CFD-Based Multiobjective Optimization of Waterjet Propelled High Speed Ships

11th International Conference on Fast Sea Transportation FAST 2011, Honolulu, Hawaii, USA, September 2011

CFD-Based Multiobjective Optimization of Waterjet Propelled High Speed Ships

Yusuke Tahara1, Takanori Hino2, Manivannan Kandasamy3, Wei He3, Frederick Stern3

1 NMRI-National Maritime Research Institute, Mitaka, Tokyo, Japan

2 Yokohama National University, Yokohama, Japan 3 IIHR-Hydroscience& Engineering, the University of Iowa, Iowa City, Iowa, USA

ABSTRACT

The present paper is complementary to a separately presented paper by Kandasamy et al. (2011), with more focus on activities of development and validation of a CFD-based multiobjective optimization method. The numerical optimization method is applied for the initial design of two waterjet propelled high-speed ships, namely, the Joint High-Speed Sealift Ship (JHSS) and the Delft Catamaran (DC). The scheme investigated in the present study is based on Evolutionary Algorithm (EA), a more suitable scheme for multiobjective optimization than other alternatives. Another important feature of EA is upward scalability in parallel computing by introducing the recent advancement of Information Technology (IT), which actually realizes a high-performance optimization framework in the present study. In addition, the concepts of Variable Fidelity/Physics (VF) and hierarchical optimization approach are adopted, so as to increase the efficiency of the whole optimization problem by using two different levels of accuracy. That is, both Unsteady RANS and Potential Flow based CFD methods together with Asynchronous Evaluator (AE) model for interface with optimization module are used in the present study. A practical geometry modelling method to yield new designs is used as successfully demonstrated in the previous work. In the following, an overview of the present method is given, and results are presented and discussed for JHSS and DC test cases. Both results appear very promising, which support overall validity and effectiveness of the optimization framework developed in the present study.

KEY WORDS

CFD Based Multiobjective Optimization; Waterjet Propelled High Speed Ship; JHSS model; Delft Catamaran model; Total Resistance Minimization; Seakeeping Merit Function Minimization

1.0 INTRODUCTION

Ship design optimization poses difficult computational problems since it commonly belongs to the class of non-linear programming (NLP) problems, for which the objective function(s) has a multimodal nature. Simulation tools and optimization algorithms can be combined together into Simulation-Based Design (SBD) environment, which

enable designers to minimize one or more user defined objective functions with constraints, under the general mathematical framework of a NLP problem. The long-term collaboration among IIHR, INSEAN (Italian Ship Model Basin) and NMRI research groups is focused on the development of a SBD toolbox, which provides High Performance Computing CFD solvers, optimization algorithms, geometry and grid manipulation automatic methods, with application to naval hydrodynamics (Campana et al., 2009). Previous versions of the tool box have been successfully used in the optimization of high speed monohull (Campana et al., 2006, Tahara et al., 2008a) and multihull (Tahara et al., 2008b, Peri et al., 2010) displacement ships and foil-assisted semi-planing catamaran ferries (Kandasamy et al., 2009a).

On the other hand, typical ship design problems are multiobjectives. For instance, goals of the design process can be resistance reduction, minimal wave height, reduced amplitude and acceleration of particular motions, etc. In addition, ship designers may also be interested to enhance certain quantities related to the engine power or to the maintenance costs. Unfortunately, the improvement of a specific aspect of the global design usually causes the worsening for some others, and the best approach is not to combine all the objectives into a single one (the so called scalarization) but to keep the multi-criteria nature of the problem and rely on the Pareto optimality concept.

Fig.1. Overview of geometry and definition of coordinate system. Top and bottom are JHSS and Delft Catamaran,

respectively.

The present paper is complementary to a separately presented paper by Kandasamy et al. (2011), with more focus on activities of development and validation of a CFD-based multiobjective optimization method in the above-

