M. INSEL
Istanbul Technical University, TURKEY. S. T. TANG
Vocational Traizing Council, HONG KONG. Z. LU
China Shipbuilding Trading Company (Guangzhou), CHINA. SUMMARY
This paper investigates the wave-making characteristics of high speed craft (HSC) in an attempt to assess the effects of wash on river banks. Three types of high speed craft concepts, namely monohull, catamaran and trimaran are investigated, examining the wash characteristics inherited in each craft type by means of a linear wave-making theory. To simplify the investigation, a monohull is used to ascertain the effects of shallow water and channel characteristics. In this study, wave spectrum across the wave frequencies have been calculated for a number of Froude numbers over the practical speed range of HSC. Based on an erosion found, the likelihood of bank erosion arising from these hip generated waves is assessed. The main parameters affecting wash characteristics are offered for high speed craft designed for river operations.
INTRODUCTION
The development of high speed passenger craft over the last two decades has been to achieve low resistance (hence higher speeds), better safety, greater comfort and lower operational costs (hence higher profits) for a given route. These craft have mainly been used in sheltered waters or short sea passages. For instance, a large concentration of HSC is found operating in the Pearl River Delta region in Southern China and growing steadily into other regions, such as Yangtze Delta and the Bohai Sea in Northern China (Lu et al 1996). As economies of these coastal regions expand, inland waterways will be increasingly utilised for transporting goods, materials and passengers. Owing to their wide deck area, good stability and speed perfonnance, catamarans have gained wide acceptance.
In fact, one of their main advantages is their low draught reqúirement, which would enable them to operate in shallow waters and rivers. However, it has been apparent from operating this type of craft in rivers that bank erosion could result when craft operates above certain speeds. In this respect, the wash characteristics, in essence the generated wave system of a craft, has found to be an important factor that should be considered in detail. The amount of wash generated should be minimized for river operations and low wash characteristics are desirable if detrimental consequences, such as damage to the river banks or even law suits, are to be avoided.
ESTIMATION OF SHIP WAVES iN RESTRICTED WATERS
Prediction of wave resistance of a surface ship by linearised theory has been utilised satisfactorily for slender hull forms by Doctors et al (1991), and by Insel et al (1994). Linearìsed theory can also be used for the prediction of the far-field wave pattern, or so called wave wake, behind the
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A Comparison of Wash Characteristics of High Speed Craft Operating
in Rivers
hull as shown by Insel and Doctors (1995). These studies have indicated that this approach gives realistic results for engineering applications at low costs.
Linearised theory of ship waves and ship wave resistance has been developed since Michell's (1898) formulation for deep-water wave resistance. Shallow water and canal wall effects were investigated by Strettensky (1936) and Lunde (1951). In this paper, an approach based on the linear theory is used to determine the far-field wave pattern and the wave resistance of a hull or a multihull.
2.1 Velocity Potential
Assuming the fluid is ideal and incompressible, the flow is steady and irrotational, the linearised boundary conditions can be expressed in a Cartesian axis system shown in Figure 1:
Laplace equation
V24)=_.
+fto
ax2 .9y2 ay2
Free surface conditions a) Dynamic free stitface condition
g(' U4);O
at z=Ob)Kinematic free surface condition
UÇ- 4=0
at z=OBottom condition
= o
atz=-H
(4)iv) Radiation condition
11m 4)
fo(i)
( x2. y2 ).00
Ofor x<O
for x>O (5)
y) Hull surface condition
Uf. 4,,= O at y=;flx,z) (6)
where the free surface is expressed as z=C(x,y) and geometry of the ship is represented by
y;f(x,z).
The velocity potential of a source with density of .t0 and located at (x,y0,z0) in shallow water canal with a depth H and a width W (Figure 1) can be obtained by considering images due to the tank walls at y01=y+2mW and y0"=-y0+(2m+1)W for of the source and its image due to the tank bottom at z'=-(2H+z0). The far field velocity potential of the source can then be fòund
and is given by Insel (1990) as: 1.
