The Myth of Aspect Ratio

Based on rigorous dimensional analysis, any dimensionless local or global quantity of the flow, such as for example
- local skin friction coefficient Cf = tau / (0.5 rho Vinf^2)
- overall drag coefficient CD = Drag / (0.5 rho Vinf^2 size^2)
- relative BL thickness delta/size
- BL shape parameter H (small H: BL is "healthy", large H: BL is "anemic")
- etc.
depends on only the following parameters:
# relative location x/size
# body shape (e.g. what's the airfoil)
# freestream angle relative to body
# Reynolds number = Vinf size / nu
If the real flow and the tunnel model flow have the same Reynolds number, their sizes are irrelevant.

The above parameter list assumes there's no free surface present.
If there is, then the dimensionless quantities will also depend on
# Froude number = Vinf / sqrt(g size)

 

The local shape parameter H(x) works pretty well at quantifying whether or not the BL is "anemic". The H(x) at any location x depends mainly on the velocity-ratio V(x)/Vinf distribution upstream of that point. This is equivalent to the Cp(x) distribution, since they are related by
Cp(x) = 1 - [ V(x) / Vinf ]^2

In turbulent flow, H(x) also depends weakly (logarithmically) on the Reynolds number, with larger Re producing smaller H values and more resistance to separation.

In all-laminar flow, there is no Re effect on H or on the separation tendency. A mosquito wing will have roughly the same CLmax as a dragonfly wing.

With a sub-scale model, it's impossible to match both Reynolds number and Froude number. I think the usual technique is to match the Froude number, trip the boundary layer to mimic larger Reynolds numbers, and hope the latter fudge doesn't matter too much. In practice it may or may not matter.

 

For the use of "anaemic" see:
Nagib, Hassan M., Chauhan, Kapil, A. and Monkewitz, Peter A.,
"Approach to an asymptotic state for zero pressure gradient turbulent bounday layers",
Phil. Trans. R. Soc. A, published online, 2007.

You can get the paper here:
http://rsta.royalsocietypublishing.org/content/365/1852/755.full.pdf html
See p.767 for their use of "anaemic".

(Mark has given more details above.)

BL trips and turbulators are another vexed area that I gave references for in a different thread.

There are probably many reasons for that. IMO it is due to (among others):
(a) Inadequacies of the ITTC 1957 line which, although it claims descent from the Schoenherr line,
is actually missing some important terms at the high Rn end,
and is just a hack at the low Rn end (included so delegates could get home from the very long 1957 conference);
(b) Interactions between Fn-dependent and Rn-dependent factors; (e.g. BL effects on wave-making and wave effects on BL development);
(c) BL separation at the stern and its influence on wave-making, and
(d) Poor testing procedures and protocols at some towing tanks.

All the best,
Leo.

 

That's what I was refering to. How close the characteristics of the tripped boundary layer correspond to the full size boundary layer should be an interesting question. I assume it's been studied in some detail.

 

Thanks for the reference. Much appreciated. I had a quick look at p 767 and have to wonder if the "fetch" issue is about some specific test setups for BL studies.

I agree with Mark's comments which were why I was surprised by what seemed to be some statements that the same Reynold's number isn't sufficient.

 

In practice the BL trips may matter (by around 4%-18% of the residuary resistance) but you might never know.

When a model is submitted to a towing tank for testing, the user does not always get back the details of how the test was conducted. Specifically, the type of BL trips or turbulators, where they were located, what corrections were applied etc.

The user gets the drag results for their small model, scales the results up to real size using some hairy methods and a dodgy friction line, and hopes that the final resistance prediction is reasonable. (I like to think of it as faith-based system under-pinned by secondary elaboration.)

All the best from sunny South Australia!
Leo.

 

I think that there could be some problems with transition too.
The formation of hairpin vortices, and their extent downstream, could also be affected by using a model (or surface) that is too short.

There are many other disputed areas in the field.
Two recent conferences on boundary layers ended in huge shouting matches between proponents of the log-law and the power law.
I'm not sure if that issue has finally been settled one way or another (or perhaps in a completely different way).

I believe your famous poet Donald Rumsfeld summarised the state of the art in one of his works

 

No absolutes eh
I wonder how many keel designs that relied on wind tunnel testing for their full development had the figures actually validated and what the error margins were.
How do you know when assumptions of ignoring the incompressibility of air come back to bite, when it’s valid and when it isn’t?

Naval research establishments have invested in large water tunnel facilities for more accurate large scale modeling at higher Re’s and they have had problems with accuracy conducting aerodynamic testing of hydromechanics… …haven’t they?


[edit] yes of course I meant compressibility of air.

 

I assume you meant compressibility of air.

