1196 978-1-4673-0199-2/12/$31.00 ©2012 IEEE

2012 International Conference on Systems and Informatics (ICSAI 2012)

Hull Form Hydrodynamic Optimization Based on Parametric Modeling Jinfeng Huang

China Ship Development and Design Center Wuhan China

Abstract-This paper discusses the hydrodynamic optimization of hull form mainly. The study has been carried out using an integrated tool for hydrodynamic optimization, incorporating a CAD modeler for definition and parametric modification of hull forms, CFD codes for the evaluation of hydrodynamic performance and software for optimization and decision making. A study includes the geometric modeling, hydrodynamic analysis, design evaluation and shape variation of a DTMB5415. Genetic Algorithm is utilized to explore the design space and to improve the hull shape. The most relevant feature of the tool is its capability to carry out and automatically evaluate parametric modifications of DTMB5415’s shape, providing an assessment of the shape variants and proposing one or several ‘Pareto optimal’ shapes. The hydrodynamic design process is implemented: An advanced parametric modeling kernel is applied for efficient form generation and variation. The hydrodynamic performance is analyzed by state-of-the-art Computational Fluid Dynamics (CFD) codes for calm water resistance. A commercial optimization system is used to integrate the various CAD and CFD tools and to carry out the optimization.

Keywords-Hull form ； Hydrodynamic optimization ； Parametric modeling；DTMB5415；Friendship；Shipflow

Achieving hull forms with a very good hydrodynamic performance has been the ambition of designers ever since the first ships went out to sea. Hydrodynamic behavior is actually the big issue of early design and one that requires skill and experience. The time and effort involved in this design phase are rather critical as they affect the competition of shipyards and consultants today more than ever.

In recent years an effort has been made to produce knowledge and tools to support early design. The key issue is to be able to easily generate variants of an initial hull and assess their hydrodynamic performance in order to take the right decisions.

In this regard, the development of tools for parameter shape modifications, the use of optimization techniques and the optimization techniques and the development of CFD tools are important and are expected to be exploited in early design activities.

This paper presents a software tool for hull form optimization based on a parameter approach to hull form design and modifications. An application is discussed in detail regarding the optimization of a DTMB5415 ship. This is carried out based on both potential flow CFD with typical design objectives and constraints.

Within this paper the synthesis model of hydrodynamic optimization is first outlined. The novel approach of parametric modeling of ship hull forms and the tools utilized for hydrodynamic analysis are then briefly described. Subsequently, the optimization environment employed to establish the synthesis model is discussed.

Following this, an example optimization are presented. The optimization of DTMB 5415 is presented in order to illustrate objectives, methods, and results.

Measures of merit is wave resistance in calm water, Displacement and Lcb were considered as inequality constraints. The set of free variables contained selected form parameters of the hull.

Various systems were utilized for this investigation: TU Berlin’s FRIENDSHIP Modeler for the parametric modeling of ship hull forms, wave resistance codes Shipflow.

I. SYNTHESIS MODEL The synthesis model of hydrodynamic optimization as presented. comprises four modules, see figure 1:

• Geometric modeling of the hull form, • Hydrodynamic analysis of the flow field, • Rational analysis of the associated performance, • Systematic change for improvement. So as to take full advantage of this synthesis model, a

complete IT (information technology) integration is needed, i.e., all modules need to be executed without manual interference. In this way many more design variants can be investigated than with traditional methods.

Figure 1. Synthesis model of hydrodynamic optimization

II. PARAMETRIC MODELING

A. GENERAL IDEA The general idea of parametric modeling is to express

shapes in terms of their desired properties. The specified

GenemetricModeling (geom、

constraints)

Shape design

Geometricdescription

Genemetric Modeling (geom、

constraints)

Flow field

Perfomance analysis

Measure of merit

Optimization strategy(NLP)

Change parameters

InitialHull form

Shape variation

Optimized hull form

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properties are treated as input to a CAD system and the modeling problem then reads: Produce a geometry such that specified properties are directly met and the shape is considered good within the design context.

