Faculty WbMT
Dept. of Marine Technology Mekelweg 2, 2628 CD DelftThe Netherlands 18th Georg Weinblum Memorial Lecture
CFD in Ship Design
Prospects and Limitations
Lars Larsson, Chalmers University of Technology'
Introduction
Computational fluid dynamics (CFD) is becoming more and more popular for analysing flow problems in almost all branches of industry. The absolute accuracy is still limited, particularly for high Reynolds numbers, but physical insight into the problem may often be gained and used to improve the design. In this respect CFD is often superior to model tests, where the absolute accuracy is higher, but where the amount of information needed to guide the designer is more limited.
The present paper deals with CFD applications to ship hydrodynamics. Here, inviscid
nu-merical methods have been used for a long time in propeller design and seakeeping calculations. Viscous methods have been less accepted in ship hydrodynamics than e.g. in aerodynamics, but during the past years, many shipyards, ship owners, and towing tanks have acquired also viscous
methods to aid the design process.
Present use of CFD in hydrodynamics
2.1 Classification of methods
CFD should include all computational methods for fluid flows, but is most often confined to Navier-Stokes methods. In my opinion, this definition is too restrictive. Fig. 1 summarizes CFD in ship hydrodynamics including all methods. Simple potential flow methods are e.g. Michell's wave resistance theory, lifting line theories in propeller design, or strip theories in seakeeping.
The last two have been useful for many years and may be considered mature tools. Panel methods are more advanced and are already established tools in resistance, propeller design,
and seakeeping. Boundary layer methods have never reached the usefulness of the potential flow
ones, but they have been used for some time for resistance calculations, propeller blade flows, and roll damping. Modern Navier-Stokes methods are just making their way into resistance
and flow and propeller effects. Euler methods play a much smaller role in hydrodynamics than
in aerodynamics. The reason is that lift is much more important in the latter field. When resistance is the major issue, it seems more appropriate to turn directly to the Navier-Stokes methods rather than trying to couple Euler and boundary layer methods. In the following, the
emphasis is on panel methods and Stokes methods for resistance and flow and Navier-Stokes methods for propellers and cavitation.
2.2 Codes regularly used in design
Computer codes which are regularly used in ship design are listed below2:
Inviscid free-surface codes: DAWSON, RAPID, SHIPFLOW, SHALLO, VSAERO,
SWAN, SPLASH, SLAW
Viscous double-model: SHIPFLOW, PARNASSOS, RANSTERN, NICE Viscous free-surface: TUMMAC, WISDAM
DAWSON and RAPID, developed by Raven (1988),(1996), have been used extensively in
com-bination with model testing at MARIN to improve hull designs. DAWSON uses a linearized
free-surface boundary condition, while RAPID solves the fully nonlinear problem. SHIPFLOW,
Larsson (1993), Larsson et al. (1989,1990,1992a,1992b), contains both inviscid and viscous
methods and is widely used. The inviscid part can
also solve the fully nonlinear problem.'Dept. of Naval Arch. and Ocean Eng., S-41296 Gothenburg, Sweden
'There are many other codes in the literature which are apparently not yet used as regular design tools
Fig. 1: Use of CFD in ship hydrodynamics. Bold face indicates areas discussed in this paper
SHALLO, Jensen (1988), Jensen and Bertram (1993), has been used by HSVA during many years. VSAERO is a well-known code in aerodynamics, originating from NASA, but since several years marketed by Analytical Methods Inc. A free-surface capability was introduced by Maskew (1989). The code has been updated for unsteady free-surface problems, Maskew et al. (1993). Due to its capability to include lift, VSAERO has been popular in America's Cup design. The same is true for SPLASH, Rosen et al. (1993). During the 1995 campaign,
SPLASH was used extensively in one of the Australian America's Cup syndicates. SWAN and SLAW use only linearized free-surface conditions. SWAN, Sclavounos and Nakos (1988), seems to be mainly used for unsteady calculations. However, during the 1992 and 1995 America's Cup campaigns, it was used in the PACT syndicate also for wave resistance, Sclavounos (1996). A
special technique takes the nonlinear effects of the large overhangs of the yacht into account. SLAW, Letcher et al. (1989), was developed for the 1992 America's Cup, but is now used by
some American yards, Stromgren (1995).
SHIPFLOW includes viscous flow methods for the double-model case. Over the forward part
of the hull the flow is computed by a boundary-layer theory while the stern flow is obtained
from a Navier-Stokes solver3, Larsson (1993). PARNASSOS is a Navier-Stokes code developed
at MARIN, Hoekstra (1989), Eca and Hoekstra (1996). Both codes seem to be used regularly
for practical design work, although not at all as frequently as the corresponding potential flow
methods. RANSTERN, Ju and Patel (1991,1992),is also used to some extent at shipyards. In
Japan, the codes developed at the Ship Research Institute have been used at the yards for some time. NICE, Kodama (1992) was extended to include a free surface by Liu and Kodama (1993). The best-known viscous free-surface code TUMMAC, Miyata et al. (1985), is used at several shipyards in the Far East. Another popular code from the same department is WISDAM, Miyata
et al. (1992), Miyata (1996).
There are many other codes in the literature, see e.g. the two CFD workshops held in 1990s, Larsson et al. (1991), Kodama et al. (1994).
2.3 Typical applications
The most common test cases for CFD methods are the HSVA tanker and the Series 60, = 0.60 hull used at the two CFD workshops. Also popular is the Wigley hull, defined by parabolic sections and waterlines. Together with the fast monohull "Athena" these three hulls were used in the cooperative experimental program coordinated by the Resistance Committee
of the ITTC. At the 20th ITTC conference in 1993, the Resistance Committee suggested in
'Except when specifically stated, Navier-Stokes methods mean here methods based on the Reynolds-averaged Navier-Stokes equations (RANS)
Resist. & Flow Prop. & Cavit. Seakeeping Manoeuvring Simple Pot. Flow Methods
Traditional Traditional Traditional Traditional
Panel Methods
Modern,
Established
Modern, Established Modern, Established Modern, Not Established Boundary LayerMethods Traditional Traditional Traditional
Navier-Stokes Methods
Modern,
Not Established
Modern,
Not Established
Future Futureaddition the tanker "Ryuko Maru" and the container ship "Hamburg Test Case".
