numerical hull series for calm water
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Numerical Hull Series for Calm Water and Sea-Keeping
Patrick Couser, Formation Design Systems Pty Ltd, Fremantle/Australia, [email protected]
Stefan Harries, Friendship Systems GmbH, Potsdam/Germany, [email protected]
Fabian Tillig, SSPA Sweden AB, Gteborg/Sweden, [email protected]
Abstract
Naval architects draw inspiration from previous designs, literature reviews, statistical regression
models and systematic series. In this paper, a complementary approach, using simulation-driven
design, is presented: exploration of the multi-dimensional design-space using first-principles
methods. The vessel is modelled parametrically with the free-variables that define the design-space.
The design-space is then populated by systematic variation of these variables. The key benefit of the
proposed method is that it allows the design team to quickly explore the design-space and build up a
knowledgebase ahead of an anticipated project. This then allows quick interrogation of the numerical
model series to substantiate design decisions during the bidding and tendering process.
Nomenclature
BWL Beam on waterline
CB Centre of Buoyancy
CG Centre of Gravity
DWL Design Waterline
GMt Transverse metacentre above CG
GZ Hydrostatic righting lever
LCB Longitudinal Centre of BuoyancyLCG Longitudinal Centre of Gravity
LPP Length between perpendicularsVCB Vertical Centre of Buoyancy
VCG Vertical Centre of Gravity
n
n-dimensional (design) space
Abbreviations
CFD Computational Fluid Dynamics
COM Component Object Model
CPU Central Processing Unit
FLOPS Floating-point Operations per Second
FFW FRIENDSHIP-Framework(Software)
GPU Graphics Processing Unit
HM Hydromax (Software)
MSI Motion Sickness Incidence,
RAO Response Amplitude OperatorSK Seakeeper(Software)
1. Introduction
The aim of this paper is to demonstrate, by means of an example application to a mega-yacht, how
numerical simulation can be used to explore the design-space early in the concept design stage of a
project and how this information may be used to gain deeper insight into the design compromises
which will have to be made.
Table I shows the principal particulars of the proposed vessel; these would typically be given by the
client: Design me a mega-yacht thats a bit faster, a bit bigger and a bit more luxurious than the one Ibought last year! As can be seen, the design requirements are quite vague, so it is of utmost
importance to gain an understanding of the design-space in which the solution will lie (or even to
ascertain the feasibility of the proposal).
1.1. Why?
Information is power! Prior knowledge of the relevant design-space for a ship-design project enables
the design team to achieve a sensible compromise that meets the customers requirements. This
knowledge can be gained in several ways. For example, an existing vessel may serve as a basis design
from which a new, improved vessel that better fulfils the customers requirements can be derived. Or,
if there is little prior knowledge or the project requires a completely novel vessel design, then it is
important for the designer to gain an understanding of the design-space by some other means. Tosummarise, the proposed approach might be used to:
Paper presented at the 10th Internat onal Conference on Computer and IT Appl cat ons n the Mar t me Industr es,
Berlin, 2-4 May 2011, Hamburg, Technische Universitt Hamburg-Harburg, 2011, ISBN 978-3-89220-649-1
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Gain an insight of the design-space early in the project; Enable rapid prototyping of ideas for novel design solutions; Provide data for decision support for possible design changes required to achieve desired
performance; and
Anticipate consequences of requested design changes.Table I: Principal particulars of the proposed mega-yacht
minimum maximum
Length between perpendiculars,LPP [m] 68.00 72.00
Beam onDWL [m] 14.00 14.25
Design Waterline,DWL [m] 3.9
Displacement in seawater atDWL [tonnes] approximately 2200
Cruise speed [kts] 16.0
Maximum speed [kts] 20.0
1.2. How?
The example presented serves to illustrate the concepts and methodology. However, there is noreason why different design aspects could not be examined or different numerical tools used. The key
is being able to automatically vary the proposed vessel in a manner so as to produce viable variants
and then be able to predict the variants performance characteristics pertinent to the design
requirements.