© 2011 American Society of Naval Engineers 263

mentioned international collaboration. The numerical optimization method is applied for the initial design of two waterjet propelled high-speed ships, namely, the Joint High-Speed Sealift Ship (JHSS) and the Delft Catamaran (DC) (see Fig.1 for geometry and definition of coordinate system). While limitations of classical optimization methods appear as complexity of problem increases, the scheme investigated in the present study is based on Evolutionary Algorithm (EA), a more suitable scheme for multiobjective optimization problem than other alternatives. Another important feature of EA is upward scalability in parallel computing by introducing the recent advancement of Information Technology (IT), which actually realizes a high-performance optimization framework in the present study. In addition, the concepts of Variable Fidelity/Physics (VF/VP) and hierarchical optimization approach are adopted, so as to increase the efficiency of the whole optimization procedure by using two different levels of accuracy. That is, both Unsteady RANS and Potential Flow based CFD methods (referred to as URANS-CFD and PF-CFD, respectively) together with Asynchronous Evaluator (AE) model for interface with optimization module are used in the present study. A practical geometry modelling method to yield new designs is used as successfully demonstrated in the previous work. In the following, an overview of the present method is given, and results are presented and discussed for JHSS and DC test cases for which realistic design optimization problem are formulated, where total resistance and seakeeping merit function are simultaneously minimized.

2.0 DEFINITION OF OPTIMIZATION PROBLEM AND NUMERICAL APPROACH

2.1 Multi-Objective Optimization Problem

Shape design optimization is typically formulated in the framework of Non-linear Programming (NLP) problem. For a general expression of N-objective function optimization problem in ship hydrodynamics, the mathematical formulation assembles all the design variables x1, x2,..., xM in a vector x

=(x1,x2,...,xM)T belonging to a subset of the

M-dimensional real space M , that is Mx (upper xu

i and lower xli bounds are typical enforced onto the design

variables). The objective of the optimization F

= (F1,F2,...,FN)T and the equality and inequality constraints h, g are functions of the design variables x

and of the state of

the system )(xu

. A general form for constrained NLP problems is then to find the particular vector x

in the

subset which solves the following:

Min:

FrReN

FrRe

FrRe

FrxuxF

FrxuxF

FrxuxF

,

,2

,1

,);(,

,);(,

,);(,

Re

Re

Re

, Mx (1)

Subject to: 0)( xhj

(j=1,…,p)

0)( xg j

(j=1,…,q) u

iili xxx (i = 1,…,M)

OPT

GM AEMOOP

BCGA

RCGA SWARM

SQP

SOOP

OPT

GM AEMorphing Scheme

CAD

OPT

GM AE URANS-CFD

PF-CFD 1

PF-CFD n

Interface with MPI Parallel Coding

Fig.2. Basic components and module interfaces.

The solution of the above problems typically requires the use of some numerical tool - the first constitutive element of the present optimization framework - to solve the system A( x

, )(xu

)=0 and evaluate the current design x

, obtaining information on the constraints too. If the function used to define the optimization problem is of fluid dynamic nature, as in our case, the step requires the evaluation of the design x

via a CFD solver, a process which is itself

computationally intensive. Within a standard nonlinear optimization algorithm - the second fundamental element of the present optimization framework - the solution of these differential equations is required for each iteration of the algorithm. In addition to these two elements, a third one is necessary: a geometry modeling method to provide a link between the design variables and a body shape. When the analysis tools are based on the solution of a PDE on some volume grid around a complex geometry this task is not a trivial one and often requires some attention. The flexibility of this element may greatly affect the freedom of the optimizer to explore the design space.

The aforementioned three elements are implemented in the present optimization framework as shown in Fig.2, i.e., those are defined in more general manner. The OPT module includes single (SOOP) and multiobjective (MOOP) optimization schemes, which covers gradient and non-gradient based schemes. The GM (Geometry Modeling) module offers capability in both CAD and morphing based design modification methods, while the latter is demonstrated in the present work. Finally, the AE module

264 © 2011 American Society of Naval Engineers

is implemented to make flexible interface with both parallel and/or serial mode PF and/or more expensive URANS-CFD. AE and CFD methods utilize MPI parallel computing architecture.

◆ △ ▽ ▼○ ◎ ■ ●□ ▲ ◇☆

◆ △ ▽ ▼○ ◎ ■ ●□ ▲ ◇☆

◆ △ ▽ ▼○ ◎ ■ ●□ ▲ ◇☆

◆ △ ▽ ▼○ ◎ ■ ●□ ▲ ◇☆

◆ △ ▽ ▼○ ◎ ■ ●□ ▲ ◇☆

◆ △ ▽ ▼○ ◎ ■ ●□ ▲ ◇☆

◆ △ ▽ ▼○ ◎ ■ ●□ ▲ ◇☆

Model 1Precise model

Model 2Intermediate

model

Model 3Approximate

model

Fig.3. Hierarchical topology-multiple models for

variable/fidelity, variable/physics approach.

y = 0.0009x0.1876

R2 = 0.4323

1.7

5E-04

1.7

6E-04

1.7

7E-04

1.7

8E-04

1.7

9E-04

1.8

0E-04

1.40E-04 1.44E-04 1.48E-04 1.52E-04 1.56E-04

PF-CFD (Rw)

URA

NS-C

FD

(Rt)

Pre-Elimination

Fig.4. Correlation of resistance between URANS- and PF-

CFD predictions. JHSS bow optimization test cases.