While most papers on CFD methods use the above hulls as test cases, there are more and
more reports on the practical application of CFD to ship design problems:
Tankers, VLCCs: Larsson et al. (1992a,b), Bertram and Jensen (1992,1994),
Ber-tram et al. (1992), Ju and Patel (1992), Minguito (1992), Larsson (1993), Tzabiras
(1993,1995a,b), Bertram and Laudan (1993), Streckwall (1993), Larsson (1994), Ishikawa (1994), Bertram (1994), Stromgren (1995)
Container ships: Bertram and Jensen (1992), Bertram and Laudan (1993), Bertram
(1994), Larsson (1994)
Ro-Ro ships: Larsson (1993), Kim et al. (1996)
Ferries: van den Berg et al. (1990), Bertram and Jensen (1994), Caprino et al. (1994) Fast mono-hulls: van den Berg et al. (1990), Thomas (1992), Larsson (1993), Saisto
(1993), Larsson (1994)
Catamarans: van den Berg et al. (1990), Miyata et al. (1993), Larsson (1994),
Papan-ikolaou et al. (1996)
SWATHs: Bertram (1992), Jensen and Bertram (1993), Bertram and Laudan (1993)
Sailing yachts: Rosen et al. (1993), Raven (1994), Sclavounos (1996), Miyata (1996),
Milgram (1996), Cowles and Martinelli (1996), Azcueta (1996)
Fishing boats: Tzabiras et al. (1995), Loukakis et a/. (1996), Tzabiras and Prifti (1996)
SES, hydrofoil boats, traditional ships, and a racing canoe: Valkhof (1992), Larsson (1993), Delhommeau (1994), Bertram (1994)
Jensen and Bertram (1993), Larsson (1994), Kim and Larsson (1994), Bertram (1994) consider restricted waters. Kim (1996), Kim and Jang (1996) apply CFD for manual hull optimization, while fully automated optimization procedures are presented by Larsson et al. (1992), Hamasaki et al. (1996), Janson and Larsson (1996), Papanikolaou et al. (1996).
The applications differ not only with respect to hull type, but also with respect to the
quantities computed. Typical quantities are:Wave/viscous resistance (Improvements of bulbs, shoulders, forebody type, shape of sec-tions, displacement distribution, transom size and planing wedges)
Lift/induced resistance (Improvements of hydrofoils and sailing yacht appendages) Sinkage and trim (Improvements of planing wedges and transom size)
Local flow (Prediction of nominal wake, propeller effects, direction of shaft brackets and fins, positioning of bilge keels)
Transition, noise and pressure signature (Naval applications)
Other quantities (Calculations for improving model tests, investigating the stability of
planing hulls, or studying environmental disturbances)
By far the most common application is the manual improvement of the forebody using a panel
method. Different bow types, with or without bulbs are investigated and the effect of moving
displacement from the shoulder area are studied. The improvement is with respect to resistance,
but many more results than the computed resistance are used to guide the designer. Kim and Jang (1996) explain this process clearly including a study of variations in the sectional area
curve and DWL shape. Less common is the improvement of the afterbody using Navier-Stokes methods, e.g. Ju and Patel (1992), Streckwall (1993), Ishikawa (1994).
The optimum size of the transom of a planing hull depends on the Froude number. The effect
of the transom size on the sinkage and trim, and thereby also on the resistance, is reported by Larsson (1994) who minimises the sum of the hydrostatic and hydrodynamic resistance
components at different speeds.
Ship designers are very interested in an accurate prediction of the nominal wake.
nately this is very difficult, Larsson et al. (1992b), Ju and Patel (1992), Bertram and Jensen (1992), Bertram et al. (1992), Streckwall (1993), Bertram (1994), Larsson (1994), Ishikawa
(1994), Loukakis et al. (1996), Tzabiras (1996a). In general, the conclusions from the CFD
workshops are confirmed, i.e. the predicted contours are too smooth, especially near the hub.
Usually, the propeller is represented by body forces in axial and circumferential direc-tions, Schetz and Favin (1977), Stern et al. (1988,1991,199.4), Zhang et al. (1992), Tzabiras
(1993,1995b,1996a,b), Tzabiras et al. (1995), Tzabiras and Prifti (1996), Loukakis et al. (1996), or simply by axial body forces, Streckwall (1993).
Rare open reports on naval applications include flow calculations for the public submarine
designs of the DARPA SUBOFF exercise, Huang et al. (1992), Bull (1996), McDonald and
Whitfield (1996), Sung et al. (1996), but detailed studies are more confidential. Our experience extends largely to computing the location of the transition from laminar to turbulent boundary
layers on the forebody. Since large pressure fluctuations are to be expected in this region, it is essential to move transition away from the acoustic window on submarines and torpedoes.
Theory and validation of the technique are presented Xia et al. (1985), but all applications are
confidential. Pressure signatures have also been computed, both for submarines and surface
ships, Feldtmann and Gustavsson (1995,1996).
Model tests may be improved by CFD. CFD can e.g. help experimenters to find the best trade-off between low blockage effects in the test facility and a high Reynolds number. By
systematic calculations a suitable model size could be found in several experiments in the SSPA
large cavitation tunnel. CFD can also help in extrapolating model-scale data to full scale, at
least for torpedo wakes in my experience. General extrapolations from model scale to very high full-scale Reynolds numbers may be more questionable.
