SID VISCOUS - Longitudinal Wave Cuts

SID VISCOUS v 1.0
=================
SID estimates the free wave spectrum and the wave resistance of a
monohull vessel from wave elevations given along a single longitudinal
cut parallel to the ship's track.

RUNNING THE PROGRAM
===================
To run the program, invoke the executable file named sid.exe.
There is no screen output, unless you have made a mess of the input
files and error messages appear.

INPUT FILES
===========
The program expects to find the plain text input file "sid.in" in the
same directory as the executable file sid.exe.

The first four values in the input file are:
gravitational acceleration, g, (m/sec/sec)
water density, rho, (kg/m^3)
Ship speed, U, (m/sec)
N: Number of x,y,z triplets to follow (integer: 201 <= N <= 16000).

The remainder of the input file must contain N values (x,y,z) where
x is distance along the cut in metres,
y is the distance from the ship's track, and
z is the wave elevation.

For example:
-0.60000E+01, -0.30480E+01, 0.47751E-04
-0.59242E+01, -0.30480E+01, 0.49019E-04
...
0.60000E+03, -0.30480E+01, -0.18081E-02

Note that the x-values must be equally-spaced along the cut.

The size of the input file could have been reduced because the y
values are all the same. Future free versions of SID may allow multiple
wave cuts that are not straight lines parallel to the ship's track.

OUTPUT
======
SID creates two plain text output files.

pq.csv
------
The P,Q functions are saved in the file named pq.csv.
1st column: theta (in radians)
2nd column: P
3rd column: Q

rw.csv
------
The free wave spectrum is
drW/dtheta = c * (P^2 + Q^2) / (cos(theta))^5
where
c= 4*rho*(g^4)/(pi*(U^6)).

Integrating dRw/dtheta from 0 to pi/2 yields the wave resistance in
Newtons. This single value is saved in the rw.csv file.

COMMENTS
========
1. Previous versions of output files are over-written, so save your
results after each run!

2. It is extremely unlikely that wave elevations could be measured
with the precision used in the examples to follow. They should be
treated as simple exercises to verify the program.

3. The program is very unforgiving: there is no error checking. Don't
put spaces between lines in the input file.

REFERENCES
==========
Lazauskas,L., "Resistance, wave-making and wave-decay of thin ships,
with particular emphasis on the effects of viscosity",
PhD Thesis, Applied Mathematics, The University of Adelaide, 20 April
2009, http://digital.library.adelaide.edu.au/dspace/handle/2440/53216

Newman, J.N., "The determination of wave resistance from wave
measurements along a parallel cut", 1st International Seminar on
Theoretical Wave Resistance, University of Michigan, Ann Arbor, 1963.

 

Example 1: Wigley Model Hull
============================
The vessel in this set of examples is a 3.048 m long Wigley model hull.
The beam is 0.3048 m, and the draft is 0.1905 m.

The wave cut is at y = -3.048 m from the ship's track as shown in
Figure 1. The negative value indicates that the cut is on the port side
of the vessel.
The wave cuts all start at x = -6.0 m, but end at different locations
in each example.

To run the examples, type the example batch file name into a console
window, or double-click the batch file you require.
Each batch files copies the appropriate example input file to "sid.in"
and then runs the executable, sid.exe.
Each example takes about 1 second on an IBM i7 PC.

ex1a.bat
--------
The input file for this example is also the default sid.in file when
you first install SID.

The vessel is travelling at 3.0 m/s, which corresponds to a
length-based Froude number of 0.549.

SID predictions of the wave resistance compare well with those
calculated by Michlet and Ulimich v 1.0.

Michlet: 27.531 Newtons
Ulimich: 27.502 Newtons
SIDv1.0: 27.575 Newtons

Figure 2 shows estimated values of P(theta) and Q(theta).
The Q function is equal to zero, or very close to it, for all theta,
because the hull is fore-aft symmetric.

The free wave spectrum in Figure 3 is very similar to that produced by
Michlet for the Wigley hull example bundled with that program. If you
are checking this yourself, you will need to use a negative value of
Ntheta to force Michlet to exclude the boundary layer displacement
thickness before it calculates the wave resistance. (I used Ntheta =
-2048 to get greater accuracy for comparison with Ulimich and SID).

