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Bilge keel–free surface interaction and vortex shedding effect on roll damping

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Abstract

Prediction of the roll damping of a ship with bilge keels using traditional techniques, such as Ikeda’s method, is no longer sufficient when the bilge keels interact with the free surface. The discrepancies occurring between this method and actual roll damping are due to free surface interaction and vortex shedding, which are not considered in this method. Reynolds-averaged Navier–Stokes (RANS) solvers can be used to capture these effects, and the widely used Ikeda’s method can be modified. In this study, two-dimensional (2D) roll damping calculations for a hull section with bilge keels, including the free surface effects, are calculated numerically and experimentally for different draft cases. The normal forces acting on the bilge keels are calculated numerically to show the free surface effect on bilge keel roll damping. The generated vortices and vortex shedding from the bilge keels are analyzed to investigate the effect of the bilge keels–free surface interaction on the roll damping coefficients. The results show that the RANS solver is capable of predicting the roll damping coefficients in good agreement with experimental results and can be further used to modify Ikeda’s method. It is concluded that the bilge keel forces decrease when the bilge keels interact with the free surface, whereas Ikeda’s method gives a constant value for each draft condition. The interaction of the bilge keels and free surface affects the generation of the vorticity and vortex shedding from the bilge keels.

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Abbreviations

\(\emptyset_{\text{a}}\) :

Roll amplitude

\(C_{\text{D}}\) :

Drag coefficient

\(\omega\) :

Roll frequency

\(C_{\text{P}}\) :

Pressure coefficient

t :

Time

l :

Moment lever of ship section

∆t :

Time step

f :

Correction factor

T :

Roll period

F BK :

Hydrodynamic unit normal force on a bilge keel

f(t):

Start-up function

C m :

Added inertia coefficient

\(I_{\emptyset \emptyset }\) :

Mass moment of inertia

\(U_{\text{BK}}\) :

Velocity at the centroid of the bilge keel

\(a_{\emptyset \emptyset }\) :

Added mass moment of inertia

\(Fn\) :

Froude number

\(C\left( \emptyset \right)\) :

Restoring moment

\(M_{\text{E}}\) :

Excitation moment

\(M_{0}\) :

Amplitude of roll moment

\(\varepsilon\) :

Phase shift

\(B_{44}\) :

Roll damping coefficient

d :

Draft

\(\rho\) :

Fluid density

\(r_{\text{BK}}\) :

Distance from roll axis to bilge keel

\(b_{\text{BK}}\) :

Bilge keel span

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Acknowledgements

Funding was provided by Yildiz Technical University and Osaka Prefecture University.

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Authors and Affiliations

  1. Faculty of Naval Architecture and Maritime Engineering, Yildiz Technical University, Istanbul, Turkey

    Burak Yıldız

  2. Graduate School of Engineering, Osaka Prefecture University, Sakai, Japan

    Toru Katayama

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  1. Burak Yıldız
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  2. Toru Katayama
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Correspondence to Burak Yıldız.

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Yıldız, B., Katayama, T. Bilge keel–free surface interaction and vortex shedding effect on roll damping. J Mar Sci Technol 22, 432–446 (2017). https://doi.org/10.1007/s00773-016-0423-9

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  • DOI: https://doi.org/10.1007/s00773-016-0423-9

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