Numerical Prediction of Steady Flow Around High Speed Vessels with Transom Sterns

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• Numerical Prediction of Steady Flow Around High
  Speed Vessels with Transom Sterns
• S.X. Du1,2, D.A. Hudson2, W.G. Price2, P.
  Temarel2 and Y.S. Wu1
• 1China Ship Scientific Research Center, Wuxi, PR
  China.
• 2School of Engineering Sciences, Ship Science,
  University of Southampton, Southampton, UK.

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Overview

• Introduction
• Mathematical Model
• Numerical Model of Transom Stern
• Mesh Generation
• Finite Element Analysis
• Variation of Appendage Shape
• Pressure Distribution and Wave Resistance
• Conclusions
• Future Work

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Motivation

• Accurate prediction of wave-making resistance
• Details of pressure and velocity distribution
  near stern
• Complex flow phenomena
• Require efficient method

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Modelling Philosophy

• Transom runs dry at high speed
• Extend idea of virtual appendage

• Use a flexible appendage
• Structural deformation with fluid pressure
• Iterate towards zero pressure on appendage
• Shape represents steady-state flow
• Three-dimensional Kelvin source for wave
  resistance of bodyappendage

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Mathematical Model (1)

• Assume potential flow
• Inviscid, homogenous, irrotational motion flow
• Outside stern region satisfy linear
  free-surface condition

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Mathematical Model (2)

• In stern region, free-surface condition is
  non-linear, giving

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Mathematical Model (3)

• Pressure given as,

• Giving wave resistance as,

• With,

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Modelling Requirements

• Flexible appendage must satisfy
• Continuous transition from transom stern to
  hollow cavity
• A local non-linear free-surface condition with
  atmospheric pressure in cavity
• A linear free-surface condition outside the
  hollow cavity region

• Appendage of Molland et. al. satisfies 1,3

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Modelling Flexible Appendage
Assume initial form of appendage
Until free-surface condition satisfied in cavity
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Application to Ship Hull

• NPL mono-hull chosen as demonstration

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Finite Element Analysis

• Three-dimensional beam framework
• Nodes coincide with hydrodynamic panel vertices
• Careful choice of Youngs modulus needed
• Maximum displacement limited
• Boundary condition at transom important

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Shape Variation of Appendage (1)
Flat-tailed appendage, Fn0.5
Step 7
Step 23
Step 15
Step 16
Step 7
Step 24
Canoe shape appendage, Fn0.5
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Variation With Forward Speed
Fn0.6
Fn0.5
Fn0.9
Fn0.7
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Pressure Distribution (1)
Step 1
Step 7
Step 23
Step 15
Pressure distribution adjacent to transom stern
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Pressure Distribution (2)
Initial step
x0.04
x0.006
x0.02
Final step
Pressure distribution at transverse hull sections
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Wave Resistance
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Summary

• Method developed to predict flow around transom
  sterns running dry
• Source distribution over hull and appendage
• Combined with finite element analysis for
  deformation of appendage
• Application to NPL hull form

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Conclusions

• Beam FE model better than shell model
• Good agreement for wave resistance
• Improved evaluation of velocity and pressure
  around hull
• Important when accounting for influence of steady
  flow in unsteady hydrodynamic problem

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Future Work

• Extend method for sinkage and trim calculation
• Include more robust finite element model
• Application to fast catamaran hulls
• Validation with experimental data for
• Free-surface elevation
• Pressure distribution around hull
• Combine with seakeeping analysis