2.2 Hierarchical Topology-Multiple Models

Since we use expensive high fidelity CFD for optimization, a more efficient scheme to exploit optimal solutions must be introduced. Approach adopted in the present study is Hierarchical Topology-Multiple Models (HTMM, Whitney et al., 2003). The approach is based on interactions among several layers, e.g., Fig.3 shows an example for the three layer case. Basically, all individuals are evaluated by using the lowest fidelity but the least time consuming (or the most approximated level) CFD in Model 3 level. Only promising individuals in the evaluation go up to Model 2 level, and are re-evaluated by using higher fidelity CFD. The process continues finally up to Model 1 level, where the most precise and time consuming CFD is used.

The HTMM was originally exercised by using inviscid CFD methods in aerodynamic applications; however in the present study, we will practice this technique with the two layer simplification and the concepts of VF/VP approach. That is, for the lower and higher fidelity layer, PF-CFD and URANS-CFD are used to evaluate the individuals. The application is found straightforward if we use the correlation between the two CFD as shown in Fig.4. It is indicated that predicted total resistance (RT) is well correlated for higher RT. Hence, after all individuals are evaluated by PF-CFD, the correlation is used to eliminate high RT designs, and

others go up to higher layer to be evaluated by URANS-CFD. This approach is used for both JHSS and DC optimization, and it appears for both cases that the total computational load is much smaller than the case where only URANS-CFD is used.

2.3 Evolutionary Algorithm - Real-coded Multi-Objective Genetic Algorithm

EA adopted in the present study is the Real-coded Multi-Objective Genetic Algorithm (RC-MOGA). The authors competitively evaluated both RC-MOGA and more classical Binary-coded MOGA (BC-MOGA) in the previous work (Tahara et al., 2008a, 2008b, Tahara and Takai, 2008). It is found that each approach offers the advantage over the other depending on the problem setup, e.g., if the design variables are given as continuous real number, RC-MOGA is more suitable. The capability RC-GA in ship design optimization is also investigated by others (e.g., Hirayama & Ando, 2007). Otherwise, in more general engineering applications details of both algorithms are discussed by Deb (2001).

Start

Generation of InitialPopulation

Decoding and Evaluationof Individuals

Selection

Crossover and Mutation

Gen.=Gen.Max ?

Stop

AsynchronousEvaluator

CPU.1

CPU.2

CPU.3

CPU.4

CPU.5

CPU.m

Different Performance

Processes

Fig.5. Parallel computing evolutionary algorithm and

asynchronous evaluation.

F1

F2

RP=1

RP=2 RP=3

RP=4

Fig.6. Pareto ranking used in MOGA

The basic algorithm of RC-MOGA in the present optimization framework is illustrated in Fig.5. As demonstrated in the previous work (Tahara et al. 2008a, 2008b), higher fitness f is given to individuals of higher Pareto ranking RP, i.e., f =1/RP (see Fig.6). A drawback of evolutionary family algorithms is increase of the computational load; however, that is overcome in the present framework by introducing parallel computing technique, i.e., Message Passing Interface (MPI) protocol with AE model. This RC-MOGA is used for both JHSS and DC optimization discussed later.


2.4 URANS-CFD Method

Adopted URANS-CFD method is CFDSHIP-IOWA version 4, which is a general-purpose, multi-block, high performance parallel computing, URANS code developed for computational ship hydrodynamics. The URANS equations are solved using higher-order upwind finite differences, PISO, and an isotropic blended k-ω/k-ε two-equation turbulence model. The free-surface is modelled using a steady and unsteady single-phase level set method to handle both complex ship geometry and complex interfacial topology due to higher Fr, bluff geometry, and/or large amplitude motions and maneuvering. For more details see Carrica et al. (2006). Overset grids are used to provide flexibility in grid generation, local grid refinement, and for bodies and/or blocks with relative motions. Recently, waterjet capabilities were implemented, including complete waterjet details, and a model for waterjet global effect and performances (Kandasamy et al., 2009b, 2010). The latter, hereafter referred to as CFD waterjet model, is used for DC optimization test case in the present study.

