Skin-Friction Formulas

hello experts, sorry i've nothing really to add
exept perhaps you ment CFD instead of FEA in your last post?
eighter way, cost, among other things scares me allrite

 

Hmm, well, I could have used the term CFD, it would just be more generalized...

CFD is the abbreviation for Computational Fluid Dynamics, which is one of research fields in fluid dynamics. It uses several tools to it's purpose, all of which work by dividing (discretizing) the observed portion of fluid domain, creating a 2D or a 3D mesh, or a set of particles in case of SPH, and then applying one or more numerical techniques on this set of discrete elements.
The terms like Finite Element Method (FEM), finite Volume Method (FVM) or Finite Difference Method (FDM), Smoothed-Particle Hydrodynamics (SPH) and others refer to a particular method used for discretization and application of physical equations on this discrete set of elementary volumes or particles.

So, in few words, CFD is a branch of fluid dynamics, FEM, FVM, FDM, SPH etc. are the tools.

 

Ooh, ooh... can I play?

This has been one of the most cogent - and respectful - threads I have read on this forum in a long time. So, onto the fun...

Let's not forget the end game, so let me propose a "mission statement": to predict total full-scale drag with the highest reliability. To reiterate: a) total drag, at b) full-scale, with c) reliability. Anything less than all three is weak.

I intentionally use "reliability" rather than "accuracy", as it has always been my mantra that well-behaved and consistent calculations (comprehensively) should trump accuracy (for any individual evaluation). For example, just look at how differing methodologies confuse the prediction of drag between buoyantly supported craft (displacement) and dynamically-supported (planing). The lack of a clear distinction of regimes means people use the wrong method and make bad predictions. Of course, if you can reduce your scope of interest, such as exclusively to monohull thin forms with no ventilated transom, then your conclusion may undoubtedly be different than if you expand your scope to include a broad collection of ship types.

So, back to the discussion of "CT-based" predictions, whereby a prediction of total full-scale drag is "assembled" from components (using the RT = CT 0.5 rho S V^2 formulation), such as friction, wave-making, transom eddies, effects of form, and all of the other small pieces that need attention. The evolutionary process of this methodology, starting with Froude, has really been a refinement on the basic approach. Differing friction lines, the introduction of the form factor, using wave-cut data for wave-making drag, etc., all have been evolutionary steps. I see no reason why the discussion of friction line should not be placed in this context.

Leo, I absolutely agree with your notion that even if the accumulated total is still fuzzy due to "noise" in their respective parts, that you should make every effort to improve each component as much as possible. That is the manner of natural selection. We all didn't evolve in whole, but in fits and starts. The opposing thumb, binocular vision, improved cognitive abilities, and walking upright all did not happen at once. Having said that, we must acknowledge that a change in each component may (will?) require a change in another component. Two examples come to mind.

The first is the "correlation allowance". This is admittedly really nothing more than a fudge factor to help the prediction of total full-scale drag have a better outcome. This correlation, however, has scope and must be applied appropriately. The CA for a planing hull will be significantly different than that of a tanker using the ITTC78 expansion with the ITTC57 friction line. And it will be different for another friction line. The use of the classical "0.0004" was developed to provide an outcome when using Schoenherr (and Schlichting-Prandtl, if I recall correctly). It is not appropriate when using the ITTC57 friction line, and ITTC proposes a CA formula for this purpose. Other CA formula have been published, which reflect the experience of a particular towing tank (e.g., Holtrop equations of MARIN's experience).

Secondly, the introduction of form factor changes things. There has been much technical discussion that using a predicted form factor (e.g., using one of the Holtrop equations), rather than an empirically-derived form factor (e.g., via a Prohaska test), will be more consistent and reliable. I would agree, but a change in friction line will probably require some corresponding change in any FF or CA algorithm (if used).

I am not suggesting that this should not be done. I just warn that we must take care to look at the whole problem when altering one of its components.