Our group investigated the dynamic stability of planing craft in the late 1980's. The
heel-ing moment caused by the dynamic pressure forces was computed at different heel angles. See
Rardanz (1994) for a similar investigation. Environmental disturbances (wash eroding river banks and disturbance velocities on the bottom of shallow waters) may be investigated and
minimized by CFD, e.g. Feldtmanrz and Gustavsson (1995,1996).
3. Limitations of current CFD methods
3.1 Accuracy
By far the most common application of CFD in ship design is the computation of the wave
pattern and the improvement of the forebody shape, based on the generated waves and the
pressure distribution. Fig. 2 shows typical results of a state of the art non-linear panel method, Janson (1997). Navier-Stokes methods are not yet competitive caused by resolution problems.
The wave cuts were taken close to the side of the ship. Calculations and measurements agree rather well for the Series 60 hull all the way from bow to stern. The bow wave is somewhat
underpredicted, due to a lack of resolution on the free surface. Janson used 25 panels per funda-mental wave length, which is according to his recommendations considering today's computer capacity (workstations). To capture the peak, more panels per wave length are required. Differ-ences occur also in the afterbody and the wake behind the hull, where the neglect of the viscous effects is the likely reason for the discrepancies. For the tanker, calculations and measurements
agree satisfactorily along the forward half of the hull. The effect of viscosity is larger for this bluff hull and the overprediction of the waves starts further forward. The bow wave peak is
probably predicted so well due to a fortuitous error cancellation due to the insufficient resolution and the neglect of the wave breaking effect. For this low Froude number, the limited computer
capacity restricted the number of panels per wave length to 15, which is probably on the low
side. Both results are from nonlinear calculations. The corresponding linear results show more wave damping and a noticeable wave length shift in the case of the tanker.
-0J00500 10c04000, h / Lpp OL00000 =11,01[000 -0.750000 0.00000 0...50000 1,00000 1.50000 2.00000 FP -0.50000 0.00000 0-50000 AP i.0000a
The results of Fig. 2 indicate that the wave pattern of displacement hulls can be predicted
accurately enough to investigate forebody modifications. However, the same approach for the afterbody is dangerous, Janson and Larsson (1996). Viscous effects may in reality completely mask the differences in the potential flow waves. For fast hulls, the effect of spray and sinkage
and trim become more important. In spite of
these additional complexities,. Larsson et al:.(1990),. Raven (1996) present useful wave predictions. In this case the major viscous effect is flow separation at the transom edge. At speeds high enough for the flow to detach, this case can
be well modelled. Then accurate analysis of the afterbody is possible and the complete wave pattern behind the hull can be obtained withsufficient accuracy to judge environmental effects..
This is fortunate, since such effects are naturally more important for fast ships.
In conclusion, the wave pattern prediction is a good tool for improving the forebody of
displacement ships and for the whole hull for fast ships wherethe flow clears the transom. To extend the applicability to problems for which the panel methods are not sufficiently accurate,
viscosity must be introduced and the only realistic way
to do this in the future is to turn to
Navier-Stokes methods with a free surface.
Even though the wave pattern may be quite useful for huh l optimization the predicted wave resistance must be treated with caution. There are several reasons for this.. Most panel methods'
compute the wave resistance by adding the contribution to the resistance from the pressure forces on all panels. The sum of all contributions (with the correct sign) is several orders of magnitude smaller than the sum of the absolute value of all contributions'. This means that
even small individual discretization errors may cause a very inaccurate final result. The most common way to account forthe total discretization error is to compute the resistance for the double-model hull without waves. By d'Alemberts paradox this resistance shall be identically zero in a non-lifting potential flow, so assurhing that the error is unchanged in the free-surface case the double-model resistance may be subtracted from the computed wave resistance.This is straight-forward if the panelization is the same in both cases, which is normally true for linear
methods, where the boundary conditions are applied on the undisturbed free surface. In the
non-linear case, however, it is difficult to devise a correction of this kind, since the panels now 4Contrary to common belief, the resistance is not the difference between two large opposing forces, one on the bow and one at the stern. For many ships, notably tankers with a long, parallel middle body, the pressure and suction forces at each end of the hull almost canceleach other.
Schiffstdchnik Bd. 44 - 097 / Ship Technology Research Vol. 44 - 1997 137
measurements 11 uomputations _ u cii FP _ Measurements II Computations 1.50000:
Fig. 2: Wave cuts close to the side of two ships. Top: Series 60, GB '= 0.6, Fri = 01.316. Bottom: Dyne
Tanker, Fr, = 0.165 2.00000 .01.00500 heipp 0.00000 A -
-follow the contour of the waves and are thus quite different from those of the double model. Linear methods, on the other hand, suffer from the inaccurate representation of the flow near
the free surface. Both the approximation of the boundary location (undisturbed surface) and
the boundary conditions (linearized) contribute to the error. For most ships the approximate location causes a reduction in the resistance, since the pressure integration up to the undisturbed waterline neglects the positive contribution to the resistance in the bow wave above thisline, while it adds a non-existing suction force in the forward direction from the area between the
waterline and the first wave through. Both effects tend to reduce the contribution to the resistance from the bow region. At the stern the effects are reversed, but smaller, since the
stern waves are normally smaller. The linearization of the equations cause an unphysical flow of energy through the free surface, Raven (1988), which could either increase or decrease the resistance.
So wave resistance calculations for slow ships are not accurate enough, at least not if the pressure summation technique is used to obtain the resistance. The waveresistance coefficient of a tanker is of the order of 10 and the discretization error, i.e. the double-model resistance, is between 10-4 and 10-5. Very careful hull panelization is required to approachthe lower level, i.e. even a non-linear calculation suffers from a large relative error. Linear results are even more unreliable yielding often negative resistances, Raven (1988).
