Theories for estimating bulb drag

[Dan S]

I have been working on a project to develop a low drag keel bulb for a specific Reynolds number that I’m interested in. The bulb will be a symmetric foil revolved around its center axis. I have used Xfoil to develop some 2D sections that look promising, but I haven’t been able to take the 2D coefficients of drag and lift and turn them into something meaningful in 3d.

Does anyone know of a way to take the 2D values and use them to estimate 3D drag and lift forces? I’m not talking exact calculations, just something close enough to show trends.

[nico]

Have a look at the Bulb design chapter, this is my BEng Yacht and Powercraft design dissertation about the design of a volvo70. You ll find something that should work well enough if your shape does not show much separation is 3D.

[jehardiman]

Get out Heorner, both volumes, lots of data on 3D bulbs at the end of wings. However, as Nico pointed out, seperation, and the resultant flow effects, is more an issue than straight up drag would indicate. There are several declassified WWII vintage DTMB hydro-reports on this issue. What is your Rn and a may be able to point out a specific paper.

[Dan S]

Originally Posted by jehardiman

Get out Heorner, both volumes, lots of data on 3D bulbs at the end of wings. However, as Nico pointed out, seperation, and the resultant flow effects, is more an issue than straight up drag would indicate. There are several declassified WWII vintage DTMB hydro-reports on this issue. What is your Rn and a may be able to point out a specific paper.

The Rn should be 385,000 plus or minus 15,000.

My goal is to hold volume constant, and thus let the Rn vary. The bulb is for a model, and I have seen some references, that say, at these Reynolds numbers, long narrow, bulbs have less total drag even thought they have higher viscous drag. The long narrow bulb also helps prevent hobby horsing.

[JesperW]

You might find this paper interesting:

http://www.aiaa.org/content.cfm?page...re97&gID=48131

(It will cost you $25)

Also, if you search litterature from the 80's, ("Progress in Aerospace Sciences"), you can find a lot of work done by A. D. Young on laminar bodies.

/jesper

[jehardiman]

Originally Posted by Dan S

The Rn should be 385,000 plus or minus 15,000.

My goal is to hold volume constant, and thus let the Rn vary. The bulb is for a model, and I have seen some references, that say, at these Reynolds numbers, long narrow, bulbs have less total drag even thought they have higher viscous drag. The long narrow bulb also helps prevent hobby horsing.

That is a pretty low Rn, not really "real world" in hydro application. Of course longer bodies will have lower drag due to the drop of Cf due to flow acceleration changing Rn at the micro velocities you are at. I think you are going to have a lot of transition data scatter. I'll look, but I don't think there is anything with a Rn that low.

[tspeer]

Originally Posted by JesperW

You might find this paper interesting:

http://www.aiaa.org/content.cfm?page...re97&gID=48131

The Parsons paper, is interesting, but his body is aimed at much higher Reynolds numbers than would be useful in a keel bulb, and probably too much laminar flow than can be achieved in water.

The best source of information on the drag of axisymmetric bodies I've found is Bruce Carmichael's, "Personal Aircraft Drag Reduction." It's published by the author:

Bruce Carmichael
34795 Camino Capistrano
Capistrano Beach, CA 92624
brucecar1@juno.com
(949) 496 5191

and available from Aircraft Spruce and Specialty Company, among others.

Carmichael's data are especially interesting because much of it was collected in water, using buoyant bodies that were released from the body of a lake to rise at terminal velocity to the surface. Much of the laminar flow drag data in the literature has been collected in air, and there's a lot of empirical evidence to show that transition occurs earlier in water than in air at the same Reynolds number.

However, one huge impediment for applying the research on axisymmetric bodies is the flow is not axisymmetric about a bulb. A nicely designed axisymmetric shape is not going to perform well if the flow separates when operating with leeway. Predicting that is a real challenge.

[jehardiman]

I don't think the data, raw or processed, from the buoyant body drag testing at Lake Pend Oreille is really going to help much. The aspect ratios may be a little on the low side and the Rn's high. Then again there is also the asymetry of the situation and the whole wave orbital issue.

[Dan S]

For the iom class this is pretty much the general bulb shape from all the top designers. http://www.gbmy.com/cballast.html

I belive David Hollum designed this foil for sails etc.

[jehardiman]

You know Dan, that looks like a Series 58 body. And you could most likely improve the drag of that photo ~30% just by adding some approprate fillets.

[Dan S]

Originally Posted by jehardiman

You know Dan, that looks like a Series 58 body. And you could most likely improve the drag of that photo ~30% just by adding some approprate fillets.

Do you know where I can find some online information about Series 58 bodies? I hope to make it to the local university library, to check out heorner (don’t have a personal copy), but I’m on call and the way work is going I bet I get called into the office. LOL why does work always get in the way of my personal life.

