Stefan Harries
Benzstr. 2, D-14482 Potsdam, Germany [email protected]
ABSTRACT
Design often means finding good compromises while the knowledge about the final product is still limited. In particular, when new ideas are developed the fast accumulation of relevant data is of high importance. In the initial design phase naval architects often rely on suitable baselines, do literature studies or utilize systematic series. In this paper a further approach shall be elaborated: systematically investigating multi-dimensional design spaces using first principle methods. An example is presented for a fast mega-yacht around 80m in length with speeds up to 20kn. Hull form development and energy consumption being of paramount importance for an entire project, the mega-yacht’s hydrodynamics was studied using a combination of non-linear free surface potential flow and boundary layer simulations. Utilizing a parametric hull model, a formal exploration was undertaken to come to know the design space. The work was realized within the FRIENDSHIP-Framework for Computer Aided Engineering coupled to SHIPFLOW as the engine for Computational Fluid Dynamics. Visualizations are done via standard relationship diagrams, including regressions, but also by means of a response surface methodology, allowing a transfinite view. This enables the design team not only to identify promising candidates for subsequent analyses but also supports their decision making when changes are requested.
INTRODUCTION
Design is making decisions on the basis of insight and options, often by finding a suitable compromise between conflicting targets. Numerical flow simulation, parametric design and increasing computer power have made formal optimization techniques popular in product development. In particular, deterministic and stochastic strategies are employed to improve designs for one or several objectives. This leads to simulation-driven design in which products or parts of them, for instance their functional surfaces, are derived from key performance measures such as resistance (e.g. Harries (2008), Peri et al (2007)), wake quality (Brenner et al (2009)), pressure rise (Palluch et al (2009)), exhaust gas concentration (Harries and Vesting (2010)), propulsive efficiency (Druckenbrod et al (2010)) or cost (Rigo et al (2008)).
Typically, the engineers set meaningful objectives and important constraints and then launch a thorough optimization that then often requires a few days of number crunching, producing several hundred (and sometimes thousands) of variants. However, an idea of the design space needs to be present beforehand so as to pose the right questions. Here, formal optimization techniques can be applied, too. However, this appears to have gotten little attention so far. Two situations come to mind directly which relate to initial design:
• Building up relevant design data early into a newbuilding project and
• Decision support for anticipated design changes.
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The first situation is particularly relevant in cases where a new design deviates considerably from any available parent. This might be because the design department has not yet been engaged in developing a certain type of vessel or, even more challenging, no reliable references can be found due to a product’s novel character. Here, first principle methods – i.e., simulations that build directly on the established laws of physics – assist greatly in deriving dependencies and showing trends.
The second situation, meanwhile, is not atypical of the dynamics that naval architects encounter with owners that change their minds rather quickly (“I would like to have…”) or with decision makers that are difficult to bring together. If new ideas come up that need to be assessed while everyone is still around the table (“what would happen if…”) then a project can be pushed efficiently if some of these changes and wishes have been anticipated, at least on the basis of an educated guess. Formal techniques of systematic design space investigation may then be utilized to work out comprehensive sets of variants beforehand. While the exact nature of the changes is naturally unknown, indicators and trends can be developed to support the decision process, possibly improving ad-hoc decisions under uncertainty.
The paper’s focus being design methodology, an example application in design space analysis and decision support is presented for a mega-yacht of LOA about 80m and LPP around 70m with speeds of 14kn (travel), 16kn (cruise) and 20kn (maximum), corresponding to Froude numbers of 0.275, 0.314 and 0.393, respectively. A fully parametric model of the mega-yacht was developed to allow for meaningful hull variations. The yacht’s calm water hydrodynamics was determined with the well-known SHIPFLOW code, using non-linear potential flow theory for the free surface wave making problem and thin boundary layer theory for an approximation of frictional resistance.
A design-of-experiments (DoE) with 200 variants was conducted to establish a data base that yields the necessary insight for a deeper understanding of the impact of changes. The FRIENDSHIP-Framework was used to (i) set up the parametric model, (ii) control the execution of the external flow solvers for a first principle ranking and (iii) provide the necessary variant management. Finally, a multi-dimensional response surface for total resistance, i.e., a meta-model, was generated applying a Kriging approach.