2.5 PF-CFD Method

Several PF-CFD methods are used in the present study. A method is WARP (WAve Resistance Prediction) developed at INSEAN. The method is based on linear potential flow theory and details of equations, numerical implementation and validation of the numerical solver are given in Bassanini et al. (1994). Extensions for multihull predictions were made (e.g. Peri et al., 1998). In evaluation of RT, ITTC’57 line is used to give frictional resistance. This CFD is used for JHSS optimization test case discussed later.

Another PF-CFD is a method developed by Tahara (2004), which is based on modification and extension of the original Dawson-type method for more general definition of numerical free-surface radiation condition, so that arbitral topology of free-surface panels can be used. This CFD is implemented into a naval architecture CAD system, and widely used in ship design field. In the present study, this PF-CFD is used for DC optimization test case. In similar manner to WARP, ITTC’57 line is used to evaluate frictional resistance of RT.

On the other hand, seakeeping performance is evaluated by using FreDOM, which is a frequency domain, Rankine-source type panel method developed in INSEAN (Lugni et al., 2004). Pitching and heaving motions are considered, hence, only starboard side domain is considered. As demonstrated in the previous work (Tahara et al., 2008b), the sea state 5 (head sea, T0=9.7s, H1/3=3.25m) is assumed in the present study, for which the following Jonswap spectrum is applied:

2

2

2

1exp

454

23/1 25.1

exp)(fT

pp

p

fTfT

HfS (2)

This is used to evaluate the RMS vertical accelerations at the bridge and flight deck. This PF-CFD is used for both JHSS and DC optimization test cases.

2.6 Shape Parameterization and Grid Re-generation

In the present study, geometry morphing approach is used to yield new designs. Inputs for this approach are several pre-designed base designs. The blending weights are related to design parameters in the optimization problem. Advantage of this approach is confirmed in the previous work (Tahara et al., 2008b). The number of design parameters is one less than that of designs to be blended, e.g., two parameters are used for three-hull-form blending as follows:

1

)1)(1(

)1(

321

3

2

1

332211

aaathatSo

a

a

a

where

PaPaPaP

(3)

where 1P

through 3P

are surface points for three basic designs, and 01 and 01 are design variables. The computational grid is re-generated similarly, by defining

1P

through

3P

to be grid points in solution domain for the base designs. This approach is used for both JHSS and DC optimization test cases.

3.0 NUMERICAL OPTIMIZATION RESULTS

3.1 Setup of Numerical Optimization

The above-described elemental components were integrated to realize an optimization framework. As mentioned earlier, two test cases, i.e, JHSS and DC test cases, were performed at NMRI by using LINUX based PC Cluster environment equipped by a gigabit network connecting 30 nodes of 2 core Xeon-3070 (64bit, 2.66 GHz) PCs. In the present optimizations, the population size of genetic algorithm coincides with number of MPI groups, each of which utilizes 4 CPUs to fully accelerate the computation. Hence, total number of CPUs used is n(m+1) + 1 = 41 (i.e., n = 4, m+1=10, where m+1 is population size). In the present study, three-block grid system is used for both JHSS and DC cases, i.e., two blocks are used for main body and stern part for JHSS case, and for half inward and outward bodies for DC case; and one block is used for background grid for both cases. The computational domain is only port half side with totally about million grid points for both cases. The same crossover rate = 0.75, a GA system parameter, is used for both JHSS and DC cases based on experiences in the previous work (Tahara, 2008b).

As mentioned earlier, two objective function optimization problems are formulated in the present study. The two


functions, namely F1 and F2 both of which are simultaneously minimized, are selected to be design tradeoff (or conflicting). Hence, the main goal of the present optimization framework is to find Pareto optimal set for the given problem. As demonstrated in the previous work, the two functions, namely F1 and F2, are related to the total resistance RT and Seakeeping Merit Function (SMF), respectively. The SMF is defined by using RAO predicted by the PF-CFD and Jonswap spectrum for sea state 5. In URANS-CFD, the aforementioned CFD waterjet model is used for DC test case. Design constraints for both JHSS and DC test cases are imposed on the principal particulars of the designs, i.e., L, B, d (draft), and displacement are kept same as those for the original design. Finally, RT correlations shown in Fig.4 and Fig.7 are used for HTMM for JHSS and DC test cases, respectively.

Rt_URANS CFD

Rt_

PF

CF

D

0.00075 0.00076 0.00077 0.00078

0.0

007

90.

0008

0.00

081

0.0

0082

Evaluated byhigher level HTMM

Fig.7. Correlation of total resistance between URANS- and

PF-CFD predictions. DC optimization test cases.