A remedy to the slow ship resistance problem may be to turn to wave cut techniques. In a preliminary study of this possibility a much more realistic resistance was predicted in the
whole speed range for a tanker, Lundgren and Ahman (1995). But at present, no significance
should be attached to the computed wave resistance for slow ships. Instead their performance
should be judged from the generated wave patterns. At higher speeds the situation is somewhat
brighter. When the wave resistance coefficient is of the order of 10-3 or larger the
double-model correction becomes relatively small and it may be assumed that the discretization error is also of relatively little significance. Wave resistance predictions at medium and high speeds
in the literature show usually a reasonable agreement between measurements and calculations.
However, the interpretation of the resultsis not obvious. The problem is that the actual wave resistance is very seldom measured. In principle it should be quite easy from a wave
cut, but
such data are rare. There is also a problem with wave breaking and spray, which reduce the
energy of the radiated waves. In most cases the predicted wave resistanceis compared with the measured residuary resistance, evaluated with the form factor method according to the ITTC
1978 recommendations.
The reasonably well predicted wave resistance shown in many papers suggeststhat it should be accurate enough for ranking purposes. There is, however, surprisingly little evidence
support-ing this conjecture in the literature. Larsson et al. (1992) and Kim and Jang (1996) presented
a successfulranking for a series of bulbs on a Ro-Ro ship. Saisto (1993) carried out wave
resist-ance calculations for round bilge high speed hulls and ranked them in the right order and Sundell
et al. (1993) report on successful rankings of several ships in a large CFD projectin Finland. I am aware of more ranking tests carried out for commercial projects at different ship yards, but
these have not been reported for confidentiality reasons. At present the ranking capability of
the potential flow solvers cannot be considered fully validated, so the safest way to make use of the wave resistance information is to use it in combination with the information from the wave pattern. Obviously, the predicted wave resistance should not be used for absolute power
predictions.
Even though the most important CFD methods in ship design are the potential flow methods, progress is being made also for viscous flows. Fig. 3 shows an example of the present capability
of Navier-Stokes methods to predict the axial velocity contours in the wake, Larsson et al.
(19921)). The outermost contours are well predicted, but the inner ones,particularly above the propeller centre are too smooth. This problem is well knownfrom the two workshops and much
of the present CFD research is directed towards improving the wake predictions. If the velocity is averaged circumferentially and the average is plotted versus radial distance from the centre
the correspondence with measurements is better, Fig. 4, but velocities are still overpredicted at the smaller radii and underpredicted further out. Averaging the radial distribution over the propeller disk almost cancels the errors. So the calculated average velocity of 0.48 is close to the measured of 0.50. General trends cannot be deduced from just one example, but in my
experience the average velocity in the propeller disk (i.e. 1 ?En, where w is the nominal wake) can be predicted rather well, see also Streckwall (199.3), Ishikawa (1994).
0.60000 7 0.40000 -Calculated 0.20000 -0.00000 -Volumetric Mean Measured Calculated eAMeasured Wake 0.50 0.48 0.1 0.8
Fig. 3. Typical results of a wake calculation using CFD. Velocity
contours in the propeller disk of
a modern tanker hull, Larsson et
al. (1992). Left: measurements. Right: calculations
Fig. 4. Radial velocity distributi-on in the wake of a modern
tan-Schiffstechnik Bd. 44 -1997/ Ship Technology Research Vol. 44 -1997 139
0.00000 0.20000 0.40000 0.60000 0.80000 1.00000 ker hull, Larsson et al. (1992)
R/RO
The inability of the Navier-Stokes solvers to predict the wake details means that it is ques-tionable whether other local flow quantities can be predicted well near the stern. Flow directions e.g. are of interest for the positioning of brackets, fins, bilge keels, etc. Fortunately, brackets are
often of interest for fast hulls, where the boundary layer leaves a submerged transom without any particular thickening and without strong embedded vortices. This facilitates the viscous
flow prediction, and even boundary layer methods may work well. Bilge keels are positioned further forward where the predictions are also more accurate. However, using CFD to design a fin near the propeller is questionable.
Viscous resistance predictions were presented at the Tokyo workshop, Kodama et al. (1994). Out of the eight methods that predicted the viscous resistance of the HSVA tanker three were
Measured Calculated
-seriously wrong and three predicted the resistance, as well as the split between friction and
pressure, quite well. A similar problem as for the wave resistance exists in the interpretation of this case: the two components cannot easily be measured separately. Therefore, the measured pressure resistance was obtained from the form factor, estimated according to the ITTC 1978
method. Since the theory of the methods was not very different, the large differences in
per-formance indicate that great care must be exercised to obtain a grid independent solution. Two of the successful authors have reported very careful grid dependence studies in other papers, Ju and Patel (1992), Ishikawa (1994). These papers and Streckwall (1993) include systematic variations of hull afterbodies and comparisons with measured data for the different shapes. In all cases, the correct ranking was obtained. Viscous resistance predictions thus seem to possible for stern optimization purposes provided the grid quality is high enough.
3.2 Applicability
Panel methods are applicable to displacement hulls at all speeds, transomhulls above the
critical speed, multi-hulls, SWATHs, hydrofoils and surface effect ships. Restricted water effects may be considered, as well as the effect of an operating propeller. Problems occur only when
either viscous or non-linear effects become important. Examples of such cases are transom stern hulls when the water does not clear the transom and wave breaking and spray at higher speeds. The only possibility to remove these restrictions in the future
will be to turn to the
Navier-Stokes equations.
Viscous methods have been used much less, but in principle they should be useful for most of the cases above. One practical problem encountered in many methods is the singularity which
occurs in the grid aft of the stern (and in front of the bow). Without special treatment this singularity cannot be included in the computational domain. Some methods may avoid the
problem if the singularity is on the boundary, and for symmetric monohulls the hull centreplane is normally a boundary. These methods will not work, however, for multihulls and twin skeg hulls. Introducing a propeller model with rotation is also a difficult task, since the flow will then no longer be symmetric.
