transom stern high speed vessel - thesis presentation

SEAKEEPING OF HIGH SPEED SHIPS WITH TRANSOM STERN AND

THE VALIDATION WITH

UNSTEADY WAVES AROUND SHIPS

Muniyandy ELANGOVAN

by

JAPAN

Social and Environmental Engineering

Introduction 1

Mathematical Formulation 2

Numerical Method 3

Experiments for the Validation of Seakeeping 4

Interaction Effect of Incident Wave in an Unsteady Wave 5

Seakeeping of High Speed Ship with Transom Stern 6

Conclusions 7

(ii) Trimaran

(i) Monohull

(ii) Unsteady wave measurement

Outline of the Presentation

(i) Hydrodynamic forces, motions and added wave resistance

1. INTRODUCTION

Aim/Purpose

• Passenger Comfort

• Safe Transport

• Accurate estimation of wave forces for structural analysis

• Prediction of operational behavior in bad weather

• Reduce the Engine power by reducing the resistance of hull

Needed Data • Ship Motions

• Hydrodynamic Forces

•Ship performance in calm water and waves

Ship Design

(Hull)

Ship Construction

Numerical Analysis

Seakeeping Analysis

Model Test

[Cheaper, less time, prototype, no limitation]

[Expensive, more time, model size, no. data points]

Real Fluid Problem

Continuity Equation

&

Navier Stokes Equation

Viscous Fluid

Laplace Equation

&

Bernoulli’s Equation

Irrotational

Inviscid

Constant density

Ideal Fluid

Physical Problem

Incompressible

Seakeeping Analysis – METHODs

Strip Method

[Ursell,F., 1949, Korvin-Kroukovski, B.V, 1949,

Tasai, F, 1959, Watanabe, Y., 1958 ]

Unified Theory, Enhanced Unified Theory

[Newman, J.N., 1978 , Kashiwagi,M.,1995]

High Speed Strip Theory

[Takaki, 1975, Chapman R.B, 1975., Maruo, 1960,

Saito et al., 1978]

2D

Green Function Method

[Inglis, R.B., & Price W.G, 1981, Kabayashi, M,

1981, Chang, 1977, Iwashita & Okhusu, 1989]

Rankine Panel Method

[Yasukawa, H. 1990, Sclavounos & Nakos, 1990,

Gadd, 1976, Dawson, 1977]

3D

Frequency Domain

Hybrid Method:

Rankine Panel Method & Green Function Method

[Iwashita, et. al.1993]

2D 3D CFD

[Sato, et. al. 1999, Weymouth, et al.2005,

Panahi, et al. 2009, Mutsuda et al. 2007]

Green Function Method

[Beck, R.F & Liapis, 1987, Powlowski and

Bass. 1991]

Rankine Panel Method

[Maskew, B.,1991,Nakos, et. al., 1993,

Yasukawa, H, 2002.]

3D

Time Domain

Hybrid Method:

Rankine Panel Method & Green Function Method

[Lin & Yue 1980, Kataoka & Iwashita. 2004]

Two dimensional potential solvers are fast and reliable for the

prediction of ship motion. When it comes to the local forces, it fails to

capture three dimensional effect.

(i)

The Green function method treats the problem in three dimensionally.

For the linear free surface, it gives good result, but it is difficult to get

the Green function for the nonlinear boundary conditions.

(ii)

In time domain, nonlinear forces can be analyzed but the computational

value is high and treatment of radiation condition also difficult. (iii)

Hybrid method also computational time is expensive and treatment of

radiation condition is difficult. It needs more memory in computer. (iv)

Considering the above points and the flexibility for the implementation

of free surface boundary condition and radiation condition, Rankine

panel method (RPM) is selected for the seakeeping analysis. In

frequency domain, weak nonlinear boundary condition can be applied.

(v)

(vi) Due to the development of numerical solver, it is equally important to

validate the result by the experimental results. Therefore, improvement

in the measurement system is also required. Unsteady wave is treated

as a higher level of local pressure estimation, which can be used for the

comparison with numerical results. Considering the needs, unsteady

wave measurement is identified to improve the measurement system.

Identification of solver and marine industry needs

Scope of Present Research

Presently, unsteady waves are measured by Okhusu’s method

[Okhusu, Kyusu University, Japan] to estimate the added wave

resistance. This formulation does not include the interaction term

between the incident wave and the steady wave. The interaction term is

derived, and effect is studied by applying to the modified Wigley hull.