Water is also compressible. The usual measure of compressibility is the speed of sound, a higher speed of sound the higher the ratio of pressure to density change.

At speeds up to Mach 0.3 or faster compressible effects can be ignored because they are very, very small. This is true in air or water. At these speeds the density changes due to the pressure changes in the flow are small enough that the differences in resulting differences in pressure from "incompressible" can be ignored for almost any hydrodynamic or aerodynamic application. This has been validated many, many times in the last eighty years or so.

 

Wind tunnel testing isn't appropriate if there is cavitation and it's important since cavitation doesn't happen in air. In that case a water tunnel would be more appropriate. But if there is cavitation on a sailboat keel then the keel needs to be redesigned. A wind tunnel test can indicate if cavitation will occur, it doesn't represent the flow properly if cavitation does occur.

Also free surface effects are not present in a wind tunnel nor a water tunnel. If they are important then a tow tank should be used.

 

Not always so, DCockey. There can be some important local deviations from the "Mach 0.3" rule of thumb, which can change the overall aerodynamic characteristics of the examined body in airflow.

Please take a look at this thread, where I have had an instructive exchange with Mr. Drela on the issue of compressibility effects over airfoils at low-speeds: http://www.boatdesign.net/forums/boat-design/naca-sections-32067-3.html#post354948
We had discussed the impact of local compressibility on various airfoils, and have concluded that the effect may be small for a NACA 0012 foil at M<0.15, but can become important at higher M's and for airfoils with sharper leading edges, where higher local speeds occur.

To better see the dependence of airfoil characteristics with Mach number (in the M<0.3 range), please see the pic I'm attaching here. It is an analysis of the NACA 0012 foil performed with an XFOIL-based software, for 3 Mach numbers: 0.0 ; 0.15 ; 0.3 . As you can see, all 3 of them are in the conventionally-assumed incompressible range. You can see how the M=0.3 graph differs significantly from the other two. The difference lays in the fact that when the freestream Mach is 0.3 there can be points on the foil surface where the flow becomes nearly transonic. The software uses the Karman-Tsien compressibility correction factor to obtain the correct Cp's.

The compressibility effects are mostly visible at high AoAs (near the stall), where the flow is subject to a major accelleration over the leading edge area of the foil.

Cheers.

 

I haven't looked at many results from naval establishments. I do seem to remember that there were plans to build a facility with a 10m fetch to test simple flat-plate BL, but it was abandoned for some reason. I can see some enormous difficulties with a system that large, and maybe results wouldn't have been useful.

There are some very amusing (for me) results for boundary layers on flat plates. I recently collated and processed data for about 170 BL profiles in the public domain, and I can reproduce a few well-known skin-friction lines by varying the von Karman constants (kappa and B0) and choosing different sets of experiments. Some choices lead to the ITTC line, others to Katsui's line, and yet others to Grigson's line. So, it depends on the faith you place in one or other of the sets of experiments.

The results for the ITTC's "Facility Bias World Wide Campaign" should be very interesting. I'm not sure why they are taking so long to release.

My guess is that there will be at least a 20% scatter for the squat of the small model destroyer and about 5%-15% for the larger model. Total resistance might vary by 10% or more. (Maybe we should run a sweep).
Why applied mathematicians should have to validate their results against such crap is beyond me

Leo.

 

Slavi, you seem to be the right person to ask...
Do you use any lifting surface programs?

I am about to release on boatdesign.net a simple program for planar wings that can be used to benchmark results for some standard simple planforms. The aim is not so much to provide a free aero program - there are far more versatile products around - but to produce pressure distributions that users can then feed into Flotilla 3.0 to estimate the wave drag and wave patterns.

I thought it might be useful to have results from some standard lifting surface programs for comparison.

Anyone else use something that is freely available?

All the best,
Leo.

 

Legal problems, perhaps? Facilities' lawyers just waiting to sue someone who would dare to say that their client's data is off by 15%-20%? There's lots of money at stake, I guess.

The answer is a question - what's the alternative?

 

I can suggest you these:

1) XFLR5, which is based on XFOIL for the airfoil analysis and has a very good and intuitive GUI. For the analysis of finite wings you can choose between a non-linear lifting-line method, two Vortex Lattice methods and a 3D panel methods. I've tried it against some known published data on finite wings and rudders, and it gave good results with both Lifting line and with VLMs. Never tried to validate the Panel method. You can find it here: http://xflr5.sourceforge.net/xflr5.htm

2) Tornado - a code which runs under Matlab. you can download it here: http://www.redhammer.se/tornado/ . They claim a good track record, and say it is being widely used for research in academic facilities. But I've never used it, so can't make comments.

Hope that's what you needed. Cheers!