A sidebar, if I may. We have two software customers that have requested us to incorporate older prediction methodologies into NavCad, simply to conform with their current practices. One very large organization - with some of the best and brightest hydro folks I know - have established a long history of successful prediction using the original Froude friction line and expansion (from the 1930s?). The other (also large) organization still uses a 2D expansion (no form factor) with the Schoenherr friction line for ALL of their work. The strength of that whole ISO9000 thing was to establish consistency in practices, which I think we call can agree helps promote reliability. It is hard to argue with someone who hangs onto a consistent practice, with deep history and knowledge of the strengths and weaknesses of their approach. (However, hanging on long after all others have moved on is probably not a great idea...)

Let me make some comments on friction lines in general. I will contend that, regardless of ITTC or other comments to the contrary, the ITTC57 is a "correlation line" and not a "friction line", and it does indeed contain some small form factor. This belief is backed up by some ACC work we did back in the mid 90s. We were evaluating test results at 1/3 scale, with dynamic wetted surface - about as good a data set as you'd want - and found that we were getting very small negative derived form factors, which of course would be a physical fallacy. We investigated using other "friction" lines (I believe we looked at the Hughes line), and the form factors became very small positive values, as one would expect. This confirmed to me that the ITTC57 line was more than just friction.

I am very bullish on the Grigson line. And, I believe that it is possible to develop a reasonable - and consistent - prediction for a corresponding form factor. Remember the end game: "to predict total full-scale drag with the highest reliability".

As a final comment, I recently read a colleague's copy of a paper presented by Neil Bose at the Marine Propulsors 2009 symposium entitled "Reliability and accuracy of ship powering performance extrapolation". He addresses many of the same issues regarding drag prediction, and expands the mission statement to include the propulsion side of the problem. If you can find a copy of the paper, it's worth a look.

Regards,

Don MacPherson
HydroComp, Inc.

 

Yeah, go on, take a shot!

That sounds like a perfectly reasonable requirement, but it's a very tall order for the near future, unless you severely restrict the type of marine vehicles.

That's not surprising. Some people swear by methods described in august books like PNA without thinking. The 2D extrapolation described in PNA is particularly bad: I certainly wouldn't recommend scaling up model residuary resistance as if it were purely wave-making.

I deliberately exclude large transom sterns from consideration for several reasons.

(a) Until we can get a handle on how simple hulls (e.g. Wigleys) behave, there's no use proceeding to more complicated shapes. Admittedly, that's not much consolation for practitioners like yourself and other NAs.

(b) I don't believe any of the transom models proposed so far.
I very much admire the experimental efforts of Couser et al, and Doctors, Day, Beck and Maki. I also like Molland's and Couser's idea of using a backward-facing step model for the flow behind a cut-off stern, but only if the hull is deeply-submerged, i.e. not influenced by the free-surface. Doctors et al have tried several variations on that theme, including a pressure coefficient method using similar coefficients to those used by Hoerner, for bullets and other projectile-like bodies. Nothing I have seen yet (including Maki's CFD attempts) works consistently and reliably.

As you know, I am a great fan of Michell, but that's because I still haven't exhausted all his theory has to offer. It is very limited in application, but for my purposes it is mathematically consistent, it produce consistent results, and it captures the correct behaviour as beam tends to zero. I love theories that sort of pin down one or more corners of a sheet that is flapping wildly in the wind. That's why I like investigating flat-plate friction rather than more difficult flows.

Evolution sometimes acts very slowly, especially when there is little pressure to change and adapt. It is now over 40 years since hydroguru J. N. Newman's plea to the ship hydrodynamics community:
"Finally, I would like to make a general comment on the state of our field as a whole. There now exists ample evidence that the separately measured components of viscous and wave resistance do not add up to the total measured resistance...
It is time... for the research community to address itself to the seemingly formidable task of studying the complete viscous free surface problem directly".

Of course, quite a lot of good research is being done, but nothing reliable has appeared that would make end-users (e.g. NA's, tank operators, and ship-builders) abandon form factor methods and other dubious methods.

