Boundary Layer Thickness 2

[Sparweb]

Hello,
I'm trying to reconcile what I read about boundary layer thickness, from some sources, with the velocity distribution/profiles from other sources.
I've been using Anderson, Intro to Flight; White, Fluid Dynamics; Hoerner; Fluid Dynamic Drag; and a bundle of NACA reports, but I can't put the two together.

In some places, the BL thickness is given as a simple formula. Often like this for turbulent layer:

d = 0.37 x / (Re_x)^0.2 (Anderson eq. 4.99)
(it's 0.36 in Hoerner Figure 2)

That equation implies there is a distinct boundary layer; below you are in it, above you are out of it. I know that's not true.

Other sources give a velocity profile... parabolic-looking for laminar and logarithmic-looking for turbulent.
That suits what I understand about the BL better, but it is of course more time-consuming to calculate.

Is there a relationship between the two methods? IE; does the simple equation correspond to a particular part of the velocity distribution? Is it 90%? Is it 99%?

Hopefully someone can provide a written source that I can use to substantiate this.



STF

 

[rb1957]

Hi Steve,

I thought boundary layer was defined by the flow velocity. When the local velocity is less than free stream then you're in the boundary layer; equal toe free stream then you're outside it. I do see it as binary, though the edge is defined by a mathematical function asymtoting to the free stream so the thickness is possibly when the local velocity is 99% of free stream.

another day in paradise, or is paradise one day closer ?

 

[btrueblood]

The boundary layer thickness, d or δ, is where the local velocity u is 99% of freestream Uo - this is the terminology used by Prandtl/Blausius for the original laminar bl solutions. My source is Engineering Fluid Mechanics, Roberson and Crowe, Houghton-Mifflin, 1980.

 

[Sparweb]

Prandtl.
I shoulda known.

I found in Von Mises a definition that it's 94% of V(free stream).
I'm starting to think that the subtle differences in the the thickness equations (the coefficients vary) from source to source are due to the authors defining the "thickness" as a different % of the freestream velocity.

STF

 

[Sparweb]

btrueblood,
Thanks for the reference. Not very good reviews of that book... but maybe that's just Amazon... would you recommend a purchase >100USD?

STF

 

[rb1957]

i'd try MIT's opencourseware ... they're bound to have courses on BL.

another day in paradise, or is paradise one day closer ?

 

[LiftDivergence]

One of the best treatments I've seen is in Theory of Wing Sections... pages 81-108.

I find it hard to shell out over 100 dollars for most books, unless they are something special. Dover has a great series which is cheap. If you are looking for something on the subject maybe try searching their catalog. They have "Theoretical Aerodynamics" by LM Milne-Thompson and "Theory of Flight" by Richard von Mises. both of which cover this to some degree.



Keep em' Flying
//Fight Corrosion!

 

[IRstuff]

I think that a continuity is the reality; nature doesn't do many absolute boundaries. But, mathematically, it's easier to essentially discretize reality.

TTFN (ta ta for now)
I can do absolutely anything. I'm an expert!

https://www.youtube.com/watch?v=BKorP55Aqvg

faq731-376 forum1529 Entire Forum list

http://www.eng-tips.com/forumlist.cfm

 

[Sparweb]

Thank you everyone!
Satisfactory answer. The difference between Prandtl's definition (99%) and von Mises' definition (94%) only amounts to a few centimeters. I plan to mount the instrument in question at least 40 cm away from the surface, so I'm very comfortable now that we can keep it out of the BL without heroic efforts.


STF

 

[btrueblood]

SparWeb,

I never took fluid mechanics, but my wife did, and kept the text book. It's a fairly useful resource, dunno if I would spend money on it or not today. FWIW, I first looked in my old heat transfer text (Holman), but even though it has fairly detailed derivations of the boundary layer solutions (laminar and turbulent), nowhere does it define d in terms of freestream velocity. I do recall seeing somebody's heat transfer analysis that alluded to the same problem, i.e. a different correlation for heat transfer from two different researchers was traced to a different definition of d. But it was a long time ago...

 

[WKTaylor]

SparWeb...

I'm curious... Is this a 'learning exercise' or are You analyzing an actual vehicle for real-world Excrescence Drag [or drag reduction]?


