# Variable decomposition approach applied to multi-objective optimization for minimum powering of commercial ships

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## Abstract

As computational fluid dynamics has matured to the point where it is widely accepted as a key tool for ship hull form design, development of simulation-based design (SBD) has been strongly motivated in the past decades. Although many successful demonstrations of SBD were presented, most cases just deal with minimization of total resistance with a formulation of single-objective optimization problem. Once the interest is in minimization of ship-scale delivered power or effective power, issue related to accuracy of the simulation appears critical in many cases, which yield unconvincing results to hull form designers. The method we propose in this paper aims at overcoming the issues. Instead of just counting on predicted power from the simulation and solve a single-objective optimization problem, we first introduce variable decomposition approach to decompose a target ship performance function into terms including embedded parameters, then formulate and solve a multi-objective optimization problem (MOOP). Any scheme to solve MOOP can be applied. In the following, an overview of the present approach is given and results are presented and discussed through comparison with available experimental fluid dynamics data and detailed analysis of flow and integral parameters. The effectiveness of the present approach is also discussed.

## Keywords

Variable decomposition approach Multiobjective optimization RANS-CFD Energy saving device Minimum powering Commercial ship## List of symbols

*L*_{PP}Length between perpendiculars (m)

*L*_{WL}Length at the waterline (m)

*B*Breadth moulded (m)

*d*Draft moulded (m)

- \(\nabla\)
Displacement (m

^{3})- \({C_{\text{B}}}=\frac{\nabla }{{{L_{{\text{PP}}}}Bd}}\)
Block coefficient

*V*_{S}Ship speed (m/s)

- \(\rho\)
Density of water (kg/m

^{3})- \(g\)
Gravitational acceleration (m/s

^{2})- \(\nu\)
Kinematic viscosity

- \(Fr=\frac{{{V_{\text{S}}}}}{{\sqrt {g{L_{{\text{PP}}}}} }}\)
Froude number

- \(Re=\frac{{{V_{\text{S}}}{L_{{\text{PP}}}}}}{\nu }\)
Reynolds number

*R*Total resistance (N)

*1*+*k*Form factor

- \(D\)
Diameter of propeller (m)

*n*Propeller rate of revolution (rps)

*V*_{a}Advance speed of propeller (m/s)

- \(J=\frac{{{V_{\text{a}}}}}{{nD}}\)
Advance ratio

- \(T\)
Propeller thrust (N)

- \({K_t}=\frac{T}{{\rho {n^2}{D^4}}}\)
Thrust coefficient

- Q
Propeller torque (N m)

- \({K_{\text{q}}}=\frac{Q}{{\rho {n^2}{D^5}}}\)
Torque coefficient

- \({\text{SFC}}\)
Skin friction correction

*t*Thrust deduction factor, e.g., \(t=\frac{{T - (R - {\text{SFC}})}}{T}\)

*w*_{n}Nominal wake, \({w_{\text{n}}}=\frac{{\int_{0}^{{2\pi }} {\int_{{\frac{{{d_h}}}{2}}}^{{\frac{D}{2}}} {ur{\text{d}}r{\text{d}}\theta } } }}{{\frac{\pi }{4}({D^2} - d_{h}^{2})}}\), where the origin is the center of propeller

*w*_{e}Effective wake fraction

- \({w_T}=\frac{{{V_{\text{S}}} - {V_{\text{a}}}}}{{{V_{\text{S}}}}}\)
Taylor wake fraction in model scale

*w*_{s}Estimated wake fraction of ship

*Q*(*O*)Propeller torque in open water (N m)

- \({\eta _0}=\frac{{T{V_{\text{a}}}}}{{2\pi nQ(O)}}\)
Propeller open water efficiency

- \({\eta _{\text{R}}}=\frac{{Q(O)}}{Q}\)
Relative rotative efficiency

- \({\eta _{\text{P}}}=\frac{{1 - t}}{{1 - {w_T}}}{\eta _0}{\eta _{\text{R}}}\)
Propulsive efficiency

- \({C_{{\text{th}}}}=T\Bigg/\left( {\frac{{\rho {V_{\text{a}}}^{2}}}{2}\frac{{\pi {D^2}}}{4}} \right)\)
Thrust coefficient

## Notes

### Acknowledgements

This work has been supported by Grant-in-Aid for Scientific Research, Japan (Project nos. 24360363 and 15H04217). The authors would like to express their appreciation to those who concern for the support and encouragement. The authors’ appreciation is extended to Mr. Kenichi Kume (NMRI) for extensive CFD data (duct series self-propulsion simulation by using unstructured meshing tool and CFD); and Mr. Yoshihisa Okada and Mr. Kenta Katayama (Nakashima Propeller Co., LTD) for valuable advice on duct optimization problem.

