Numerical Prediction of Steady Flow Around High Speed Vessels with Transom Sterns S.X. Du 1,2, D.A....
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Transcript of Numerical Prediction of Steady Flow Around High Speed Vessels with Transom Sterns S.X. Du 1,2, D.A....
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.
OverviewOverview
• 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
MotivationMotivation
• Accurate prediction of wave-making resistance
• Details of pressure and velocity distribution near stern
• Complex flow phenomena
• Require efficient methodCompromise between theoretical rigour and
practical computational method
Modelling PhilosophyModelling 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 body+appendage
Mathematical Model (1)Mathematical Model (1)
• Assume potential flow– Inviscid, homogenous, irrotational motion flow
• Outside stern region – satisfy linear free-surface condition
0on 0 02
22
zzx
Fn
0 nWBody boundary condition
Kelvin wave source potential on surface of hull and appendage
Mathematical Model (2)Mathematical Model (2)
• In stern region, free-surface condition is non-linear, giving
0 where021
),(21 2 apFnyxaWW
),(on 0 0 yxaz nW
)(
),(
xFn
gLUFn
yxa
W
giving ,
stern transomdry the behind surface free the is
Mathematical Model (3)Mathematical Model (3)
• Pressure given as,
pFnz 2
21
21
WW
• With,
SU
RC ww 2
21
• Giving wave resistance as,
.21
21 23 dsnFnzgLR x
Sw
b
WW
Modelling RequirementsModelling Requirements
• Flexible appendage must satisfy1. Continuous transition from transom stern
to hollow cavity
2. A local non-linear free-surface condition with atmospheric pressure in cavity
3. A linear free-surface condition outside the hollow cavity region
• Appendage of Molland et. al. satisfies 1,3
Modelling Flexible AppendageModelling Flexible Appendage
Assume initial formof appendage
Calculate velocity and pressure distribution
Use pressure to deformappendage shape
Re-mesh appendage Until free-surfacecondition satisfied
in cavity
Application to Ship HullApplication to Ship Hull
• NPL mono-hull chosen as demonstration
L(m) L/B B/T CB CP S(m2)
1.6 9.0 2.0 7.42 0.397 0.693 0.338
31L
‘Flat-tailed’ appendage
‘Canoe-shaped’ appendage
Finite Element AnalysisFinite Element Analysis
• Three-dimensional beam framework
• Nodes coincide with hydrodynamic panel vertices
• Careful choice of Young’s modulus needed
• Maximum displacement limited
• Boundary condition at transom important
Shape Variation of Appendage (1)Shape Variation of Appendage (1)
Step 7
Step 7
Step 15 Step 23
Step 16 Step 24
Flat-tailed appendage, Fn=0.5
Canoe shape appendage, Fn=0.5
Pressure Distribution (1)Pressure Distribution (1)
Step 7
Step 15 Step 23
Step 1
Pressure distribution adjacent to transom stern
Pressure Distribution (2)Pressure Distribution (2)
Pressure distribution at transverse hull sections
x’=0.006 x’=0.02 x’=0.04
Initial step
Final step
SummarySummary
• 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
Conclusions 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