NOMENCLATURE
B Maximum beam
CB Block coefficient
CF Frictional resistance coefficient CM Sectional area coefficient at midships CPfor Prismatic coefficient of the forebody CT Total resistance coefficient
CW Wave resistance coefficient from pressure integration
CWwaveCut Wave resistance coefficient from wave cut analysis
DWLfullness Coefficient of the curved part of the design waterline in the forebody Fn Froude number
FP Forward perpendicular
KM Transverse metacentre above keel LOA Length over all
LPP Length between perpendiculars Rn Reynolds number
RT Total resistance
RWwaveCut Wave resistance from wave cut analysis
S Wetted surface area
T Design draft
XCB Longitudinal center of buoyancy
∇ Displacement volume
ℜ2 Two-dimensional (parameter) space ℜ3 Three-dimensional (Cartesian) space ℜn n-dimensional (design) space
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CAD Computer Aided Design CAE Computer Aided Engineering CFD Computational Fluid Dynamics DoE Design-of-Experiments DWL Design waterline FOB Flat of bottom FOS Flat of side
RSM Response Surface Methodology / Response Surface Model SAC Sectional area curve
2d Two-dimensional 3d Three-dimensional KEYWORDS
Mega-yacht, CAD, CAE, CFD, Simulation-driven Design, Response Surface Methodology, Resistance PARAMETRIC MODEL
A fully parametric model was developed within the FRIENDSHIP-Framework for a round bilge mega-yacht.
Assuming a classical twin-screw design with bulbous bow and skeg, the bare hull was subdivided into a forebody and an aftbody region, joined at the maximum section, see Figure 1. For simplicity the skeg, shafts, brakets, propellers, rudders, thrusters and other appendages were neglected. The bulb was fitted to the bare hull within a region of transition aft of the forward perpendicular.
Figure 1: Parametric model of round bilge mega-yacht
A fully parametric model does not assume a given parent hull (as opposed to partially parametric modeling). It can be adjusted to match a baseline, too, but is more frequently used to build up the entire geometry from scratch.
Functional surfaces often display a common building code into a certain direction. The planar sections of a ship hull usually change very little when going incrementally in longitudinal direction, save for deliberate discontinuities.
(Similarly, the profiles of a propeller do not change that much when going in radial direction.)
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As depicted in Figure 1 the topology of the presented model consists of the following curves in longitudinal direction:
• Positional curves, namely flat of bottom (DECK) when starting with the keel and going
• Integral curves, namely the sectional area curves for the bare hull (SAC) and the bulb (SACofBULB)
• Differential curves, namely the sectional flare at the design waterline (DWLflare) and t (flareOfBULB).
These longitudinal curves provide the necessary input for the modeling of sections and, hence, the building of surfaces. Within the FRIENDSHIP-Framework
FSplines allow the generation of fair curves with flexible end points, tangents and area values. Essentially
parameters treated as equality constraints developed for collecting information availa point on the surface for any pair of surface to ℜ3 as would, say, Bézier or B-spline surfaces
particular representation with regard to the curves they capture
SYSTEMS (2009) for details. In this way, the entire hull form is defined by a set of around 50 parameters such as LPP, B, T, CM, CPfor, DWLfullness, LBulb and so forth
Figure 2: Bare hull with bulbous bow
Figure 2 shows the body plan, waterlines, a side and a perspective view of a representative instance of the parametric model. Changing geometry is a matter of selecting one or several of the parameters that define the geometry and letting the FRIENDSHIP
no more than a few seconds since a mechanism is utilized known as lazy fetching: All elements know their current
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he topology of the presented model consists of the following curves in longitudinal
Positional curves, namely flat of bottom (FOB), design waterline (DWL), flat of side the keel and going upward,
Integral curves, namely the sectional area curves for the bare hull (SAC) and the bulb (SACofBULB) Differential curves, namely the sectional flare at the design waterline (DWLflare) and t
These longitudinal curves provide the necessary input for the modeling of sections and, hence, the building of Framework two special entities were applied: FSplines
allow the generation of fair curves with flexible (and possibly small) sets of parameters such as start and ssentially they are planar B-spline curves optimized for fairness
equality constraints, see Harries (1998). Meanwhile, MetaSurfaces are novel
developed for collecting information available in two distinct directions. They yield the Cartesian coordinates of any point on the surface for any pair of surface coordinates u and v, basically giving an unambiguous
spline surfaces, too. However, they are more flexible as they do not assume any particular representation with regard to the curves they capture, see Palluch et al (2009)
In this way, the entire hull form is defined by a set of around 50 parameters such as and so forth.