## References

- 1.Proceedings 25th international towing tank conference, Fukuoka, Japan, 14–20 September, 2008Google Scholar
- 2.Proceedings 26th international towing tank conference, Rio de Janeiro, Brazil, 28 August–3 September, 2011Google Scholar
- 3.Proceedings 27th international towing tank conference, Copenhagen, Denmark, 31 August–5 September, 2014Google Scholar
- 4.Hart CG, Vlahopoulos N (2010) An integrated multidisciplinary particle swarm optimization approach to conceptual ship design. Struct Multidiscip Optim 41:481–494CrossRefGoogle Scholar
- 5.Kuhn J, Collette M, Lin W-M, Schlageter E, Whipple D, Wyatt D (2010) Investigation of competition between objectives in multiobjective optimization. Proc 28th Symp Nav Hydrodyn 2:1233–1244Google Scholar
- 6.Zhang B-J, Ma K (2011) Study on hull form optimization for minimum resistance based on niche genetic algorithms. J Ship Prod Des 27:162–168CrossRefGoogle Scholar
- 7.He XD, Hong Y, Wang RG (2012) Hydroelastic optimization of a composite marine propeller in a non-uniform wake. Ocean Eng J 39:14–23CrossRefGoogle Scholar
- 8.Hollenbach U, Reinholz O (2011) Hydrodynamics trends in optimization propulsion. In: Second international symposium on marine propulsors SMP’11, Hamburg, GermanyGoogle Scholar
- 9.Stuck A, Kroger J, Rung T (2011) Adjoint-ased Hull Desogn for wake optimization. Ship Technol Res 58(1):34–44CrossRefGoogle Scholar
- 10.Luo W, Fu B, Guedes Soares C, Zou Z (2013) Robust control for ship course-keeping based on support vector machines, particle swarm optimization and L2-Gain. OMAE 2013, NantesCrossRefGoogle Scholar
- 11.Xu Y, Sun Y, Wei Y, Guan H, Liu M, Cai W (2012) Study on ship–ship hydrodynamic interaction by ANN optimization. MARSIM 2012, SingaporeGoogle Scholar
- 12.Kim HJ, Choi JE, Chun HH (2016) Hull-form optimization using parametric modification functions and particle swarm optimization. J Mari Sci Technol 21(1):129–144CrossRefGoogle Scholar
- 13.Chrismianto D, Kim DJ (2014) Parametric bulbous bow design using the cubic Bezier curve and curve-plane intersection method for the minimization of ship resistance in CFD. J Mar Sci Technol 19(4):479–492CrossRefGoogle Scholar
- 14.Diez M, He W, Campana EF, Stern F (2014) Uncertainty quantification of Delft catamaran resistance, sinkage, and trim for variable Froude number and geometry using metamodels, quadrature and Karhunen–Loeve expansion. J Mar Sci Technol 19(2):143–169CrossRefGoogle Scholar
- 15.Han S, Lee YS, Choi YB (2012) Hydrodynamic hull form optimization using parametric models. J Mar Sci Technol 17(1):1–17CrossRefGoogle Scholar
- 16.Kandasamy M, Peri D, Ooi SK, Carrica P, Stern F, Campana EF, Osborne P, Cote J, Macdonald N (2011) Multi-fidelity optimization of a high-speed foil-assisted semi-planing catamaran for low wake. J Mar Sci Technol 16(2):143–156CrossRefGoogle Scholar
- 17.Tahara Y, Tohyama S, Katsui T (2006) CFD-based multi-objective optimization method for ship design. Int J Numer Methods Fluids 52:449–527CrossRefzbMATHGoogle Scholar
- 18.Tahara Y, Peri D, Campana EF, Stern F (2008) Computational fluid dynamics-based multiobjective optimization of a surface combatant. J Mar Sci Technol 13(2):95–116CrossRefGoogle Scholar
- 19.Tahara Y, Peri D, Campana EF, Stern F (2011) Single and multiobjective design optimization of a fast multihull ship: numerical and experimental results. J Mar Sci Technol 16(4):412–433CrossRefGoogle Scholar
- 20.Campana EF, Peri D, Tahara Y, Stern F (2006) Shape optimization in ship hydrodynamics using computational fluid dynamics. Comput Methods Appl Mech Eng 196:634–651CrossRefzbMATHGoogle Scholar
