Shallow water effects for SWATH ships

Volker Bertram, Institut fürSchiffbau' Walter Grollius, Duisburg Model Basin for Inland Water

Lämmersieth 90, D-22305 Hamburg, Germany

2Klöcknerstr. 77, D-47057 Duisburg, Germany

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Shipbuilthng-1. Introduction

SWATH (small waterplane area twin hull) ships are designed for good seakeeping even ;t high speeds. Shallow water effects can be important for SWATH ship operations if fast

SWATH ships operate in coastal areas or rivers. Existing SWATH ships with a displacement of more than 100 tons can be classified into two groups: slow SWATH ships operating at Froude numbers 0.2 F < 0.3 and fast SWATH ships operating at Froude numbers 0.7 < F,, < 0.8,

Bertram (1993). Fast SWATH ships are usuallyrelatively small (less than 400 tons) and used

as passenger ferries. These fast ferries for short or medium distances operate in coastal areas

where the depth limitationaffects the hydrodynamics Questions arising in this context are:

How does the resistance increase? How does sinkage increase?

How does the trim momentchange?

Traditional model experiments to answer these questions are time-consuming and costly. Could a computational method be a substitute ofsufficient accuracy? Previous SWATH corn-putations on deep water showed recent improvements in predicting capabilities even though

fully nonlinear solutions were not possible due tobreaking waves, Bertram (1993). Computa-tions for slow ships in shallow water even with side walls captured major effects well but our experience was limited to under-critical speeds (Froudenumber based on water depth smaller

than 1). Therefore, computations for a SWATH ship on shallow water were now compared to model experiments for a wide range of depth Eroude numbers F,11 covering under- and

over-critical speeds. Computations were performed before model tests.

2. Computational

Method

The computational method considers the steady flow of an ideal fluid around a twin-hull ship. The field equation for this potential flow is Laplace's equation that holds everywhere in the fluid domain. A well-posed problem formulation requires additional boundary conditions:

Water does not penetrate the wetted hull surface (Neumann condition) Water does not penetrate the bottom of the sea(Bottom condition) Water does not penetrate the water surface (Kinematic condition) There is atmospheric pressure at the water surface (Dynamic condition) The ship is in equilibrium(Equilibrium condition)

At the end of the strut the flow separates (Kutta condition)

Waves appear only in a sector behind the ship (Radiation condition)

There is uniform flowfar away from the ship (Decay condition)

The computational model of a Rankine panel method accounts only for part of the free water surface. This introduces an artificialboundary. Waves created by the ship must pass

through this boundary without reflection ("open boundary" condition).

The problem is complicated because Kutta condition (6) and dynamic condition (4) are

nonlinear and the exact boundaries of ship hull and water surface are a priori not known.

An exact solution would require fully nonlinear methods which are not available if areas with

breaking waves are large. This is always the case for fast SWATH ships.

Positive experience for deep water, Bertram(1993), justifies a simplification:

Schiffstechnik Bd. 41 - 1994 / Ship Technology Research Vol. 41 - 1994

55

Shallow Water Effects

for SWATH Ships

The Kutta condition is enforced by requiring the cross flow component in horizontal y-direction to vanish at the end of the strut of each _{SWATH demihull.}

Dynamic and kinematic condition are combined and linearized. The resulting simple Kelvin condition is enforced at the undisturbed water plane z = 0.

Trim is fixed for SWATH ships. This generally applied assumption for SWATH ships reflects assumed corrections by the crew to keep the ship on an even keel by ballasting

or using control foils.