In trying to include many real effects, such as surface roughness, we should try to be as true as we can to the physics of the problem. To me that means first finding an accurate method that works on perfectly smooth, flat surfaces, and then modifying the BL velocity profile to accommodate various types of surface roughness.

I'm not saying that is an easy matter, in fact it is incredibly difficult, but I don't think that we should just throw our hands up and apply fudge factors willy-nilly without at least considering what else is available.

Warning heeded!

I'm not sure about Holtrop's CA formula, but I'll side with Grigson on Holtrop and Mennens's other formulae:

"There is no physical basis for such formulae, a fact about the wave resistance admitted on p.92 (of the H&M paper)".
and
"The formulae are mathematical interpolation formulae for the model bank at NSMB. As such they are very useful. But the data for k originating from models other than the giant 10m-12m models... will suffer from the
defects of the ITTC57 line when used to find k".

It's almost impossible to shake off that ITTC57 animal grabbing your leg.

Without giving anything more away, are the Schoenherr users Japanese?

The change to the ITTC line after 1957 apparently caused quite a lot of pain among tank operators and ship-builders. Grigson himself was (fondly) described by Prof. D. Faulkner (vice-pres. of RINA) as a "bete noire" among towing tanks. I have no doubt that any further changes to recommended friction and form drag procedures will also be met with furrowed brows.

Good! I have found similar tendencies with some very thin and slender hulls.

But I still contend that the Schoenherr line is purely empirical, and that it is based on some very dodgy experimental data, and therefore so is the ITTC57 line.

Schoenherr used results from towed flat planks, so:
(a) there should have been very little if any form drag arising from the 3D nature of the flow on a curved body.
(b) the data contained spurious edge effects (at the front, sides and ends of the planks) which are are not the same as separation effects near the stern of a full 3D body, and
(c) he did not have any data for Rn > 5X10^8, so the line is just an extrapolation at high Rn.

To me this is the fundamental question on this particular matter:
How do you know that the ITTC line contains any allowance for form effects?

I could as easily contend that it is a poorly-constructed, empirical skin-friction line, and that it is just a guess to say that its tendency to over-prediction at low Rn is due to form effects.

Thanks. I know that Bose and a student also looked at Grigson's line several years ago, and used it in powering predictions for some full-size (fishing?) boats. I emailed him today to get a copy of his latest effort.

I am still undecided on Grigson.
I started out my research into this stuff by confirming his calculations using the same boundary layers as he did. (Trust, but verify!) Later I added another 80 or so BL velocity profiles, and then used a slightly more accurate analysis to arrive at my variant of his line.

That's still not enough for me to decide completely in Grigson's favour.
There are a variety of unusual, little-known issues such as the "anaemia" of some experimental boundary layers I need to think about first. I've had to find real work lately, so that kind of fundamental research is on hold for a while.

The 25th ITTC in 2005 made a good case for some work done by Osaka et al, but I'm not convinced by it because of the small Rn of the experiments.

What I found very amusing (in a nerdy, Asperger's kind of way) was that I could get different friction lines depending on what values I chose for two fundamental boundary layer "constants", i.e. kappa (the von Karman constant) and B0, which is an intercept in the log-law.

The values of those constants are still quite uncertain, and many authors refer to "the most popular values of kappa and B0" as if these matters can be decided by a show of hands at a town-hall meeting. If that is how science should be done, then we can all be climate change experts too!

I'm glad you aren't completely against the idea of re-examining skin-friction methods. I've seen the "but it's only an interim solution" for so long now, I think of the ITTC line as the Punxsutawney Phil of drag prediction.

I wonder if I could sneak that last criticism through peer-review. :idea:

All the best,
Leo.

 

Leo, is it correct to interpret your previous series of notes as a search for a physically stringent, purely analytical method to find the basic friction of a theoretically smooth surface, excluding the influence from all other factors?

