Skin-Friction Formulas

Hello Jehardiman,
The graph you see in my previous post, if you are talking about that one, is my version of Rick W.'s original graph (visible here: http://www.boatdesign.net/forums/design-software/michlet-30472-4.html#post333745 ), the latter one presenting some imho really abnormal error bands.
Rick did it in order to demonstrate the increasing inaccuracy of the force measurement in a towing tank, in the reagion of low speeds - which is ok as a general principle. The main argument behind the original graph is that, assuming a 1% dynamometer precision measured at full-scale and kept as a constant-value down to low speeds, the absolute uncertainity will logically increase. I agree with that but disagree with the numerical values of error bands in Rick W's graph, which are, in my opinion, due to calculation errors or due to some wrong assumption regarding the full-scale force value.
My version, under the same assumptions, presents error bands in the low Froude number region of around 25-30%, which is what can (imho) be reasonably expected when testing a single model in such a vast range of Fr's.
The S I have used is the static wetted surface, V is ship/model translational speed.

 

Seems some wine did you good, Daiquiri, up and smiling again........

Now these formulae only deal with the "smooth surface" Cf, which does not exist, other than as an envelope limit. All our hydro "peers" (Nikuradse, Prandtl, Blasius........) have dealt with the fluid friction problem both for internal and external flows. We have to account for real world surface roughness as well when using scale models.

Attached please find a classic Cf diagram from "van Lammeren, Troost and Koning: Resistance, Propulsion and Steering of Ships", 1948. From this it is obvious that any comparison in overall scale must also consider the roughness scale as well as the proportions between laminar and turbulent surface regions.

 

The graph shows a similar result only you are showing Ct whereas the graph I showed was only the Cw as used in the paper under question.

You need to remove the frictional drag to arrive at what was shown in the paper and my post on the Michlet thread.

This gets to the point I am making in the previous post on this thread. If the drag components of a model are separated so the components can be scaled appropriately, and there is a few percent error in determining the frictional component in the model and the full scale, what does that do to the error band at full-scale. I can see how it could be easily 20% in error if small models are used.

Having a frictional component with a few percent error may not be significant in determining the power requirement for most boats but if it is being used as the basis for scaling from a small model then there is every chance the prediction from the model will be poor.

When I appreciate that the underlying systemic errors can be so large I get some comfort that my model testing is not as bad as I thought. However compared to using even a moderately good analytical model it is a waste of time.

Rick

 

I looked at that data and the data was derived from 1.6m long models. That means for a Fn of 0.25 Rn = 1.68E6 which is square in the middle of the turbulent transition zone so I would expect that much scatter in Ct. Cf scatter in that region is noiminally 0.0028 to 0.005. The fact that the maximum measured error over the readings is +/-25% should be expected.

 

I have no problem your argument regarding roughness and that it should be accounted for.

My work is concerned with the theoretical 2D skin-friction problem in turbulent flow and how experiments are conducted with smooth plates. The boundary layer trip used in the experiments is the first difficulty - roughness effects are a long way down the list after that.

A more modern reference than the one you gave (thanks!) is the PhD thesis:
Candries, M., 2001. Drag, boundary layer and roughness characteristics of marine surfaces coated with antifoulings.

All the best,
Leo.

 

As an ignorant person myself, I am always happy to help out a brother!

The notion of the ITTC line being a correlation line was killed in 1978. I believed the same myth myself for a long time, so don't feel too bad.

The ITTC now recommend the line as a skin-friction estimator for single screw ships and from which to calculate form factors. It cannot be both a skin-friction line and a correlation line - that is a contradiction in terms.

Here's a reference for how the ITTC line was used with re-enry vehicles by one set of workers:

Pettersson, K. and Rizzi, A., Reynolds number effects identified with CFD methods compared to semi-empirical methods", 25th Int. Congress
of the Aeronautical Sciences ICAS 2006-2.3.4, 2006, pp. 14.

I'll try to find my electronic copy when I get time.

Leo.

 

Daiquiri,
Here's the paper I mentioned on re-entry vehicles.

Leo.

I think this is the one. I need to check it and some others.

 

Does transition play a role?
Shouldn't BL trips have promoted flow to fully turbulent?

I'm very wary about using the ITTC line and others in this Rn region. How they can be used with confidence to extrapolate to full-size is beyond me.

Leo.

 

Thanks, I know PONA's side of the story.

1. I disagree that they are all a mix of 2D, 3D, and pipe-flow.

Schoenherr's line, and therefore the ITTC line, are empirical lines based on a
truncated version of von Karman's equation; the empirical data on which they are based is not reliable as it contains edge effects on the towed planks.