The design-space investigation thus comprises three main tasks:
1. Definition of a suitable parametric model which can be used to generate feasible designvariants from a small number of key parameters.
2. Numerical analysis of the vessel using simulation tools which can provide an assessment ofthe vessel performance characteristics of interest (in this case, hydrostatics, resistance and
sea-keeping). These tools need to be selected so that they can provide sufficiently reliable
data within available time and computational resource constraints.
3. Automation of vessel design variation, analysis, results gathering and post-processingtasks.
The FRIENDSHIP-Framework (FFW Friendship Systems, 2009) is used to firstly define the hull
geometry in a parametric manner which can then be systematically varied and secondly to
systematically vary the design, control the analyses and collate the results for all the design variants.
1.3. What is Important?
What is of interest and importance to the designer will depend on the individual project being
undertaken. In this example, static stability as well as resistance and also passenger comfort when thevessel is under the influence of waves are considered.
The vessels calm water resistance was estimated using SHIPFLOW (Flowtech 2004, 2009), whilst
sea-keeping characteristics and hydrostatic stability were predicted using Seakeeper (SK) and
Hydromax(HM Formation Design Systems, 2011).
1.4. Computer Hardware
It is interesting to look at the increase in computer performance over time; this is shown in Fig. 1 for
the last 30 years (SUPERCOMPUTER 2011; Thibault et al. 2009; Koomey et al. 2009). There
continues to be exponential growth in not only the performance of supercomputers but also that of
personal micro-computers. What is also interesting is the application of GPUs rather than CPUs tosolving CFD flows (Thibault et al. 2009). GPUs can be optimised for floating-point calculations and
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matrix inversion much more than CPUs (which are required to perform a much broader range of
operations). The rate of increase in performance of GPUs is greater than that of both CPUs and
Supercomputers.
The rapid development of computer hardware and the advent of computer clusters and clouds (e.g.
Amazon Elastic Compute Cloud EC2) and other distributed systems now mean that the hardware
resources necessary for the type of numerical investigations described in this paper are now
accessible to even the smallest design teams.
Fig. 1: Super- and Micro-computer performance with time
2. Methodology of the Investigation
In this section, we shall look in some detail at the numerical method used for the design-space
investigation. The key concept to take from this paper is the methodology; different analysis software
can be substituted and different performance measures will be appropriate for different projects.
2.1. Parametric Modelling
The general hull-form chosen for the example mega-yacht was a classical twin-screw design with
bulbous bow and skeg. Appendages were not included at this initial phase of the design. The bulb was
modelled in some detail, since it had a significant impact on the hull resistance. The bulb was blended
into the main hull over a region of transition aft of the forward perpendicular. The main hull itself was
split into fore- and aft-body regions joined at the section with maximum cross-sectional area. A full3D model of this geometry was realised in the FFW.
The model was parameterised so the geometry could be manipulated by a small number of key
features which the designer would wish to vary. These parameters are the free-variables of the n-
dimensional design-space to be investigated and were used to generate design variants within that
space. The parameters (or free-variables), with their range of variation are given in Table II and the
primary curves describing the model are shown in Fig. 2. The body plan, plan, profile and perspective
views of a representative instance of the parametric model are shown in Fig. 3. Full details of the
parametric model are described inHarries (2010).
