Transom Drag

Discussion in 'Hydrodynamics and Aerodynamics' started by jesdreamer, Dec 14, 2015.


  1. Leo Lazauskas
    Joined: Jan 2002
    Posts: 2,696
    Likes: 149, Points: 63, Legacy Rep: 2229
    Location: Adelaide, South Australia

    Leo Lazauskas Senior Member

    There are some similarities to cavitating struts, but there are also
    notable differences.

    You are absolutely correct: the fictitious hollow models are simple
    engineering methods that can give reasonably good, fast estimates of
    the drag. Various methods have been proposed, notably Couser et al,
    L.J. Doctors, and more recently Vorus and Taravella.

    However, some of these authors sometimes over-sell their methods a
    little. They claim that the methods *do* approximate the true flow
    behind the transom, but when examined closely the models often rely on
    additional parameters. For example, the model developed at Uni of
    Southampton used a parameter to vary the length of the hollow in such
    a way as to get the best fit to the experimental resistance. That's
    very sensible, acceptable, and there is nothing to criticize. Doctors
    also uses hollow lengths that vary with Froude number in his papers.
    However, it doesn't mean that the hollow length is close to the actual
    values as I'll show below.

    In general, simple models give quite good estimates of the drop in the
    water level at the transom as speed increases. Vandenbroeck and Tuck's
    estimate of when a 2D transom runs fully dry is quite good. Doctors
    found some fairly simple fits to the measured drop in water level, and
    they seem to apply well across a fairly wide range of transom beam-to-
    depth ratios. (His formulas can be found in the papers I attached to
    earlier posts in this thread.)

    The length of the hollow is much harder to estimate, and I haven't
    seen any good estimates using simple mathematical models. Admittedly,
    it is a very difficult flow regime and we shouldn't expect linear
    models to be very successful.

    The attached figure (from Simon Robard's thesis) shows the length of
    the hollows for 3 beam-to-draft ratios of NPL hulls used in Couser's
    work, and measurements by Doctors et al. (The hulls used in the
    measurements are slightly different to the curves in Couser's work,
    but they are close enough for our purposes). As you can see, the hollow
    lengths that give the best approximation of the resistance are very
    different to the measured hollow lengths. Therefore, using variable
    hollow lengths that give good resistance estimates cannot be said to
    also approximate the true flow very well.

    Another difficulty that isn't mentioned in many papers is how to
    estimate the hollow length that gives good estimates of the resistance
    *before* the resistance is known. It's easy to get good agreement with
    many quantities after experimental values are available, as anyone who
    has read CFD papers knows! :)

    There are also some models, like the one by Taravella, McKesson and
    Vorus, that don't quite match the expected physics. Their hollow model
    gives quite good predictions for some flow quantities, but the flow
    doesn't satisfy the Kutta condition at the transom. On the other hand,
    Doctors' "firehose" model satisfies the Kutta condition, but it
    doesn't match the experimental data as well.

    So, yes, some transom hollow models can give good, engineering estimates,
    but you have to be careful how you use those models. As always, using
    them for hulls or transoms that are far outside the range they were
    based on is not advisable. And sometimes it's not clear how good the
    estimates will be before experiments are available.

    I took a different approach in Flotilla, and used a combination of
    theoretical flow calculations, and some empirical constants.
    I am now trying to include the effects of shallow water, finite-width,
    and squat. I hope to release it sometime next year but I am having
    a devil of a time trying to account for the effect of solitons suddenly
    shooting ahead of the hull in shallow channels. That can cause the hull
    to bounce around and makes modelling the flow at the transom very messy.
     

    Attached Files:

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