Effect of Friction Lines on the Resistance of a Friction Plane

Thanks Leo. I have been using michlet since its early release. I did not do Procedure 1 & 2. My fault.

 

Attached are two text files of experimental total resistance coefficients as functions of Froude number from Candries' thesis.
These should be used to check your own calculations.

I used a little program named "engauge" to get the points from magnified graphs in the pdf file of his thesis. Any differences from the original are due to me. Always check for yourself!

I tried Prohaska's method to get form factors for the two drafts, however, there are very few points in the correct Froude number region. And, as the 26th ITTC warns, experimental data at low Fr can be subject to very large errors.

Leo.

 

Leo, I don't know how Michlet converts splines into panels, but it would seem that the struts' tip conditions would be different in Michlet (beveled) than on the model (flat). I was wondering if it would make sense to increase the draft in Michlet by enough to match surface areas. The bevel also affects prismatic coefficient a bit. Don't know how to finesse that one except to put some rocker in the keel line. Did you happen to check how well your five splines reproduce the model with respect to C_p?

 

The strut is approximated well using the spline. If you look at the off1.mlt output file you will see that there is no bevel.
There is, of course, no need to use splines for a vertical strut. You can just use use a table of offsets once you are happy with the number of stations and waterlines.

It is easy to check that the volume is accurate. For example, try a vertical parabolic strut. Michlet calculates the CB and Cp exactly.

 

I thought the lowest waterline always had 0 offset and the bottom panels formed a chine at the next waterline up. Since you had 101 waterlines and the thickness averaged about 1%.....

ok, there's my mistake, I was thinking thickness 1% of draft- its 1% of length - six times less bevel than I had imagined.

 

In Michlet, the bowmost station always has 0 offset.

You should still use a large number of stations and waterlines to get an accurate estimate of surface area.

I should also point out that a lot of the resistance work can and should be done "offline."

For example, once you have a good estimate of the wave resistance and surface area, it is quite easy to paste the results into Excel and then add the skin-friction using the ITTC line or some other lines. There is no need to keep using Michlet to calculate the total drag. That's too slow!

Using a spreadsheet it is also easy to try different values of form factors to see whether they improve the correlation with the experiments.

Leo.

 

To Leo "the great boffin"

I have tried to learn something from Candries' experiments that could be used for the resistance-prediction of a yacht hull. In the case of the smooth surface there is little news. The measurements of the small plate are doubtful, I have attached a comparison with the total drag from other authors, using the measured momentum deficit thickness.
Candries' friction force data for the large plate depend heavily on the calculated wave resistance that needs to be subtracted from the total drag. He is just happy that his CFD-program uses the same assumptions as Schönherr and the CFD-results for the frictional forces coincide with the Schönherr-line.

In any case the hull of a yacht is quite different from the hull of commercial ships. These ships have a large middle part with long parallel sides that allow the usage of the flat-plate equations for the calculation of the frictional resistance, may be improved by a form factor that accounts for the influence of the afterbody. On the contrary a yacht hull has streamlines that are curved and the waterspeed varies continuously along the hull. The boundary layer is also influenced by the changing curvatures. Therefore I posted a note in DCockey's thread concerning the Delft series. I think the Delft-method for calculating frictional resistance might be right for tankers but is just too crude for yachts.

When you use your michlet program and restrict its usage to thin ships you are also on the safe side regarding the frictional resistance. Flat-plate equations might be applicable.

Regards
Uli

 

I agree with you, Uli.

Finding an appropriate value of the form factor seems to be the key, but that is not a simple task.

Firstly, getting accurate data at low Froude numbers is subject to great inaccuracies. The 26th ITTC says that there can be 20% variations in estimated form factors for "simple" hulls. For hulls with immersed transom the variation can be much more. And for hulls with bulbous bows, the standard methods are next to useless.

Secondly, and more worrying, is that several researchers have found that form factors are dependent on the Reynolds number. That undermines a very cherished assumption by those who like to use form factors, especially when they rely on small model hulls for towing tank tests.

I'm still not quite sure what that means for the ITTC line, which supposedly includes an allowance for form effects at low Rn.

I also agree 100% with you that flat-plate skin friction is more likely to work well with thin ships. That's why I prefer to leave stubby hulls to those who dabble in the darker arts.

Thanks for the pdf file of results. I looked at the same set of data as you did, however, I did not try to produce a total CF curve directly: I concentrated more on the local skin-friction cf.

What amused me greatly was that I could end up with three different CF curves (ITTC, Katsui or Grigson) by choosing pairs of "popular" values of the von Karman constant and the intercept B0. As Grigson mentions, this notion of "popular" values is not good science - it is more like a shouting contest at a town-hall meeting!