L
E mmsin(co)}
KmcDSOm U m.0 (7)cosh (Km(Z+H)) cus (m ity/W)
far even in
cosh (Km!!) sin(miry/W)
far odd m
where
cos(cù r0)
for even in
m.ffT cos(mtYOIW).(m
X0)th0far
m«m ces (c r1,)
far even in
=ffom sin(miy0IW)
sm(wm r0) 0far odd m
m s -K-u 16it u e cosh (Km(H+Z0))Wg (1- Kflsech
2(Kj!).Sjfl2O)0KmC0SOh1) wm= Km coswhere Km and 0m are solution of
Km K0 SCC2Om ti(KJf»0
and Km SiflOrn imlW 2.2 Far-Field Wave System in a Shallow CanalThe far field wave elevation can be found from dynamic free surface condition and is given by Insel (1990) as:
m 11m. ces (in ity/W) for even in
mcomsm]
sin(mliyIW) for odd in
Thus the wave system of a source, or source distribution, at any position of the canal can be represented by a finite number of discrete wave components with angle of 0m and wave number of IÇ (Figure 2). m&id '1m are the amplitudes of the symmetric wave components relative to the tank centerline, whilst maflCl Pm are that of the asymmetric wave components. For a symmetric hull form relative to the canal centerline, a and p. will be zero. However for a symmetric ship advancing on one side of the river oem and will not be zero. For practical calculations m (equation 12) can be truncated at a finite number M. The use of a finite number of wave components is justified: if the harmonic number is increased, the angle of wave reaches very high values. (Om>70) and increase of angle by increasing m would be very small.
Evaluation of wave coefficients is performed for a combination of source-sink distribution where source strength is derived from thin ship assumption over the panels distributed on the centerplane of the hulls (typically 21x51 panels). The numerical code also includes routines to trim and increase/decrease draught of the hull form at any speed.
Udf
- 2n d
2.3 Wave Resistance of a Ship Model in a Shallow Canal
Wave resistance can be obtained by considering energy changes as given in Insel (1990):
2.4 Far Field Wave Patterfl Of a Multihull
Far field wave elevations of a multibody configuration can easiiy be calculated by discretising each body individually and performing the integrations on equation 8 and 9 on all the hull surfaces.
= EN
COS(ClI)m x0) for even rn
ffotrn cos(mnYO/W).( XO)tho o
for o
rnffMOtm sin(mny1/W)
th &
(16)s
Wave elevation and wave resistance can still be calculated from equation 12 and 14 respectively. This approach can, be utilised fOr catamarans, trimarans or for any combination of symmetric hulls located on r off the centre plane of the tank.
2.5 Assessment of the Method
Based on the method outlined above, wave system of a monohull/multihull can be expressed as a superposition of discrete waves advancing with an angle to the tank centerline from 0-45 degrees (transverse waves) to 45-80 degrees (divergent Waves). The waves above 80 degrees (standing waves) are not normally encountered in ship waves Typical wave amplitude distributions are shown in Figure 3a and 3b for Fn= 0.3 and 0.5. The transverse waves, which contribute substantially to wave-making resistance, are thé main concern.
The use of linearised theory for slender hulls has indicated that the linearised theory canj over/underpredict the wave resistance for certain Froude numbers. Doctors et al (1994) has suggested use of a correctiòn factor based on tanktesting. Insel and Doctors (1995) applied such corréçtions for a mathematically defined hull forni and obtained good correlation on the distribution of wave resistance across the wave ahgle and good correlation between measured and cálculated wave traces. two examples of such correlation are given in Figure 3a, 3b for wave resistance distribution and Figure 4a, 4b for wave traces taken at Froude number of 0 3 and 0 5 The correlation suggests that linearised theory can be used for qualitative comparisons without any modifications, and could be corrected for quantitative comparisons. As the aim of this paper is to asses the relative performance, no corrections have been applied to the simulations.
3. AN EROSION FUNCTION
Wpg [+Ti(1-.