(i)

To treat the transom stern condition, until now there is no proper

boundary condition to treat the transom stern by panel method. From

the experimental observations, a new boundary condition is derived to

treat the transom effect mathematically in numerical method.

(ii)

Transom boundary condition is applied to monohull and numerically

predicted hydrodynamic qualities have been compared with

experimental data for validation. This application has been extended for

trimaran as well.

(iii)

2. MATHEMATICAL FORMULATION

Governing Equation

Laplace Equation

2.1 Definition of Problem

Fig.1 Coordinate system n

(i) Body boundary condition

(ii) Free surface [KC & DC] (iv) Control Surface

(v) Bottom Surface

(iii) Radiation condition

2.2 Velocity Potential

Fig.2 Double body flow Fig.3 Uniform flow

where

Unsteady Velocity Potential

Total Velocity Potential

, ,

(i) Double Body Flow Potential

(ii) Steady Velocity Potential

Free Surface

Hull Surface

Free Surface

Hull Surface

2.3 Boundary Value Problem

(iii) Steady Velocity Potential

[Baba, E., 1976]

DBF

NK

Free Surface

Hull Surface

(i) Unsteady Velocity Potential [Yasukawa, H, 1990]

[Timman & Newman, 1962]

2.3 Boundary Value Problem (Cont.)

DBF

NK (ii) Unsteady Velocity Potential

where ,

,

(i) Steady wave

(ii) Steady pressure

(iii) Steady forces and moment

2.4 Hydrodynamic Parameters

(iv) Unsteady Wave

(v) Unsteady Pressure

2.4 Hydrodynamic Parameters (Cont.)

where

where

,

,


(vi) Added mass and Damping Coefficient

(vii) Wave Exciting Forces and Moments


(viii) Ship motion

where

,

3. NUMERICAL METHOD

3.1 Computation of Velocity Potential

(i) Direct Method

(i) Indirect Method

where ,

Q = (0, 0, -d)

L = 2.0 m

d = L / 10 = 0.2 x

y

z

Fig.4 Free surface with point source

3.2 Point Source Problem

[ Bessho, M., 1977] (i) Analytical Formulation

where

where

Green Function

Wave Term

3.2 Point Source Problem (Cont.)

,

[Bertram, V, 1990] (ii) RPM – Panel Shift Method

Velocity Potential

Free Surface

Integral Equation


[Scalvounos & Nakos, 1990] (ii) RPM – Spline Interpolation Method

Velocity Potential on the free surface

Radiation condition

Integral Equation


Fig. 5 RPM-PSH: Wave pattern at Fn = 0.2, Ke L =5.0, t = 0.447

3.3 Numerical Results

RPM-PSM RPM-SIM

Fig. 6 Wave pattern at Fn = 0.2, Ke L =5, t = 0.447

RPM-PSM RPM-SIM

3.3 Numerical Results (Cont.)

Fig.7 RPM-SIM: Wave pattern at Fn = 0.2, Ke L =30, t = 1.095


RPM-PSM RPM-SIM

Fig. 8 Wave pattern at Fn = 0.2, Ke L =30, t = 1.095

RPM-PSM RPM-SIM


3.4 Integral Equation for Ship

Velocity Potential

Integral Equation

where

,

4. EXPERIMENTS FOR THE VALIDATION OF SEAKEEPING

Unsteady waves are generated by both the diffraction of incident

wave and the motions of the ship due to the incident waves

1

Unsteady Wave Measurement

Okhusu proposed a method for measuring ship generated unsteady

waves and the evaluating the wave amplitude function which can be

used for estimation of added wave resistance.

3

Unsteady wave patterns physically show the pressure distributions

over the free surface that can be considered as local physical value.

This unsteady wave is superior to pressure measurement on the hull

surface from the point of view of the cost and the convenience.

Therefore it is valuable to utilize the unsteady waves in order to

validate the numerical computation methods more precisely.