This means that the language the designer uses is based on high-level and problem-oriented vocabulary instead of the low-level elements associated with a specific mathematical representation. Rather than producing a hull form via points (e.g. offsets, vertices etc.) and subsequently evaluating the geometry (e.g. form parameters, basic longitudinal curves, various ship lines, fairness etc.),the naval architect defines the parameters and lets the system determine the corresponding geometry. The form parameter approach thus reverses the conventional modeling technique。

B. CAD Tool : FRIENDSHIP MODELER FRIENDSHIP system have been developed at TU Berlin.

The system follows the classic naval architect's technique of describing a ship's geometry in terms of longitudinal curves–so-called basic curves–from which all design sections are derived. Basic curves comprise positional, differential and integral information. The design waterline, the center plane curve and the deck are straight-forward examples of positional basic curves. The sectional area curve is the most prominent integral curve. An example for a differential basic curves is the curve of sectional slopes at the design waterline. A flexible set of basic curves is available to accommodate different hull topologies. The shape of the envisioned hull is exclusively defined in terms of form parameters from which the basic curves are laid out. The basic curves then contain all information necessary to subsequently create an ordered set of design sections. A surface description of the hull is derived using the design sections in an interpolation, approximation or association scheme. The idea of the modeling process is illustrated in figure 2.

Figure 2 Parametric modeling process

The FRIENDSHIP system is completely based on B-spline curves and surfaces. Each B-spline is determined from form parameters by optimizing suitable fairness criteria. B-spline vertices are treated as free variables while form parameters represent equality constraints. Since fairness is an intrinsic part of the generation process all shapes are smooth and display excellent quality. No interactive vertex

manipulation is required. The advantage of the approach when compared to traditional modeling techniques is that hull shapes are generated and modified in a highly-concerted manner, allowing to evoke both fine-tuned and considerable changes in geometry by varying just a few selected form parameters, thus making the FRIENDSHIP system a valuable choice for formal hydrodynamic optimization.

III. HYDRODYNAMIC ANALYSIS

A. GENERAL IDEA At the preliminary design stage the evaluation of

hydrodynamic performance is carried out on the basis of numerical simulations. For a thorough investigation calm-water resistance need to be taken into account.

B. WAVE RESISTANCE In deep waters, ship is sailing at the speed of U in still water in uniform. Assume that the fluid is inviscid, irrotational flow of incompressible, the velocity potential exists as φ .Construct the following definite solution of this problem :

2 0φ∇ = Within the fluid domain V (1)

1 1( )2

Vg

η φ φ φ= ⋅∇ + ∇ ⋅∇ On the free surface SF (2)

( ) 0zV gφ η φ∇ − ⋅∇ + = On the free surface SF (3)

V nnφ∂ = ⋅

∂ On the surface of the hull (4)

)0,0,0(=∇φ At infinity (5) In (4), n is the unit normal vector of the hull

surface. ( ,0,0)V U= 。 The fluid velocity potential φ is available when solving

the above problem. Then the fluid disturbance velocity φ∇can be got. According to the Bernoulli equation, fluid pressure distribution can be got.

1( )2xp U gzρ φ φ φ= − ∇ ⋅∇ + (6)

The fluid pressure points along the wet surface of the hull, the fluid forces and moments suffered by the hull can be got:

1 2 3( , , )SB

F F F F pnds= = ∫∫

1 2 3( , , ) ( )SB

M M M M p r n ds= = ×∫∫ (7)

Ship wave resistance:

1 1wSB

R F pn ds= − = −∫∫ (8)

Dimensionless wave resistance coefficient:

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212

ww

RCV Sρ

= (9)

Heave force and trim moment:

2 1 3( )SB

M p zn xn ds= −∫∫

3 3SB

F pn ds= ∫∫ (10)

NURBS-based high-order panel method has been used to solve the fluid velocity potential. The fluid velocity potential at the field point p :

1 1 1( ) ( )( )4 q

SB SF

p q dsr r

φ σπ +

= −′∫∫ (11)

In(10): ,r r′ is the distance between field point p and source point q ,meeting point q′ respectively. ( )qσ is the strength of the distribution source.

The amount of the flow field (such as the hull surface type value, the fluid velocity potential and the source intensity distribution, etc.) are expressed by NURBS

, , , ,0 0

, , ,0 0

( ) ( )( , )

( ) ( )

m n

i j i j i k j li j

m n

i j i k j li j

d N u N vp u v

N u N v

ω

ω

= =

= =

=∑∑

∑∑ (12)

Where, ,i jω is the coefficients for NURBS weights ,i jd is

the control vertices, , ( )i kN u is k -order B-spline basis.

Calculate discretely in the parameter space ),( vuΓ . Discretized ),( vuΓ into M N× grid points. Express the (11) discretely according to (12) and substituted into (2) - (4) to get the fluid velocity type. Then yield the hull wave resistance according to (8) and (9).

IV. OPTIMIZATION Optimization is the formal process of finding a good

(possibly the best)solution from a set of feasible alternatives. It follows a rigid format that allows a unified problem formulation but relies on the possibility to capture the problem mathematically in respect to the following important terms:

(1)Measure(s)of merit The objective function(s),i.e., criterion/criteria, by which a solution is assessed.

