### Parallel-middle-body and Stern-form Relative Significance in the Wake Formation of Single-screw Large Ships

*Ketut Suastika, Fajar Nugraha, I Ketut Aria Pria Utama*

**Abstract**: The relative significance of

the parallel middle body and stern form in the wake formation of single-screw

large ships and their contribution to the ship’s viscous resistance are studied by using computational fluid dynamics (CFD). A

10450-DWT tanker is considered by varying the ratio of the

parallel-middle-body’s length to the ship’s length (

*L*) and by varying the shape of the stern form from a

_{mb}/LV-like to a U-like underwater stern transom section. In all the calculations,

the principal dimension and the displacement of the ships are kept constant. A

larger value for the parallel-middle-body relative length (

*L*) of ships with the same stern form results in a

_{mb}/Llarger drag coefficient but does not affect the nominal wake fraction

significantly. A change in the shape of the underwater stern form,

from a V-like to a U-like section, results in a much larger drag coefficient

ascribed to the much larger wake fraction. The stern form dominantly affects

the nominal wake fraction and the ship’s viscous resistance compared to the

parallel-middle-body relative length.

**Keywords**: CFD; Parallel middle body; Ship resistance; Stern form; Wake fraction

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#### References

Anderson, J.D., 1995. Computational Fluid Dynamics: The Basics with Applications. McGraw-Hill, New York

Aydin, M., 2013. Development of a Systematic Series of Gulet Hull Forms with Cruiser Stern. Ocean Engineering, Volume 58, pp. 180–191

Banks, J., Phillips, A.B., Turnock, S.R., 2010. Free-surface CFD prediction of components of ship resistance for KCS. In: The Proceedings of the 13th Numerical Towing Tank Symposium, 10 October, Duisburg, Germany

Benedek, Z., Balogh, B., 1968. The Scale Effect on Nominal Wake Fraction of Single-Screw Ships. Periodica Polytechnica/Mechanical Engineering, Volume 12(1), pp. 27–37

Choi, J., Kim, J., Lee, H., Choi, B., Lee, D., 2009. Computational Predictions of Ship-speed Performance. Journal of Marine Science and Technology, Volume 14(3), pp. 322–333

Choi, J.E., Min, K., Kim, J.H., Lee, S.B., Seo, H.W., 2010. Resistance and Propulsion Characteristics of Various Commercial Ships Based on CFD Results. Ocean Engineering, Volume 37(7), pp. 549–566

Dymarski, P., Kraskowski, M., 2010. CFD Optimization of Vortex Generators Forming the Wake Flow of Large Ships. In: The Proceedings of the 13th Numerical Towing Tank Symposium, 10 October, Duisburg, Germany

Dyne, G., 1974. A Study of Scale Effects on Wake, Propeller Cavitation, and Vibratory Pressure at Hull of Two Tanker Models. In: The SNAME Annual Meeting, 14–16 November, New York, USA

Eca, L., Hoekstra, M., 2009. On the Numerical Accuracy of the Prediction of Resistance Coefficients in Ship Stern Flow Calculations. Journal of Marine Science and Technology, Volume 14(1), pp. 2–18

Guldhammer, H., 1962. Formdata: Some Systematically Varied Ship Forms and their Hydrostatic Data. Danish Technical Press, Copenhagen

Hoekstra, M., 1975. Prediction of Full Scale Wake Characteristics Based on Model Wake Survey. International Shipbuilding Progress, Volume 22(250), pp. 204–219

Holden, K.O., Fagerjord, O., Frodstad, R., 1980. Early Design-stage Approach to Reducing Hull Surface Forces Due to Propeller Cavitation. Transactions SNAME, Volume 88, pp. 403–442

Holtrop, J., Mennen, G.G., 1982. An Approximate Power Prediction Method. International Shipbuilding Progress, Volume 29(335), pp. 166–171

Hoyle, J.W., Cheng, B.H., Hays, B., Johnson, B., Nehrling, B., 1986. A Bulbous Bow Design Methodology for High-speed Ships. Transactions SNAME, Volume 94, pp. 31–56

Huang, F., Yang, C., 2016. Hull Form Optimization of a Cargo Ship for Reduced Drag. Journal of Hydrodynamics, Volume 28(2), pp. 173–183

Kostas, K.V., Ginnis, A.I., Politis, C.G., Kaklis, P.D., 2015. Ship-hull Shape Optimazation with a T-Spline Based BEM Isogeometric Solver. Computer Methods in Applied Mechanics and Engineering, Volume 284, pp. 611–622

Larsson, L., Stern, F., Bertram, V., 2003. Benchmarking of Computational Fluid Dynamics for Ship Flows. Journal of Ship Research, Volume 47, pp. 63–81

Melville-Jones, B., 1937. The Measurement of Profile Drag by the Pitot-Traverse Method. The Cambridge University Aeronautics Laboratory (R & M No. 1688), Technical Report of the Aeronautical Research Committee for the Year 1935–1936, Volume I

Menter, F.R., 1994. Two-equation Eddy-viscosity Turbulence Models for Engineering Applications. AIAA Journal, Volume 32(8), pp. 1598–1605

Mitchel, R.R., Webb, M.B., Roetzel, J.N., Lu, F.K., Dutton, J.C., 2008. A Study of the Base Pressure Distribution of a Slender Body of Square Cross Section. In: The Proceedings of the 46th AIAA Aerospace Sciences Meeting and Exhibition, 7–10 January, Reno, Nevada, pp. 1–8

Park, S., Park, S.W., Rhee, S.H., Lee, S.B., Choi, J.-E., Kang, S.H., 2013. Investigation on the Wall Function Implementation for the Prediction of Ship Resistance. International Journal of Naval Architecture and Ocean Engineering, Volume 5, pp. 33–46

Seo, J.H., Seol, D.M., Lee, J.H., Rhee, S.H., 2010. Flexible CFD Meshing Strategy for Prediction of Ship Resistance and Propulsion Performance. International Journal of Naval Architecture and Ocean Engineering, Volume 2, pp. 139–145

Suastika, K., Nugraha, F., 2017. Effects of Parallel-middle-body Relative Length and Stern Form on the Wake Fraction and Ship Resistance. Applied Mechanics and Materials, Volume 862, pp. 278–283

Utama, I.K.A.P., 1999. Investigation of the Viscous Resistance Components of Catamaran Forms. PhD Thesis, University of Southampton

Versteeg, H.K., Malalasekera, W., 2007. An Introduction to Computational Fluid Dynamics: The Finite Volume Method. Longman Scientific, Harlow, UK

Wang, Z.-Z., Xiong, Y., Wang, R., Shen, X.-R., Zhong, C.-H., 2015. Numerical Study on Scale Effect of Nominal Wake of Single Screw Ship. Ocean Engineering, Volume 104, pp. 437–451

Zhao, Y., Zong, Z., Zou, L., 2015. Ship Hull Optimization based on Wave Resistance using Wavelet Method. Journal of Hydrodynamics, Volume 27(2), pp. 216–222