I think most of us can agree that all the "friction lines", "correlation lines" or whatever have a history of empirism; somewhere in their evolutionary stoneage there is an experiment. They also include, in one way or another, the influence from factors like shape, volume, distance from initial disturbance et c.. If we really want a physically firm base for friction calculation, the theoretical lower envelope is still missing, and I think that is the essence of this discussion.

That means that we have to go down to the molecular level to gain insight; in a sense to leave the classical hydrodynamics. We have to describe the process of how the asymmetry of the intermolecular forces on both sides of the fluid/solid barrier interact, and what kind of freedom to move, that may develop. The first issue that comes to my mind is the influence of the interaction between the surface tensions of the two substances. There is a radical difference beween "surface events" when the solid surface is hydrophobic instead of hydrophilic versus the fluid. As a result, tests with exactly similar surface roughness but different surface chemistry/material will show different friction.

For example, in cavitation research, this has provided some interesting answers, explaining non-linear phenomena that we could not understand with the classical cavitation theories. In this context we have to seek alliance with the surface chemists, dealing with glue and paints; they know quite a lot about this (but they speek a weird language.......).

 

The essence of what I am saying is that we can do better than using the ITTC57 line with fairly simple models that are currently available.

You are absolutely correct that we have to resort to experiments. Even in simple 2D boundary layer theory we have to make many assumptions and use empirical constants, e.g. log-law or power law to describe the velocity profile? What value of the von Karman constant describes the data best? No-slip condition or partial slip at the wall?

I agree that there are many interesting avenues down which further research can proceed and that some of these will mean we have to leave classical models behind. In some cases, it might be necessary to abandon some very cherished assumptions and models. such as the continuum hypothesis. To model the effects of simple geometric roughness is a tough problem even without the molecular effects you described.

I like your thinking about establishing a lower limit, but I''m not sure what is allowed to achieve that limit. You mentioned different surface treatments and materials. Is that all that is allowed to find this putative lower limit? Or can we also include charging the surface using other electrical means so that some of the surface has a positive charge and other parts are negatively charge?

Is vibrating the surface allowed? How much? Until we instigate sonoluminescence in just the way we want it and for every part of the hull?

So many interesting studies and so little time!

All the best,
Leo.

 

Naah, why overdo it..... As long as we strive for a stringent analytical expression for the applications, where we today resort to empirical tools, let's leave static electricity and vibrating surfaces to the next generations. The sonoluminiscence is well left to some of the miniscule marine plancton organisms, that use it to enhance their sex appeal........

 

I read your paper and effects of the TBL on energy flow. Quantifing the transfer of energy to the TBL, and what that means, it is a gremlin that haunts the area around the transition zone, Rn 1e5 to 1e7. As this is an area that I often work in, I have had a large amount of discontent with existing theory which lead me to my own methods.

However, I must point out that I am A Naval Architect and Engineer, and I wish to bound the problem, not get the "exact" answer as I "know what I don't know". To say you want "physics based" friction line yet from your paper I see no reference to handling pre-existing turbulence. The 2-D TBL Defect Intergrals use a von Karman constant, yet you empericaly selected one based upon a curve fit even though you stated that the T3 data was "scattered" due to free-stream turbulence (Appendix C.1, 2nd Para). This tells me that the formulation is not "physics based" but rather a better curve fit...just like all pervious data (Another thing I look for in papers is the Answer= complicated equation *(1+ fudge factor) formulation).

In a real sense, a "math model" can never be a "physics model" because we will never know all the physics. This does not limit thier usefulness though. While circulation theory, Navier Stokes, and even F=ma are just mathamatical contrivences of patently fradulent models, they useful to the engineer because they get an answer that is good enough. Making a new model, flawed though it may be, not necessarily a bad thing, as a better initial value allows us to reduce rule of thumb markup derived from known results. Environmental conditions are the major driver of loads for large vessels in this Rn area. If we were gods and could know the position and velocity of every mote in the universe, then we could have a true physics based solution, after all, electrons know the fundmental laws and follow them. However, in real water, turbulence is a stoichastic process and we must admit the lack of our ability deal determinasticly with the inflow "free-stream" to our boundary layer problem.