2

Unsteady wave measurement analysis is made considering the

number of wave probes and the unsteady wave second order term

4

4.1 Introduction

Fig.9 Layout of ship motion, forces and moment measurement system

(a) Motion free measurement setup (b) Forced motion measurement setup

Fig. 10 Diagram - Unsteady wave measurement arrangement

Wave Probes

4.2 Unsteady wave measurement

2nd order wave

1st order wave Steady wave

Total wave (i) Steady wave, (ii) Diffraction wave, (iii) Radiation wave

(3 unknowns)

(5 unknowns)

4.2 Unsteady wave measurement (Cont.)

(i) Total wave (up to 1st order)

(ii) Total wave (up to 2nd order)

4.2 Unsteady wave measurement (Cont.)

where

Modified Wigley hull(blunt) mathematical expression

Fig. 11 Plan view of the modified Wigley hull

Fig. 12 Wave probe dependency study

at y/(B/2)=1.4; Fn=0.2, l/L=0.5, c=p

4.3 Experimental Results

Fig. 13 Diffraction wave - 2nd order term

at y/(B/2)=1.4; Fn=0.2, l/L=0.5, c=p

4.3 Experimental Results (Cont.)

5. INTERACTION EFFECT OF INCIDENT WAVE

IN AN UNSTEADY WAVE

Okhusu proposed unsteady wave measuring method, which does not

include the interaction term of the incident wave and steady wave.

1

Interaction effect of Incident wave in an Unsteady wave

Here, interaction term formulation is carried out to see the influence

of incident wave and steady wave in the unsteady wave analysis by

computed DBF and measured NK wave.

2

Hydrodynamic forces, moment, ship motions and waves are

numerically computed and compared with an experimental result to

validate the Rankine panel computational code.

3

5.1 Introduction

5.2 Influence of Steady and Incident wave in an Unsteady wave

(ii) Unsteady wave elevation

where

,

(iii) Unsteady wave elevation (diffraction)

where ,

(i) Measured unsteady wave

5.3 Treatment of influence term in Numerical Method

(i) Double body flow formulation

(ii) Neumann Kelvin formulation

then,

then, ,

Unsteady wave elevation

Unsteady wave elevation

Interaction Term

DBF

[Double body flow formulation]

Fig. 14 Perspective view of modified Wigley hull

5.4 Treatment of influence term in DBF

Fig. 15 Interaction between Double body flow and Incident wave

at y/(B/2)=1.4; Fn=0.2, l/L=0.5, c=p

5.4 Treatment of influence term in DBF (Cont.)

Interaction Term

[Neumann Kelvin formulation]

at y/(B/2)=1.4; Fn=0.2

NK

Fig. 16 Measured steady wave

5.5 Treatment of influence term in NK

Fig. 17 Interaction effect between Kelvin wave and Incident wave

at y/(B/2)=1.4; Fn=0.2, c=p

l/L=0.5 l/L=0.6

l/L=0.7

NF = 140 x 38 = 5230

NH = 70 x 20 = 1400

Fig. 18 Perspective view of modified Wigley hull

5.6 Computational Domain

Fig. 19 Computational grid

Fig. 20 Steady Kelvin wave pattern of modified Wigley model (blunt) at Fn=0.2

5.7 Numerical and Experimental Result (Cont.)

Fig. 21 Added mass and damping coefficient due to

forced heave motion at Fn=0.2

5.7 Numerical and Experimental Result

Fig. 22 Added mass and damping coefficient due to

forced pitch motion at Fn=0.2


Fig. 23 Wave exciting forces and moments at Fn=0.2, c=p


Fig. 24 Ship motions at Fn=0.2, c=p.


Fig. 25 Heave radiation wave at Fn=0.2, KL = 30


Fig. 26 Diffraction wave at Fn=0.2, l/L=0.5, c=p


Fig. 27 Heave radiation wave at y/(B/2)=1.4 for Fn=0.2, KL = 30, 35

Fig. 28 Diffraction wave at y/(B/2)=1.4 for Fn=0.2, l/L=0.5 , 0.7, c=p


[forced motion, | x3 |=0.01m, | x5|=tan^(0.01/0.42), |x7|=0.01 m]

Fig. 29 Total unsteady wave at y/(B/2)=1.4 for Fn=0.2, c=p

5.8 Influence of Amplitude of Incident wave

l/L=0.7

l/L=0.9

[forced motion, | x3 |=0.01m, | x5|=tan^(0.01/0.42), |x7|=0.01 m]