(2)Free variables The independent decision variables that can be modified directly and that uniquely describe the optimization problem.

(3)Constraints The restrictions imposed on the search space which reduce the possible combinations of free variables to those that are considered feasible; one may further distinguish bounds(i.e., upper and lower limits of each variable),equality constraints and inequality constraints.

The general idea is that many optimization problems can be formulated as the search for the minimum or the maximum

of one or more suitable measures of merit. The measures of merit depend on a set of significant free variables that are systematically changed in order to identify one or several maximums or minimums. Often the search space is restricted by a set of constraints imposed on the free variables and, sometimes on the objective function itself. The objective functions are usually calculated by means of sophisticated simulation programs, here by means of CFD codes.

In order to set up the synthesis model of hydrodynamic optimization, see figure 1,an environment is needed which integrates the various modules of modeling, analysis, evaluation and variation. This paper uses Friendship to achieve the integration and optimization of each module.

V. EXAMPLE OF DTMB5415 HULL LINE OPTIMIZATION ON RESISTANCE PERFORMANCE

David - Taylor pool (DTMB) 5415 ship model has almost the same shape with the U.S. Navy ship DDG51.DTMB5415 Hull line is a typical high-speed line for military vessels, which has a huge sonar cover and a square tail. The resistance performance optimization problem is: Optimize its shape while meeting certain constraints to improve the resistance properties. The main dimensions are listed in Table 1.

Table 1: DTMB5415 main elements Waterline

length Lwl (m)

Bwl (m) Draft(m)

Block coefficient

C b

Displacement (t)

5.700 0.769 0.372 0.344 0.574

A. DTMB parametric geometry model In this paper, Friendship software has been used to

achieve DTMB5415 parametric modeling of the whole ship, as shown in Figure 3 .The global parameters constituting the ship are listed in Table 2.

Figure 3 DTMB5415 parametric model Table 2 Llist of the global parameters

No. Global parameters

Significance

1 baseKeel Bottom baseline height 2 draft Draft 3 maxLength Maximum length of the hull 4 maxbeamAtDeck half-width value at the deck 5 midXpos X coordinate at the maximum cross-section

6 XAftbase The vertical position of baseline end point in the tail

7 XAp the X coordinate of end point on waterline at the tail

8 Xforbase X coordinate of first end point on baseline 9 XFp X coordinate of first end point in waterline

10 XPeak x coordinate of the first front point Positions of these characteristic parameters in

corresponding in the hull geometry are shown in Figure 4.

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Figure 4 The main geometric parameters reflected in the ship

hull

B. set design variables This study is to optimize the sonar shield shape and select

the parameters which control the change of sonar shape as design variables. The corresponding changing ranges are shown in Table 3.

Table 3 Definition for design variables

No. Variable value

Variable name Variable

upper limit Variable

lower limit The initial

value 1 X_domeTip 0.38 0.406 0.39485 2 dome_TipElevation 0.04 0.09 0.0723 3 xtemlow 0.407 0.415 0.409818 4 xminlow 0.49 0.54 0.515 5 domelowaftmidZ 0.02 0.04 0.03100467 6 XmaxH 0.485 0.53 0.50788434 7 domeupMaxH 0.145 0.155 0.149959 8 domeupaftH 0.117 0.133 0.1251 9 domemaxHprofile 0.160 0.170 0.165

10 domeupforfulns 0.60 0.76 0.68 11 domeaftmidH 0.135 0.15 0.143 12 fulnsatstemlow 0.75 0.79 0.77 13 domelowfulnsmid 0.81 0.84 0.828 14 domeupfulnsBeg 0.716 0.75 0.73725 15 domeupfulnsEnd 0.655 0.695 0.675 16 domeupC1fullness 0.1 0.25 0.15 17 domelowForfullness 0.3 0.4 0.36 18 fulnsdomepffore 0.76 0.8 0.7835 19 domeElevationMid 0.062 0.082 0.072 20 domeupForeTan 8 16 15.2 21 domeBeamtipfulns 0.7 0.85 0.8 22 Xmaxbeam 0.513 0.553 0.533 23 domeMaxbeam 0.115 0.135 0.1257 24 domeaftbeam 0.065 0.09 0.07503 25 domebeamc2TanEnd -18 -14 -16

C. Definition of target parameters As the ship belongs to high-speed boats, wave resistance

accounts for the main ingredients in the total resistance. Therefore, wave resistance coefficient C w has been the chosen as the target for optimization.