The major problem with viscous methods is the full-scale prediction. In principle, CFD methods offer the attractive possibility to predict resistance and flow at full scale, thus
cir-cumventing the approximate procedures for extrapolating model scale experimental data to full scale. Predictions at full scale are not straightforward, however, due to the much reduced viscous length scale in ship flows as compared to model flows. The viscous length scale for a large ship is typically two orders of magnitude smaller than that at model scale, relative to the dimensions
of the hull, i.e. the grid has to be two orders of magnitude denser for the same resolution. If this was to be applied in all three directions the total number of grid pointswould increase by
a factor of one million! Further, more time steps or iterations are likely to be needed.
Fortunately, the viscous length scale is important only normal to the hull and mainly in the region close to the surface. Therefore, a natural strategy is to keep a rather coarse grid in the two tangential directions and use a very stretched grid in the normal direction with a
large concentration of points near the hull. The problem withthis strategy is that the grid cells near the hull become very thin, relative to their lateral dimensions. The aspect ratio gets very
large. This causes problems for most numerical methods and the solution does not converge.
To reduce the problem, wall functions may be used near the hull surface. The thinnest cells are thereby avoided and the aspect ratio problem is reduced.
Full-scale predictions were requested by the organisers of the 1990 workshop, Larsson et al. (1991), but only 3 out of 17 methods provided such results, and one of these was seriously in
error. The other two results looked reasonable, but no quantitative assessment could be made
due to lack of measured data. This is a general problem when evaluating full scale predictions. Attempts to measure the flow in the propeller plane, Lammers et al. (1989), Tanibayashi (1990),
Kux (1990), covered only a small sector. An exception is the "Ryuko Mare', for which data
are available at a transverse plane in front of the propeller, Namimatsu et al. (1973). This hull is obsolete, however.
The experience from the workshop shows the difficulties encountered when trying to compute
full-scale cases, and there are only a few papers presented later. To validate their full-scale predictions, Ju and Patel (1991) applied their method to a high Reynolds number experiment
with an axisymmetric body, Coder (1982,1988). This experiment was carried out in a nitrogen
wind tunnel operating at a pressure of 80 kPa and a temperature of 145°C. The highest
Reynolds number reached with the 6.13m model was 1.046 x 109, i.e. a Reynolds number of a fairly large ship. Ju and Patel managed to predict the measured data quite well and computed then the flow around the HSVA tanker at several Reynolds numbers up to 5 x 109. They
attribute their success to the use of the law of the wall and to the finding that this law seems to be valid to larger values of y+ at higher Reynolds numbers. Apparently the valid range for the wall law is an order of magnitude larger at full scale. This facilitates the grid generation
and the aspect ratio problem considerably.
Systematic calculations for a series of afterbodies at both model and full scale were presented by Ju and Patel (1992), other full-scale results from methods employing the wall law by Tzabiras
(1991,1993) and Sames (1995). Sames used the same grid at both scales, but with the no-slip condition (i.e. without the wall law) at model scale. The change in viscous length scale between model and full scale increases y+ by a factor of about 100 and this corresponds quite well with
the increase in y+ for a wall law approach compared to a no-slip approach. Eca and Hoekstra
(1996) calculated the HSVA tanker at model and full scale using the no-slip condition at both
scales. This called for extreme stretching at full scale, particularly since y+-values as low as 0.1 were used for the first points off the wall. The aspect ratios for the innermost cells in this case were as high as 107, which is about 103 times larger than the values at which numerical problems normally occur. The reasons for the robustness of the method are not obvious from the paper, but the approach differs considerably from that of most other methods in that the
"Reduced Navier-Stokes equations" are solved.
3.3 User-friendliness
A problem in introducing CFD at the design department of a shipyard is the little time that can be spent on CFD analyses by the hydrodynamicist. Most yards have only a few projects a year and in every project the CFD analyses are mainly concentrated to the verysqueezed
initial design period. Consequently the designers have little time to get acquainted with the code and to practise. The code thus has to be user-friendly, perhaps more so than in other
branches of industry. An aircraft or an automobile project, e.g. have a design period of several years, whereas a ship has to be designed in a few months.
The request for user-friendliness has prompted some of the commercial code vendors to introduce expert advice into the code, e.g. SHIPFLOW has an automatic running mode for
standard ships of different kinds. In the automatic mode the code only requests the hull shape, the speed and some limited information about special features, such as bulbs. No information
on the grid generation is required. Of course, this facilitates the use of the code greatly, and
since the grid parameters are set by the code in a systematic way it is easy to compare results for different computed cases. The disadvantage is that the parameter setting has to be rather conservative. A run in the automatic mode must always work, even though the results could
have been more accurate, had the grid been designed individually by an experienced user. The normal running mode must therefore also be available.
A current research project intends to facilitate the use ofCFD as a ship design tool, Larsson (1996). A final goal is to develop a "designer's workbench" integrated into the designer's working environment. To speed up the design process, powerful shape variation tools will be developed
and a rapid communication will be established between the geometry modeller and the CFD code. Guidance on shape changes will be provided based on design evaluation criteria from
the CFD output. Further, databases with earlier computations and measurements will become available and empirical corrections to predicted global quantities, such as the resistance com-ponents, will be introduced.
4. Present research
The present research in hydrodynamics CFD is directed towards removing or reducing the
effect of the limitations presented in the previous section. The centre of effort is shifting from potential flow theory towards free-surface Navier-Stokes methods. I will briefly review the
present research on Navier-Stokes methods, with particular emphasis on the work in our research group.
4.1 Grid generation
All the methods of the 1990 and 1994 workshops, Larsson et al. (1991), Kodama et al. (1994), used single block structured grids. This is not surprising, since the effort spent on more advanced grid generators is far smaller in ship hydrodynamics than e.g. in aerodynamics. Exceptions are the codes developed with submarine applications in mind, Gallagher (1993), Sung et al. (1996), McDonald and Whitfield (1996), Bull (1996), where the importance of appendages has forced
the developers to go for more advanced gridding techniques. Other examples of multiblock
calculations in hydrodynamics are Tzabiras (1993), Weems et al. (1994), Cowles and Martinelli (1996).
