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Radiation and Diffraction Velocity Potentials for Multi-hulled Vessels in 2-D

  • Research Article - Mechanical Engineering
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Abstract

The blended approach has the potential to provide the engineering solutions for design optimization keeping in view the current demand of the extensive computer resources for fully nonlinear computations. This study investigates two-dimensional boundary value problem for multi-bodies radiation and diffraction velocity of multi-hulled vessels using blended method. In blended scheme, fully nonlinear Euler equations of motion are solved with nonlinear hydrodynamic forces acting on multi-hulled vessels. Lid is employed over the body segment to suppress the eigenvalue mode, thus eliminating singularities in source strength being used on multi-hull bodies presenting geometrical discontinuities. Comparison between the blended technique and its validation against analytical calculations and experimental work are presented and found in good agreement. It is concluded that blended technique is an efficient and accurate alternate method to provide time simulations of ship motion and other essential parameters for design optimization.

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Abbreviations

U :

Mean forward speed

x, y, z :

Inertial coordinate system

\({\eta_{1}}\) :

Surge

\({\eta_{2}}\) :

Sway

\({\eta_{3}}\) :

Heave

\({\eta_{4}}\) :

Roll

\({\eta_{5}}\) :

Pitch

\({\eta_{6}}\) :

Yaw

x 0 :

X-axis in earth fixed coordinate

t 0 :

Time in earth fixed coordinate

n j :

Unit normal

F :

Force

S :

Surface/segment

\({\Phi}\) :

Total velocity potential

\({\nabla}\) :

Laplace operator

D :

Total/cumulative derivative

\({\varphi}\) :

Perturbation velocity potential

V :

Ship unsteady oscillatory velocity vector

u,v,w :

Subscripts used for velocity in x, y and z directions

\({\xi}\) :

Instantaneous wave profile

p :

Total pressure

\({\kappa}\) :

Wave number

\({\beta}\) :

Heading angle

Z :

Complex points on the body surface

Z o :

Complex points in the fluid water domain

\({\sigma R, D}\) :

Constant source strength

n :

Inward normal

A i,j , B i,j :

Added mass and damping coefficients

d :

Damping

m :

Added mass

N :

Calculated numerically

O :

Experimental data

b :

Node points on the body

r :

Complex data (gain)

i :

Complex data (imaginary)

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Authors and Affiliations

  1. Department of Industrial Manufacturing Engineering and Management, National University of Sciences and Technology, PN Engineering College, PNS Jauhar, Karachi, Pakistan

    M. Saeed Khalid & Salman Nisar

  2. Department of Naval Architecture and Marine Engineering, University of Michigan, Ann Arbor, MI, USA

    A. Troesch

Authors
  1. M. Saeed Khalid
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  2. Salman Nisar
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  3. A. Troesch
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Corresponding author

Correspondence to Salman Nisar.

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Khalid, M.S., Nisar, S. & Troesch, A. Radiation and Diffraction Velocity Potentials for Multi-hulled Vessels in 2-D. Arab J Sci Eng 41, 4573–4582 (2016). https://doi.org/10.1007/s13369-016-2184-5

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  • DOI: https://doi.org/10.1007/s13369-016-2184-5

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