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Computational fluid dynamics-based multiobjective optimization of a surface combatant using a global optimization method

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Abstract

The main objective of this article is to describe the development of two advanced multiobjective optimization methods based on derivative-free techniques and complex computational fluid dynamics (CFD) analysis. Alternatives for the geometry and mesh manipulation techniques are also described. Emphasis is on advanced strategies for the use of computer resource-intensive CFD solvers in the optimization process: indeed, two up-to-date free surface-fitting Reynolds-averaged Navier-Stokes equation solvers are used as analysis tools for the evaluation of the objective function and functional constraints. The two optimization methods are realized and demonstrated on a real design problem: the optimization of the entire hull form of a surface combatant, the David Taylor Model Basin—Model 5415. Realistic functional and geometrical constraints for preventing unfeasible results and to get a final meaningful design are enforced and discussed. Finally, a recently proposed verification and validation methodology is applied to assess uncertainties and errors in simulation-based optimization, based on the differences between the numerically predicted improvement of the objective function and the actual improvement measured in a dedicated experimental campaign. The optimized model demonstrates improved characteristics beyond the numerical and experimental uncertainty, confirming the validity of the simulation-based design frameworks.

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Abbreviations

B n (t):

Bezier curve of degree n

D P, D O :

Experimental value of the parent and the optimized designs

E Δ :

Difference between the measured and the expected improvements

f, f 0, etc.:

Fitness function

\( \vec F \) = (F 1, F 2, ..., F N )T :

Multiobjective functions

F n = \( {U \mathord{\left/ {\vphantom {U {\sqrt {gL_{PP} } }}} \right. \kern-\nulldelimiterspace} {\sqrt {gL_{PP} } }} \) :

Froude number

\( \bar f(t) \) :

Average fitness of a population

g :

Gravitational acceleration

h, g :

Equality and inequality constraint functions

L PP :

Ship length

M :

Number of design variables

m :

Number of processors

n :

Population size

N :

Number of multiobjective functions

N i,p , N i,q :

Normalized B-spline basis functions of degree p and q

p, q :

Number of equality and inequality constraint functions

P, Q, R :

Grid clustering and stretching functions

P i,j :

Location vectors of nonuniform rational B-spline (NURBS) control points

P o, δP :

Original and displacement location vectors

r :

Penalty parameter

R n = UL PP /v :

Reynolds number

R P :

Pareto ranking

R T :

Total resistance

S(u, v):

3D surface defined by NURBS

S, D :

Simulation value, and date value

S P, S O :

Numerical simulation value of the parent and the optimized designs

U :

Ship speed

u, v :

NURBS parameters

U S, U SN, etc.:

Uncertainty

\( \vec u(\bar x \to ) \) :

Velocity components, normalized by ship speed U

w i,j :

Weights

X, Y, Z :

Nondimensional Cartesian coordinates, normalized by ship length L PP

\( \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}} {x} \) = (x 1, x 2, ..., x M )T :

Design variables

\( \vec x,\vec y \) :

Points in the multiobjective function space

x 0, x k+1 :

Original and new Bezier patched surface

x i (t):

Frequency of genotype B i at generation t

x u i , x l i :

Upper and lower bounds of design variables

χ :

Subset χ of the M-dimensional real space \( \Re ^M \)

ΔS, ΔD :

Differences in value between the parent and the optimized designs

λ*:

Nondimensional wavelength

ν :

Kinematic viscosity

ρ :

Density of water

ξ 1, ξ 2, ξ 3 :

Computational coordinates

ξ 3, ξ 5 :

Heave and pitch peaks of response amplitude operator for head seas for λ* ≥ 0.4

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Authors and Affiliations

  1. Department of Marine System Engineering, Osaka Prefecture University, 1-1 Gakuen-cho, Osaka, 599-8531, Japan

    Yusuke Tahara

  2. Italian Ship Model Basin, INSEAN, Rome, Italy

    Daniele Peri & Emilio Fortunato Campana

  3. IIHR—Hydroscience and Engineering, University of Iowa, Iowa, USA

    Frederick Stern

Authors
  1. Yusuke Tahara
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  2. Daniele Peri
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  3. Emilio Fortunato Campana
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  4. Frederick Stern
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Correspondence to Yusuke Tahara.

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Tahara, Y., Peri, D., Campana, E.F. et al. Computational fluid dynamics-based multiobjective optimization of a surface combatant using a global optimization method. J Mar Sci Technol 13, 95–116 (2008). https://doi.org/10.1007/s00773-007-0264-7

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  • DOI: https://doi.org/10.1007/s00773-007-0264-7

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