Fig.8. Problem definition of the present multiobjective

optimization. JHSS bow optimization test case.

3.2 Case 1 – JHSS Bow Optimization

The first test case is JHSS bow optimization. Main objective here is to perform initial evaluation of the present optimization framework with relatively simple problem setup. Fig.8 shows problem definition of the present test case. Modification region is limited to bow region, and waterjet effects are not considered in CFD. Fig.9 shows comparison of bow shape together with surface pressure contours for the original and pre-designed base designs. Trends in geometry modification and bow surface pressure distribution are clearly correlated with trends in F1 and F2

(see Fig.10 for F1 and F2). Input designs for the present optimization are the C.1, C.2, and C.3. designs.

Original (C.1)

Modified (C.2)

x

z

0.00 0.05 0.10

-0.0

3-0

.02

-0.0

10

.00

cp1.00.90.80.70.60.50.40.30.20.10.0

-0.1-0.2

Modified (C.3)

x

z

0.00 0.02 0.04 0.06 0.08 0.10

-0.0

3-0

.02

-0.0

10

.00

cp

1.00.90.80.70.60.50.40.30.20.10.0

-0.1-0.2

x

z

0.00 0.02 0.04 0.06 0.08 0.10

-0.0

3-0

.02

-0.0

10

.00

cp

1.00.90.80.70.60.50.40.30.20.10.0

-0.1-0.2

Fig.9. Comparison of surface pressure contours for base

geometry (URANS-CFD results). JHSS bow optimization test cases.

C3

Original

C1

C2

0.00018 0.00019

0.2

50.

26

0.2

70

.28

0.2

9

F1 : Total resistanceF2 : Seakeeping merit function

F2

F1

ID-204

Fig.10. Solutions from the present multiobjective optimization. F1 vs. F2 – Total resistance (RT) vs.

Seakeeping Merit Function (SMF). JHSS bow optimization test case.

After optimization is performed up to 40 generations, 400 new designs are automatically generated. Fig.10 shows distribution of the designs, where red squares indicate design on Pareto optimal set. All designs on the Pareto set will be candidates for final selection by designers, considering design tradeoff between F1 and F2. On the Pareto optimal set, F1 minimum design indicates -7.3%O (%original value) and +6.9%O for F1 and F2, respectively; and F2 minimum design indicates -5.5%O and -3.0%O for F1 and F2, respectively. As an example, the F2 minimum design, denoted as ID-204, is selected for detailed evaluation. The blending weights (a1, a2, a3) are (35%, 65%, 0%), i.e., ID-204 design is created by C.1 and C.2 designs, with the more influence of the latter. Fig.11 and Fig.12 show comparison of geometry, surface pressure, and


RAO between the original and ID-204 designs. The trends in total resistance are consistent with trends in flow field around bow, i.e., new design indicates reduced bow wave crest that yields smaller wavemaking resistance. The results shown for this test case are in general found satisfactory, hence extension to solve more complex problem is considered. The results are discussed in the following section.

Fig.11. Comparison of RAO, surface pressure contours, and

frictional streamlines between the original design and a selected optimal design on Pareto set (ID-204) (URANS-

CFD results). JHSS bow optimization.

Fig.12. Comparison of geometry between the original and

optimal (ID-204) designs. JHSS bow optimization.

3.3 Case 2 – Delft Catamaran Optimization

The test case discussed here is Delft Catamaran (DC) optimization. Fig.13 shows the problem definition. First, differences of RT between with and without (w/wo) CFD waterjet model are discussed. Fig.14 shows comparison of wave field for the original DC design, where insignificant differences are seen between the two. However, the differences are more significant in RT as shown in Fig.15, where values for the several pre-designs are also included. This is apparently caused by the significant changes in sinkage and trim due to waterjet effects, which in a case totally reverse the trend in RT as seen for 707. These results lead to an important fact that, for the operation condition considered in the present study, inclusion of waterjet effects in simulations is necessary for realistic design optimization.


optimization. Delft Catamaran optimization test case.

Original (With WJ)

Original (Without WJ)

Fig.14. Comparison of wave field (URANS-CFD results).

Delft Catamaran optimization test case for with and without CFD WJ model.