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Table II: The free variables that are used to define the parametric model
minimum maximum
Length between perpendiculars,LPP [m] 68.00 72.00
Beam onDWL [m] 14.00 14.25
Midship area coefficient 0.82 0.89
Prismatic coefficient of fore part of hull 0.60 0.63DWL half angle of entrance [deg] 14.0 18.0
DWL fullness coefficient 0.58 0.62
Bulb area to midship area ratio 0.092 0.098
Bulb fullness coefficient 0.75 0.85
Longitudinal position of section with max. cross-sectional area [%LPP] 44.0 48.0
Fig. 2: Parametric model of round bilge mega-yacht
Fig. 3: Example of typical bare hull with bulbous bow generated from the fully parametric model
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2.2. Performance Prediction
The numerical tools used to calculate the vessel performance are described below. The tools
presented cover three of the main areas of interest during initial design: resistance, sea-keeping and
static stability. However it would be entirely feasible to include other tools to compute other
performance parameters, for example production cost, manoeuvring, etc. The scope of the
performance parameters to be considered depends on the time available to complete the study as well
as the tools available and the level of detail of the ship model required to produce meaningful results.
2.2.1. Flow Simulation and Resistance Prediction
When predicting calm-water resistance, there is generally a trade-off between accuracy and the
computational effort required. Since only the bare hull was modelled, it was considered appropriate to
employ potential flow theory to solve the non-linear wave resistance problem with free sinkage and
trim combined with a thin boundary layer theory calculation for the frictional resistance, further
details are given in Harries (2010). When fine-tuning appendages, such as brackets, later in the
design, a RANSE calculation should be undertaken to accurately capture the viscous phenomena, for
example Brenner (2008).
The flow simulations were computed on a standard dual core notebook and took about four to five
minutes per variant and speed. With a CFD license for both cores, around 200 designs could be
computed in one overnight job. A typical panel arrangement and results are shown in Fig. 4.
Fig. 4: Typical panel arrangement of free surface and hull
with wave-wake height contours and hull streamlines at FN = 0.393
2.2.2. Motions in Waves and Comfort Measures
The vessel motions due to waves were predicted using Seakeeper a linear strip theory method in the
vein ofSalvesen et al. (1970). Two scenarios were considered (details are given in Table III):
1. Vessel at anchor or in a marina in a very slight sea-state the so-called Party condition.(Note that mooring forces were not considered.)
2. Vessel underway at a cruising speed of 16kts in a higher sea-state, as might be encounteredwhen traveling between two such Party locations the Cruise condition.
The motion sickness incidence (MSI) after two hours exposure was computed at different longitudinal
positions along the length of the vessel (Fig. 5). That is the percentage of people who can be expected
to vomit after having been subjected to the motions for a period of two hours, as calculated by themethod proposed by OHanlon and McCauley (1974) andMcCauley et al. (1976). The performance
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measure extracted from the analysis was simply the minimum MSI along the length of the vessel for
each of the two scenarios considered; assuming that the vessel layout could be adjusted so that MSI-
critical systems (e.g. the bar) could be sited accordingly.
Table III: Two scenarios considered for the sea-keeping calculations
Party Cruise
Vessel speed [kts] 0.0 16.0
Characteristic wave height [m] 0.5 2.0
Modal period [s] 2.0 7.1
Wave heading Head seas
Wave spectrum type 1-Parameter Bretschneider
Fig. 5: Typical MSI distribution over the length of the vessel
The sea-keeping model used 41 equally spaced sections through the hull. Conformal mapping wasused to model the sections and compute the sectional added mass and damping in heave (five
mapping terms were used to give a good fit to the hull sections). The vessel heave and pitch response
amplitude operators (RAOs) was then calculated at 200 frequencies and these were used to calculate
the MSI. The calculations, for 200 variants, were computed on an average desktop computer using
SK, again in an overnight job controlled by the FFW.
2.2.3. Hydrostatic Stability Criteria
Virtually all vessels must comply with hydrostatic stability criteria specified by class. A small subset
of intact-vessel stability criteria, which are typically applied to this class of vessel, were selected from
theLarge Commercial Yacht Code (Maritime and Coastguard Agency 2007) intact stability standards
for monohull vessels, section 11.2.1.1. These criteria are summarized in Table IV.