Schoenherr's data was limited to Rn < 5X10^8 and he made up for gaps in his data by using different experiments that were not the same as his base data, e.g. Kempf's towed plank experiments and towed catamaran planks. Again, spurious edge effects were not accounted for.

The Hughes line is a strange one. It was a disaster when first released because it too contained spurious edge effects. I think that Gadd or Hogben (memory failing!) quickly corrected the experimental data, and re-worked the formula, but it is still not very reliable. For example, it gives results that are far below the others in the table I attached earlier. Paraphrasing Grigson, the Hughes line is still used to this day to shitcan other methods.

The last two columns of the table I gave, Grigson's line and my re-analysis of his work (I added many new high-fidelity boundary layers), are purely 2D smooth plate stuff. See for example, Chapter 3 and 4 and Appendices in:
http://digital.library.adelaide.edu.au/dspace/handle/2440/53216

2. The ITTC line was adopted as an interim measure so delegates could get away after a very long ITTC meeting in 1957. R.N. Newton proposed the line, and delegates acepted it, because they wanted an explicit formula that was a bit steeper than Schoenherr's at low Reynolds numbers. Incidentally, the David Taylor Model Basin was already using the Schoenherr line at that stage.

The way you use "Schoenherr plus a little" sounds like what R.N. Newton did to arrive at the ITTC line. Not my kind of science, but others are welcome to choose their own favourite flavour.

3. The excuse that the ITTC line is not a skin-friction line, but a "correlation" line was disposed of by the ITTC in 1978. It recommended the line as a skin-friction estimator for single screw ships and from which to calculate form factors. It cannot be both a skin-friction line and a correlation line - that is a contradiction in terms. (I think I have learned a new mantra!)

4. You make the same mistake as Daiquiri did in assuming the ITTC line is used only for your favourite marine applications. As Tolstoy said, "To a cobbler there's nothing like leather"

If you are happy with a non-physics based line that gives you estimates that are satisfactory for your purposes, then by all means use it. It's easy to use with a hand-held calculator, which is a big plus over other methods.

5. I must be blind to some Naval Architect's in-joke.
I don't see how using one skin-friction line instead of another leads to any
particular kind of boat, ACC, Swiss bathtub, or other.

Please enlighten me so I can have laugh along with people at the cool table.

All the best,
Leo.

 

A 500m long towing tank full of ether would be a fun place to work problem for a smoker!

I haven't seen any experiments, but there should be some done to quantify the effect of some interesting real ship problems involving fluids with different viscosities, e.g. the behaviour of ship-waves in a sea that has an oil-slick on top.

There is also the problem of ships travelling through a sea that has a thin layer of ice slush with a very high effective viscosity. That affects both the skin-friction and wave-making. I've done a little mathematical work on that problem but IMO, experiments would be very tough to do properly.

Leo.

 

Michlet predictions use the still water line. Patrick Couser's (experimental) Ct was also non-dimensionalised used static wetted area, but Ship Report 71 does discuss at length the issue of using the running wetted area.

There is an issue of consistency in some mathematical models that is not often appreciated. For example, in thin-ship theory, certain equations and boundary conditions are satisfied on the undisturbed waterplane and the static waterline projected onto the hull centreplane.

Some people argue that using the running wetted area will give better estimates of the total resistance, but I would counter that it is cherry-picking one factor while ignoring others. In fact, sometimes it will improve predictions, and at other times it will be worse. That's just a consequence of an inconsistent mathematical model.

IMO, if you want to use the running wetted area in thin-ship or other linear models, you should also use the dynamic waterline in estimating wave resistance, and that then raises the whole issue of how to account for sinkage and trim, and the "moving dish problem", i.e. how much does the water squat around a hull at speed.

There are also very vexed issues to do with how transom sterns should be modelled in a consistent manner.

These matters, like the appropriate skin-friction line, are far from settled.

As I said in another post, even eminent hydrodynamicists (e.g. L.J. Doctors and A.H. Day) have difficulties with sinkage and trim in their models, and whether it would be better to use experimental values or predicted values.
See page 18 of this document from the 2000 Int. Workshop on Water Waves and Floating Bodies:
http://www.iwwwfb.org/Abstracts/iwwwfb15/iwwwfb15_discussions.pdf

I spoke to Lawry Doctors a few months ago, and he said he often does not include sinkage and trim in his work because (1) it takes a long time to calculate and (2) it doesn't always give better estimates. (Of course, I'm sure he includes squat in situations where it is essential to so.)

Thanks, JEHardiman, you just made me avoid real work for another hour.

Regards from warm, sunny Australia, Northern Hemisucker!
Leo.

 

Sorry Leo, but this time we are on different positions (which is always a good thing, that's the only way we have to increase our knowldegde ).