The hull of a ship is normally a very smooth surface and the computational domain outside
the hull and in the wake may be transformed into a rectangular block without difficulties. A single block, structured grid thus seems well suited for this case. However, there are reasons to consider more complex grids. One obvious reason is that the hull always has some kind of appendage fitted to it, such as the propeller and the rudder. These have so far been neglected,
but many ships, notably displacement twin-screw ships and most planing hulls, have appendages which strongly influence performance. Another case where a single block grid may be difficult to fit in is the transom stern hull at low speeds. Submarines and sailing yachts also have important
appendages. The second reason for introducing more complex gridding techniques is that the
grid singularities in front of and behind the hull may be removed, thus simplifying the work of the solver considerably.
A more advanced grid may be created by block-structured or completely unstructured grids. The latter approach undoubtedly has the largest flexibility, but there are several drawbacks: in-creased memory requirements due to the necessary connectivity information, inin-creased comput-ing time due to the unstructured matrices occurrcomput-ing in implicit solvers, difficulties to implement higher-order numerical schemes and more difficult implementation of multi-grid (convergence
acceleration) techniques. In many internal flow situations, the boundary of the computational domain is so complicated that the greater flexibility outweighs the drawbacks of the unstruc-tured approach, but this is not the case for the flow around the hull. That is why unstrucunstruc-tured
grids are not used in ship hydrodynamics. An exception is Hino et al. (1993).
The traditional multi-block techniques employ patched component grids, i.e. the blocks
match each other at common boundaries. Although it is not fully clear from the presentations,
most of the multi-block methods mentioned above seem to be of this type. An exception is
Weems et al. (1994) employing a composite or overlapping grid ("Chimera grid"). However, no results are shown for this feature. Overlapping grids offer considerably more flexibility than the traditional patched block methods and represent the best alternative to completelyunstructured grids. Using an overlapping grid, regions with large gradients may be covered with separate
sticking out from the hull surface may be covered with a thin grid extending backwards into the
wake. In this grid the boundary layer and wake are resolved, while the boundary layer of the main hull is computed in a hull-fitted grid, in turn embedded in a Cartesian background grid.
The component grids may also be movable, a feature which may be utilised in the calculation of the flow around a propeller operating in the wake behind a hull.
The overlapping grid calls for a more advanced "book-keeping" than the traditional patched
grids. All points in the component grids have to be classified as either regular discretization
points, interpolation points or "dead" points, which may be deleted. Related to each interpola-tion point is a set of weights used for the weighted interpolainterpola-tion between the surrounding points in the overlapping component grid. The minimum number of points needed in each overlap is
set by the order of the numerical method used by the solver. E.g. second-order accuracy calls for three points in the coarsest of the two overlapping grids. Special problems occur if more than two grids overlap in a certain region and this problem is solved by assigning a priority to all component grids. The 2-D multi-block overlapping grid generator of Petersson (1997)
has recently been extended to 3-D. Fig. 5 shows, as a 2-D example, the grids around two foils.
Around each foil a body-fitted 0-grid has been generated and behind the foils there is a high
density rectangular grid. These three grids are embedded into background rectangular grids of two different densities. In this way the boundary layers and wakes can be resolved with high
accuracy, without wasting any grid points in regions away from the bodies, where simple rect-angular grids are used. In the figure all interpolation point are indicated by circles. These also represent the edges of the grids. All points outside the circled ones have been deleted. Several 3-D cases have been computed as well, but the interpretation of 3-D plots is so difficult that the simpler 2-D case has been chosen for this presentation.
Linked to this grid generator is a Navier-Stokes solver. It employs a finite-difference, second-order accurate numerical method with a SIMPLE scheme for pressure/velocity- coupling. Wall functions are not used and all variables are computed in a collocated grid. Central differencing
is used for all terms and the minimum amount of artificial dissipation needed for stability is computed using a theory by Henshaw et al. (1990). The first 3-D results of the new method
are reported in Regnstrom et al. (1996). Fig. 6 shows results of the Navier-Stokes solution for the 2-D foils of Fig. 5. The figure shows a blow-up of the streamlines in the most complicated region around the small foil, where several grids overlap. Note the smoothness of the streamlines across interpolation zones. A similar approach was employed by Malmliden (1994), where an overlapping grid generator was Used together with a Navier-Stokes solver. However, the results
suffered seriously from grid resolution problems and were inaccurate. Korpus (1995) briefly
describes overlapping grid computations for submarines and surface ships.
4.2 Turbulence modelling
CFD methods are not yet accurate enough for predicting the details of the flow in the wake behind the hull. The velocity distribution in the propeller disk, normally slightly above the
centre, is too smooth. The "hooks" in the measured distribution are not captured well enough.
In reality, the hooks are created by a vortex hitting the propeller plane at this position. The vortices are created near the bilge on the afterbody in front of the propeller and numerical methods tend to underpredict the strength of the vortices, thus underestimating their stirring
effect on the wake.
Two reasons have been suggested for the failure to predict the vortex strength accurately: nu-merical accuracy by Kim and Choudhury (1994) and turbulence modelling by Deng et al. (1993),
Deng and Vissoneau (1996) and Sotiropoulos and Patel (199.4,1995). Kim and Choudhury
showed that the third-order QUICK scheme for discretization of the convective terms produced much better results than lower-order schemes in their 61 x 39 x 29 points grid on the afterbodies of the HSVA and Dyne hulls used at the Tokyo workshop. However, they were not able to re-produce the hooks of the wake contours on the HSVA hull, even with the most accurate scheme,
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a) a) a) -0 ci, E 0 C) (0a failure attributed to inaccurate inflow conditions (only the afterbody flow was computed).
Their results, are not consistent with those of several other researchers.