Regards, Wil Taylor

o Trust - But Verify!
o We believe to be true what we prefer to be true. [Unknown]
o For those who believe, no proof is required; for those who cannot believe, no proof is possible. [variation,Stuart Chase]
o Unfortunately, in science what You 'believe' is irrelevant. ["Orion", Homebuiltairplanes.com forum]

 

[Sparweb]

Definitely real world.
A blend of many long and short term goals.... reality check of a CFD analysis that we will be subcontracting, getting started on the loads for preliminary stuctural analysis even before the CFD people give us their data.... educational task for a summer student... lots of reasons.

STF

 

[WKTaylor]

Berrwy Berrwy Intewesting.

As a service/liaison enginerd I've had to understand [ROT] aero-drag/lift aberrations/asymmetry effects for various military acft... especially when a ‘bird’ has been pronounced a ‘sick old dog'.

IE: skin/panel mismatches, rough paint [or erosion-coating] finishes, external [air-flow side] patches, etc...; or a flight control surface can't be balanced; or engine performance is sub-par; unusual aerodynamic noises or vibrations; external store carriage; ice/snow/rain/sand accumulation/effects/removal; etc. It is amazing what 'garbage' can accumulate-on/affect a jet in-service!

For giggles, You may find the following 'other references' [stumble-on stuff] useful...

AIAA 2014-2866 A Study of Airplane Excrescence Drag [GA]

AFWAL-TM-84-203 PREDICTION OF AERODYNAMIC DRAG

AGARD-AG-264 Aircraft Excrescence Drag

AGARD-LS-67 Prediction Methods for Aircraft Aerodynamic Characteristics (REF chapter 'Boundary-Layer Calculation Methods and Application to
Aerodynamic Problems' by J.Steinheuer)

AGARD-R-654 Special Course on Concepts for Drag Reduction

AGARD-R-723 Aircraft Drag Prediction and Reduction

AGARD-R-786 Special Course on Skin Friction Drag Reduction

Dan Raymer’s Aircraft & RDS

http://www.aircraftdesign.com/

DARCorporation

http://www.darcorp.com/

[DAR Corp & Roskam's books]

NAVAIR 00-8T-80 Aerodynamics for Naval Aviators

http://www.faa.gov/regulations_policies/handbooks_manuals/aviation/media/00-80t-80.pdf

Numerous ESDU short-courses

https://files.engineering.com/getfi...b34-11258a0eb2bd&file=ESDU_catalogue~2017.pdf

Regards, Wil Taylor

o Trust - But Verify!
o We believe to be true what we prefer to be true. [Unknown]
o For those who believe, no proof is required; for those who cannot believe, no proof is possible. [variation,Stuart Chase]
o Unfortunately, in science what You 'believe' is irrelevant. ["Orion", Homebuiltairplanes.com forum]

 

[Sparweb]

Wil,
So it's not really excrescence drag that we're concerned about; not exactly. Our customer wants to sample air from an undisturbed airstream, and expects a CFD analysis of the dimensions of the BL to locate the probe... But I think we could use a 6-inch longer mast and stop worrying... So while I am inclined just get the job done and play safe, the customer is quite happy to study the phenomenon in detail. A rare opportunity for me to compare the old classic books with the newest CFD analysis. Given the importance they are placing on the data quality, we may also end up with a test flight to compare CFD predictions with actual measurements... a data trifecta!

STF

 

[rb1957]

this to avoid using the airplane's systems ? they'll at least give you a good "truth" to compare with your installation's data.

another day in paradise, or is paradise one day closer ?

 

[berkshire]

Why not just drop a " Bomb" on a line ?
B.E.

You are judged not by what you know, but by what you can do.

 

[Sparweb]

We're doing this purely for science.

Here's an example of what's going to be built (not our aircraft, not our customer, not our instruments, but the same idea, attached to the FUSELAGE):

STF

 

[rb1957]

where ever you mount this, you can use the a/c systems to validate (during the test phase) that the instrument is reading correctly.

another day in paradise, or is paradise one day closer ?

 

[Sparweb]

Berkshire,
Great question!
I had a customer many many moons ago that operated a "clothesline" CASA 212 with these hanging off the back. Made them up a new cradle for the fat one.
Google "tem aircraft survey" for more about those guys.

STF

 

[Sparweb]

Wil,
I've been going through your bibliography, and I found a few more gems that you may find interesting.

AGARD Flight Test Instrumentation Series Volumes 1 & 2, on Pressure and Flow Measurement
NATO Search page

STF