NUMERICAL SIMULATION OF HIGH SPEED SHIP WASH WAVES Kunihide Ohashi, National Maritime Research Institute, Japan Jun Hasegawa, National Maritime Research Institute, Japan Ryohei Fukasawa, National Maritime Research Institute, Japan

SUMMARY

An investigation of wash waves of a high speed craft is carried out. At first, the measurement of wave height using three wire resistance probes is carried out. Each probe is placed at the different position from the ship center line. These measurements are carried out in deep and shallow water conditions. The quantity of trim and wash wave height in deep and shallow conditions is discussed. Next, the numerical simulation of wash waves is carried out. A CFD codes which has developed in NMRI is applied to the prediction of wash waves. The wave height distribution is obtained by re-generation of computational grid from reference grid. The reference computational grid covers very wide domain to resolve the wash waves. Longitudinal wave profile is compared with measured result. Through the comparison of computed and measured results, the applicability of the present method is discussed. 1. INTRODUCTION The operation of high speed craft may be constrained in lower speed to avoid the creation of high wash waves. It would be useful to be able to predict wash waves before the craft in service. Many efforts are being made for understanding of wash waves in deep and shallow water conditions.(1)(2)(3) In the present study, an investigation of wash waves of high speed craft is carried out. Present investigation is mainly to establish an operational guide for crew. At first, measurement of wash waves is carried out. Wash waves in deep and shallow water conditions are measured. The measurement results of trim and sinkage are used in numerical simulation. Next, the numerical simulation of wash waves using computational fluid dynamics is carried out. To treat a transom stern, some modeling is needed. A ship stern is extended to ship aft as if a ship hull is existed. Through the comparison of computed and measured results, applicability of present method is examined. 2. MEASUREMENT OF WASH WAVES 2.1 SHIP MODEL The ship model is high speed craft with single chain type. Main particulars of ship and model are listed in Table 1.

Table 1 Main particulars The material of model is wood, and as appendages, shaft brackets and shafts are attached. 2.2 MEASUREMENT SYSTEM The measurements at deep water condition are carried out in the #2 towing tank of NMRI. The dimensions of the tank are, length 400m, width 24m and depth 8m. Resistance wire probes for measurement of wash waves are positioned 2.0m(y/L=0.792), 3.0m(y/L=1.192), 6.0m (y/L=2.396) from the center line of model (Figure 1). Forward speed of carriage is from abt. 2.0m/s (Fn=0.4) to

abt. 7.0m/s (Fn=1.4). Froude number Fn is based on ship length L. The measurements are carried out in these speed, wave disturbance of tank wall is eliminated in analysis.

Figure 1 Layout of probes with ship model (Deep water)

The model is towed at sinkage and trim freed condition. The towing rod is set to longitudinal center buoyancy, and the rod angle is adjusted to shaft angle while the measurement. The laser distance meter is used to determine exact moment when the model passed the wave measurement probes. Reflective plate is attached to carriage, when the carriage passed at the point of laser distance meter, pulse is marked and recorded in the measurement system. Near stern wave measurement is also carried out in deep water condition. Wave height is measured by servo type which the probe heaves with wave surface. Measurement results are used for modeling of transom stern in computation. The measurements in shallow water condition are carried out in the #3 towing tank of NMRI. The dimensions of the tank are, length 150m, width 12m. Depth is examined with real sea, then decided to 0.64m. Measurements are almost as same as deep water condition, except for the number and position of probe, and carriage speeds. Only one probe is used for this measurement, and is positioned at 1.0m (y/L=0.416) from the center line of model (Figure 2). Forward speed of carriage is from abt. 2.0m/s (Fn=0.4) to abt. 4.5m/s (Fn=0.9) which are determined by the examination of the shallow water effect based on depth Froude number

ghVFnh /= (Figure 3). h is a depth of water.