[tspeer]

Here's a paper that might be relevant,

Dalton, C., and Zedan, M. F., "Design of Low Drag Axisymmetric Shapes by the Inverse Method," Aerodynamics of Transportation, the Joint ASME-CSME Applied Mechanics, Fluids Engineering and Bioengineering Conference, June 18-20, 1979. Published by the American Society of Mechanical Engineers.

The methods they use were developed by Zedan, "Flow Around Axisymmetric Bodies: The direct and Inverse Problems," Ph.D. Dissertataion, University of Houston, 1979. The drag calculation is a fairly straight-forward integral boundary layer approach. It starts with the surface velocity distribution computed from the source distributions, then applies Thwaites' method for the laminar boundary layer to get the momentum thickness and shape factor, Crabtree's transition criterion, and Nash's turbulent boundary layer relation to get the shape factor. Patel's method for a thick boundary layer is used from there to the tail, and Young's formula predicts the drag coefficient from the final boundary layer thickness and characteristics.

Other related papers are:

Zedan, M. F.; Seif, A. A.; Al-Moufadi, S.; "Drag Reduction of Airplane Fuselages Through Shaping by the Inverse Method," Journal of Aircraft, 1994,
0021-8669 vol.31 no.2 (279-287).

Parsons, J. S, and Goodson, R. E., "The Optimum Shaping of Axisymmetric Bodies for Minimum Drag in Incompressible Flow," Purdue University Report, ACC-72-6, June 1972.

Their approach to designing a low-drag axisymmetric body is similar to designing a low-drag airfoil section using an inverse code like XFOIL's MDES method. You specify a favorable pressure gradient from the nose to as far back as you think you can get away with, and then use a pressure distribution from there to the tail to recover from the peak velocity in as short a distance as possible without incurring turbulent separation. The length of the favorable pressure gradient may be driven by laminar to turbulent transition at the design Reynolds number, or by the distance needed for the recovery region.

The concave pressure recovery results in a short body for the volume it has to contain, reducing wetted area. The favorable pressure gradient delays boundary layer transition, so there is a laminar boundary layer over as much of the wetted area as possible.

Zedan and Dalton show how their method can reproduce the F-57 body of Parsons and Goodson, then proceed to use the inverse method to come up with an improved shape. It's coordinates are in the attached file. The F-57 came very near to transition in the first 10% of its length, so there was a distinct danger of premature transition and loss of laminar flow over much of the body. The modified shape is more robust.

[tspeer]

Originally Posted by Dan S

[color=#000066]Do you know where I can find some online information about Series 58 bodies? ...

They aren't in Hoerner.

The coordinates for the Series 58 bodies 4162 and 4165 are in the attached files. (From Moore, Wilburn L., "Bodies of Revolution With High Cavitation-Inception Speeds - For Application To The Design Of Hydrofoil-Boat Nacelles," Report 1669, David Taylor Model Basin, Sept. 1962.)

However, I think one can do better for a keel bulb. The 4165 was designed for a far higher volume Reynolds number than a bulb, so maintaining laminar flow was not a consideration at all. It has a modest adverse pressure gradient from 30% of the length all the way to 90%, which is very conservative.

The 4162 is less conservative, and actually has a hollow in the middle of its pressure distribution. It has a steeper pressure gradient than the 4165 aft of around 75% chord, and the pressure recovery is convex, which may be more susceptible to separation. The hollow in the pressure distribution of the 4162 may be a good thing when you combine it with a keel strut. The junction between the two will produce higher velocities, so the hollow in the 4162's velocity distribution will help compensate for the interfernce with the keel strut.

The best approach would be to use something like Zedan's method to design a shape that would take into account promoting laminar flow over at least part of the forebody, interference with the keel strut in the middle, and a short tail to minimize the wetted area.

Of course, an even better shape to take account of the keel would not be axisymmetric. It might be somewhat flattened or even dished on the top where the strut attaches, to help cancel the interference effects, but fuller on the bottom like a purely axisymmetric shape.

And then one might want to take into account leeway and heel...

[jehardiman]

Originally Posted by Dan S

Do you know where I can find some online information about Series 58 bodies?

DTMB Series 58 (a total of 24 bodies) and it's companion paper on parallel midbody have been declassified, but seem not to be included in most reference lists, I can't find them on the internet (and as they form the basis for most modern US submarines, I can see why). I'll have to get an exact title for you and you may have to go to a library that handles tech publications. One of the big things that Series 58 shows is that most of the lowest drag shapes are directionally unstable. This means that rudder angle must be added to keep them on course. This increases overall drag, but is not included in the drag analysis. Be warned!

[jehardiman]

Try to get you hands on these reports

Resistance Experiments on a Systematic Series of Streamlined Bodies of Revolution - For Application to the Design of High-Speed Submarines, Morton Gertler, DTMB Report C-297, April 1950

Additional Tests of the Series 58 Forms, Part I, Resistance tests of a Parallel Middle Body Series, C.A. Larson, DTMB Interim report C-738, November 1955.