Applications and Limitations of Potential Flow Codes
for the Wave Making Problem
Volker Bertram, IfS Gerhard Jensen, HSVA
1. Introduction
TECHNISCHE UNJVERSITEIT Laboratoiium voor Scheepshydromechanlca Archlef Mekelweg 2, 2628 CD De!ft Te 015.786813 - Fax: 015781838CFD is developing faster than any other field of ship hydrodynamics. "Applications and Limi-tations" can therefore only show the picture of the present situation (1993) and will be outdated very quickly. Nevertheless we consider it usefull to show some actual applications of our own
experience and to try a glance into the not too far future. We limit ourselves to panel methods as they are most certainly the most widely used approach for practical application.
To judge the results we have to introduce typical representations first. Then we will show a few cases of applications to practical modern ship hulls. In the closing chapter we will try to analyse the rate of development in non-viscous CFD for ships.
2. Representation of results
Most panel methods yield the source strength on the panel as the direct result. Summation of the velocities induced by all panels plus the parallel stream give the velocity at desired field points and especially on the collocation point(s) of each panel. Using Bernoulli's equation pressures and wave heights are computed at these points. Finally integration of the pressure yields forces and moments which can be used as resistance and to compute dynamical trim and sinkage (squat). Usully for this integration the pressure as well as the surface normal are assumed constant within each panel.
Sometimes the maximum value of the flow velocity across the water surface or some other error
criterion to check the quality of the non-linear solution are presented.
Panel methods for wave resistance computation yield a vast amount of data, typically velocities
at several thousand points. Of course this amount of data must be aggregated and presented in form of suitable plots. Usually only few plots are sufficient.
The typical plots include:
Pressure distributions on the ship hull
The computed pressures on the fore body are generally considered to be quite accurate.
A colour plot of interpolated isobares (pressures are proportional to the velocity squared) are used to recognize critical over velocitiesand steep pressure gradients. These areas are
often found near the shoulders of the vessel were they induce deep wave troughs. Steep pressure gradients correspond to steep wave slopes which will generally radiate into the field. Over velocities near the bottom may have a negative influence on the formfactor.
Interpolation of pressure between the panel centers gives a more realistic impression of the pressure distribution. It may however suggest a higher accuracy than the grid can
deliver. Therefore a plot of the grid must accompany the pressure plot, lithe steps in
the colouring are too small (or even smooth), which looks nice, a comparisonof different
variants is much more difficult. Pressure distributions are often presented in different
views, Fig. i and 2. - Wave profile
Basing on their experience with model tests ship designers are used to judge the hull form of ships based on the wave profile along the hull. When comparing design alternatives the
wave profile shows where a better interference has been achieved (e.g. Fig 3). To increase
clarity the vertical scale usually amplified. Also in case of the wave profile interpolation may suggest a higher data density than is really computed. Wave profiles along the hull can be computed in at least three different ways:
For each panel on the hull the wave height corresponding to the local velocity is computed. If this height intersects the panel a horizontal line is drawn.
The row of collocation points on the water surface next to the hull is plotted. For commonly used grids this row may be a significant percentage of the breadth from
the hull.
The transverse wave profile is extrapolated onto the hull.
For Froude Numbers higher than 0.2 there are generally no significant differnces between
options (1) and (2). HSVA will generally show both and an interpolation in one plot. Directly on the bow the results may not be physical. For a speed of 20 kn a stagnation pressure corresponding to a wave height of 5.4m would be expected for potential flow. As the collocation points generally do not describe the stagnation point at wedge shape water lines this value is not reached in the numerical results. In the real flow surface tension and wave breaking or spray formation will generally prevent the wave height to reach this value. This effect is usually limited to a very small region and the second or third panel along the waterline should show realistic results already.
- Velocity plots on the hull surface
Vector plots of velocity (Fig. 4) distributions give similar impressions of the flow direction
as tuft tests. Due to 3-dimensionality of the flow and the need to project the vectors onto
some view plane the quantitive judgement is difficult achieve. The plot of the pressure distribution (pressure is proportional to the velocity squared) helps to give some more
insight.
An additional use of velocity plots is the location of discretization errors, recognizable
by unplausible directions or lengths of the arrows. Unusual absolut values of the velocity
are generally easier recognized in the pressure plots.
- Wave pattern
The presentation of the wave pattern as contour lines (lines of equal wave height) (Fig. 6) is used to see from where waves (containing energy) are radiated away from the ship.
Those areas are too be treated in an optimization.