Table IV: Stability criteria considered
Section Description Required value
11.2.1.1.1a Area under GZcurve from 0 to 30 deg. heel shall not be less than 0.055 m.rad
11.2.1.1.1b Area under GZcurve from 0 to 40 deg. heel shall not be less than 0.090 m.rad
11.2.1.1.2 Area under GZcurve 30 to 40 deg. heel shall not be less than 0.030 m.rad
11.2.1.1.3 Maximum GZat 30 deg. or greater heel shall not be less than 0.2 m
11.2.1.1.4 Angle at which maximum GZoccurs shall not be less than 25 deg.
11.2.1.1.5 Initial metacentric height (GMt) shall not be less than 0.15 m
In order to obtain a meaningful performance measure of stability, the maximum vertical centre ofgravity (VCG) at which all criteria were just passed was calculated for a range of displacements. A
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typical curve of maximum allowable VCG against displacement, for three representative design
variants, is shown in Fig. 6. The measure of performance used was the area under the maximum
allowable VCG curve integrated over the displacement range of 1800t to 2600t. This measure was
chosen because early in the design process, neither the VCG nor the displacement would be known
with certainty; the measure gives some indication of the scope of VCG change that can be
accommodated whist still passing the criteria.
Damage stability has not been considered at this stage because this would depend on the
compartmentation layout which would not be available early in the initial design. Once a design
variant has been selected for detailed design development, the internal layout and compartmentation
would have to be chosen so that damage stability requirements were met.
The analysis was performed inHMusing a range of heel angles at each displacement to calculate the
GZcurve for a given VCG. The vessel was free-to-trim ensuring a longitudinal balance ofCG and CB
(theLCG being derived from theLCB of the upright vessel). The VCG was then systematically varied
to determine the maximum value ofVCG at which all the stability criteria were still passed. Managed
by the FFW, the calculations, for 200 variants, were computed in a matter of several hours.
Fig. 6: Typical MSI distribution along the length of the vessel
2.3. Software Integration
The FFWand the simulation software are developed by different software vendors. However, in order
to automate the task of generating design variants and analyzing their performance, it is essential that
the software systems are able to communicate. Under Microsoft Windows there exists a paradigm for
inter-process communication. This is known as the Component Object Model (COM). For full detailsof COM, the interested reader is referred toBox (1998). COM allows access to suitably COM-enabled
applications via a common interface from a variety of programming languages: C#, VBA, etc. and
also the FFWs own macro language.
Suitable macros were developed in the FFW to export the hull geometry and then import this
geometry and run the analyses inHMand SK. The results of the analyses were then read back into the
FFWfor post-processing to calculate the final performance measures for each variant. Fig. 7 shows a
screenshot of the FFW, HMand SKin action.
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Fig. 7: Screenshot of FRIENDSHIP-Framework, Hydromax and Seakeeper in use
2.4. Design of Experiments
The design-space was investigated using a Design of Experiments approach to populate the domain
with variants. The principal particulars of the vessel are given in Table I and the nine free-variable
which were used to define the variants are given in Table II. These nine free-variable thus establish a
nine-dimensional space 9. A Sobol algorithm, Press et al (2007) was used to give a quasi-random,
yet uniform sampling of these variables over the desired range (see Table II). The performance was
calculated for 200 variants. A typical distribution of variants (for one free-variable) is shown in Fig.
8; as expected, the Sobol algorithm provides a uniform, quasi-random sampling over the design-space. The design of experiments approach covers the design-space more economically than a regular
grid approach a regular grid of just two parameter variations in 9 dimensions would require 512 (29)
variants.
Fig. 8: Typical distribution of a free-variable using the Sobol algorithm
2.5. Response surfaces
The design-space exploration generates a large quantity of data and represents a not insignificant
amount of computational effort (especially if sophisticated numerical simulation tools have been
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used). It is useful then, to reuse this data, potentially for automated optimisation or other similar
applications. There are several ways in which this data can be captured so as to be able to determine
the vessel performance measures for a set of specified values of the free-variables. These include:
statistical regression; artificial neural networks (e.g. Couser 2004) and response surfaces. All of these
methods effectively allow interpolation of the performance measures of the design given a set of
values of the design parameters (free-variables) without having to redo the numerical simulation, thus
saving a lot of computational effort.