2K0!!).E []
4 smh(2K0F1) mP,m CO520m 2K,,/I -2 smb (2KJf) (13) (14)Erosion of river banks is a complex problem. It is affected by boththe.flow speed and waves. In the present work only waves are considered for the sake of simplicity. The erosion mass rate
Tim
Um
(bulk transport) due to a simple wave as suggested by the function given by Abbott and Price (1994) can be written as:
EMR =aC Ç2SIn24
(17)where
a : constant
C : wave celerity wave amplitude
wave direction normal to the bank (Figure 5)
Assuming that this equation is applicable to rivers and the effect of wave group is superposition of each wave, erosion due to a ship wave system can be expressed as:
the upper terms are applied for even m while the lower terms are applied for odd m. If angle of wave is zero degrees, i.e. transverse waves, erosion is zero. Same applies to 90 degrees waves, i.e. waves parallel to the banks. The most critical waves are between 15 degrees to 60 degrees (Figure 6). lt follows that greater mean wave amplitude does not necessarily mean a greater risk of erosion, as most of the Ship waves consist of transverse waves which make up most of wave resistance, but relatively low erosion propensity.
4. HULL FORMS ON WASH CHARACTERISTICS
Wave resistance and wash characteristics have known to be greatly affected by the choice of hull-form: a slender or a streamline hull would create less waves. However, in multi-hull configuration, wave inteiference effects could play a vital role in the selection of a suitable hull form and dimensions. In this section, their effects on erosion are examined.
4.1 Hull types
Three hull configurations, namely a monohull, a catamaran and a trimaran have been
investigated. Each configuration has its own unique wave spectrum: monohulls have smaller transverse waves and stronger diagonal waves, while multihulls can achieve smaller diagonal waves by means of wave interactions but suffers from transverse wave interactions.
Monohull : A simple mathematically defmed monohull forni, known as Wigley Hull (Figure 7), is utilised in the current work. The hull has parabolic waterlines and cross sections. Length to beam ratio is 5, and beam to draught ratio is 3.2 (Figure 8a). Block coefficient is 0.4444 making this slender hull a suitable choice for this preliminary study.
Catamaran : A catamaran, made up of two symmetrical demihulls, has thesame form as
E
>Cm C
Sin(2D,,,) (18)by substituting CV Cos O, it can be written as: M
EDCE
m.O 2 2,mm'
Lam+mimonohull but only half as wide as the monohull (Figure Sb), i.e. LIB:10 and BIT:] .6. In this configuration both monohull and catamaran have the same displacement, Froude number (Fn) and Reynolds number for the same speed The separation to Length ratio of 0 3 has been accepted fôr the current work.
Trirnarall : A trimaran
consists of a central hull which is the same as a demihull of the catamaran and each side hull which has half of the displacement of catamaran demihull (Figure 8c). Hence the trimaran lias thé equivalent displacement as monohull and catamaran. The width of the trimaran has been kept similar to the catamaran.The results of wave resistance and erosion function calculations are presented in Figure 9a and 9b Wave resistance reduction of catamaran concept has been achieved by using two slender hull forms comparing to a fuller monohull. The total resistance of catamaran may be higher than the monohull due to wetted surface increase for equivalent displacement However the reduction in erosion has greatly influenced by the craft type Tnmaran concept has the worst resistance characteristics due to an increased Wetted surface area and wave interactions. Still, fOr high speed operations Fn>0 5, trimarans would have an advantage over monohulls as it has a lower erosion rate.
The distribution of wave resistance and erosion functiOn. across the wave angle is given Figure lOa and lOb for Fn= 0.35, FIgure lia and lib forFn=O.50, Figure 12a and 12b for Fn=O.80. For the lowest speed (Fn=035) trimaran has the highest wave resistance and erosion whilst catamaran has the smallest due to its thin hulls. The reduction comparing to monohull is apparent for all three Froude numbers Hence, catamarans would be the most suitable configuration for river operations.
4.2 Hull form
To have an appreciation fhow huilform wOuld affect erosibn, the prismatic coefficients, beam and draught of the monohull are used for this part of the study.
Hull fullness: The effect of hull fullness has been tested based on prismatic coefficient which varied 0.7 to 0.9 by means of varying parallel middle body length forthe monohull. Figure 13 demonstrates howthe erosion factor changes with prismatic coefficients. The y axis has been taken as erosion function/prismatic coefficient ratio (or erosion function/displacement) to achieve a comparison based on erosion per displacement (C corresponds to CBas CM is constant for all
the forms). For the low Froude numbers the erosion per displacement is high for high prismatic coefficients. However the difference is negligible, or even favourable for high prismatic coefficients for Fn> 0.45. Hence, for high speed operations, a fuller hull may not bring about a higher erosion risk.