The design water line with marks of sections should be included to allow orientation in the wave pattern. Often we see that wave heights behind the vessel are higher than near
the bow, which is in many cases not observed in the real flow. The reason for this is
the missing damping in potential flow, the typical bluntness of the waterline, but mainly the missing thick and separating boundary layer at the stern so that stagnation pressure cannot be reached in real flow. This is not an error in the solution but underlines that potentail flow results are not very useful at the stern.
Another important use of these plots is the control of certain features at the outer limits of the free surface grid. Reflections at the sides or waves in front of the ship indicate an
insufficient fulfillment of the radiation condition and the condition of the open boundary.
- Perspective views of wave pattern
Perspective views of wave paterns may be with hidden lines, ray tracing and semy trans-parent water surface are quite popular. For the development of better hull forms they do not supply any additional information.
The computed wave resistance reacts very sensitvely to numerical errors. When using pressure integration basically the difference of the forces on fore and after body is computed. As these
forces are aproximately equal and about an order of magnitude larger then the resistance the
relative errors are significantly enhanced.
- Errors in the pressures come from the discretization and the assumption of constant pressure
and normal on the hull. This applies especially where strong pressure gradients occur (near corners, e.g. the bow) and where the hull surface curvature is large as compared to the panel
size (e.g. bulbous bow).
Integration of the hydostatic pressure according to the same method up to the zero speed water line often results in a logitudinal force which may have the same order of magnitude as the wave resistance at low Froude Numbers. If this force is accounted for the results may be
more realistic. An alternative method for the wave resistance determination could be the wave
patern analysis from longitudinal or vertical cuts. As they base on linear wave theory and a certain directional characteristic they can only be applied in the far field, which may often be outside the discretization. Further research is certainly required.
The vertical force is not as much affected by the spreading of the error. Therefore the predicted sinkage generally fits the measured values over wide range of FroudeNumbers within 10%. The
trimming moment is numerically sensitive again. The trimming moment is quite sensitive again; in addition viscous forces can have some influence. This effect is even stronger in shallow water.
Summarizing we state:
It is not expected that potential flow methods give resistance predictions to the degree of
accuracy required by ship yards. They can be used however to compare pressure distributions
and wave heights of different hull forms in order to optimize hull forms. In the bow region the grid spacing should be smaller than elsewhere. Squat is predicted quite accurate.
Commercial reports on wave resistance computation are expected to include:
Information to be used for hull form optimization.
Isobars on the hull (preferably in colour) for all relevant areas. Oblique views from underneath have proven to be quite suitable. Relevant parts e.g. the bulb should be
presented in additional magnifications.
Wave profile along the hull along with some information on how the wave proffle was determined.
Velocity distribution on the forebody.
When different variants were investigated the change in computed wave resistance should
be stated.
For special applications squat is of interest.
Information for qualitiy control
A short description of the method including information about the conditions that are
fulfilled numerically.
Plots of the grids on the hull and the water surface.
The number of iterations to obtain a non linear solution can help to judge convergence
properties.
Contour plots of the water surface to identify unphysical effects at the outer boundaries of the discretization.
Plot of the velocity distribution at the stern to see whether unrealistic velocities e.g. at the transom may have influenced the results on the forebody.
6. Information about the sensitivity of the results on grid-variations
Generally the report should include plots of the major lines like stem contours, design waterline
and constrution frames to ease connection of the results to the lines drawings.
3. Applications
The following examples are all taken from the regular industrie and research work at the Hamburg Ship Model Basin (HSVA) and have been computed using the program SHALLO jointly developed by the authors.
3.1 Slow Ships
Full and slow hull forms have long been not accesible to reliable computions. Only 5 Years ago Jensen (1988a) failed to get a non-linear solutuion for the ilS VA-Tanker (CB = 0.85) at
a speed corresponding to FN = 0.85. Raven (1990) demonstrated the paradox of negative
resistance for tankers computed with the Dawson method (double model linearization) which was not due to discretization errors but due to enerr flux across the free surface and therefore
calls for non-linear solutions. In 1991 HSVA computed non-linear solutions for the E3-tanker
project at very low Froude-Numbers.
