Skin Friction Lines - Some Comparisons

Discussion in 'Hydrodynamics and Aerodynamics' started by Leo Lazauskas, Feb 15, 2013.

  1. Leo Lazauskas
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    Leo Lazauskas Senior Member

    The two attached figures show 5 popular friction lines and several
    lines calculated by Eca and Hoekstra (E&H) using a variety of
    turbulence models in the CFD program "PARNASSOS". See:
    "The numerical friction line",
    J. Marine Science and Technology,
    Vol. 13, 2008, pp. 328-345.

    Also shown are very recent values calculated by Kuoh et al in:
    Kuoh, Jen-Shiang, Chen, Yen-Jen and Chau, Shiu-Wu,
    "Numerical study on scale effect of form factor",
    Ocean Engineering, Vol. 36, 2009, pp. 403-413.

    In the first graph it is difficult to see how the various lines
    differ, so in the 2nd plot I have shown the ratio of those lines to
    the ITTC 1957 line. (Therefore, the ITTC line is a horizontal line
    equal to 1.0).

    The ITTC, Hughes, Katsui and Grigson lines are defined and discussed
    in The Final Report of the Resistance Committee to the 26th ITTC.

    The ITTC line is

    C_FITTC57(X) = 0.075/(X-2)^2

    where X is an abbreviation for log10(Rn), and Rn is the
    Reynolds number.

    The ITTC line is considered to be a correlation line and not a pure
    friction line, i.e. it contains a component of form drag. It can be
    written as:

    C_FITTC = C_FHughes * (1 + 0.1194)

    where the Hughes line is a "pure" friction line given by

    C_FHughes = 0.067/(X-2)^2

    Therefore the form component in the ITTC line is about 12% of the
    skin friction predicted by the Hughes Line.

    Katsui's Line is given by


    Grigson's Line is a bit more complicated: refer to the ITTC Resistance
    Committee Report.

    Note that there are no comparisons with measured values in these
    graphs. It is more usual to show experimental values of the local
    skin-friction which I will do in the next post on this thread.

    I don't want to enter into a debate about the relative merits of the
    various lines and methods, however:

    1. It is clear that the Hughes Line is significantly different to the
    other lines. In the next post I will show that it does not agree well
    with measured values of local skin-friction. I think there is good
    evidence that this line should not be used for routine work. For some
    people it might be of "engineering accuracy", but there are better
    alternatives available.

    2. Katsui's line and the SST turbulence model predictions are very
    close for the higher Rn range.

    3. Grigson's Line and Wilcox's turbulence model are also very similar
    at higher Rn.

    4. Using any of the lines to extrapolate from low Rn model hulls to
    full-size ships requires considerable experience and/or faith.

    Attached Files:

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    • fig2.gif
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  2. Leo Lazauskas
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    Leo Lazauskas Senior Member

    The local skin-friction is defined as

    c_f = tau/(0.5*rho*U^2)

    where tau is the local shear stress at the wall, rho is fluid density,
    and U is the free-stream velocity.
    It can also be written as the derivative of the distance x from the
    leading edge of the flat plate times the total friction, C_F, i.e.

    c_f = d(x C_F)/dx

    Note that the local skin-friction c_f is NOT the same as the total
    friction C_F.

    For example, the local skin-friction of the ITTC line is

    c_fITTC = C_FITTC * [1 - 0.869/(X-2)^2]


    C_FITTC is the ITTC line, and X is an abbreviation for log10(Rn).

    Many people, including some very eminent professors of naval
    architecture, have failed to appreciate the difference between c_f
    and C_F. More recently, posted some of my collection of
    historic friction lines to their wiki and got it wrong! (It was still
    incorrect as of a few days ago.)

    Local skin-friction can be measured directly using techniques such as
    oil-film interferometry, or floating balances.
    If boundary layer velocity profiles are used to estimate skin-friction,
    then predictions will depend on the way in which the profiles are
    processed. (I will not bore you here with that controversial topic:
    at least one symposium at Princeton was abandoned when it degenerated
    into a shouting match between advocates of two different approaches.)

    The attached graphs compare predictions with direct measurements
    of c_f. In all cases the boundary layer was tripped to ensure turbulent
    flow. These trips add their own drag and are one of several reasons
    for differences between experiments at different facilities.