‐14.0%

‐12.0%

‐10.0%

‐8.0%

‐6.0%

‐4.0%

‐2.0%

0.0%

ORI 101 602 707 PF1 PF2

ddd

0.000660

0.000670

0.000680

0.000690

0.000700

0.000710

0.000720

0.000730

0.000740

0.000750

0.000760

ORI 101 602 707 PF1 PF2

F1(RT)_WJ

F1(RT)

‐0.004500

‐0.004000

‐0.003500

‐0.003000

‐0.002500

‐0.002000

‐0.001500

‐0.001000

‐0.000500

0.000000

ORI 101 602 707 PF1 PF2

Sink_WJ

Sink

0.000000

0.005000

0.010000

0.015000

0.020000

0.025000

0.030000

0.035000

0.040000

ORI 101 602 707 PF1 PF2

Trim_WJ

Trim

Fig.15. Comparison of geometry, resistance, sinkage and

trim (URANS-CFD results). Delft Catamaran optimization test case for with and without CFD WJ model.

Based on the above-described results, two base designs are selected, namely 101 and 602 (hereafter referred to as B2

and B3 designs). These are input designs of the present optimization framework together with the original design (B1). Note that the designs 707, PF1 and PF2 shown in Fig.15 are excluded this time since those do not indicate significant reduction of RT for the case with waterjet effects, and more importantly, those do not satisfy the equal draft constraints. Fig.16, Fig.17, and Fig.18 show comparison of geometry, wave field, and RAO for the base designs. General trend in modification is forward shift of LCB, and reduction of RT is likely achieved by reduction of sinkage


and trim along with reduction of low pressure region on hull surface due to reduced wave trough near the stern. As shown in Fig.19, B2 and design indicate -4.0%O and -33.9%O for F1 and F2, respectively; and B3 design -4.5%O and -16.5%O for F1 and F2, respectively.

Fig.16. Comparison of geometry used for MOOP. Delft

Catamaran optimization test case.

Original (B.1)

Modified (B.2-101)

Modified (B.3-602)


Delft Catamaran optimization test case with CFD WJ model.

Fig.18. Comparison of RAO (PF-CFD - FreDOM - results).


After optimization is performed up to 36 generations, 360 new designs are generated. Fig.19 shows distribution of the designs, where Pareto optimal set, indicated by red squares, are successfully obtained with a number of designs for the final selection. On the Pareto optimal set, F1 minimum design indicates -4.6%O and -19.4%O for F1 and F2, respectively; and F2 minimum design appears to be B2, i.e., -4.0%O and -33.9%O for F1 and F2, respectively. For more detailed evaluation, a design on the Pareto set, namely ID-94 is selected. The blending weights (a1, a2, a3) are (0.5%, 60%, 39.5%), i.e., ID-94 design is mostly created by B.2

and B.3 designs, with the more influence of the former. The design indicates -4.5% and -25.9% for F1 and F2, respectively. Fig.20 shows comparison of area distribution (CP curve) between the original and ID-94 designs; and Fig.21 shows comparison of body plan and waterline for the designs. Again, the general trend in modification to yield ID-94 is forward shift of area distribution, which moves LCB 1.0%L forward.

Detailed comparison of flow fields between the two designs, i.e, the original and ID-94 designs, are shown in Fig.22 through Fig.28. Trends in wave field is that relatively small differences are seen near the bow but near the stern, i.e., wave trough is significantly reduced for ID-94 and that leads to reduced area of low pressure region on the hull near the stern. This clearly yields reduction of RT for the design. On the other hand, there is no significant difference in boundary layer flows between the two designs, which results in insignificant difference in frictional resistance. That is, reduction of RT is achieved by reduction of pressure resistance, or more specifically wavemaking resistance. It is noteworthy that, as shown in Fig.28, the above-mentioned important differences in wave field between the two designs are well predicted by the PF-CFD. This is likely a proof of success of the present HTMM approach, where information from URANS-CFD and PF-CFD is effectively combined.

B3

B1

B2

ID 094

B3

Original Design

F*1

F* 2

0.96 0.98 1

0.8

1

Fig.19. Solutions from the present multiobjective optimization. F1 vs. F2 – Total resistance (RT) vs.

Seakeeping Merit Function (SMF). Delft Catamaran optimization test case.

Fig.20. Comparison of geometry used for MOOP (Optimal

– ID-94). Delft Catamaran optimization test case.


Y

Z

-0.15 -0.1 -0.05 0 0.05 0.1 0.15-0.06

-0.04

-0.02

0

0.02

0.04

After BodyFore Body

(B.1 Design)

Y

Z

-0.15 -0.1 -0.05 0 0.05 0.1 0.15-0.06

-0.04

-0.02

0

0.02

0.04

After BodyFore Body

(ID-94 Design)

X

Y

0 0.2 0.4 0.6 0.8 1

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

URANS-Based Optimization

ID-94

Original (B.1)

Fig.21. Comparison of geometry between the original and optimal (ID-94) designs. Delft Catamaran optimization test

case for with and without CFD WJ model.

