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SUPERYACHT #10
Autumn 2006

Article selected from our quarterly magazine dedicated to the largest and most luxurious boats with information, interviews, technical articles, images and yachting news


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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 pre-existing 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 i-th 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:
  1. 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;

  2. 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 anti-roll 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.

  3. 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 i-th 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 many-sided 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 over-negative 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 sub-grouping of that of departure. The number of possible solutions to the optimisation problem will depend on the dimensions of this sub-grouping 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 cost-benefit ratio must be evaluated for each objective.

 


Figure 5. Calculation mesh of a CFD code on the study of propeller-rudder 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 trade-off 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 Navier-Stokes". RANS models solve averaged Navier-Stokes 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 non-stationary flows (acronym U- RANS) which permits extending these models' field of application.

Potential or non-viscid codes. Potential models solve equations of motion of a body immersed in an "ideal" fluid, non-viscid 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 i-th 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:

RF = ½ CF ρ U² S

in which: CF 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 water-supply 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.