    Although there are many flaws and faults with the experiments, it is
    clear that the Hughes line is a very poor predictor of c_f for the
    entire range of Reynolds numbers.

    I don't want to recommend any one of the lines over the others.
    Personally, I prefer my own variant of Grigson's Line for a variety
    of reasons that I won't go into here. One good reason is that it
    predicts slightly greater resistance at high Rn and that it is better
    to err on the side of caution in powering predictions, particularly
    when extrapolating from small models to full-size.

    Whether any of the lines is suitable for your personal work depends
    very much on the "engineering accuracy" required for the task at hand!

    Attached Files:

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  3. Petros
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    Petros Senior Member

    very interesting work Leo. shows from 7 to 10 percent variation between the methods.

    Do you have any experimental measurements to super impose of the CFD predictions?
  4. Leo Lazauskas
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    Leo Lazauskas Senior Member

    Thanks, Petros.
    I am slowly putting together a collection that I will post here
    when I get time.

    In the meantime, have a look at the attached paper by Eca and
    Hoekstra, and Figure 4 in particular. You can see that the
    predictions for real ships lie a bit above Grigson's Line which
    predicts the highest C_F of the methods I showed in the previous
    Last edited: Aug 12, 2015
  5. Remmlinger
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    Remmlinger engineer

    Leo, we started a discussion about local skin friction one and a half year ago -, you might remember. It seems that you have meanwhile done a deep dive into the historic research and brought some jewels to the surface. It would be interesting to see, how Österlunds ( measurements fit into your pictures. To treat Hughes fairly, I think one should not only consider his friction line, but better his original measurements. If his measured values are extrapolated to a plate with infinite width, these values fit the picture in a much better way than his line.
    As always impressed,
  6. Leo Lazauskas
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    Leo Lazauskas Senior Member

    Thanks, Uli.
    1. I actually tried to omit some of the historic stuff that I have.
    (I thought I had hit pay-dirt with one senior Boeing aeronautical
    engineer who retired after 50 years with the company, but she lost
    everything in an arson attack. The original data sheets were lost and
    I haven't had time to digitise the graphs of what remained.)

    Some older experiments are quite unreliable. I (and Grigson) believe
    that some of those experiments were the main cause for the ITTC Line
    not being a very good friction line. Yeah, yeah, I know it's a
    "correlation line".

    For example, the ITTC Line is based on the Schoenherr "Law" which is an
    empirical formulation. The form of the equation is not correct because
    it omits certain terms that should be included up to ship-scale.
    At high Rn it is based on Kempf's experiments with pontoons which
    included edge effects. von Karman selected only 6 of the measurements
    which lie on a straight line to estimate certain coefficients.

    2. Osterlund's experiments were excellent. They were made in a wind
    tunnel with an ambient turbulence of about 0.02% which is very low for
    this type of work. Unfortunately, the Rn range was not very extensive.
    But they are a triumph, to be sure!

    Incidentally, the discussion of how the results should be scaled ended
    up in the shouting match between professors from Stanford Uni and a Swedish
    contingent from KTH. I think the reconvened symposium might also have
    ended the same sad way. Of course both sides are wrong: "Essentially all
    models are wrong, but some are useful", as George Box famously stated.

    I did examine those and other modern experiments quite a while ago.
    The 1st attached figure shows the results of my analysis for 3 pairs of
    log-law constants (kappa and B0) and fits to the wake portion of the
    boundary layer.

    You can see that I can get a very good fit to the various experiments,
    depending on which pair of constants are chosen. The bands in the graphs
    are +/- 2% and most of the experiments fall within those reasonably
    tight bounds.

    When converted to total friction lines (i.e. C_F not c_f), I get three
    contenders shown in the 2nd figure.
    Note that the first pair of constants gives a close approximation to
    the ITTC line at high Rn; the second pair is close to Katsui's Line, and
    the 3rd is close to Grigson's Line.
    Thus, and it still amuses me immensely, we can arrive at any of the lines
    under consideration by the recent ITTC depending on what faith we place in
    the experiments.