Fig.22. Comparison of RAO (PF-CFD – FreDOM -

results). Delft Catamaran optimization test case with CFD WJ model.

Original (B.1)

Optimal (ID-94)



Original (B.1)

Optimal (ID-94)



Original (B.1)

Optimal (ID-94)



Original (B.1)

Optimal (ID-94)

Fig.26. Comparison of pressure field (URANS-CFD

results). Delft Catamaran optimization test case with CFD WJ model.

Original (B.1)

Optimal (ID-94)

Fig.27. Comparison of axial-velocity field (URANS-CFD results). Delft Catamaran optimization test case with CFD

WJ model.


Original (B.1)

Optimal (ID-94)

Fig.28. Comparison of wave field (PF-CFD results). Delft

Catamaran optimization test case with CFD WJ model.

4.0 CONCLUDING REMARKS

The numerical optimizations of the initial design of two waterjet propelled ships are carried out, i.e., JHSS and Delft Catamaran (DC) test cases, by using the optimization framework developed in the present study based on advanced free-surface URANS and PF solvers and evolutionary algorithms. For both test cases, practical multiobjective optimization problems are formulated with realistic design constraints, i.e., total resistance RT and seakeeping merit function SMF are simultaneously minimized. The problems are successfully solved by the present optimization framework and the both results appear very promising, e.g., Pareto sets are successfully obtained with enough number of designers’ final selection. A selected design on the Pareto set for DC case indicates significant and meaningful reduction of RT and SMF, i.e., about 5% and 26% reductions, respectively. Together with a fact that the trends in design modification and flow fields are consistent, the above-mentioned results support overall validity and effectiveness of the optimization framework developed in the present study.


optimization. Delft Catamaran three speed optimization test case.

Rt_RANS_SP1

Rt_

RS

_S

P1

5.500E-04 5.550E-04 5.600E-04 5.650E-04

5.9

60E

-04

5.98

0E

-04

6.0

00E

-04

6.0

20E

-04

Rt_RANS_SP2

Rt_

RS

_S

P2

7.400E-04 7.500E-04 7.600E-04 7.700E-046.80

0E

-04

6.9

00E

-04

7.00

0E

-04

7.1

00E

-04

7.20

0E

-04

Rt_RANS_SP3

Rt_

RS

_S

P3

5.400E-04 5.450E-04

5.1

50E

-04

5.2

00E

-04

5.2

50

E-0

4

Fig.30. Correlation of resistance between URANS- and PF-

CFD predictions. Columns, Fr=0.3, Fr=0.5, and Fr=0.7, respectively. Delft Catamaran optimization test case.

B3

B1

B2

Original Design

F*1

F* 2

1 1.01 1.02 1.03 1.04

0.9

60

.97

0.9

80.

991

1.0

1

B3

B1

B2

Original Design

F*1

F* 3

1 1.01 1.02 1.03 1.04

0.9

80

.99

1

B3

B1

B2

Original Design

F*2

F* 3

0.96 0.97 0.98 0.99 1

0.9

80

.98

50

.99

0.9

95

1

Fig.31. Solutions from the present multi-objective

optimization. F1, F2, and F3 are total resistance (RT) for Fr=0.3, 0.5, and 0.7, respectively. Delft Catamaran three

speed optimization test case.


At present, our future effort in the present international collaboration is directed toward the next goal to complete more challenging problem, e.g., 3-speed multiobjective problem are formulated and solved. Fig.29 shows the problem setup for such a problem, and preliminary results are shown in Fig.30 and Fig.31. Further evaluation of the results is in progress. Planning of experimental campaign to validate the results is also in progress, and will be reported in near future.

REFERENCES

Bassanini, P., Bulgarelli, U.P., Campana, E.F. & Lalli, F. (1994). “The Wave Resistance Problem in a Boundary Integral Formulation.” Surveys on Mathematics for Industry, 4, pp. 151-194.

Campana, E.F., Peri, D., Tahara, Y. & Stern, F. (2006). “Shape Optimization in Ship Hydrodynamics using Computational Fluid Dynamics.” Computer Methods in Applied Mechanics and Engineering, 196, pp. 634–651.