Deng et al. (1993) showed that an ad hoc reduction of the. eddy viscosity in the core of
the bilge vortex dramatically improved the velocity distribution in the wake. Their method was second-order accurate and did not include wall functions, as that of Kim and Choudhury.
Deng's et al. results focused the interest on the turbulence models Until then there were, with
very few exceptions only the Baldwin-Lomax and k-E models in use. More accurate models were clearly needed. Sotiropoulos and Patel (1994,1995) and Chen etal. (1994) introduced Reynolds stress models yielding clear improvements. Fig. 7 shows the improvements in the prediction of
the velocity distribution in the central part of the wake by going from the k-E model to the Reynolds stress model .The results are for the Dyne tanker. As usual the simpler model predicts
too smooth contours, missing entirely the low speed island at the 0.4 contour, which is well
predicted by the Reynolds stress model. For the HSVA hull, the wake hook and hence the
vortex strength are overpredicted.
Introducing a Reynolds stress model into a Navier-Stokes method is not always straight-forward, Deng and Vissoneau (1996). The momentum equations represent a subtle balance
between terms of different origin. E.g. the Reynolds stress gradients may be equally important
as the pressure gradients. Therefore, the normalpressure/velocity coupling must be modified to a pressure/turbulence/velocity coupling. Predictions based on the Reynolds stress model
tend to overpredict vorticity and, in fact, using the original two-equation k-w model of Wilcox (1993), Deng and Vissoneau also obtain results as good as with the Reynolds stress mode) with much less effort.
In general, however, a Reynolds stress model should perform better than a two-equation model like the k-E model because the latter uses a scalar value for the eddy viscosity. If the flow has, a, high degree of turbulence anisotropy, each ,component of the Reynolds stress must
be computed separately as in the Reynolds stress model. In rotating flows the turbulence is known to be anisotropic, and this speaks in favour of the more complicated model when predicting the vortices hitting the propeller plane. An alternative to the Reynolds stress model is an algebraic stress model, where all components are computed separately, but using algebraic
relations derived by modelling all the terms in the Reynolds stress equations.
Svennberg (1996) investigates the best compromise between computer effort and accuracy,
testing nine turbulence models On the following cases: a single vortex at the centre of a wind
tunnel, two counter-rotating vortices in a flat plate boundary layer, and the HSVA hull., Fig. 8, shows results for the single vortex. The measured data show practically no change in the axial
and the tangential velocity between an inflow and a downstream station. There is thus no
diffusion of the vortex. This is well predicted by the Reynolds stress model (RSM) of Launder and Shima (1989). However, the standard k-E (KE) model predicts considerable diffusion,. These results support the findings by Sotiropoulos and Patel (1994,1995).
4.3 Free-surface boundary 'condition
Free-surface boundary conditions were introduced into Navier-Stokes methods, more than
thirty years ago, Harlow and Welch (1965). Successors to their Marker And Cell (MAC) method have been in use ever since, particularly for internal flow problems like sloshing. However, ship wave calculations appeared more recently, Miyata et al. (1985), Hino (1989). During the early nineties, free-surface conditions were introduced into several codes, Miyata et al. (1992), Tahara and Stern (1992), Hinatsu (1992),. Shin et al. (1992), Alessandrini (1993), Chen et al. (1993), Campana et al. (1993), Farmer et al. (1993), Hino et aL (1993), Liu and Kodarna. (1993). The real breakthrough came in 1994 at the Tokyo workshop, Kodarna et al. (1994), where ten
meth-ods with free-surface capabilities were presented. Important contributions after the workshop are Watanabe et al. (1994), Hino (1994), Alessandrini and Delhornmeau (1990,, Tahara and
Experiment .00 0.01 0.02 am 0.04 0.05 0.06 0.07 0.08 0.00 .0.01 -.02 -0.03 -.04 -0.05 k-e model Exp. data Inflow data KE RSM Exp. data Inflow data KE RSM Reynolds-stress model
Fig. 7. Velocity contours in the wake of the Dyne tanker. Predictions by Sotiropoulos and Patel (1995). Measurements by Denker et al (1991).
Fig. 8. Free vortex in a wind tunnel. Measurements by Phillips and Graham (1984). Predictions by Svennberg (1996) using two turbulence models.
Top: tangential velocity. Bottom: axial velocity
0.0' 0.03 0.04 0.05 0.06 0.07 0.08 -0.01 02 -0.03 .0.04 -0.05 :0. Y 0.01 -0.02 -003 -0.04 -0.05 0.02 0.04 10.05 006,0%0.08 5
Stern (1996) and a comprehensive review of the free-surface developments in Miyata's group at the University of Tokyo, Miyata (1996). The general problem with free-surface Navier-Stokes calculations for ships is the insufficient resolution of the waves. In fact, the results of the work-shop showed that potential flow methods are presently superior to the Navier-Stokes methods in predicting the wave pattern. Even with as much as 600 000 grid points, the low Froude number (0.16) waves of the Series 60 model were almost completely damped out away from the hull. At
a higher Froude number (0.32) the predictions were considerably better, but still not as good as those of the potential flow methods. The wave profile on the hull, on the other hand, was
quite reasonable, also at the lower speed.
The resolution problem has been noted by many of the authors above, and the problem is specifically addressed in Hino (1994). Mori and Hinatsu (1994) discuss the problem in their comments to the workshop results and point out that the resolution requirements are larger for the diverging waves than for the transverse waves. Since most grid convergence studies
have been made in two dimensions, their results cannot be immediately transferred to the ship case. Earlier studies on two-dimensional waves, Shin and Mori (1988), Lungu and Mori (1993),
indicated that at least 30 points were required per fundamental wave length. At a Froude
number of 0.16 this transforms into a grid spacing of 0.005, which would be appropriate in the longitudinal direction. However, in the transverse direction, this Froude number would call for
a spacing of 0.001. A minimum computational domain, two ship lengths long and half a ship
length wide would then require 200 000 points on the surface! In fact, more recent 2-D solutions, Kang (1996), indicate that the number should be even larger. Fortunately, the number of grid
points is inversely proportional to the Froude number to the fourth power, so the situation is
considerably brighter at higher Froude numbers.