    In the next slab of posts and data I will include the most recent experiments
    by Orlu which support Osterlund's findings. Again, they do not cover a very
    wide range of Rn.

    3. I have seen some recent re-analysis of the Schoenherr Line but I have not
    had time to digest it. See:
    Nishioki, Michio,
    "Rotta skin friction law and Schoenherr formula"
    Fluid Dynamics Research, Vol. 41, 2009, pp 1-9.

    There also some new experiments using similar techniques to Kempf's in a
    bigger towing tank. See:
    Kiyoto Mori, Hiroki Imanishi, Yoshiyuki Tsuji, Tomohiro Hattori, Masaharu
    Matsubara, Shinsuke Mochizuki, Masaru Inada and Tadashi Kasiwagi,
    "Direct total skin-friction measurement of a flat plate in
    zero-pressure-gradient boundary layers",
    Fluid Dynamics Research, Vol. 41, 2009, pp. 19.

    Their conclusion was that the experimental local friction was about 6% lower
    than the Karman–Schoenherr formula, but that it is consistent with the values
    obtained by other direct measurement techniques.

    4. My original motivation for this thread was to examine how well the Hughes
    Line compares with experiments. It might agree with the extrapolated
    measurements you mentioned, but it doesn't stack up well against all the other
    experiments. I don't like the implicit implication that the Hughes Line is a
    good "pure" friction line. It's not - it is pretty awful compared to many other
    simple alternatives.

    5. Surely it should be an easy task to come up with a simple friction line for
    flat plate boundary layers. It's not like we are including roughness and 3D
    effects. If only we could account for the forest of hairpin vortices :)

    Attached Files:

  7. Leo Lazauskas
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    Leo Lazauskas Senior Member

    Uli, I know of the analysis you are referring to:
    Gadd, G.E.,
    "A new turbulent friction formulation based on a re-appraisal of Hughes' Results",
    Trans. RINA, vol 109, 1967, pp. 511-539.

    That new line is

    C_F = 0.0113/(X-3.7)^1.15

    where X is log10(Rn).

    However, that is not the way the ITTC write their line so I have omitted it.
    I'll add it to my to list of historical lines and show it together with about a
    dozen others that have been proposed over the years.
  8. Remmlinger
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    Remmlinger engineer

    Are you referring to the paper of William George from Chalmers who claimed that there is no log law and that the Karman-constant is not constant and all scientist in the last 80 years were wrong? I prefer the position of Nagib and Monkewitz. Österlund had offered an explanation so that no side would lose face (see attachment).

    This is the point, it all depends on reliable experiments. It makes me wonder, that I have not seen in the papers the simple check against the momentum equation. If the quantities Cf and delta 2 (=momentum deficit thickness) are measured, the momentum equation requires that
    Cf = 2* d(delta2) / dx
    If I differentiate the momentum def. thickness along x, I get the diagram in the attachment. Nether Österlund nor Smith-Walker show a good agreement. May be the definition of the outer edge of the boundary layer for the determination of the momentum deficit plays a role?

    When I got Österlunds results I updated my boundary layer calculation code - I use an integral method. The code needs an estimate for Cf as a function of Re d2 (Reynolds number based on momentum def. thickness). The result of the change was barely noticeable. The calculated total resistance of the model-hull was identical "within engineering accuracy";). To understand this, I drew delta2 as a function of x in dimensionless form, see attachment. There is a 6% variation between the two datasets. In the end, total resistance is equivalent to delta2 at the stern and as long as I calculate the resistance of the model in the towing tank, both datasets give good results for the towing force, which differs much less than these 6%. The error creeps in, when I extrapolate these results to full scale. I think it is better to repeat the boundary layer calculation for the full size yacht and hopefully staying within the validity of the Cf=f(Re d2) function.

    btw, to loose everything in a fire is a threat to be taken seriously. I did sent the source code of some of my programs in an e-mail to my own address. This way it is saved on the server of my internet provider in a fire protected building.

    Attached Files:

    Last edited: Feb 17, 2013
  9. Ad Hoc
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    Ad Hoc Naval Architect

    Leo, I hate to defend such a “poor performer”, but I think you’re being a bit overly presumptuous of Hughes’s method/line, as Remmlinger has pointed out.