Also note that Michlet presents the free wave spectrum in kilo Newtons
for -90 deg. < theta < 90 deg. as shown in Figure 4. The area under the
curve is equal to the wave resistance in kilo Newtons.

ex1b.bat
--------
In this example the vessel is travelling at 1.0 m/s, which corresponds
to a length-based Froude number of 0.183. This is about as low as we
can go with the present version of SID.

After running the example, plot the P,Q functions to see the relatively
poor approximations for small values of theta. Despite that, the value
of the predicted wave resistance is quite reasonable.

Michlet: 0.5112 Newtons
Ulimich: 0.5108 Newtons
SIDv1.0: 0.5131 Newtons

ex1c.bat
--------
In this example the vessel is travelling at 5.0 m/s, which corresponds
to a length-based Froude number of 0.915. Although this is an
unreasonably large Froude number for this type of hull, it is still
useful for verification purposes.

The value of the predicted wave resistance compares very favourably
with Michlet and Ulimich estimates.

Michlet: 37.502 Newtons
Ulimich: 37.458 Newtons
SIDv1.0: 37.487 Newtons

USEFUL EXERCISES
================
1. Reduce the number of wave records to see how it affects predictions
of P,Q, the free-wave spectrum, and the wave resistance.
You can do this by changing the third entry in the input file.
Increasing the number of wave records would require calculating
wave elevations yourself using, for example, Michlet or Flotilla.

2. Adding random and/or systematic noise to the z-values will show how
predictions could be affected when real on-water data is used as input.

 

Example 2: DTMB 5415 Destroyer
==============================
The vessel in this example is an imaginary 8570 tonne, 142 m long
destroyer hull with a large sonar dome and a small transom stern.
The hull offsets are based on the model DTMB 5415 hull. See Figure 1.
The beam of the vessel is 18.0 m; the draft is 8.5 m.

ex2a.bat
--------
The vessel is travelling at 15.0 m/s, which corresponds to a
length-based Froude number of 0.402.

The wave cut is at y = -200.0 m, and it extends from x = -200.0 m to
x = 15800.0 m.

SID's prediction of the wave resistance is about 10% lower than
Michlet's because Michlet's predictions for transom stern hulls
includes some components that do not manifest themselves in the wave
pattern. SID's predictions do, however, agree very well with those of
SWPE.

Michlet: 1349330 Newtons
SWPE: 1224817 Newtons
SIDv1.0: 1226194 Newtons

Although the values in the hollows of the free wave spectrum curve are
small, they are significantly greater than zero, in contrast to the
curves for the Wigley hull shown in Example 1. The reason for this
behaviour in the present example is due to the vessel's transom stern.

Clearly we have obtained, "...more information from the wave pattern
than from the single number which is the wave resistance. Experienced
naval architects can interpret the measured spectrum by itself, and
use it as a basis for improving and refining hull designs."
J.N. Newman, "Marine Hydrodynamics", 1977.

 

Example 3: LA Class Submarine
=============================
This example is for a 6400 tonne, 110m long LA class submarine.
The beam of the hull is 9.64m; the draft (from baseline to the top of
the conning tower) is 16.133m.

ex3a.bat
--------
In this example the vessel is travelling at 10 knots (5.144 m/s),
which corresponds to a length-based Froude number of 0.157.

The vessel is submerged so that the conning tower is just touching the
undisturbed free surface. See Figure 1.

The wave cut is at y = -50.0m.

SID predictions of the wave resistance compare well with those
calculated by Michlet and SWPE.

Michlet: 33933.2 Newtons
SWPE: 33964.8 Newtons
SIDv1.0: 33932.0 Newtons

Figure 2 shows estimated values of P(theta) and Q(theta).
The grid-scale oscillations at small theta are due to the low Froude
number. Using a much longer wave cut would reduce these oscillations
at the expense of longer computation times.

The free wave spectrum in Figure 3 is very similar to that produced by
Michlet for the LAsub example bundled with that program. If you
are checking this yourself, you will need to use a negative value of
Ntheta to force Michlet to exclude the boundary layer displacement
thickness before it calculates the wave resistance.
(I used Ntheta = -1024 to calculate the wave resistance).

 

Very interesting, Leo. It scares me to even just imagine the amount of math involved in that reverse analysis.

And I just have to express the first thought I've had when I spotted this thread: most sincere compliments for the choice of the software's name.