Beam variation : By varying the beam, erosion per displacement (based on LIB=l0) is given in Figure 14 A slender form of high L/B ratio suggests low erosion risk However other design constraints, such as machinery arrangement and stability requirements would impose practical limits to this parameter. this constraint may be overcome with a twin-hull configuration,. see Doctors and Renilson (1993), by using extremely low beam demi-hulls to reduce erosion risk.
Draught variation : The erosion function per displacement (based on B/T=1.6) is given in Figure 15 for a monohull by keeping length to beam ratio constant at 10 As it is expected the
erosion risk rises with decreasing B/T ratio, hence decreasing L/T (L/B B/T) ratio, i.e. less slender. However the draught of the craft should be decided on the limitations of water depth, slenderness of the hull and stability.
EFFECTS OF CHANNEL CHARACTERISTICS ON WASH
In addition to basic hull configurations and dimensions, changes in river characteristics would also affect river bank erosion: its width, depth and cross-section profile.
Channel Width : The hydrodynamics of ship waves changes as the channel width narrows. However, these changes could not be a linear one, as depicted by the graphs in Figure 16. The graphs suggest that after a certain width, W/t =1.5, the likelihood of erosion reduces with increasing distance, but below a certain distance, erosion could also have favourable erosion characteristics. This could be explained by the fact that as the channel width reduces, the wall begins to act on the hull, making the configuration more akin to a twin-hull, bringing about
interference effects. As a result, resistance could be lower under favourable conditions and erosion lessens. However, this may not be easily realised as the river banks are rarely smooth vertical walls. The data also suggests that for Wit> 5, likelihood of bank erosion due to width restrictions is greatly reduced.
Channel Depth: The effects of channel depth, better known as shallow water effects, is a classical ship hydrodynamic problem. Here, fairly well-understood phenomena is expected, that is when depth Froude number is equal to unity the highest erosion is encountered. If a craft is operating through the various depths, substantial changes in erosion must be expected. Higher erosion will be encountered for subcritical depths (i.e.Fnh<1 .0) and less erOsion for supercritical depths (Fnh>l .0). E.g. for Froude number of 0.6 (which is about 22 knots for 36 m long craft), 30 % more erosion is calculated for DIL:0.3 (10.8 m deep) and 75 % less erosion is calculated for DIL:0. I (3.6m deep) comparing to assumed deep case of Dit: 1.0 (36 m deep). These are well born out in the graphs of Figure 17. The risk of erosion becomes low for high speeds as long as depth Froude number is above 1.0.
Cross-section Profile: Channel shapes, other than those depicted here as vertical walls, should be investigated. However, within the present theoretical framework or any formulation of the classical approach it would be very difficult to model other shapes. A first attempt has been made in Doctors and Renilson (1993) to approximate the sloping side walls in an average manner. However, the results were not well-predicted by theory. Based on limited experimental evidence, sloping banks tend to reduce resistance. It is envisaged that boundary element approach could be more appropriate, though a penalty in terms of computing time is to be expected. For the present investigation, this parameter would be left for future investigation.
CONCLUSIONS
In this investigation, an attempt has been made to use linear theory to assess the likelihood of erosion caused by ship generated waves on river banks The results strongly suggest that catamarans would cause the least erosion amongst common HSC hull configurations over the practical speed range.
about greater erosion risks. More importantly, wave angles between about 30-60 degrees tend to reinforce greater erosion. Of all the parameters tested, shallow water effects showed dramatic changes particularly at depth Froude number around I O Channel width is also a prime parameter in erosion A hull of high length to beam ratio (L/B), i e a slender form may show substantial improvements in erosion characteristics.
A slender hull catamaran would be most suitable for high speed passenger transportation among the craft types reviewed in this work. However a comprehensive assessment must be performed for a concept design by usmg expected river width and depth as well as craft length and hull fOrm. Additionally the effects of propulsion system on the wave system must also be considered as surface piercing bodies such as Z drives may cause substantiâl waves.