Following the work ofHarries (2010) a response surface, meta-model method has been used. The n-
dimensional (where n is the number of free-variables) response surfaces for the performance
measures are fitted using a Kriging approach, see Tillig (2010). Once the response surface has been
generated, interpolation is more or less instantaneous (compared with a CFD or sea-keeping
calculation which might take a few minutes to several hours to perform). Continuous iso-parametric
curves and surfaces can then be generated from the response surface making it easier for the designer
to visualise the design space: the designer is able to see the effect of continuously varying one or two
free-variables rather than seeing discrete results for variants where all the free-variables have been
modified (which is the raw output from the design of experiments investigation of the design-space).
3. Results
This section presents some results for the mega-yacht example. One should not forget that these
findings are only meaningful in the context of the chosen parametric model (the established design-
space) and that they rely on the validity of the simulations. Even though these simulations are built on
first principles, there are notable simplifications, for instance the wave resistance and sea-keeping
analyses, as used in this example, ignore viscosity.
3.2. Correlations
Some samples of the raw results from the Sobol investigation of the design-space are presented by
means of correlation plots (as shown in Figs. 9 to 14). These correlation plots can highlight generaltrends in the data but it should be noted that the points represent discrete variants where all of the
free-variables have changed; thus these diagrams do not accurately represent the continuous variation
of a single variable. The band-width of the scatter of points about the mean line gives an appreciation
of the difference that can be achieved due to variation of all the other free-variables. It should be
noted that even when there is reasonably strong correlation between performance and a free-variable,
there is often a significant range of performance (which thus depends on the other free-variables). For
example, in Fig. 11, at a length of 70m the Cruise MSI can vary between 4% and 5%. This also
implies that there is always room for improvement even though one (or several) free-variables need to
be fixed at a certain point in the design process. The range of performance can be taken as an initial
indication of how much potential for optimisation is available.
3.2.1. Principal Hull Geometry
Fig. 9 presents the vessel displacement against the length between perpendiculars. A general trend
towards higher displacement for longer vessels can be seen. Nevertheless, as discussed above, there
are instances of vessels with higher and lower displacements (for a fixed LPP) that depend on the
values of the remaining free-variables.
3.2.2. Calm Water Resistance
Fig. 10 shows the correlation between vessel length and predicted wave resistance coefficient. As
might be expected the longer the vessel, the lower the resistance. The interested reader is referred to
Harries (2010) for further details and results of the resistance calculations performed.
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Fig. 9: Typical correlation of a performance measure with a free variable (Displacement and Length)
Fig. 10: Strong correlation between Wave resistance coefficient and LPP
Fig. 11: Strong correlation between MSI and LPP
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Fig. 12: Very weak correlation between MSI and Beam
Fig. 13: Strong correlation between Stability performance measure and LPP
Fig. 14: Un-correlated relationship between Stability performance measure and Bulb Fullness coef.
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3.2.3. Sea-Keeping
As might be expected, the MSI shows a reasonably strong inverse correlation to the vessel length: as
the vessel length increases, the motion sickness incidence decreases, Fig. 11. Sometimes it may be
found that there are surprising correlations (or lack thereof); for example Fig. 12 shows that the
correlation between MSI and beam is not very strong, contrary to what might be expected.
3.2.4. Hydrostatic Stability Criteria
A strong inverse correlation between vessel length and stability was found Fig. 13. This is probably
due to the fact that the displacement range for the stability calculations was fixed irrespective of
vessel length. Shorter vessels would be broader and/or deeper in the water generally resulting in
greater intact stability (up to the angles of heel investigated). Other parameters showed little or no
influence on stability (Fig. 14) indicating that they can be varied to improve other performance
measures without penalising the stability performance.