    If I recall correctly (I used to have the paper, can’t find it now..typical!!), Hughes' “pure friction” line is bit of misnomer, since he refers to 2D flow. He was also trying to define a “form factor”.

    The general assumption being that the traditional Froude method where the whole of the residuary resistance (Cr) is assumed to be the same for model and ship. Whereas in the Hughes’ method the Cr that is attributed to viscous effects is reduced in the model to ship transfer. Since the Hughes method gives much lower ship predictions and one uses a larger “correlation allowance”, i.e. his form factor.

    Hughes form factor being r = (1 + k).

    Where k = (Cvm – CFo)/CFom

    Cvm = Viscous resistance
    CFo = frictional

    And r = the ratio of viscous resistance to friction resistance, assumed it to be independent of Rn, and various values of CFo are obtained, by a constant 'times' the CFo value. And of course his CFo is subtly different to the ITTC1957, as you’ve noted.

    Thus whilst I agree the Hughes line is not ideal at all, it does require more than just a simple plotting of the 0.066/(logRn – 2.03)^2. It’s fiddly with different CFo curves and then finding the “run in” point of Ct/CFo , since Hughes assumed the Cr to be vanishingly small at low Fn.

    Thus, it isn’t a one line fits all.

    The JMST paper 2008 by Eca & Hoekstra do state in their conclusions that despite excellent agreement with the k-w model the usual “transition” occurs at a lower Rn than expected - nothing is perfect :eek:. But interestingly do go on to say that they have some slight reservations of a pure numerical friction line being widely adopted but it is useful in determining form factors. Which is ostensibly what Hughes was doing, and indeed many others. Pay ya money, take your choice :D
  10. Leo Lazauskas
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    Leo Lazauskas Senior Member

    The George and Castillo paper was one. Barenblatt and Chorin from
    Stanford were also very vocal critics of the way in which
    Österlund's experiments were scaled.
    There were claims that all fluid mechanics text books would have to
    be scrapped. Of course, that hasn't happened!

    I also like the approach you mentioned. They, and others are still
    trying to calm down the warring parties. See:
    I. Marusic, B. J. McKeon, P. A. Monkewitz, H. M. Nagib, A. J. Smits,
    and K. R. Sreenivasan,
    "Wall-bounded turbulent flows at high Reynolds numbers:
    Recent advances and key issues",
    PHYSICS OF FLUIDS 22, 2010,

    I think it does play a role. I don't like using d95, or d99.
    Like Grigson, I extrapolate to the "true" edge of the BL.
    If you are really keen, have a look at Chapters 3 and 4 and
    Appendices B and C of my thesis which shows my approach.

    I think you are fairly safe for the range of Rn you are interested in
    for yachts. Using direct measurements of cf also helps. It is much
    messier if you use velocity profiles because that's when all sorts
    of assumptions have to be made. The "wake" component is
    particularly difficult to model.

    Of course, the situation is much worse for high Rn and, as you said,
    when extrapolating a long way beyond the experiments. I agree, too,
    that it is often better to repeat calculations at full scale, rather
    than relying on extrapolation. It is not too bad for us; CFD users might
    have to wait a lot longer and pay big electricity bills for their results :)

    When it cools down here a bit, I'll post comparisons of the Hughes Line that
    Gadd derived, and an earlier version due to Wieghardt. It's too hot to think
  11. Remmlinger
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    Remmlinger engineer

    Hughes' experimental results

    I had to shovel snow for an hour today, so I am all powered up!
    I think I still owe you an explanation for my remark about Hughes' results.
    There is a paper by Davies and Young (see att.) that states that Hughes overestimated the edge effects in the analysis of his test results. Using their formula gives much better agreement of Hughes' data with the other friction lines (see the pdf).

    Attached Files:

  12. Leo Lazauskas
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    Leo Lazauskas Senior Member

    Thanks, AdHoc and Uli.

    AdHoc: I appreciate that there are subtle differences in Hughes'
    approach, and I also understand that it can be reasonably reliable
    when used cautiously and consistently by experienced practitioners.
    Grigson is scathing of the line "...a seriously wrong line which
    is still resurrected to cast doubt on other lines."
    However, he does concede that "...for many years one model basin of
    good repute used the Hughes line".
    The implication being that they were competent and knew what they were
    doing then, but no longer use it.