Further work is also being carried out by authors on the influence of river bank slopes on erosion, the pressure loading due to waves on the river/harbour bank walls and the motions of small craft on the river/harbour walls due to passmg high speed craft.
DISCLAIMER
The views expressed are those of the authors,, for which they are alone should be held responsible.
REFERENCES
Abbot M.B. and Price W.A., (1994), Coastal, Esturial and Harbour Engineers' Refere,ice Book, E&FN Spoon, Oxford.
Doctors L.J., Renilson MR-, Parker G. and Hornsby N., (1991), Waves and Wave I?esistance of a High Speed River Catamaran, Proc First International Conference on Fast Sea Transportation (FAST 91), Norwegian Institute of Technology, Trondheim Norway, Vol1.
Doctors L J and Remlson M R, (1993), The Influence ofDemihull Separation and River Banks on the Resistance of a Catamaran, Second International Conference on Fast Sea Transportation (FAST 93), The Society Of Naval Architects of Japan, Yokohama, Japan. Insel M., (1990), An investigation into the Resistance Components of High Speed ('aÍamaraizs Ph.D. Thesis, Department of Ship Science, University of SoUthampton, U.K. Insel M., Molland A.F. and Wellicome J.F., (1994), Wave Resistance Prediction of a catamaran by Linearised Theory, CADMO 94, Southampton, UK.
Insel M. and Doctors L.J., (1995), Wave Pattern Prediction of Monohulls and
Catamarans in Shallow Water canal by Linearised Theoiy, 12th Australasian Fluid Mechanics Conference, Sydney, Australia.
Lu B. Z., Tang A.S.T. and Insel M., (1996), A techhic4l and economic Apprdisal offbur HMSV routes in China, 12th Fast Ferry International Conference, Copenhagen.
Lunde J.K., (1951), On the Linearized Theory of Wave Resistance for Displacement Ships in Steady crndAccelerated Moti on Transactions of SNAME, Yol:59
Michell J H (1898), The Wave Resistance of a Ship Philosophical Magazine, London, Series 5, VoI:45.
Srettensky L.N., (1936), On the Wavemaking Resistance Of a Ship Moving Along in a Canal, Philosophical Magazine and Journal of Science, Vol:22, Seventh Series.
Figure 3a: Wave amplitude across the wave Figure 3b: Wave amplitude across the wave
\PA\rd'.
-Figure 4a:Measured and ca1cu1ted wave elevations (Fn:O.30)
Figure 5: Erózion due to waves
J
i
Figure 4b: Cahulated and measured wave elevations (Fn:O.50)
V
I
_
Figure 6: Distribution of angular parts of eroñon and wave resistance functions
across the wave angle
Figure 1: Axis system and canal dimensions Figure 2: Angle and direction of wave components
Figure 7: Mathematical hull form (Wigley Hull)
B/2
B/2
Figure 8b: Catamaran form
L
Figure9a: Erosion function across the Froude number range for monohull,
catamaran and tiimiran
across wave angle (Fn:O.35)
T
B/S-D.3L B/2
f-Figure 8a: Monohull form
L/
L
Figure Sc: Trimaran form
across wave angle (Fn:O.3 5)
T
D.3L
i
0.3 0.4 0.5 0.5 D D
Figure 9b: Erosion function across the Froude number range for monohull,
catamaran and trimaran
Figure 1 Oa:Wave resistance distribution Figure lOb: Erosion function distribution
Figure 1 la: Wave resistance distribution Figure lib: Erosion fùnction distribution across wave angle Fn:O.5O) across wave angle (Fn:O.50)
Figure 12a: Wave resistance distribution Figure 12b: Erosion function distribution across wave angle (Fn:O.80) across wave angle (Fn:O.80)
Figure 13: Effect of hull fuilnes on erosion Figure 14: Effect of length to beam ratio
Figure 17: Effect of river depth on erosion function
Figure 15: Effect of beamto draught ratio Figure 16: Effect of river width on erosion
on erosion function function