are hull with bulbous bow generated by means of fully parametric modeling
2 shows the body plan, waterlines, a side and a perspective view of a representative instance of the parametric model. Changing geometry is a matter of selecting one or several of the parameters that define the FRIENDSHIP-Framework determine the new hull form. On a standard notebook this takes no more than a few seconds since a mechanism is utilized known as lazy fetching: All elements know their current he topology of the presented model consists of the following curves in longitudinal
flat of side (FOS) and deck Integral curves, namely the sectional area curves for the bare hull (SAC) and the bulb (SACofBULB), Differential curves, namely the sectional flare at the design waterline (DWLflare) and top flare of the bulb
These longitudinal curves provide the necessary input for the modeling of sections and, hence, the building of FSplines and MetaSurfaces.
sets of parameters such as start and s optimized for fairness with the input novel surface entities ble in two distinct directions. They yield the Cartesian coordinates of any giving an unambiguous mapping from ℜ2 However, they are more flexible as they do not assume any
and FRIENDSHIP In this way, the entire hull form is defined by a set of around 50 parameters such as
fully parametric modeling
2 shows the body plan, waterlines, a side and a perspective view of a representative instance of the parametric model. Changing geometry is a matter of selecting one or several of the parameters that define the determine the new hull form. On a standard notebook this takes no more than a few seconds since a mechanism is utilized known as lazy fetching: All elements know their current
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status of being either up-to-date or out-of-date and are aware of their clients and, hence, act as suppliers that provide information to other elements in the model’s hierarchy. Every single change of any (design) element is spread throughout the entire dependency tree. If an element is asked to deliver one of its properties, for example a double value, it may readily do so if up-to-date. If the element is out-of-date, however, it asks all its direct suppliers for their input. Should one, several or all of its suppliers happen to be out-of-date, too, the call for updates is propagated downwards. (Recursions are avoided by a one-way dependency check at the time of creation of each element.) A selection of the Dependencies is presented in Figure 3 (right part) as a zoomed in portion of an entire screen shot (left part) that displays the ObjectTree on the left, the Dependencies view in the upper part of the central window and, in addition, the offsets used for hydrostatics calculations. The free variable DWLfullness, i.e., the fullness of the curved part of the design waterline starting at the forward point of intersection with the flat of side and leading all the way to the forward perpendicular, is selected (see zoomed in portion). An FSpline called DWLfwd is identified as a client of DWLfullness (as would be expected). One level further on in the hierarchy, there is an entity called DWLcontainer that apparently is a client of DWLfwd and, consequently, of DWLfullness, too. (Note that free variables, by definition, do not have any suppliers but clients only.)
Going deeper down into the hierarchy (not shown here), the surfaces of the forebody also depend on DWLfullness (via DWLcontainer and DWLfwd). Figure 4 illustrates the effect of changing DWLfullness in a single parameter variation. Here the design waterline becomes more slender from left to right while all other input is maintained. This means that also the sectional area curve is kept. Hence, new sections follow the modified waterline but feature the same area.
Differences can best be observed by looking at the section for which the curvature distribution is displayed as porcupines. Looking from left to right in Figure 4, the transition between curved and flat regions at the flat of side grows more pronounced while the buttocks become more curved towards the bow. (The pictures are taken for the same region of the hull in exactly the same perspective. The arrows emphasize the areas of interest.)
Figure 3: Selected dependencies within the parametric model and zoomed in portion
FLOW SIMULATIONS
Flow simulations need to be chosen in a trade-off between accuracy and effort. Currently, in order to understand the impact of changing main dimensions in the initial design of a fast vessel it should suffice to employ potential flow theory to compute the non-linear wave resistance problem with free sinkage and trim. Since the boundary layer of a fast round bilge monohull should not be substantial this can be combined with a calculation of the frictional resistance via thin boundary layer theory. At a later stage, for instance when fine-tuning brakets, a RANSE calculation should be undertaken to capture the viscous phenomena well enough, see e.g. Brenner (2008).
For the flow simulations of the mega-yacht SHIPFLOW XPAN and XBOUND by FLOWTECH (2004, 2009) were utilized. SHIPFLOW follows a zonal approach and allows an increase of complexity for the flow analysis depending on the design phase. Besides, it is tightly integrated within the FRIENDSHIP-Framework, see e.g. Abt and Harries (2007) for details, making it ready-to-go for the systematic investigation.
