    8
    Views:
    4,451
Forum posts represent the experience, opinion, and view of individual users. Boat Design Net does not necessarily endorse nor share the view of each individual post.
When making potentially dangerous or financial decisions, always employ and consult appropriate professionals. Your circumstances or experience may be different.