Frontal area resisantance vs. Wetted surface

Hello
I wonder what ideas are there around the factor of frontal area resistance and wetted surface resistance. Generally I speak the bulb keel case, and particularly: frontal area (looking to aft) would be increased by bigger diameter of torpedo bulb, but wetted surface would be smaller (mostly on bulb; fin is another case and is affected by profile mostly). I mean weight is constant, so the bulb would have two options - longer and more narrow, or shorter and thicker.
SO, what are the appreiciated points - less frontal or less wetted?

boa

 

Both the drag due to frontal area and the drag due to wetted area come from losses in the boundary layer. You can, indeed trade wetted area for frontal area, provided that you maintain attached flow. This was the subject of Bruce Carmichael's research in the 1960's. He came up with some low fineness ratio bodies that had very low drag.

Carmichael, Bruce H "Underwater Vehicle Drag Reduction through choice of Shape". AIAA 2nd Propulsion Joint Specialist Conference, Colorado Springs, USA, June 1966, Paper No. 66-657.

Parsons used an optimization routine and a CFD code to shape axisymmetric bodies for minimum drag. A comparison between Carmichael's Dolphin and Parsons' X-35 bodies is shown in the attached figure. (Note the Reynolds number. "Your mileage may vary.")

PARSONS, J.S., GOODSON, R.E., and GOLDSCHMIED, F.R., "Shaping of axisymmetric bodies for minimum drag in incompressible flow," Journal of Hydronautics 1974, 0022-1716, vol.8 no.3 (100-107).

Take a look at Design of Fuselage Shapes for Natural Laminar Flow, Drag Reduction and Shape Optimization of Airship Bodies.

One way that's been successfully used is to adopt 2D airfoil shapes by taking the coordinates to the 3/2 power. This tends to make a shape that is more pointed than the airfoil from which it was derived.

One problem in designing minimum drag shapes, is you can get almost any answer you want, depending on what you assume for the base pressure. And a bulb has to operate efficiently over a wide range of speeds. It would not be good to design a bulb for a high Reynolds number, putting the maximum thickness way back to provide a long favorable pressure gradient on the forebody and a steep adverse pressure gradient on the aft body, only to find that the aft body experienced massive separation and drag at lower speeds.

Another problem is a keel bulb does not see axial flow. The bulb has to operate at a leeway angle. This brings with it cross-flows that will make the boundary layer separate earlier, and interference between the bulb and keel strut that can reduce or increase the induced drag. These factors, along with the desire to make the bulb center of gravity as low as possible, also make non-axisymmetric shapes interesting possibilities.

 

I have used Michlet to look at wave drag on a sumberged hull and it fits with what I have measured with an eliptical nosed parabolic tail on a submerged hull having fineness ratio of 8. This was not a "laminar flow" hull. The drag was much higher than my prediction because I did not allow for wave drag. You need to be a few diameters below the surface before wave drag becomes negligible and Michlet demonstrates this.

I did not try optimisation of the submerged hull with Godzilla but it would be interesting to see what it comes up with. Could be just a sphere!

Irrespective, if you are considering a keel bulb then you could have surface effects and hull interference effects that alter the shape from the ideal laminar flow body. Once wave factors come into play there are usually benefits to increasing fineness ratio.

Rick W.

 

I would recommend avoiding some of the extreme pointed "optimum" NFD shapes. This is because many have directionaly unstable flow patterns and also extremely poor off axis moments and drag. There is a reason high speed submarines have blunt forebodies.

 

There is a Godzilla example bundled with the program that allows you to optimise for skin-friction only (i.e. no need to submerge the object to eliminate wave effects). The optimum is not a hemisphere as you expected, but rather more elliptical. Reynolds effects are responsible because of the trade-off between the lowest possible surface area and the benefits of going to a higher Reynolds number by increasing the length slightly.

Regards,
Leo.

 

Dalton, Charles and Zedan, M.F.,
Design of low-drag axisymmetric shapes by the inverse method,
J. Hydronautics, Vol. 15, Nos.1-4, Jan-Dec. 1981, pp. 48-54.

Hess, John L.,
On the problem of shaping an axisymmetric body to obtain low drag
at large Reynolds numbers,
J. Ship Research, Vol. 20, March 1976, pp. 51-60.

Nakayama, A. and Patel, V.C.,
Calculation of the viscous resistance of bodies of revolution,
J. Hydronautics, Vol. 8, No. 4, Oct. 1974, pp. 154-162.

Mattner, T.W Tuck, E.O and Denier, J.P.,
Optimal nose shaping for delayed boundary-layer separation in
laminar plane-symmetric and axisymmetric flow,
15th Australasian Fluid Mechanics Conf., Uni of Sydney, Australia, 13-17 Dec. 2004.

Smith, A.M.O.,
Stratford's turbulent separation criteria for axially-symmetric flows,
J. App. Math. and Physics (ZAMP), Vol. 28, 1977, pp. 929-939.

Zedan, M. Fouad and Dalton, Charles,
Viscous drag computation for axisymmetric bodies at high Reynolds
numbers,
J. Hydronautics, Vol. 13, No. 2, April 1979, pp. 52-60.


Just a few more references for you, Tom.

All the best,
Leo.

 

A longer more slender bulb has more wetted surf area but more distributed weight and I think they are used more for heavier weather sailing where skin friction is not that impostant and when the boat is being moved about by waves it slightly dampens the movements compared to a stubby bulb with little wetted surf area and mass more centered beneath the keel. Also the modern bulbs are kind of trapezoidal to try and get the centre of gravity as low as possible since it's by far the heaviest part, usually.?