5.8 Influence of Amplitude of Incident wave (Cont.)

Fig. 30 Total unsteady wave at y/(B/2)=1.4 for Fn=0.2, c=p

l/L=1.1

l/L=1.4

[Maruo, H, 1960]

[Okhusu, M, 1977]

(i) Added Wave Resistance

(i) Kochin Function

5.9 Estimation of Added wave Resistance

where

where ,

at y/(B/2)=1.4; Fn=0.2, l/L=0.5, c=p

Fig. 31 Kochin function computed with diffraction wave

5.9 Estimation of Added wave Resistance (Cont.)


Fig. 32 Added wave Resistance at Fn=0.2, c=p

Steady wave resistance (average) = 0.4382 kgf, L = 2.5 m


Fig. 33 Added wave Resistance at Fn=0.2, c=p

Steady wave resistance (average) = 0.4382 kgf, L = 2.5 m

Derived interaction effect of incident wave and steady wave in the unsteady

wave have been applied for unsteady wave analysis in various ways

1). Influence of 2nd order term in the wave. - not dominant

2). Interaction effect between double body flow and incident wave. – small

3). Interaction effect between Kelvin's wave and incident wave – Remarkable

1

Steady wave, diffraction wave, radiation wave and unsteady pattern which are

numerically computed are compared with experimental data, and it is matching

well with experiment. Only in the amplitude, there is a small difference.

2

The experiments were carried out for a modified Wigley model and the obtained

results of hydrodynamic forces, ship motions, unsteady wave fields and added

wave resistance were used for the validation of the present RPMs. Through the

comparisons, it was confirmed that the present RPM code is effective for the

seakeeping estimations.

3

5.10 Concluding Remarks

6. SEAKEEPING OF HIGH SPEED SHIP WITH TRANSOM STERN

TRANSOM STERN BOUNDARY CONDITION

HIGH SPEED - MONOHULL

To treat the transom stern condition, until now there is no

proper boundary condition to treat the transom stern by panel

method. A new boundary condition is derived from the

experimental observation to treat the transom effect

mathematically in numerical method.

1

Transom stern Boundary Condition

6.1 Introduction

(i) Steady Problem

Steady Velocity Potential

[Hughes & Bertram, V, 1995]

Fig. 34 Transom steady wave

6.2 Transom stern boundary condition

(ii) Unsteady Problem

Monohull in the Experimental Lab.

Unsteady Velocity Potential

Fig. 35 Snap shot of the transom stern in the motion measurement test

Total wave – smoothly separating from the dry transom

(i) Diffraction Velocity Potential

Diffraction wave plus incident wave is equal to zero

6.3 Formulation of Transom stern condition

(ii) Radiation Velocity Potential

At Transom: Unsteady wave elevation = Vertical unsteady displacement

Only z comp.

where

6.3 Formulation of Transom stern condition (Cont.)

Fig. 36 Treatment of Transom stern boundary condition

6.4 Treatment of Transom stern condition (Cont.)

Monohull

Fig. 37 Plan view of the monohull

6.5 Hull Data

NH = 1480 (74 x 20)

NF = 3888 (162 x 24)

NFA = 297 (99 x 3)

Fig. 39 Computational Grids

Fig. 38 Perspective view of Monohull

6.5 Hull Data (Cont.)

Fig. 40 Steady wave at Fn = 0.5 Fig. 41 Measured sinkage and trim

6.6 Numerical and Experimental Result

Fig. 42 Added mass and damping coefficient due to forced heave motion at Fn=0.5


Fig. 43 Added mass and damping coefficient due to forced pitch motion at Fn=0.5


Fig. 45 Ship motions at Fn=0.5, c=p.


Fig. 46 Wave pressure on the hull at Fn=0.5, l/L=1.1, c=p


Fig. 47 Total unsteady pressure at Fn=0.5, l/L=1.1, c=p


Fig. 48 Wave pressure at Fn=0.5, l/L=1.1, c=p


at Fn=0.5, KL=30, x3 = 0.02 m

Fig. 50 Comparison of measured and computed wave pattern

at Fn=0.5, l/L=0.7, c=p, H/l=1/20

Fig. 51 Comparison of measured and computed wave at y/(B/2) = 1.52

at Fn=0.5, KL=30,

x3 = 0.02 m

at Fn=0.5, l/L=0.7,

c=p

Fig. 52 Added wave resistance (Fn=0.5, c=p) with transom and sinkage & trim effect