 

Very kind, Slavi, but it's actually quite a bit easier than you think.
There is no annoying hull to worry about

I'm glad you don't think it's rotten.

 

What's the hardest part about implementing the integrals numerically? Do you have a way to check the 'quality' of the numerical solution? What parameters/variables are the equations most sensitive to numerically?

 

The length of the cut and the number of points per wavelength
can affect the quality of the final result, but I use special
techniques to get around that. Although it's not a big issue
for the free version, there are some tricks to do with viscosity
that help too.

The other major "trick" is to invert the correct formula. Some
people incorrectly use the far-field complex amplitude. The
controversy over that issue should have been settled once and for
all back in 1963, but there are very recent papers that still use
the the wrong method. I am fairly certain that towing tanks use the
correct method in routine work.

 

Can you elaborate on the "special techniques" you use to get around the problems of the 'length of the cut' and number of samples per wave? Are your projects open source?

EDIT:
You should add your solver to the OpenFOAM CFD suite and call it "Michlet_FOAM" or something like that.

 

It would take far too long to elaborate. There are different methods depending
on the type of viscosity formulation. Some are used with Lamb's formulation,
others are used for surface layers, as in simulations with thin layers of oil-slick
or ice slush.

Sorry, I'm happy to provide executables on a donation basis, but my projects
aren't open source. They are really just hobby interests I cobble together while
watching B-grade scifi. The lack of comments in the code would embarrass me
and infuriate everyone else.

 

SID does not depend on thin-ship theory, so any reference to Michell would
be inappropriate. The code works for beamy vessels that violate the small
slope assumption. All that is necessary is that the wave cut is far enough
away from the vessel so that non-linear effects are negligible and wave
slopes are small. I only used Michlet and UliMich to verfiy that SID
converges to the correct wave resistance for thin ships.

I could connect it to OpenFoam, but it would be more fun for me to get SID
working with hovercraft, multihulls, and Surface Effect Ships. One possible
application of SID and its variants is to extend CFD calculations into the far
field, but I suspect others might have already done that.

IIRC, Kevin Maki and his Uni of Michigan colleagues have already made an
OpenFoam version of Michell's integral.

 

What I actually had in mind in referencing the potential solution to CFD was incorporating Doug Read's work with artificial neural networks as a correction to the linear theory (the NN's were trained from Ship Flo and the corrections are based on hull form coefficients).

Thanks for the tip about Kevin Maki's work.

 

I think that Friendship Systems are also working on optimisation using
parametric modelling and hooks to a variety of CFD codes.
https://www.friendship-systems.com/products/friendship-framework

 

SID also works with hovercraft (ACV) and other pressure distributions.
To install Example 4 to follow, unzip the file and copy ex4a.in to the examples
sub-directory, and the ex4a.bat file to the directory where the other batch files
reside.

 

Example 4: Model Hovercraft
===========================
The vessel in this example is a 2.070m long model air-cushion vehicle
(ACV) used by Everest and Hogben in their experimental studies.
The beam of the hull is 1.372 m. The nominal pressure is p0=28.7485 Pa.

ex4a.bat
--------
In this example the vessel is travelling at 2.7033 m/s which
corresponds to a length-based Froude number of 0.6.

The wave cut is at y = -4.0m.

SID predictions of the wave resistance compare well with those
calculated by Flotilla v 3.0 which is available on boatdesign.net.

Flotilla: 0.3075 Newtons
SIDv1.0: 0.3065 Newtons

Figure 2 shows estimated values of P(theta) and Q(theta). The free wave
spectrum is given in Figure 3.

The Newman-Poole wave resistance coefficient C_NP is obtained by
multiplying the wave resistance by (rho*g)/(B * p0^2).
For this example we have C_NP = 2.6481 which is within the experimental
scatter and close to the value predicted by CFDship shown in Figure 3.

REFERENCES
==========
Bhushan, S., Stern, F. and Doctors, L.J.,
"Verification and validation of URANS wave resistance for Air Cushion
Vehicles and comparison with linear theory",
J. Ship Research, 11 Oct. 2011.

Everest, J.T. and Hogben, N.,
"Research on hovercraft over calm water",
Trans. RINA, 1967, pp. 311-326.

Newman, J.N. and Poole, F.A.P.,
"The wave resistance of a moving pressure distribution in a canal",
Schiffstechnik, Vol. 9, 1962, pp. 1-6.