- 21.Kandasamy M, Peri D, Tahara Y, Wilson W, Miozzi M, Georgiev S, Milanov E, Campana EF, Stern F (2013) Simulation based design optimization of waterjet propelled Delft catamaran. ISP 60:277–308Google Scholar
- 22.Diez M, Campana EF, Stern F (2015) Design-space dimensionality reduction in shape optimization by Karhunen–Loeve expansion. Comput Methods Appl Mech Eng 283:1525–1544CrossRefGoogle Scholar
- 23.Kim K, Leer-Andersen M, Orych M (2014) Hydrodynamic optimization of energy saving devices in full scale. In: 30th symposium on naval hydrodynamics, Hobart, Tasmania, Australia, 2–7 November, (CDROM)Google Scholar
- 24.Gothenburg 2010 (2010) A workshop on numerical ship hydrodynamics, Gothenburg, Sweden, 8–10 December, (CDROM)Google Scholar
- 25.Tokyo 2015 (2015) A workshop on numerical ship hydrodynamics. 2–4 December, (CDROM), TokyoGoogle Scholar
- 26.Kasahara Y (2015) Hull form design utilizing CFD for improvement of EEDI. In: International workshop on ship technologies related to energy efficiency design index (EEDI), Tokyo, JapanGoogle Scholar
- 27.Ichinose Y, Tahara Y, Kasahara Y (2015) Numerical study on flow field around the Aft part of hull form series in a steady flow. In: 18th numerical towing tank symposium, Cortona, Italy, (CDROM)Google Scholar
- 28.NMRI CFD 2015 (2016) User manual and related information. National Maritime Research Institute, MitakaGoogle Scholar
- 29.HEXPRESS (2016) User manual and related information. http://www.numeca.com/
- 30.Ichinose Y, Kume K, Tahara Y (2016) A development and analysis of the new energy saving device “USTD”. In: Proceedings of the 19th numerical towing tank symposium (NuTTs’16), St. Pierre d’Oleron, France, 3–4 October, (CDROM)Google Scholar
- 31.Tank Test Report (2015) Tank Test No. 15-04, (Japanese, unpublished). National Maritime Research Institute, MitakaGoogle Scholar
- 32.Tahara Y, Saitoh Y, Matsuyama H, Himeno Y (1999) CFD-aided optimization of tanker stern form—2nd report: minimization of delivered horse power. J Kansai Soc Nav Archit Jpn 232:9–18Google Scholar
- 33.Breslin JP, Andersen P (1994) Hydrodynamics of ship propellers. Cambridge University Press, Cambridge, p 194Google Scholar
- 34.Spalart PR, Allmaras SR (1994) An one-equation turbulence model for aerodynamic flows. La Recherch Aerospatiale, No. 1Google Scholar
- 35.Wilcox DC (1994) Simulation of transition with a two-equation turbulence model. AIAA J 32(2):247–255CrossRefzbMATHGoogle Scholar
- 36.NAPA (2016) User manual and related information. http://www.napa.fi/
- 37.RHINOCEROS (2016) User manual and related information. http://www.rhino3d.com/
- 38.GRIDGEN (2016) User manual and related information. http://www.pointwise.com/
- 39.Tahara Y (2015) CFD-based hull form/appendage optimization by using deterministic and stochastic optimization theory. In: 12th international marine design conference, Tokyo, Japan, 11–14 May 2015 (CDROM)Google Scholar
- 40.Tahara Y, Shingo S, Kanai A (2017) CFD based optimal design method for energy saving devices by using overset grid technique and nonlinear optimization theory. J Jpn Soc Nav Archit Ocean Eng 26:1–16Google Scholar
- 41.Deb K (2001) Multi-objective optimization using evolutionary algorithms. Wiley, HobokenzbMATHGoogle Scholar
- 42.Hess JL, Smith AMO (1962) Calculation of non-lifting potential flow about arbitrary three-dimensional bodies. Douglas Report No. E S 40622. Douglas Aircraft Company, Santa MonicaGoogle Scholar