Model Ship Loa(m) 2.702 20.0 B(m) 0.608 4.5 D(m) 0.311 2.3

2m

12m

Tank side wall

Ship model 3m

6m

291

-7.00

-6.00

-5.00

-4.00

-3.00

-2.00

-1.00

0.00

0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60Fn[-]

Trim [%L]

Deep Water

Shallow Water

0.00

0.20

0.40

0.60

0.80

1.00

2 3 4 5 6 7 8 9 10

FnH=0.7FnH=1.0Fn based carriage speed

depth of water(m)

Fn

7.0=hFn means the point where the shallow water effect begins to appear. 0.1=hFn means critical speed which the wash waves height increases dramatically.

Figure 2 Layout of probes with ship model

(Shallow water)

Figure 3 Shallow water effect

2.3 MEASUREMENT RESULTS Figure 4 and Figure 5 show the measurement trim and sinkage. Aft trim and sink are positive. Fore trim of shallow water is larger than trim of deep water in lower Froude number. Also sinkage of shallow water becomes larger. Figure 6 shows measurement results of wash wave height in deep water condition. x/L=0 means fore perpendicular of the ship. It is clearly seen wash waves are consisted from bow and stern waves etc. Figure 7 shows measurement results of wash wave height in shallow water condition. Wash waves are available in two velocities due to the tank wall reflection.

Figure 4 Measured result of trim(%L)

-2.50

-2.00

-1.50

-1.00

-0.50

0.00

0.50

1.00

0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60

Fn[-]

Shinkage [%L]

Deep Water

Shallow Water

Figure 5 Measured result of sinkage(%L)

Fn=0.4

-0.040

-0.030

-0.020

-0.010

0.000

0.010

0.020

0.030

0.040

-5 0 5 10 15 20 25

x/L(FP 0)

Wave height h/L

y/L=0.792y/L=1.192y/L=2.396

1m

6m

Tank side wall

Ship model

292

Fn=0.5

-0.040

-0.030

-0.020

-0.010

0.000

0.010

0.020

0.030

0.040

-5 0 5 10 15 20 25

x/L(FP 0)

Wave height h/L

y/L=0.792

y/L=1.192

y/L=2.396

Fn=0.6

-0.040

-0.030

-0.020

-0.010

0.000

0.010

0.020

0.030

0.040

-5 0 5 10 15 20 25

x/L(FP 0)

Wave height h/L

y/L=0.792y/L=1.192y/L=2.396

Figure 6 Wash wave measurement result (Deep water)

Fn=0.4

-0.040

-0.030

-0.020

-0.010

0.000

0.010

0.020

0.030

0.040

-5 0 5 10 15 20 25

x/L(FP 0)

Wave height h/L

Fn=0.45

-0.040

-0.030

-0.020

-0.010

0.000

0.010

0.020

0.030

0.040

-5 0 5 10 15 20 25

x/L(FP 0)

Wave height h/L

Figure 7 Wash wave measurement result (Shallow water)

Tank side wall reflection

Tank side wall reflection

293

3. NUMERICAL SIMULATION 3.1 CFD CODE The flow solver used in this study is called NEPTUNE(4) which is under development at National Maritime Research Institute. The governing equations are 3D Reynolds averaged Navier-Stokes equations for incompressible flows. Coupling between pressure and velocity is made by artificial compressibility approach. The final form can be written as follows.

0=∂

)-(∂+

∂

)-(∂+

∂

)-(∂+

∂

∂

zgg

yff

xeeq ννν

t (1)

and Twvup ][=q

In the above, all variables are non-dimensionalized using the reference density 0ρ , velocity 0U and length 0L . The velocity components (x,y,z) direction are expressed as (u,v,w). The inviscid fluxes e, f and g, viscous fluxes ev, fv and gv are defined as,

uwuvpuuβ+

=2

e ,

vwpv

uvvβ

+= 2f ,

pwvwuwwβ

+

=

2

g (2)

zx

xy

xxv

τττ0

=e ,

yz

yy

xyv

τττ0

=f ,

zz

yz

zxv

τττ0

=g

where β is a parameter for artificial compressibility and ( ) ( )ijjitij xuxuνRτ ∂/∂+∂/∂+/1= . R is Reynolds