Campana, E.F., Peri, D., Tahara, Y., Kandasamy, M. & Stern, F. (2009). “Numerical Optimization Methods for Ship Hydrodynamic Design,” Trans. SNAME Annual Meeting, Providence. Rhode Island, USA.

Carrica, P., Wilson, R.V. & Stern, F. (2006). “Unsteady RANS Simulation of the Ship Forward Speed Diffraction Problem.” Computers and Fluids, 35, pp. 545-570.

Deb, K. (2001). Multi-Objective Optimization using Evolutionary Algorithms. John Wiley & Sons.

Hirayama, A, & Ando, J. (2007). “Study on Reduction of Wave-making Resistance in Multiple Load Conditions using Real-coded Genetic Algorithm.” Proc. PRADS2007, 2, pp. 1050-1056.

Kandasamy, M., Ooi, S.K., Carrica, P., Stern, F., Campana, E., Peri, D., Osborne, P., Cote, J., Macdonald, N. & de Waal, N. (2009a). “URANS based optimization of a high speed foil assisted semi planning catamaran for low wake.” Proc. 10th International Conference Fast Sea Transportation, FAST 2009, Athens, Greece.

Kandasamy, M, Takai, T. & Stern, F. (2009b). “Validation of detailed water-jet simulation using Urans for large high-speed sea-lifts.” Proc. 10th Int.Conference on Fast Sea Transportation, FAST 2009, Athens, Greece.

Kandasamy, M., Ooi, S.K., Carrica, P. & Stern, F. (2010). “Integral Force/Moment Waterjet Model for CFD Simulations.” ASME J. Fluids Eng, in press.

Kandasamy, M., He, W., Tahara, Y., Peri, D., Campana, E., Wilson, W. & Stern, F. (2011). “Optimization of Waterjet-Propelled High Speed Ships - JHSS and Delft

Catamatran.” Proc. 11th International Conference Fast Sea Transportation, FAST 2011, Honolulu, Hawaii, USA.

Lugni, C., Colagrossi, A., Landrini, M. & Faltinsen, O.M. (2004). “Experimental and Numerical Study of Semi-displacement Mono-hull and Catamaran in calm water and incident waves.” Proc. 25th Symposium on Naval Hydrodynamics, St. John's, Canada.

Peri, D., Roccaldo, R. & Franchi, S.I. (1998). “Influence of the submergence and the spacing of the demihulls on the behaviour of multihulls marine vehicles: a numerical application.” Proc. PRADS '98, Den Haag, The Netherlands.

Peri, D., Campana, E.F., Tahara, Y., Kandasamy, M. & Stern, F. (2010). “New developments in Simulation-Based Design with application to High Speed Waterjet Ship Design.” Proc. 28th Symposium on Naval Hydrodynamics, Pasadena, USA.

Tahara, Y. (2004). “A Rankine-Source Panel Method for Steady Ship-Wavemaking Problem – Technical Notes on NAPA Potential Flow CFD Module -.” Proc. NAPA User Meeting, Turku, Finland.

Tahara, Y., Peri, D., Campana, E.F. & Stern, F. (2008a). “Computational fluid dynamics-Based multiobjective optimization of a surface combatant.” J. Marine Science and Technology, 13(2), pp. 95-116.

Tahara, Y., Peri, D., Campana, E.F. & Stern, F. (2008b) “Single and Multiobjective Design Optimization of a Fast Multihull Ship: numerical and experimental results.” Proc. 27th Symposium on Naval Hydrodynamics, Seoul, Korea.

Tahara, Y. & Takai, T. (2008). “High-Performance Multi-Objective Evolutionary Algorithms for Computational Fluid Dynamics-Based Design Optimization.” Proc. 3rd PAAMES and AMEC2008, Chiba, Japan, pp. 313 – 323.

Whitney, E.J., Gonzalez, L.J., Srinivas, K., Périaux, J. & Sefrioui, M. (2003). “Adaptive Evolution Design Without Problem Specific Knowledge: UAV Applications.” Proc. EUROGEN 2003, Barcelona, Spain.

ACKNOWLEDGEMENTS

This work has been supported by the U.S. Office of Naval Research (Grant Number N00014-09-1-0979 and N00014-08-1-0491) under the administration of Dr. Ki-Han Kim and Dr. Peter Cho; and Grant-in-Aid for Scientific Research, Japan (Project Number 21360436). The authors would like to express their appreciation to those who concern for the support and encouragement.


Documents

CFD-Based Multiobjective Optimization of Waterjet Propelled High Speed Ships