SUPERYACHT #10 Autumn 2006
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Article by Mario Felli


Optimisation and experimentation: new frontiers of ship design / 2

Test Tank at INSEAN (National Institute for Marine
Architecture Studies and Experiments). Experimentation is a useful
tool during the designing of a ship: directly, through performance
verification, and indirectly through validation of CFD models.
(Photo supplied by G. Aloisio)

To complete what was described in the June issue
of "Superyacht" with regard to aspects characterising the design of a vessel and
new design trends, this article aims to provide a more detailed
description of the problems involved in selecting an optimisation
algorithm. As noted extensively in part one of this article, in
modern approaches to design the search for an optimal solution
that globally maximises vessel performance is a complex and many
sided process based on the joint use of experimental verification
and numerical simulation. Vessel design is evolving progressively
towards a process of global optimisation, characterised by an
integral vision of all the problems and parameters that contribute
to the performance of the vessel system. So in this scenario a
"trial and error" approach is inevitably inadequate and in any
case, due to its "iterative" nature, we come up against costs that
are too heavy with regard to time schedules and verification of
congruity with the design specifications. In other words, the
passage through experimental verification cannot be integrated de
facto into a design process of this type, so it would inevitably
be "sacrificed" and perhaps required only to verify the
"definitive" configuration (figure 1).
Figure 1. Block diagram of a vessel design. On the basis of the
design specifications (1) and of the designer's experience (2)
[which often sets out from preexisting configurations] the final
geometry of the vessel is defined (5). This approach is unlikely
to assume the characteristics of an iterative process due to the
high costs of experimental verification of performance phase and
congruity with the design specifications.
This design approach then consists of an iterative process whose
feedback is in fact entrusted chiefly to the designer's instinct
and experience rather than to backup from appropriate measuring
instruments, so it does not guarantee achievement of an "optimal
solution". In this context we must include the need for the aid of
optimisation algorithms, and therefore the need to "set" the trial
and error design scenario in the virtual reality of numerical
simulation (figure 2).
Figure 2. Block diagram of the design of an "optimal" vessel. The
objective value of the design variables (1) is iteratively
compared with the current one at the ith step (2). If the
difference is greater than zero we proceed to a further step of
optimisation (3) which gives a new geometry of the model (4)
characterised by its own value of the design variables (6). The
value of these variables calculated with a CFD solver or
experimentally measured (5) is once more compared with the design
values, closing the iteration. The process ends with optimised
geometry (7) when the current value of design variables
corresponds to the objective one.
There are clear advantages to be gained from this new approach:
 an integral vision of the actions and effects brought to bear
on the vessel system which also takes into consideration any
interaction between "conflicting" solutions: the adoption of
optimisation algorithms may therefore handle
contemporaneously a grouping of parameters and variables,
often interdependent, something that would be otherwise
impossible even for an expert designer;
 the certainty of proceeding by means of a process of
iterative improvement that converges towards the optimal
solution: the designer's modifications of an unsatisfactory
solution can in fact sometimes turn out to be fairly
inefficacious, or rather have negative repercussions on a
general vision of the vessel system's performances. Returning
to the example of passive control systems (see the June
number of "Superyacht"), a variation in the form of antiroll
bilge keels or stabilising fins with view to improving vessel
stability could have a negative fallout on hydrodynamic and
hydroacoustic performances and on propulsive efficiency.
 the possibility of integral management of vessel design in
the virtual reality of numerical simulation: in this way the
design process would be partially relieved of having recourse
to experimentation for verification of intermediate solutions
(in fact an untenable solution due to the prohibitive costs
and time schedules required by construction and systematic
verification of a model at the ith step of the design
process to supply information on correspondence to the design
objectives and on any modifications to be carried out for the
next step).
The scenario of a design project completely set in the virtual
reality of numerical simulation is a fairly ambitious and complex
objective which is studied in the main shipbuilding research
centres. One point is to understand how much numerical simulation
can faithfully represent physical reality. Analysis of the
variables that influence accuracy of numerical simulation is a
highly complex and manysided aspect involving both the quality of
the chosen theoretical model and the implementation and conditions
of use of the numerical algorithm (quality of calculation grids
etc.). The exact solution of the equations that govern the motion
of a vessel (and in general of a body in a fluid) involves a
computational burden that is sometimes unsustainable, depending
strictly on the desired degree of accuracy, on the operational
conditions necessary for representation of the physical problem in
question and, of course, on technological aspects linked chiefly