Finally, it is interesting that the 26th ITTC admits that there may be better skin-friction lines, but the real issue is to get better estimates of form factors. IIRC, they have recommended that task as a priority for the next ITTC.

Leo.

 

Here's an idea on how to obtain improved estimates of Cf, though requiring considerable more effort than using a simple curve.

A streamline based boundary layer model could be marched along the hull surface streamlines to estimate local cf, and the results integrated for an overall Cf IF the streamline shape and velocities are known.

But where to obtain the streamline shape and velocities from? Perhaps they don't need to be known exactly. Assuming the streamline based boundary layer model is reasonably good, then the streamline shape and velocity would not have to be exact to get an improved estimate of Cf over a simple one curve fits all approach. Either a potential flow code or a RANS code would be run to obtain the (approximate) streamlines and (outside the boundary) velocities on/near the hull surface. If data is available from a test of the profile of the free surface at the model it could be used to adjust/improve the potential flow/RANS code results. The streamline shapes would then be calculated and the boundary layer model marched along the streamlines to obtain the local skin friction, which in turn would be intergrated for overall Cf. (If a potential flow code is used for the overall flow then the boundary layer displacement thickness can be calculated and used to improve the flow calculations.)

This proceedure would be followed at both the scale model and full size Renoylds numbers, and then the usual procedures followed to scale the test results, but using the Cf from the calculations rather than values from a curve, adjusted or not.

 

I think that the methods you have proposed have been tried over the last 40 years and in a variety of ways but without much success. IIRC, Patel and Landweber tried several streamline tracing methods back in the 1970s. There are many difficulties, not least that of inaccuracies propagating as one marches along streamlines. I have tried similar methods, for fun, using thin-ship theory, but I certainly wouldn't recommend it.

If you are keen, search for Landweber and Patel, and follow the trail of papers! The IIHR should have some early reports in their online archives.

 

I'm not surprised that others have tried similar ideas. It was a thought on how to include "3D" effects in calculating/estimating Cf.

In the 1980's I used streamline tracking and boundary layer intergration as included in VSAERO, which has the potential panel method and streamline boundary layer model coupled. I was interested in predicting separation rather than skin friction and had moderate success. I was using the commercial version of VSAERO (AMI), not the public distribution version.

 

Very interesting thread

The form factor is not the only issue if it comes to the drag prediction of yacht hulls. They can also exhibit larger portions of laminar flow at low speeds. I have used Patels method for axisymmetric turbulent boundary layers to calculate the skin friction along the hull. I know that the hull is not a body of revolution, but it is "less wrong" than the flat plate assumption.
To get the frictional drag (total drag - wave drag) it is not sufficient to integrate the skin friction cf as DCockey proposed, you need to add an estimate for the pressure drag. I have used proposals from Hoerner. The results can be seen in the attachement.
An alternative method was given by Granville. He calculates frictional drag using momentum thickness, shape factor and flow velocity at the stern.

In any case, using the Delft-method might result in an erroneous extrapolation to full size.

Curious for your comments
Uli

 

Grigson's line seems to do well here.

Have you tried using a double-body method to get the viscous pressure resistance?

 

How is "pressure" drag separated from "wave" drag?

If I go back to the basics the overall drag can be considered as longitudinal sum of the integral of the longitudinal component of the shear stress vector over the wetted surface, and the integral of the longitudinal component of the pressure vector over the wetted surface. This equation is exact. I'm using two integrals for a reason. The presence of a free surface and the resulting waves and changes in flow field affect the intergrals. The challenge of course is that the pressure distribution and shear stress distribution are generally not known everywhere over the wetted surface.

My question is how are the two integrals split into the three quantities of "skin friction", "pressure drag" and "wave drag?

Is "skin friction" the shear stress integral? Or is the "skin friction" the portion of the shear stress integral which is dependent on Re only and is not Fn dependent?

Is the "pressure drag" mentioned above the portion of the drag due to the pressure which is Re dependent? I assume it must be, otherwise there wouldn't be any wave drag (other than possibly that due to shear stresses).

Is the "wave drag" the portion of the pressure integral and the shear stress integral which is dependent on Fn alone and is not Re dependent.

Another approach is to divide drag into three terms:
A - Fn dependent, Re independent
B - Fn independent, Re dependent
C - Fn dependent, Re dependent

Froude's hypotheis is that C is negligable and can be neglected. In that case A is generally called "wave drag" and B is frequently called "skin friction" and life is simplier.

The problems of course arise when C can't be neglected. It generally includes contributions from both the shear stress integral and the pressure integral. Recognizing this may be helpful in determining how to model it.

 

Replaced By Post Below