HIGH SPEED - TRIMARAN

INCLUDE TRANSOM STERN BOUNDARY CONDITION

Trimaran

Fig. 53 Plan view of Trimaran

6.7 Hull Data


Fig. 54 Perspective view of Trimaran

6.7 Hull Data (Cont.)

Fig. 56 Steady Kelvin wave pattern at Fn = 0.5

6.8 Numerical and Experimental Results

6.8 Numerical and Experimental Results (Cont.)

Fig. 58 Steady pressure on the hull at Fn = 0.5 Fig. 57 Steady wave view at Fn = 0.5

Fig. 59 Added mass and damping coefficient due to forced heave motion at Fn=0.5


Fig. 60 Added mass and damping coefficient due to forced pitch motion at Fn=0.5


at Fn=0.5, KL=30, x3 = 0.02 m

Fig. 62 Heave Radiation wave


Fig. 63 Diffraction wave

at Fn=0.5, l/L=0.7, c=p, H/l=1/20



Fig. 64 Perspective view of Monohull

6.9 Hull Data

(Sinkage and Trim)

Fig. 66 Ship motion at Fn=0.5, c=p.

6.10 Numerical and Experimental Results

Fig. 67 Wave pressure on the hull at Fn=0.5, l/L=1.1, c=p

(with TSC, sinkage and trim effect) (with TSC, without sinkage and trim effect)


(with TSC, sinkage and trim effect) (with TSC, without sinkage and trim effect)



Numerically computed results of hydrodynamic forces, ship motions,

unsteady wave fields and added wave resistance were compared with

experiment and good agreement is observed.

2

6.11 Concluding Remarks

Transom stern boundary condition is derived based on the experimental

observation and applied for high speed monohull 1

In the Kochin function calculation for the added wave resistance, the

amplitude of H1 is less than 10% of H2 for the conventional ships advancing

at low forward speed. It is easily noticed that the amplitude of H1 is larger

than that can be seen in the conventional ships. It is suggested that the

contribution of H1 is valuable for the added wave resistance estimation.

4 The accuracy of the seakeeping estimations was fairly improved by taking

account of the effect of the sinkage and trim incorporated with the present

transom stern condition

3

Transom condition is applied for the trimaran and predicted hydrodynamic

forces are showing good agreement with experimental result

Sinkage and trim also considered for numerical calculations of wave

pressure and unsteady pressure and compared with experimental results.

Influence of main hull is observed in the outriggers in pressure plot.

5

6

7. CONCLUSIONS

CONCLUSIONS

The interaction effect between the incident wave and double-body flow in

steady flow is not remarkable. The consideration of its effect scarcely

affects the analyzed diffraction wave.

1.

In the analysis of diffraction wave, the effect between the incident wave

and the steady Kelvin wave is remarkable, and the effect can be also

confirmed in the Kochin function. This affects the estimation of the added

wave resistance about 4% in magnitude.

2.

The experiments were carried out for a modified Wigley model and the

obtained results of hydrodynamic forces, ship motions, unsteady wave

fields and added wave resistance were used for the validation of the

present RPMs. Through the comparisons, it was confirmed that the

present RPMs are effective for the seakeeping estimations.

3.

CONCLUSIONS (Cont.)

A flow model was proposed to satisfy the phenomena denoted in point 4.,

and a corresponding boundary condition was derived.

5.

It was confirmed that the Rankine panel method with transom stern

condition well explains the experimental results. Additionally, the

accuracy of the seakeeping estimations was fairly improved by taking

account of the effect of the sinkage and trim incorporated with the

present transom stern condition.

6.

The proposed method is applied to the trimaran and the results are

compared with experiments. The effect of sinkage and trim is taken into

account with the transom stern condition. The comparisons of obtained

results with experiments show good agreements for the trimaran.

Interaction effect between the main hull and outriggers are observed

around stern part only in the unsteady pressure distributions.

7.

From the high speed monohull analysis, It was confirmed from the

present experiments (H/l=1/50) that the transom stern was completely

dry even when the ship is freely oscillating in waves provided that ship

advances at high speed. All the waves that consist of the incident wave,

steady wave, radiation waves and diffraction wave flow away smoothly

from the bottom part of the dry transom stern.

4.

Thank You

transom stern high speed vessel - thesis presentation

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seakeeping of high speed