    I guess my main gripe is the way the ITTC line has been presented by
    the current ITTC as the Hughes line + a correction term. I think it is
    open to misinterpretation.

    I also don't like the ITTC line because it leads to negative form
    factors for very slender hulls. I have never had that difficulty with
    other methods. Of course, experienced NA's and others know this is just
    an artefact of the ITTC line, but it is not a good look.

    We could argue endlessly about the distinction between the ITTC Line and
    a "true" planar friction line, but I like Grigson's take on it:

    "What is the significance of the formula? To discover this one must see
    how in fact it is used. It operates to provide the foundation on which
    k and C_R are determined at model scale, and by which at ship scale
    C_VS is determined, C_R being unchanged. The ITTC Line is used exactly as
    any friction line giving C_F in 2D time-mean flow would be used. There is
    no physical distinction between the ITTC Line and a planar smooth friction
    law. Any other distinction is purely verbal."

    Finally, if the ITTC line is not a friction line, then what should we use
    in its place?

    The corrections of Hughes' data by Davies and Young in the paper you
    gave are just one of many such attempts. Wieghardt (1955) and Gadd (1967)
    have also tried.
    Personally, I think that there is no need to use Hughes' data at all,
    corrected or not. There is too much fiddling to get it to look right and there
    is enough other better data available.

    We should also be a bit wary of the Smith-Walker data. Nagib has shown that it
    is possible that their boundary layers are "anaemic", i.e. they were possibly
    not fully-developed turbulent flows at the highest Rn in their set. However,
    there is not much else available at those Rn, so it's hard to leave them out.

    I also think that the Schoenherr Line should be dumped: it certainly
    should never be used to support or cast doubt on other methods because
    it is fundamentally flawed. I really don't understand why it has survived for
    so long.

    Just to complete the set, the attached figure shows some historical friction
    lines as fractions of the ITTC line.

    Hughes was very critical of Gadd's modification.
    Gadd's modified line is really only applicable for Rn < 10^8:
    differences between that line and the ITTC line become quite large
    for Rn > 10^8.5.

    Granville came up with a line that is very similar to the ITTC line:

    C_F(X) = 0.0776/[(X-1.88)^2) + (60.0/Rn)

    where X is log10(Rn). I'm not really sure why he decided to devise
    that particular formula. Grigson showed that it is not all that good
    when compared to experiments.

    Attached Files:

  13. Remmlinger
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    Remmlinger engineer

    My proposal would be to forget about the many different "lines" for a moment and to agree on experimental data that can be considered reliable.
    If we have trustworthy experimental data, it is no big thing to find an interpolating curve that fits these data.

    PS. I will try to get this paper
    may be that gives an indication
  14. Leo Lazauskas
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    Leo Lazauskas Senior Member

    Nagib and his colleagues have published several papers in the last 3 or 4 years. That is a good one.

    I used a method due to Kendall and Koochesfani to better collapse the
    Osterlund data. IIRC, Nagib has shown that it can only get down to an
    accuracy of +/- 1.5%. That is good enough for my purposes, and the results
    I showed were contained within a band of +/-2%, so Nagib's assertion seems
    right to me. He can probably squeeze out a slightly better result because he
    has all the details of how the experiments were conducted.

    I agree that finding reliable sets of data is very important. However, all of
    the sets I have are subject to some criticism. For example, Barenblatt and
    Chorin were not critical of Osterlund's measurements, but on how they were
    Some of their criticisms were very petty. E.g. they said that Osterlund's
    kappa=0.384 was much lower than values reported by other researchers.
    They conveniently ignored the fact that Karman obtained an almost
    identical value 60 years earlier.
    They also were wary that the experiments were over a fairly narrow Rn
    range, and that all the experiments were conducted at the same facility.
    That's a fair enough criticism. But I think there have been some re-tests by
    Orlu and others elsewhere that tend to support Osterlund's findings.
    Fascinating detective work for us, Sherlock!

    (Email me at my cyberiad address if you are having trouble getting some
    papers and I'll see what I can do.)

  15. Remmlinger
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    Remmlinger engineer

    You Sherlock, I Watson!
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