to the power of the computer system. So what happens is that
approximate models are used which "simulate" the physics problem
on the basis of a compromise solution between characteristics and
the nature of the amplitudes to be obtained. By way of example,
let's consider the problem of numerical simulation of the
performances of a propulsor and of determination of a vessel's
resistance to forward progress. In the first case the choice of a
CFD model that neglects viscid effects (potential models) is a
solution that can yield information on the thrust and torque of
the propulsor with a fair degree of accuracy and with low
computational costs, widely justifying its use in comparison with
the more costly viscid models. In the second example, the use of a
potential model gives an underestimate of resistance to progress
inasmuch as it neglects the contribution of the friction component
(linked, precisely, to viscosity): in this case the choice of a
viscid model is a preferential solution. How much do the results
of numerical simulation differ from the effective values of the
physical problem under examination? In our examples: what error is
committed in neglecting the viscid effects in representing the
performance of a propeller? How much does the resistance value
calculated with a RANS model differ from the values measured in a
towing test? In this context experimental validation of CFD models
takes an absolute foreground role, "certifying" the quality of the
theoretical model adopted (viscid, potential etc.) and of the
numerical algorithm (as the theoretical model is converted into a
calculation instrument) with the values measured experimentally
(figure 3).
Figure 3. Validation of a potential code on the analysis of field
of velocity upstream of the rudder. Experimental validation of CFD
models certifies quality of numerical simulation and is therefore
very useful in the phase of development and implementation of a
CFD code.
The foregoing clearly demonstrates how the search for a compromise
between computing costs and accuracy of numerical simulation is a
highly delicate aspect in the choice of optimisation algorithm:
also in this case the iterative process requires, at every step, a
verification of the solution with regard to the desired values and
therefore clashes with the contrary needs to cut computational
costs without overnegative effects on the quality of the process itself.
Having stated this premise with the intention of clarifying the
scenario and the problems inherent to the design of an "optimal"
vessel, it is worthwhile pausing to briefly describe the aspects
peculiar to an optimisation algorithm and to better qualify the
meaning of the adjective "optimal" in this specific case. A highly
detailed description of these aspects would be understandable only
to those with knowledge of fairly elaborate theoretical concepts
so, where necessary, I shall try to sidestep mathematic rigours
and formalisms in order to facilitate understanding for less
expert readers. The departure point of an optimisation algorithm
concerns identification of a space of "design" variables that
physically describe the specific problem to be optimised (e.g. for
minimising total resistance: speed of progress, geometrical
variables, roughness of the ship's bottom, draught etc.) and the
mathematical formulation of an expression which analytically
translates operational objectives and limitations as a whole.
Figure 4. Optimisation of the form of a vessel's bow bulb to
minimise wave resistance value. The value of pressures on the
vessel's bow and of the wave profile were obtained numerically by
means of a RANS code.
The first group includes a more or less heterogeneous collection
of specifications describing the vessel performances desired:
these specifications may regard, for example, the hydrodynamic
performance of a hull in terms of resistance to progress rather
than manoeuvrability and stability with a sea running, or the
vessel's hydroacoustic or hydroelastic performances. The second is
represented by a grouping of functional limitations (e.g. maximum
height of wave profile, minimum distance of the vortical
structures of the stabiliser fins from the propulsor shaft) and
geometrical ones (e.g. vessel size, displacement, volumes required
for payload) the effect of which is to restrict the dimension of
the "design" variables space to a subgrouping of that of
departure. The number of possible solutions to the optimisation
problem will depend on the dimensions of this subgrouping and
therefore on the number and typology of the objectives and
limitations set. In some cases, in particular, there will be no
solution to the optimisation problem and it will be necessary to
remodel objectives and limitations. Definition of objectives of
course is a step in which one must take account of both the
engineering need to maximise vessel performances and the practical
possibility of implementing and completing the optimisation
process within reasonable time schedules. Fairly heavy costs are
involved in the introduction of a heterogeneous grouping of
objectives (e.g. setting objectives on total resistance value,
vibrations aft and roll stability) as against the evident
advantage of directing design towards a process of global vessel
optimisation: the different nature of the individual problems and
the eventuality of interaction between variables that define the
physical behaviour thereof call for a fairly complex formulation
of the objective functions and equally complex verification of
correspondence to design specifications. In this sense careful
analysis of the optimisation problem and possible methodological
solutions for application to a specific problem is a very
important phase in which the costbenefit ratio must be evaluated
for each objective.