I understand that your original post refers to the ITTC'57 line, which is a correlation line, not the friction line. It is a numerical fit of observed data and already contains an effect of hull form factor, which makes it different from the flat-plate friction line. ITTC Commitee itself, in every official document or discussion I've come upon, calls it "correlation line".
Check out ITTC website, recommended procedures and definitions section, and also "Practical Ship Design" by D.G.M. Watson (Elsevier) page195, and also "Practical ship hydrodynamics" by Volker Bertram (Elsevier) page 72 ...or a myryad of other pubblications, even very recent ones.

If you are talking about ITTC'78 performance prediction METHOD, then it does use ITTC'57 formula (corrected with yet another form-factor) for evaluation of frictional resistance, but still remains valid for ship hulls only (unless explicitly proven otherwise, which I still need ot see). That's because ITTC'57 is a ship-model correlation line, as explained above. Hence it cannot be reliably used for other purposes than for correlating model tests with full-scale ships.

There is no ITTC lines in that paper and (of course) no reentry vehicles over there. It is a paper on CFD applied to airplanes. Reentry vehicles operate at hypersonic speeds, behind a strong shock-wave where air temperatures reach several THOUSANDS Kelvin (or °C, if you prefer). How would you use ITTC line in that environment?

All the best,

S.

 

1. I poked my head out of the gopher hole so people could take shots at me. Thanks for playing!

2. I thought I might have the wrong paper for re-entry vehicles. I'll keep looking.

3. The reference to the ITTC line in the Pettersson and Rizzi paper is not immediately obvious.

I have to argue my there via a few steps, so bear with me. (I will also use some remarks and notes gleaned from Grigson's 1999 RINA paper to support my argument because he was instrumental in starting the re-examination of
skin-friction lines.)

On p. 8, 2nd column, 3rd para of the CFD paper, it says:
"The semi-empirical skin friction method used here is the Karman-Schoenherr equation and compressibility effects are corrected with the Sommer-Short estimate using a recovery factor of 0.89."

I don't do anything with compressibility, but you might know something about the Sommer-Short method.

Now, the ITTC57 line claims descent from Schoenherr's line.

Delegates at the 1957 ITTC wanted a line that was identical to Schoenherr for Rn > 10^7, but steeper below 10^7. (Hardly a scientific way of doing things, but I guess that's why it was labelled as an "interim solution".)

R.N. Newton came close to that requirement with his ITTC57 line.

The ITTC57 line and the Schoenherr line are identical for large Rn, e.g. (with Rn in millions):
Rn ITTC57 Schoenherr
100 2.083 2.072
200 1.889 1.884
600 1.632 1.632
and identical (to 3 decimal places) for all Rn > 600 million.

The form of Schoenherr's law has been taken from von Karman's equation which itself has dropped terms that are significant up to ship scale.
"Thus the form of the equation is not correct...All these objections apply equally to the ITTC 1957 line", Grigson, p. 81.

Maybe it's time to find something less interim.

4. The ITTC can call its line whatever it likes, but the fact remains that it is *used* as a pure skin-friction line.

"The ITTC has in fact accepted that its line is a friction equation in planar flow. Because it is the formula to be used to obtain k in the ITTC 78/87 method for determining the performance of single screw ships, there can be no form factor implicit in the 1957 ITTC57 2-D friction line. That would be a contradiction in concept.", Grigson, p. 113.

Therefore, I maintain it can be used for skin-friction prediction of flows other than around ships. Not that I would do that because I think it is (relative) rubbish.

5. I find it amusing when sophisticated CFD ship codes use the ITTC line for skin-friction. All that code, all that effort, and then they rely on an empirical hack See the attached paper from 2006 describing experience with a RANS solver.

Leo.

 

No, never - you don't deserve that. We are just discussing.

Yes, an old but valid method for correcting Cf for Mach number and wall temperature. If you are interested in it, the original report by Summer and Shot can be found at NACA Technical Reports server: http://ntrs.nasa.gov

It is contrary to information given by many other references (like the ones I've cited in the previous post), are you sure it is not mr. Grigson's personal considerations rather than a generaly accepted fact? But anyways, it is very interesting and I'll check it out, thanks. Do you perhaps have the title of Grigson's paper where he says that?

I'm just trying to imagine the computing cost of a direct finite-element simulation of the boundary-layer around a ship hull... It would be scary, imho.
Like I said, we are living in an imperfect and often unpredictable world... And (though maybe you will not agree), let me add - that's the beauty of it.

All the best,
S.

 

The paper I attached to my last post uses it as a pure skin-friction line.
For every paper you cite that denies it is a skin-friction line, I can probably find a recent one where the line is used in that way.

And don't we argue like perfect gentlemen. We are an example to all!
Leo.