Abstract
This paper investigates the interference effects of wave systems on a multi-hull vessel in shallow water. A numerical analysis is made using the URANS code CFDSHIP-Iowa V.4 on the DELFT Catamaran model 372. The test matrix for numerical computations includes two separation distances (s = 0.17; 0.23) and the depth values of h/T = 8.2, 2.5 and 2, at several speeds ranging within Fr H = 0.775–1.739. Numerical results are compared with the experimental data of the Bulgarian Ship Hydrodynamic Center, and verification and validation for resistance, sinkage and trim are also performed. Results show that, at critical speed (Fr H ≈ 1), the presence of a finite depth significantly affects the catamaran total resistance, which, in shallower water, increases considerably with respect to deep water. At low h/T, small effects of the water depth on resistance occur at subcritical and supercritical speeds. The interference effects seem to be more relevant in shallow, rather than in deep water, with maximum IF values registered at critical speeds (Fr H ≈ 1). Similarly to deep water, the lower the separation distance the greater the interference value. Moreover, in shallow water some negative interference is observed at Fr > 0.5. Wave patterns and wave profiles are analyzed and a comparison is made between several configurations of catamaran and a mono-hull vessel, in order to analyze how water depth and separation distance determine resistance and interference. Finally, a vortex instability study is also included.
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Abbreviations
- C f :
-
Frictional resistance coefficient
- C p :
-
Pressure resistance coefficient
- C r :
-
Residuary resistance coefficient
- C T :
-
Total resistance coefficient
- D :
-
Experimental data value
- E :
-
Comparison error
- f :
-
Karman shedding frequency (Hz)
- f′ :
-
Non-dimensional Karman shedding frequency (=1/τp)
- Fr :
-
Froude number \( \left( {=\frac{U}{{\sqrt {gL} }}} \right) \)
- Fr H :
-
Height Froude number \( \left( {=\frac{U}{{\sqrt {gh} }}} \right) \)
- g :
-
Acceleration of gravity (=9.81 m/s2)
- H :
-
Half wake width (m)
- h :
-
Water depth (m)
- IF:
-
Interference factor
- 1 + k :
-
Form factor
- L :
-
Model length (m)
- P :
-
Estimated order of accuracy, pressure (N/m2)
- R :
-
Ratio between solution changes
- R T :
-
Total resistance (N)
- S :
-
Separation distance between the hulls (m), wet surface area (m2), simulation value
- s :
-
Non-dimensional separation distance (=S/L)
- St H :
-
Strouhal number (=f H/U S)
- T :
-
Model draft (m)
- U :
-
Ship speed (m/s)
- U D :
-
Experimental data uncertainty
- U G :
-
Grid uncertainty
- U I :
-
Iterative uncertainty
- U S :
-
Shear layer velocity (m/s)
- U SN :
-
Simulation numerical uncertainty
- U V :
-
Validation uncertainty
- z:
-
Non-dimensional wave elevation by L
- ρ :
-
Water density (kg/m3)
- σ:
-
Non-dimensional sinkage
- τ:
-
Trim (rad)
- τp :
-
Non-dimensional instability period \( \left( {={\text{period}} \times \frac{U}{L}} \right) \)
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Acknowledgments
This work was supported by the Office of Naval Research, Grant N000141010017 under the administration of Dr. Patrick Purtell. The authors appreciate BSHC who provided the EFD data for this study.
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T. Castiglione, W. He and S. Bova contributed equally to this work.
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Castiglione, T., He, W., Stern, F. et al. URANS simulations of catamaran interference in shallow water. J Mar Sci Technol 19, 33–51 (2014). https://doi.org/10.1007/s00773-013-0230-5
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DOI: https://doi.org/10.1007/s00773-013-0230-5