A Rarikine panel method with additional horseshoe vortices solves the problem stated so

far. The conditions are fulfilled by: Neumann collocation

Bottom _{mirror images of all elements with bottomas reflection plane}

Kelvin collocation

Equilibrium _{not, sinkage is calculated once without repeating}

calculations. Trim is fixed

Kutta _{collocation at 0.5 typical grid spacing behind strut}

Radiation staggered grids

Decay automatically

Open boundary staggered grids

Bertram (1993) gives the mathematical model _{with all essential formulae.}

3. Results

A research program of the German ministry for _{Research and Technology (BMFT)} investi-gates fast and unconventional ships. Part of the program is concerned with systematic model series for SWATH ships and funded the _{present work.}

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Fig.1: General hull geometry of the _{SWATH ship models}

For these tests a model kit of simple hull and strut elements was used. The hulls have circular cross sections with effiptical change of radius at the bow_{and parabolic change at the stern. The}

length of the parallel middle body with constant radius determines the prismatic coefficient of the hull. The struts with vertical _{sections have a parabolic bow and stern of each 25%}

length. Fig.1 shows a sketch of the general hull geometry. Computations and shallow water

experiments were applied to a typical SWATH configuration from the deep water _program. The main dimensions of the SWATH ship (model) _{were L = 2.5m, DH = 0.2m, t,}

_{= 0.lm,}

B, = 0.8m, d = 0.16m. LNH

coefficient Cp = 0.768.

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Schiffstechnik Bd. 41 _{- 1994 / Ship Technology Research VoI. 41 - 1994} Li I ipse

4

1 2 3 4 5 6 8 g o 12 13 14 15 16 17 18 19 20

Fig.2: Panel model of SWATH ship

A gap between strut and hull in the aftbody was closed in the panel model, Fig.2. The errors in the global solution due to the change of geometry will be small as this region is

poorly approximated by potential flow anyhow. The panel model extends considerably above the still water line so that even for high Froude numbers the wetted surface will not exceed the discretized part of the hull. Froude numbers F ranged from 0.2 to 1.0 for a water depth of O.43m giving a range of depth Froude numbers FIL,, from 0.48 to 2.43. Model tests were

performed at the Duisburg Towing Tank in a tank of 9.8m width.

The computed wave resistance was always smaller than the measured residual resistance,

Fig.3. The difference becomes most pronounced for the region of transcritical speeds where the

maximum of the resistance coefficient appears. It is subject to discussion to what extent this

discrepancy is due to physical (viscous) effects. However, our panel method predicts for real ship

geometries resistance with insufficient accuracy. (The same is true for all otherstate-of-the-art codes.) Recent research of Söding (1993) indicates that a source/sink method should enforce

an average condition over a surface patch rather than a condition at one point to improve

accuracy. Incorporation of this approach may improve agreement for resistance considerably. Computations reproduced sinkage surprisingly well, Fig.4. There appears a narrow range of

overcritical speeds with dynamic lift (negative sinkage). The computations reproduced this lift.

Experimental data show extreme scatter in this region making a comparison of quantitative

values difficult. Trim moment (Munk moment) was extremely well captured, Fig.5. This agreement is surprising as trim is generally considered to be numerically sensitive and influenced

by viscous effects. The present analysis seems to contradict this statement for SWATH ship; qualitative and quantitative agreement is sufficient for practical design purposes. The moment is made nondimensional by displacement V and length L. It is positive for increased draft at the bow. The point of reference lies on the center line of the lower hull amidships.

The experimental results have to be considered unreliable in the transcritical regime. In a towing tank of limited width the flow becomes highly unsteady in the transcritical regime. The wave pattern opens to an angle of 900 for the critical Froude number 1. The energy is "trapped" and accumulates. Periodically single waves ("solitons") are formed that propagate faster than the ship. As a result, forces on the ship show large fluctuations, e.g. 30% in the resistance. Also, experimental data were not corrected for the blockage effect of the limited tank width.

References

BERTRAM, V. (1993), A computational fluid dynamics method for SWATH ships, Conf. FAST'93,

Yokohama

SÖDING, II. (1993), A method for accurate force calculations in potential flows, Ship Technology Research 40/4

Fig.4: Sinicage for SWATH ship, experiment, o computation

M/(pgVL)

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Fig.3: Wave/residual resistance for SWATH ship, experiment, o computation

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Fig.5: Trim moment for SWATH ship, _{experiment, o computation}

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58 _{Schiffstechnik Bd. 41 - 1994 / Ship Technology Research Vol. 41 - 1994}

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