number defined as νLU /00 where ν is the kinematic viscosity. tν is the non-dimensional kinematic eddy viscosity which is determined by the Spalart-Allmaras one equation model. Spatial discretization is based a structured cell-centered finite volume method. Inviscid fluxes are evaluated by the Roe scheme and MUSCL extrapolation is adopted to attain the third order accuracy, while viscous fluxes are centrally differenced. The equation is solved by an approximate Newton relaxation method with a symmetric Gauss Seidel iterative approach. The code employs multigrid approach and local time stepping method to accelerate convergence to a steady state solution The nonlinear free-surface conditions are implemented and re-gridding technique is used to treat the free-surface deformation. 3.2 COMPUTATIONAL GRID AND CONDITIONS Figure 8 and Figure 9 show the computational grids. Computational domain and grid detail are listed in Table 2.

XY

Z

Ship hull

Figure 8 Computational grid near hull(deep water)

XYZ

Bottom of domain

Ship hull

Figure 9 Computational grid near hull(shallow water)

Table 2 Computational domain and grid detail

The computational domain covers the wash waves. Minimum spacing is 5×10-3 at FP, 1×10-2 at AP and 1×10-2 in normal directions. Froude number is set to Fn=0.4, 0.5, 0.6. Trim and sinkage of measurement results are used in each case. Thus ship trim and sinkage are fitted to measurement result. A transom stern of the ship is treated by the extension of ship hull to backward of ship. The amount of this extension is examined by the comparison of wave height where the right after the ship. In the case of Fn=0.4, the amount of extension is 5%L, 10%L in Fn=0.5 and 20%L in Fn=0.6 respectively. In the case of shallow water, boundary condition at bottom of computational domain is 0=∂/∂ np and

Computational Domain

-1.5≤x≤11.0 -5.0≤y≤0.0(Deep water) -7.0≤y≤0.0(Shallow water) -1.9≤z≤0.12(Deep water) -0.27≤z≤0.12(Shallow water)

Grid points 415×33×281(Deep water) 415×33×281(Shallow water)

294

(u,v,w)=(1,0,0). 3.3 RESULTS

Fn=0.4

-0.06

-0.05

-0.04

-0.03

-0.02

-0.01

0.00

0.01

0.02

0.03

0.04

1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8

x/L(from Ship Stern)

Wave height h/L

Measured y/L=0

Measured y/L=0.592

Computed y=0

Computed y/L=0.592

Fn=0.6

-0.06

-0.05

-0.04

-0.03

-0.02

-0.01

0.00

0.01

0.02

0.03

0.04

1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9

x/L(from Ship Stern)

Wave height

h/L

Measured y/L=0

Measured y/L=0.592

Computed y=0

Computed y/L=0.592

Figure 10 Comparison of near stern wave profile

Figure 10 shows comparison of near stern wave profile. Computed results show good agreement with measurement results, thus present amount of extension of ship hull can be used for prediction of wash waves. Figure 11 and Figure 12 show comparison of wash wave profile in deep water condition. Computed results show agreement with measured result except y/L=2.396 in Fn=0.4. The deviation may be caused by the divergence of wave height. Figure 13 shows comparison of wave profile in shallow water condition. Computed results show agreement with measured results and simulate the crests decay well. From Figure 14 to Figure 19 show the computed wave contour in deep and shallow water conditions. Waves are diverged with Kelvin wave angle in deep water condition. On the other hand, waves in shallow water conditions show quite unique characteristics. Large transverse waves are generated in Fn=0.5 which is a critical speed. As in the case of Fn=0.6 which is supercritical speed, wave length become longer. Finally, Figure 20 shows the comparison of maximum wave height. The maximum wave height is defined as the largest wave height in measured and computed results. Computed results show agreement with the measured results. Also, Computed results of wave height become large at the critical speed in shallow water condition. 4. CONCLUSION Measurement and prediction of wash waves have been carried out. Computed results show agreement with