The waves diminish as exp(z1Fri2), where z is the distance below the undisturbed free surface. Therefore only a thin region close to the surface has to be discretized with the high
resolution. An appealing solution is thus to apply the overlapping grid technique and introduce a few grid layers near the surface with increasing spacing in the vertical direction.
Free-surface Navier-Stokes methods may be classified in different ways, but a very distinct
feature dividing the methods into two categories is the treatment of the grid at the surface. In the MAC method and its successors, the Volume Of Fluid (VOF) method and the more recent density function method, the grid is fixed and the location of the free surface in the grid is tracked in different ways.. The other approach is to deform the grid to fit to the free surface at all times. In recent years this latter technique has become dominant because it is
generally considered less diffusive. Another advantage is that the free-surface boundary layer may be resolved with high accuracy. The advantage of the fixed grid methods is that they save computer effort, since the grid does not have to be regenerated at every step.
Most moving grid methods suffer from problems if strong non-linearities occur, such as over-turning waves and breaking. A new fixed grid, surface tracking technique that should be able to cope with multi-valued wave shapes and topological changes occurring when water drops break off is the "level set" technique developed at UCLA, Sussman et al. (1994). No results involving gravity waves have been reported so far. The basic idea behind the level set method is to define a scalar, the level set function, in the whole computational domain, which includes both fluids
(in this case air and water). Initially, the scalar value is equal to the distance from the point in question to the interface. Thereafter a separate differential equation is solved for the scalar
after solving the flow equations in both fluids simultaneously. The new equation specifies the
total derivative of the scalar to be zero, or in other words, every fluid particle is assigned a unique value which is not changed during the computation. Sometimes the scalar field has to
be reinitialized, but that has nothing to do with the basic principle. Since the particles initially
on the free surface will stay there forever, the position of the surface at every later stage can be found as the zero level of the scalar function. The change in physical properties across the
interface is smeared out in a thin band at the interface. Fig. 9 shows the breakoff of a water drop from a wave generated by a bump on the bottom of a canal. Four different time steps showing the break-off are displayed. These results are only qualitative. A higher resolution is required for quantitative results, but the example shows the method's inherent capability of
handling difficult non-linearities, including also changes in topology.
5. The future
Possibilities in a longer range are tightly linked to the future development in computer speed and storage capacity, but long term predictions of computer capacity are scarce, due to the large uncertainties involved. The best prediction offered at present is based on the past development rate, namely a doubling in speed every 18 months (Moore's law). This corresponds to an order of magnitude every five years and holds for each individual processor. The rate could be increased
if the number of processors is increased. In December 1996, the world's first Tflop machine was demonstrated by the Intel Corporation, Miller (1996). The machine had 7 264 Pentium
Pro processors and achieved a speed of 1.06 Tflops. A performance increase by two orders of magnitude is predicted for 2005.
"Stokes methods" in this paper are methods based on the Reynolds Averaged Navier-Stokes (RANS) equations. In the RANS methods, all spatial and temporal scales related to the turbulence have been removed through averaging over suitable length and time scales. The cost for this is the appearance of the Reynolds stresses, which have to be modelled. Unfortunately,
the results are rather dependent on the performance of the turbulence model under different conditions. The basic idea behind the methods on the next level, the Large Eddy Simulation (LES) models, is that as much as possible of the flow dynamics shall be computed, without
having to resolve the smallest scales. It is thus assumed that the necessary model for the small scales is more universal, or has less influence on the mean velocity and the integrated quantities of interest.
The most accurate calculations are those where the full range of scales is resolved in the
Navier-Stokes equations by Direct Numerical Simulation (DNS). But for a full-scale ship, the
smallest length and time scales in the boundary layer are of the order of 10-6 m and 10-5s respectively. Fortunately, they are only important close to the hull. Further out, the relevant scales are larger. This should be compared with the number of grid points needed to resolve
channel flows using both LES and DNS at different Reynolds numbers, Wilcox (1993):
Fig. 9: The break-off of a water drop
pre-dicted by the level set technique. Wavegen-erated by a bottom bump. Note the shift in
the vertical direction between the time steps.
(Only qualitative results; resolution
A LES solution for a Reynolds number of 230 000 calls for 108 grid points. This is within
reach. The largest cases which have been computed today are approaching this number. Since
the Reynolds number in this case is based on the channel height it would correspond to a
Reynolds number based on the boundary layer thickness for a ship hull (or perhaps twice that number). This value is relevant for typical model-scale cases. LES calculations for ship models should thus be possible relatively soon and even DNS simulations might be carried out within
the not too distant future, at least in laboratories with access to the fastest supercomputers.
Obviously, more time is required before these methods may be in general practical use. Full-scale
calculations of either type will not be possible within the foreseeable future.
6. Conclusions
CFD is already 'an established tool for forebody design, including bulb shape, shoulder shape, shape of sections and forebody type In this case, potential flow methods are
employed and the recommendations for design are based primarily on flow variables, such as pressures, velocities and wave heights'.
Afterbody design using the same methods is possible for planing hulls, where viscous effects are small. For displacement hulls viscous flow methods are required and promising
results have been presented using carefully designed grids.. The ongoing developments described in the paper are likely to make viscous flow methods as useful as potential flow methods are today. Improvements of afterbodies and propellers may then be carried out routinely.
Other applications for which CFD is already useful include lift/induced resistance for sailing yachts and hydrofoils, local flow predictions for positioning shaft brackets, fins, bilge keels etc, environmental disturbances such as wake wash and beach erosion and
naval applications like transition prediction and pressure signature.
For absolute power predictions towing tank experiments will be needed in the foreseeable future, but CFD is better for design purposes since it provides more guidance to the user on how to improve the design.
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