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Figure 4: Zoomed in region in the forebody Figure 5 shows the panelization of both
streamlines (lower part) at 20kn, corresponding to
XPAN and XBOUND the default settings were taken (apart from an increased tracing points). Wave resistance was calculated from
analysis (for cross-validation). The total resistance
cuts and the frictional resistance RF from boundary layer analysis All other resistance components were simply neglected since
The underlying assumption therefore is that variants perform similarly with regard to appendage resistance etc. – which should be reasonably
The flow simulations were done on a standard dual core notebook and took about
and speed, convergence of the free surface problem typically being achieved within 10 to 12 iterations. With a CFD license for both cores around 200 designs could be computed in one overnight job.
DESIGN SPACE INVESTIGATION
A systematic design space investigation was performed via a Sobol algorithm, Press et al (2007). Nine free variables were considered such as length, maximum beam, sectional area coefficient at midships etc., see Table
for details, establishing a nine-dimensional space
when main dimensions are somewhat established but not yet completely fixed. The vessel’s design draft, however, was kept constant at 3.9m.
200 variants were studied – each for three speeds, resulting in a total of 600 CFD runs. The speeds of interest were travel speed of 14kn for large ranges, cruising speed of 16kn and, very importantly, maximum speed of 20kn high performance. For hydrostatics and
the maximum speed with a total of 7000kW of installed power (corresponding to two MTU 16V595 TE 70 at 4680 HP each).
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Zoomed in region in the forebody close to the FOS for DWLfullness = 0.58, 0.60 and 0.62 both the free surface and the hull (upper part) along with resulting waves and streamlines (lower part) at 20kn, corresponding to Froude number Fn = 0.393 for LPP = 70m. For b
the default settings were taken (apart from an increased number of streamlines and associated tracing points). Wave resistance was calculated from both pressure integration over the hull and transverse wave cut he total resistance RT was computed by summing up the wave resistance from wave
from boundary layer analysis at full scale with Reynolds number
All other resistance components were simply neglected since the focus was put on comparing and judging variants.
nderlying assumption therefore is that variants perform similarly with regard to appendage reasonably accurate at this stage.
The flow simulations were done on a standard dual core notebook and took about four to five minutes per variant and speed, convergence of the free surface problem typically being achieved within 10 to 12 iterations. With a CFD license for both cores around 200 designs could be computed in one overnight job.
A systematic design space investigation was performed via a Sobol algorithm, Press et al (2007). Nine free variables were considered such as length, maximum beam, sectional area coefficient at midships etc., see Table
dimensional space ℜ9. All variables are potential candidates for change at the point when main dimensions are somewhat established but not yet completely fixed. The vessel’s design draft, however,
each for three speeds, resulting in a total of 600 CFD runs. The speeds of interest were travel speed of 14kn for large ranges, cruising speed of 16kn and, very importantly, maximum speed of 20kn high performance. For hydrostatics and -dynamics an actual draft of 3.6m was prescribed so as to be able to reach the maximum speed with a total of 7000kW of installed power (corresponding to two MTU 16V595 TE 70 at 4680
= 0.58, 0.60 and 0.62 the free surface and the hull (upper part) along with resulting waves and
For both SHIPFLOW number of streamlines and associated pressure integration over the hull and transverse wave cut resistance from wave Reynolds number Rn = 7.2 108. on comparing and judging variants.
nderlying assumption therefore is that variants perform similarly with regard to appendage resistance, air
four to five minutes per variant and speed, convergence of the free surface problem typically being achieved within 10 to 12 iterations. With a CFD
A systematic design space investigation was performed via a Sobol algorithm, Press et al (2007). Nine free variables were considered such as length, maximum beam, sectional area coefficient at midships etc., see Table 1 (red box) . All variables are potential candidates for change at the point when main dimensions are somewhat established but not yet completely fixed. The vessel’s design draft, however,
each for three speeds, resulting in a total of 600 CFD runs. The speeds of interest were travel speed of 14kn for large ranges, cruising speed of 16kn and, very importantly, maximum speed of 20kn for an actual draft of 3.6m was prescribed so as to be able to reach the maximum speed with a total of 7000kW of installed power (corresponding to two MTU 16V595 TE 70 at 4680
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Figure 5: Panelization of free surface and hull along with waves and streamlines at Fn = 0.393
Figure 5: Panelization of free surface and hull along with waves and streamlines at Fn = 0.393