Up to now the lowest Froude-Number computed at HSVA was for a river cargo vessel
(Fig. 5). The principal dimensions are Lpp = 104.5m,B = 10.95m,T = 3Mm. The
wa-ter depth was 5m and the channel width 83.2m. In the discretisation the concave propeller
tunnel was was smoothed. The investigated Froude- Number was FN = 0.12. The water surface was discretized using 927 panels only. Nevertheless the results were quite good and converged
in a few steps. The wave patern shows little shallow water effect (the depth Froude Number is 0.55) but some blockage effect and reflections of the waves at the channel walls. On the sides of the vessel the water surface is generally lowered, but modulated by the wave pattern. The sinkage was underpredicted by 17% and the trim by 21%. This may be due to boundary layer effects which increase the blockage. In addition the water surface height at the forward end of the grid is not zero, which shows that with restricted waters the free surface grids should be larger than usual, which increases the number panels.
The wave resistance is an order of magnitude lower than the measured residual resistance. Nevertheless it is difficult to determine a form factor for a blunt ship on shallow water as even
at small velocities some waves are generated, so that the wave resistance cannot be singled out
of the experimental results.
3.2 Container Vessel
The optimization of forebodies of Container vessels is very useful and routinly done using SHALLO and is often quite sucessful (Jensen 1988b). A quite impressive example may be
the following: In a first design step a vessel with a block coefficient CB = 0.61 had been
designed. The prospective owner considered a reduction in cargo capacitiy to further reduce power by reducing the block coefficient to CB = 0.58. Against expectations a higher wave resistance was predicted for the more slender hull. Fig. 3 shows the wave elevation along the
hull featuring significantly steeper waves with a deep trough near section 12. This corresponds
to the unfavourable pressure distribution shown in Fig. 1. Therefore the fuller hull form was
considered for further investigation. Some form modification wererecommended to reduce the
trough at the shoulder.
The ITTC standard test case of a container vesseiwas usedfor validation. In 1991 the ship flow
ra
smooth automatic discretisation. (Fig. 7). The rpedicted wave resistance showed errors up to 100%. In 1992 the computation was repeated using a newly developed panel generatorbased on NAPA-ship design program. The grid has 516 panels. It is smoother and significantly
refined at the bow. The results are much better as shown in Fig. 8. This demonstrates that
the grid generation and the experience of the user have a significant influence on the quality of
results and that the used grids should be clearly documented when presenting results.
3.3SWATH-Vessel
For the flow about a SWATH-ship (SWATH=Small Waterplane AreaTwin Hull) an additional
condition is the Kutta condition at the rear end of the struts. Due to the flow induced by
one hull on the other the flow is not symmetric for each hull. Similar as for foils an addi-tional condition is required to assure the flow leaves the trailing edge tangentially. The most simple condition is to require the transverse flow velocity to be zero (Joukowsky-Condition),
Bertram(1992).
Among the large number of published theoretical prediction methods for SWATH vessels most
base on the "slender-body-theory", the "thin-ship theory" or combinations of both. In the
regime of moderate Froude- Numbers these methods show extremeoscillations in the resistance
which do not correspond to experimental results. At Froude-Numbers beyond 0.4 they show quite good agreement with experiments. Although 3-d panel methods generally allow the description of flows about complicated geometries (e.g. elephant foot cross section). Due to their much higher cost in discretization and computer time there is no reason to use them for
fast SWATH.
In a extensive research project a systematic series of SWATH-vessels was developed and tank
tested. A typical candidate has the following principal dimensions: Length of body 25.0 m
Diameter 1.6 m Strut thickness 0.8 m
Distance between center lines 8.0 m
Fig. 9 shows the discretization of the hull. Fig. 10 shows the wave pattern for two Froude Numbers. Fig. 11 shows the measured values as compared to the computational results. For
Froude-Numbers up to 0.4 the agreement is quite fair. For higher Froud-Numbers the agreement is not satisfactory.
SWATH-vessels seem to be at the limit of todays possibilities. Very fine discretizations are required at ship and strut ends.
3.4 Reefer Vessel
Another very succesful investigation was for a reefer vessel. A design for Froude-Number 0.29
had been developed by a customer and tank tested in an other facility when HSVA's services
called for because the vessel used 15% more power at the design speed than available according
to the contract. Time was extremely short. The model was braught to HSVA to validate the model test results and simultaneously potential flow computations were started for the original hull form and for a modification and for an alternative design by HSVA. Fig. 12 shows a very unfavourable pressure distribution and corresponding wave elevations along the hull for the
original hull, while the HSVA design shows much better results. Thus after 2 weeks of analysis
and lines design it was clear which path to follow. A new model was built and tested. The
ship yard will be able to fulfill the contract.
If used in the early design stage potential flow analysis could have avoided costly model tests and delays for the project.