3.3. Response Surfaces
Once the n-dimensional response surfaces have been fitted to the discrete data obtained from the
design-space exploration, continuous iso-parametric curves and surfaces can be generated for
continuous variation of only one or two free-variables (the others remaining constant). In Figs. 15 to
17, all but two free-variables are kept constant resulting in iso-surfaces through the design space. In
each diagram the range of each free-variable has been normalised to 1.0.
In most cases the response surfaces follow what might be expected: Fig. 15 shows that the delivered
power requirement is reduced for longer and generally narrower vessels; and Fig. 16 shows that MSI
is reduced for longer vessels, with the optimum beam being about the middle of the range. However
in the case of the stability performance measure response surface, Fig. 17, the effects of length and
beam are more complex. It should be noted that since the entire design-space exploration is not
covered by the variants tested, care should be taken to ensure that the response surface is used forinterpolation, and not extrapolation. The sharply raised corners in Fig. 17 are due to extrapolation
with insufficient variants to adequately describe the response surface in these regions.
Fig. 15: Response surface for Power vs. Length and Beam
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Fig. 16: Response surface for Sea-keeping vs. Length and Beam
Fig. 17: Response surface for Stability vs. Length and Beam
4. Taking Things Further / Practical Application
In this paper we have presented an example using a mega-yacht initial design project. Relatively
simple numerical simulation tools have been used to investigate three aspects of the design process:
calm-water resistance (using potential flow and boundary layer theory), sea-keeping (using strip-
theory) and static stability. However, there is no reason why the same methodology cannot be applied
to different problems using different simulation tools.
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The FRIENDSHIP-Framework is very useful in that it facilitates a parametric model of the hull
geometry and allows this geometry to be systematically varied. It then manages sending the geometry
to and retrieving the results from the external simulation tools. The COM interface provides a
relatively simple mechanism for inter-process communication on the Microsoft Windows platform.
(The coupling between the FFWand the analysis software, SKandHM, was achieved using COM.)
Although not presented in the current work, using the resulting response surfaces to drive an
optimisation search is entirely possible and would be the logical next step of the design process (see
Harries (2010) for an example).
5. Conclusions
One of the most challenging tasks for the ship designer is to gain an insight into the non-linear
relationships between competing objectives, constraints, free- and dependent-variables so as to be
able to obtain a suitable final design that meets the customers requirements. The methodology
described in this paper shows how first-principles simulations, coupled with a parametric model of
the vessel can facilitate rapid exploration of the design-space. The methodology can be summarised
as follows:1. Creation of a suitable parametric model of the vessel. The parameters chosen to be free-variables entirely define the vessel and span the design-space of interest. They can be
regarded as the free-variables of an optimisation problem.
2. Performance measures and constraints such as hydrostatics and hydrodynamic performanceare identified and determined by means of numerical simulations based on the vessel
obtained from the parametric model.
3. The design-space is then systematically and automatically explored using formal methods.4. The results of the design-space exploration are captured by response surfaces that allow for
very rapid interpolation of the performance measures for any of set of values of the free-
variables.
5. Once the design-space is known and understood, the data can be used to answer what if?type questions as well enabling optimisation searches to be performed quickly.
The key things to take from this paper is the methodology. The details of the specific parametric
model and analysis tools used are of less importance because they can (and should) be adapted and
tailored to the specific needs of the individual project. However, what this paper aims to show is how
an in-depth knowledge of the design-space in which one finds oneself can be gained by more formal
and extended use of numerical simulation. Of course, as computational power continues to increase
and the accuracy of numerical simulation techniques continues to improve, it will be appropriate to
change the hardware and software used to perform the design-space exploration. It is believed by the
authors that the approach described in this paper will aid naval architects during their design tasks by
providing familiarity with novel design ideas more quickly and allowing them to make appropriate
design modifications to match evolving client requirements more easily.
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