Which brings up my AC coment. First, NA's sit at the geek table. 2nd, becuase so much CFD and FEA was used to calculate performance and strength, and so much of real loads would be based upon environment, they had to limit the racing environment to conditions that were "the known unknowns" were manageable within the precieved error limits of thier models. Math model vessels do poorly in real water unless you successfuly manage the fudge factors. This is the true history behind the friction lines.

 

Glad to hear that!

That's why I am very wary of experiemnts with small models. Trying to avoid difficulties with transition by using BL trips just introduces other great uncertainities.

I selected several "constants" and that's what I found very amusing - I could get different lines (ITTC, Grigson, Katsui etc) depending on which set I chose in the analysis.

I showed the T3 data as a reference, but I didn't use it in curve fits. I tried to use only high-fidelity data (e.g. +/- 2% errors) in those fits.

The T3 data is interesting in its own right. As you say, free-stream turbulence is an issue in real scenarios at sea, and we are a long way from devising anything approaching acceptable physical and mathematical models. Even repeating experiments with the same free-stream turbulence is very difficult, especially if we want comparisons between different testing facilities.

If I was a god who could do that I wouldn't bother with boats. I'd just make my own jetpack!

Sure, and so we have to resort to curve-fits and other statistical methods while remaining as close to the physics we have available to us at the time.

I don't know anyone (apart from students who have just discovered CFD) who think that we understand anything much about turbulence.

I completely agree. And having to resort to large form factors is a measure of just how bad we (I here mean applied mathematicians) are at modelling real scenarios.

All the best,
Leo.

 

I agree, trying to model sharkskin, riblets and other "simple" surfaces is hard enough for now.

While we are digressing...
Sonoluminescence is not used by micro-organisms as far as I know, although some shrimps are real stunners!

I mean the still unsolved physical phenomenon of creating light in water using sound, e.g. http://en.wikipedia.org/wiki/Sonoluminescence

Leo.

 

I am fully aware of the sonoluminiscence phenomenon, Leo, and I have observed it in cavitation experiments. Marine biologists have claimed some plancton species actually use a flexible body cavity to induce the luminiscence by cavitation, which was what I associated to, ...in vain it occurs!

 

Here's another one for the table , did anyone here go to that symposium?

 

I didn't go, but I got that interesting paper yesterday.

It builds on the work done by the same authors for the Specialist Committee on Powering Performance Prediction at the 24th ITTC:
http://ittc.sname.org/proc24/Volume II/Volume II - Specialist Committee on PPP.pdf

Leo.

 

I’ve been following this thread with great interest. I have not finished reading all the papers which you have given reference to in this thread, but I’m working on it. Even though I don’t have a lot to contribute at this time, I thought that I would share my current thoughts. Perhaps you can guide me.

Starting with a relative simple model of Resistance which was given in another thread: > Boat Design > center of flotation calculation and implications?

It seems that Frictional drag is by definition the component proportional to the wetted surface area. If so, then the confounding aspects of characterizing frictional resistance lies in its convolution with the other aspects of resistance. Frictional resistance would be fairly easily characterized, if all the other components of resistance were well defined and characterized.

It seems to me that we don’t need a new equation for Frictional Resistance, but we need a new model for resistance. - a thermodynamic model which includes three dimensional hull geometry, Reynolds number and Froude number. A useful model should only require these three inputs for a hull on the surface. Boundary layer thickness, separation point, vortexes and waves, are all outputs or characteristics of the model. We can assume standard temperature and pressure, density of water, etc.

I have some ideas on how to approach this, but what do you think of this relative nieve line of thought so far?

~ Michael

 

I forgot...
You could use hot water to reduce the kinematic viscosity and that way increase the Reynolds number. That way you might be able to get away with using a smaller model, but at the cost of heating a very large bath. Warm ether would probably be even better, but scary as hell.

Leo.