4. History and Future
A major reason to use CFD is time. It is generally expected that CFD gives quicker answers about the hydrodynamic properties of a ship design than model tests. Qualitatively everybody concerned is aware that CFD application has become faster within the last years, quantitative
information is however hardly available in literature.
The individual steps for a ÇFD project are as follows:
Transformation of the lines drawing into a CAD description
Generation of panel grid
CFD-Computation (batch) Documentation (plots, report)
In 1984 at the University of Hamburg wave resistance computations were started. The first
practical application for a slightly submerged sumbmarine took about a week for digitizing the
hull form for the then available hull form description system EUMEDES. Based on this in an
interctive proces each panel was manually defined. Each run on the VAX 11/780 took about 12
hours of CPU time (linearized solution). They often were repeated with different parameters or grids. Then with a specially designed program which required a lot of interactive input for views scaling of velocity arrow and distance of iso-lines plots were generated and plotted on a pen plotter. The total time was more than a month.
As should be expected from a University major concern and development was aiming at
improv-ing the computation itself, like introducimprov-ing new open boundary conditions and non-linearity. A new panel type was introduced which solved the permanent problem at the ships ends with the previous one. In combintation with the increased experience now only one or two attempts
were sufficient go get an acceptable grid. This experience was introduced into semi-automatic grid generators for body and water surface.
1991 at HSVA we used a HP Apollo 720 wich allowed us to get a non-linear solution in maybe
2 CPU-hours. The total time from step 1 to 4 was reduced to about 4 days.
This shows that the computation time was reduced by a much greater factor then the rest and only takes a small part of the total time. Therefore effort is now necessary to reduce the other steps. We are now working on the reduction of the other steps:
The first step (Digitizing of hull form) could be fully omitted if the designer supplies the hull
form in a suitable electronic format. At HSVA we now use the NAPA-ship design system which
is also in use by many ship yards and has a number of data interfaces to other formats. For the future it would be desirable to have a neutral hull form description standard.
Based on the NAPA description an automatic panel generator was programmed which only requires very little manual input. The resulting grids normaly need only very little manual
correction. The grid generation on the free surface is performed fully automatic. Thus the
total time for grid generation was reduced to about 1 day.
The documentation and analysis of the results was further automatized so that a standard
report can be produced within I to 2 work day. Of course the judgement of the results, the development of recommendations and quality control will be left to the experts, so that the potential for further reduction is limited.
To efficiently use external potenitial flow calculations by a lines designer it is required that electronic means of information transfer are used. Then it is expected that within the foresee-able future a designer on the ship yard may have professional CFD-results on his desk on the next day.
r
Literature
BERTRAM, V. (1992), Wellenwiderstandsberechrzung für SWATH-Schiffeund Katamarane,
Jahrbuch der STG
JENSEN, G. (1988a), Berechnung der stationären PotentiaLstrômung urn ein Schiff unter
Berücksichtigung der nichtlinearen Randbedingurig an der freien Wasseroberfäche, Diss.,
IFS-Bercht 484, Univ. Hamburg
JENSEN, G. (1988b), Berechnung des Wellenwiderstands fur praktische Schiffsformen,
Jahrbuch STG
RAVEN, H.C. (1990), Adequacy of free surface conditions for the wave resistance problem, 18th
Fig. 1. Pressure distribution on a Container-Vessel, CB=O.61, Fn=O.24
s
Fig. 2. Pressure distribution on a Container-Vessel, CB =0.58, Fn =0.24A
2 3 ô
Fig. 3. Wave elevation along hull for two container vessels, Fn =0.24,
CB=O.61
CB=0.58
-U = 24.0 kn
7 6 9 0 U 2 3 3 6 7 5 9 20--/
Fig. 4. Velocity distribution on the extremly long protruding bulb of
largepr
à
1111
w.-m
irr
Fig. 6. Wave pattern of an inland waterway
vessel at Fn =0.12, FnH0.55
in as
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o oo O o o O + o S O.
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Fig. 8. Computed and measured wave resistance, trim and sinkage for
TTC-Test-Ship
o Measurement, Grid 1, Grid 2
CW,CR + S 8 AT/L o + e o + S o O ot
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Fig. 9. Discretization of SWATH configuration.
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Fn = 0.28
4 3 2
i
o CR/Cw 1000 Ó 0'. 1 0'.2 0.3 0'.4 0'.5 0'.6 0.7 0'.8 0.9Fig. 11. Wave resistance of SWATH vessel
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