Figure 5. Calculation mesh of a CFD code on the study of
propellerrudder interaction: the numerical solution is supplied
in a discrete grouping of points along a suitably developed
calculation grid.
Figure 6. Seakeeping test in rough weather at the INSEAN
rectilinear tank. Experimental simulation of rough sea conditions
is carried out in a rectilinear tank by means of a wave generating
system. (Photograph by G. Aloisio).

For example, in the case of a racing yacht where performances in
terms of toughness and manoeuvrability are uppermost, to insert an
objective regarding noise levels on board would heavily and
uselessly jeopardise the optimisation process. Contrarily, the
coupling of manoeuvrability and toughness with comfort is a
strategic objective in Superyacht optimisation.
Once the optimisation problem has been formalised in terms of the
functions objective and the operational limitations, it is
important to choose an instrument capable of describing, for each
step in the optimisation process, the modified geometry of the
hull and the CFD code calculation grid. A few words on this
subject: the domain in which a CFD simulation is represented
consists of a discrete grouping of points whose characteristics
(reciprocal distance, position etc.) play a highly important role
in determining the performances of the simulation itself (figure
5), both in terms of accuracy and of computational costs.
Construction of the calculation grid is also a fairly complex
aspect: at each step of the optimisation process, redefinition of
the vessel's form makes it necessary to remodel the calculation
grid to adapt it to the new geometry. In this case too, moreover,
seeking a tradeoff between opposed requisites is a crucial point
which the designer must tackle: choose a very dense grid to ensure
a greater degree of simulation accuracy, or favour a streamlining
of the iteration process thus reducing computational costs? The
answer isn't simple and requires specific knowledge of the
problems that characterise the development of a CTD code
(computational costs, physical characteristics of the problem to
be analysed, stability etc.) which is beyond the scope of this
article. The efforts made daily by research to supply the designer
with increasingly efficient and fruitful codes for improving
vessel performances has produced exceptional results in recent
years. The study of techniques for streamlining costs of the
optimisation process, while at the same time increasing efficiency
and potentialities, is a subject of considerable interest in the
shipbuilding research sector.
The right investment strategy for the shipbuilding world lies in
these new design instruments.
Glossary
CFD. CFD (Computational Fluid Dynamics) is an applied physics
discipline that came into being around the 1960's. As the name
suggests it is the study, by means of computer, of the dynamics of
a fluid in which there may be physical phenomena such as heat
transfer, acoustic irradiation, vibration transmission, cavitation etc.
Validation. Validation of CFD models is the experimental
verification of results obtained through numerical simulation on
an assigned engineering problem. This process of "certification"
of simulation quality is typically carried out by comparing the
values of the output variables of the numerical model with those
measured experimentally, under the same operating conditions and
at corresponding points of the field.
RANS Codes. Acronym of "Reynolds Averaged NavierStokes". RANS
models solve averaged NavierStokes equations and can therefore
simulate the fluid dynamics of a body immersed in a viscid and
turbulent fluid, only with regard to the average and stationary
current. There is a variant for nonstationary flows (acronym U
RANS) which permits extending these models' field of application.
Potential or nonviscid codes. Potential models solve equations of
motion of a body immersed in an "ideal" fluid, nonviscid and
irrotational. The ability to correctly describe the physics
involved is limited in comparison with more sophisticated models
(such as RANS). The advantage however is that the solution of
equations that describe the field of motion is relatively simple,
and that complex applications and configurations are possible with
reduced computational costs.
Feedback. The feedback concept is typically used in the study of
automatic controls. The fundamental idea in feedback or
retroaction is to modulate a signal, noting the effects it has on
the system on which it is acting: a signal that acts on a system
with view to the latter behaving in the desired way must therefore
depend on both a command signal and on the effective behaviour of
the system. This can occur only through an action of feedback, a
retroaction, that returns to the system input the information
regarding the output (see also figure 3). In the specific case,
commensuration of the system's effective behaviour (value of the
design variables at the ith step of the optimisation process)
with regard to the objective (objective value of design variables)
requires "measurement" of the effects (e.g. through experimental
surveys or CFD simulations) in order to direct the optimisation
model towards the "optimal" solution.
Friction resistance. Friction resistance is the resultant of the
tangential stresses on the surface of a moving body in the
direction of motion, due to the effect of viscosity. Friction
resistance is described by the following formula:
R_{F} = ½ C_{F} ρ U² S
in which: C_{F} represents the friction coefficient, ρ fluid density,
S the "quickwork" surface and U the speed of the vessel.
Form resistance. Form resistance is the resultant of the normal
pressure stresses on the surface of a body in the direction of
motion.
Total resistance. The sum of friction resistance, form resistance
and wave resistance.
Roll stability. A vessel's tendency to right itself following a
disturbance that produces roll (e.g. waves on the beam, extensive
sideways shifting of the payload or, in the case of watersupply
ships and tankers, problems of sloshing).
Calculation mesh. A numerical code gives the solution to a fluid
dynamics problem in a discrete grouping of points called a
calculation grid or mesh. In contrast the analytical solution of
a system of partial differential equations (as in the case of
fluid dynamics equations) consists of expressions that describe in
a continuous way the variations of the dependent variables.