D. Set constraint Choose the change of displacement and vertical position

of buoyancy center as constraint value to ensure the optimized ship's displacement and vertical position of buoyancy center does not change a lot, which are defined as follows:

(1) Displacement constraints: 1%

DispDispDisp

o

o ≤−

(2) Vertical position of buoyancy center constraints:

%1≤−

o

o

LcbLcbLcb

Of which:

oDisp Disp were the initial displacement and the optimized displacement,

oLcb Lcb were the initial vertical position of buoyancy center and the optimized vertical position of buoyancy center. In optimization, the change of displacement and vertical position of buoyancy center are within a certain range. According to the constraint of plus or minus 1% ,the four binding parameters are defined in Table 4 below.

Table 4 Definition of constraint parameters

Order Number

Constraint name Meaning Constraints Constraint

parameter

1 maxDisp Maximum displacement <=0.558253 displacement

2 minDisp Minimum displacement >=0.547198 displacement

3 maxLcb

maximum of vertical

position of buoyancy

center

<=3.55729 lcb

4 minLcb

minimum of vertical

position of buoyancy

center

>=3.48685 lcb

E. Optimization algorithm In this paper, the gradient algorithm (T-Search) has been

chosen as the optimization algorithm. This optimization algorithm is a optimal solution within a small range of search. When searching, a suitable direction is found for each time. The chosen direction should make the search fastest, while ensuring the search range is in the feasible region. In order to achieve this goal, search along the direction of the constraint tangent and ensure there is no constraint violations. In the optimization process, the maximum number of calculation times is 100.

F. Results of resistance optimization After 20h of computing, optimization results are in Table

5, Table 6 below. Comparison of the free surface wave contour map and the side longitudinal waveform before and after optimization are shown in Figure 5,comparison of the surface before and after optimization is shown in Figure 6.

Table 5 Optimization result

No. Variable Description Variable value

Control parts Variable name The initial

value Optimized

value 1

Sonar position

X_domeTip 0.39485 0.38636 2 dome_TipElevation 0.0723 0.05889 3 xtemlow 0.409818 0.4148 4 xminlow 0.515 0.5067

1200

5 domelowaftmidZ 0.03100467 0.02506 6 XmaxH 0.50788434 0.52099 7 domeupMaxH 0.149959 0.14613 8 domeupaftH 0.1251 0.13173 9 domemaxHprofile 0.165 0.16408

10 domeupforfulns 0.68 0.6086 11 domeaftmidH 0.143 0.13709 12 fulnsatstemlow 0.77 0.7697 13 domelowfulnsmid 0.828 0.8164 14 domeupfulnsBeg 0.73725 0.72873 15 domeupfulnsEnd 0.675 0.69410 16 domeupC1fullness 0.15 0.24096 17 domelowForfullness 0.36 0.33804 18 fulnsdomepffore 0.7835 0.793 19 domeElevationMid 0.072 0.07982 20 domeupForeTan 15.2 15.9 21 domeBeamtipfulns 0.8 0.73386 22 Xmaxbeam 0.533 0.5494 23 domeMaxbeam 0.1257 0.12567 24 domeaftbeam 0.07503 0.08338 25 domebeamc2TanEnd -16 -17.92

Table 6 Comparison between constraint and objective

name Initial value

Optimized value Changing value

Constraint lcb 3.28005 3.2912 Backward

0.339%

Disp 0.552726 0.549639 Increase 0.5585%

Objective Cw（10-3

） 0.89321677 0.67616622 Decline 24.30%

Figure 5 comparison of the free surface wave contour map and the side longitudinal waveform before and after optimization

Optimization Original

Figure 6 Comparison of the surface before and after optimization

From the comparison results we can see that the optimized ship's wave resistance decreased 24.3%, vertical position of buoyancy center move forward slightly and the number of waveforms reduces near the optimized hull. Figure 10 illustrate the amplitude of wave slices in the vicinity of the optimized bow becomes smaller.

VI. CONCLUSION In this paper, Friendship system software platform has

been used to complete the DTMB 5415 hull form optimization. Following conclusions: (1) Friendship based full hull line parametric modeling is feasible and the hull line can be transformed automatically through modifying the characteristic parameters. (2) The optimization search of the ship space has been completed by using gradient-based algorithm. Even though it can get good result, further study is needed to judge whether it is a global optimal solution. (3) optimization of the ship takes long, further research is needed to improve the optimization efficiency. (4) The optimization goal of this paper is wave resistance coefficient and further study is required for multi-objective optimization methods.

ACKNOWLEDGEMENTS The author is gratefully thankful to the research team

members and the Support of The 111 Project (B08031), National Natural Science Foundation of China (No:51039006).

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