measured results. Present prediction method is practical one but give useful information about wash waves. Although Sinkage and trim data are needed for present method, these data can be estimated by an empirical method or simulated directly in computation in near future. 5. ACKNOLEDGEMENT Japan Coast Guard and Sumidagawa Shipyard Co, .Ltd. have sponsored this research, and are thanked to their permission for this publication. REFERENCES 1. Whittaker, J.T., Doyle, R., Elasser, B., ’A Study of the Leading Long Period Waves in Fast Ferry Wash’, Hydrodynamics of High Speed Craft Wake Wash & Motion Control, RINA International Conference, 2000 2. Raven, H.C., ’Numerical Wash Prediction using a Free-Surface panel Code’, Hydrodynamics of High Speed Craft Wake Wash & Motion Control, RINA International Conference, 2000 3. Keuning, J.A., Visser, D.B., ’An Approximation Method For th Wake Wash of Planing of Monohulls’, Hydrodynamics of High Speed Craft Wake Wash & Motion Control, RINA International Conference, 2000 4. Hirata, N., Hino, T., ’An Efficient Algorithm for Simulating Free-Surface Turbulent Flows around an Advancing Ship’, Journal of the Society of Naval Architects of Japan, Vol.185, 1999

295

Fn=0.4

-0.040

-0.030

-0.020

-0.010

0.000

0.010

0.020

0.030

0.040

-5 0 5 10 15 20 25

x/L(FP 0)

Wave height h/L

Measured y/L=0.792

Computed y/L=0.792

Fn=0.4

-0.040

-0.030

-0.020

-0.010

0.000

0.010

0.020

0.030

0.040

-5 0 5 10 15 20 25

x/L(FP 0)

Wave height h/L

Measured y/L=1.192

Computed y/L=1.192

Fn=0.4

-0.040

-0.030

-0.020

-0.010

0.000

0.010

0.020

0.030

0.040

-5 0 5 10 15 20 25

x/L(FP 0)

Wave height h/L

Measured y/L=2.396

Computed y/L=2.396

Figure 11 Comparison of wave profile(Deep water, Fn=0.4)

296

Fn=0.6

-0.040

-0.030

-0.020

-0.010

0.000

0.010

0.020

0.030

0.040

-5 0 5 10 15 20 25

x/L(FP 0)

Wave height h/L

Measured y/L=0.792

Computed y/L=0.792

Fn=0.6

-0.040

-0.030

-0.020

-0.010

0.000

0.010

0.020

0.030

0.040

-5 0 5 10 15 20 25

x/L(FP 0)

Wave height h/L

Measured y/L=1.192

Computed y/L=1.192

Fn=0.6

-0.040

-0.030

-0.020

-0.010

0.000

0.010

0.020

0.030

0.040

-5 0 5 10 15 20 25

x/L(FP 0)

Wave height h/L

Measured y/L=2.396

Computed y/L=2.396

Figure 12 Comparison of wave profile(Deep water, Fn=0.6)

297

Fn=0.4

-0.040

-0.030

-0.020

-0.010

0.000

0.010

0.020

0.030

0.040

-5 0 5 10 15 20 25

x/L(FP 0)

Wave height h/L

Measured y/L=0416Computed y/L=0416

Figure 13 Comparison of wave profile(Shallow water, Fn=0.4)

Figure 14 Computed wave contour (Deep water, Fn=0.4)

Figure 15 Computed wave contour (Shallow water, Fn=0.4)

298

Figure 16 Computed wave contour (Deep water, Fn=0.5)

Figure 17 Computed wave contour (Shallow water, Fn=0.5)

Figure 18 Computed wave contour (Deep water, Fn=0.6)

299

Figure 19 Computed wave contour (Shallow water, Fn=0.6)

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Fn

Maximum wave height (hmax/L)

Measured y/L=0.792(Deep water)Measured y/L=1.192(Deep water)

Measured y/L=2.396(Deep water)Measured y/L=0.416(Shallow water)

Computed y/L=0.792 (Deep water)Computed y/L=1.192 (Deep water)Computed y/L=2.396 (Deep water)

Computed y/L=0.416 (Shallow water)

Figure 20 Comparison of maximum wave height

300