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EFD and CFD for KCS heaving and pitching in regular head waves

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Abstract

The KCS container ship was investigated in calm water and regular head seas by means of EFD and CFD. The experimental study was conducted in FORCE Technology’s towing tank in Denmark, and the CFD study was conducted using the URANS codes CFDSHIP-IOWA and Star-CCM+ plus the potential theory code AEGIR. Three speeds were covered and the wave conditions were chosen in order to study the ship’s response in waves under resonance and maximum exciting conditions. In the experiment, the heave and pitch motions and the resistance were measured together with wave elevation of the incoming wave. The model test was designed and conducted in order to enable UA assessment of the measured data. The results show that the ship responds strongly when the resonance and maximum exciting conditions are met. With respect to experimental uncertainty, the level for calm water is comparable to PMM uncertainties for maneuvering testing while the level is higher in waves. Concerning the CFD results, the computation shows a very complex and time-varying flow pattern. For the integral quantities, a comparison between EFD and CFD shows that the computed motions and resistance in calm water is in fair agreement with the measurement. In waves, the motions are still in fair agreement with measured data, but larger differences are observed for the resistance. The mean resistance is reasonable, but the first order amplitude of the resistance time history is underpredicted by CFD. Finally, it seems that the URANS codes are in closer agreement with the measurements compared to the potential theory.

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Abbreviations

\( a_{n} \) :

n’th order of amplitude

\( B_{\text{wl}} \) :

Model beam

\( B_{X} \) :

Bias limit

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

Block coefficient

\( {\text{d}}t \) :

Time step

\( D \) :

Distance between carriage wave gauge and LCG

\( f_{\text{e}} \) :

Frequency of encounter

\( f_{\text{n}} \) :

Natural frequency

\( {\text{Fn}} \) :

Froude number

\( F_{X} \) :

X force

\( {\text{FS}} \) :

Fourier series expansion

\( g \) :

Gravity constant

H :

Wave height

\( I_{yy} \) :

Total moment of inertia of the model

\( k \) :

Wave number

\( L_{\text{pp}} \) :

Model length between perpendiculars

\( L_{\text{wl}} \) :

Model length of waterline

\( M \) :

Number of repeats

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

Mass of model

\( p,q,r \) :

Roll, pitch and yaw rate

\( p_{G} \) :

Order of accuracy

\( P_{X} \) :

Precision limit

\( \text{Re} \) :

Reynolds number

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

Grid refinement ratio

\( R_{\text{G}} \) :

Grid convergence ratio

\( {\text{RM}} \) :

Running mean

\( S \) :

Model surface area

\( S_{L} \) :

Minimum solution of considered grid

\( S_{r} \) :

Standard deviation

\( S_{U} \) :

Maximum solution of considered grid

t :

Time

\( T_{\text{e}} \) :

Encounter period

\( {\text{TF}}_{i} \) :

Transfer function in i’th mode

\( T_{\text{m}} \) :

Model mean draught

\( T_{\text{p}} \) :

Peak period

\( u,v,w \) :

Surge, sway and heave velocities

\( U_{0} \) :

Model speed

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

Carriage velocity

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

Grid uncertainty

\( U_{X} \) :

Total uncertainty

\( x_{i} \) :

i’th degree of freedom

\( x,y,z \) :

Axial, transverse and vertical coordinates

\( X_{\text{G}} \) :

Longitudinal center of gravity (LCG)

\( X_{i} \) :

Measured variable

\( Y \) :

Approximated variable

\( Y^{ + } \) :

Wall distance

\( Z_{\text{G}} \) :

Vertical center of gravity (VCG)

\( \delta_{{{\text{RE}}_{\text{G1}} }}^{*} \) :

Grid error

\( \Updelta \) :

Model displacement

\( \Updelta_{\text{G}} \) :

Maximum change between grids

\( \Updelta_{\text{HSC}} \) :

Convergence of RM values

\( \Updelta_{\text{SC}} \) :

Statistical convergence

\( \varepsilon_{{{\text{G}}ij}} \) :

Difference between i’th and j’th grid

\( \phi \) :

Level set function

\( \gamma_{Yn} \) :

n’th order phase

\( \eta \) :

Water viscosity

\( \lambda \) :

Wave length

\( \nabla \) :

Model volume

\( \rho \) :

Water density

\( \theta \) :

Pitch angle

\( \theta_{i} \) :

Influence coefficient of i’th variable

\( \zeta \) :

Surface elevation

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Acknowledgments

This research was sponsored by a FORCE Technology, Office of Naval Research (ONR) contract N00014-07-C-0035 and grant N00014-09-1-1055 under the Naval International Cooperative Opportunities in Science and Technology Program (NICOP). Additionally, this work was supported in part by a grant of computer time from the DOD High Performance Computing Modernization Program at NAVO MSRC. Thanks to Pablo Carrica, IIHR for assistance related to code issues.

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Authors and Affiliations

  1. FORCE Technology, Hjortekærsvej 99, Kongens Lyngby, Denmark

    Claus D. Simonsen, Janne F. Otzen & Soizic Joncquez

  2. IIHR, The University of Iowa, 100 C. Maxwell Stanley Hydraulics Laboratory, Iowa City, IA, USA

    Frederick Stern

Authors
  1. Claus D. Simonsen
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  2. Janne F. Otzen
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  3. Soizic Joncquez
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  4. Frederick Stern
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Correspondence to Claus D. Simonsen.

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Simonsen, C.D., Otzen, J.F., Joncquez, S. et al. EFD and CFD for KCS heaving and pitching in regular head waves. J Mar Sci Technol 18, 435–459 (2013). https://doi.org/10.1007/s00773-013-0219-0

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  • DOI: https://doi.org/10.1007/s00773-013-0219-0

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