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Development of Empirical Formulation for Bow Flare Slamming and Deck Wetness for Displacement Vessels

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Abstract

The paper presents an empirical method to calculate bow flare slamming pressure and the green water load. Many empirical formulae for various types of vessels have been provided by rules of ship classification societies. In the present work, attempt is made to develop generalized formulations for all types of displacement vessels. Extreme sea conditions are considered. Bow flare pressure is derived in terms of flare and waterline angles. Specific condition for limiting waterline angle is derived based on 2D numerical simulations. Deck wetness is derived in terms of static and dynamic swell-up and the relative motion. Variation of static swell along the length is determined based on potential solution based analyses considering variation in vessels’ hull. 2D wedge simulations are carried out to validate the formulation of dynamic swell-up. Results of the calculated bow flare and deck pressures are compared with various ship classification society formulations and the trends are found to be in good agreement in general barring at bow flare where lower pressure is found in most of the presented cases. Also IACS UR S21A (2018) governing minimum pressure for deck scantlings is found to be conservative in few of the presented cases. Although scantlings assessment is not performed, the presented new formulations may help in realistic assessment of scantlings.

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Abbreviations

L :

vessel length, m

B :

vessel breadth, m

C b :

block coefficient of the vessel at design draft

U :

vessel design speed, m/s

Fn :

Froude number = \( U/\sqrt{gL} \)

h s :

static swell-up, m

ζ B :

elevation due to bow wave, m

ζ s :

sinkage due to speed, m

ζ :

wave elevation, m

λ w :

wave length, m

L e :

length of entrance on water plane, m

h d :

dynamic swell-up, m

l :

distance of the CG from the considered section, m

s(l):

vertical displacement at l, m

z :

heave displacement, m

θ :

pitch displacement, rad

ω :

wave frequency, rad/s

ω e :

encounter wave frequency, rad/s

Z(l):

freeboard height above design waterline at l, m

Subscripts:

“sig” and “ext” denote significant and extreme values respectively.

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Acknowledgements

The authors express their earnest gratitude to the Indian Register of Shipping (IRS), Mumbai, for supporting the reported work. Authors would like to thank Mr. A. R. Kar, Vice President of the Research Division of IRS for his valuable guidence.

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  1. Research and Innovation Centre, Indian Register of Shipping, Mumbai, 400 072, India

    Sharad Dhavalikar, Prasada N. Dabbi, Deepti Poojari, Ramkumar Joga & Sachin Awasare

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Correspondence to Sharad Dhavalikar.

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Dhavalikar, S., Dabbi, P.N., Poojari, D. et al. Development of Empirical Formulation for Bow Flare Slamming and Deck Wetness for Displacement Vessels. J. Marine. Sci. Appl. 17, 414–431 (2018). https://doi.org/10.1007/s11804-018-0045-1

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