CONTROLLABILITY AT TOO HIGH SPEEDS IN TOO SHALLOW WATER

Albert J. Jurgens (MARIN, The Netherlands) Arie de Jager (IHC HOLLAND dredgers BV, The Netherlands)

Abstract: Nowadays vessels will have to run at higher speeds in shallow water. Furthermore, it is known that vessels lose controllability while sailing at too high speeds in shallow water: squat causes a too large trim forward and instability loops in general grow. The target of the present project was to determine at which water depths and at which speeds the manoeuvrability dominates the behaviour of the trailing suction hopper dredger. For this project, extensive captive static and dynamic model tests were carried out in a range of water depths, with two vessels. A large range of speeds and trim conditions were model tested and a mathematical model was created. The mathematical model is used in fast time simulations to find the limits of controllability.

1. INTRODUCTION

During the operation of a trailing suction hopper dredger, the ship encounters a wide variation of water depths. Additionally, the ship has to operate in restricted water ways. The environment is not only restricted with respect to the water depth, but also in width during e.g. dredging operations in harbours or channels. This imposes stringent demands on the manoeuvrability of the ship. Regular groundings made investigation necessay. To obtain more insight into the physics with respect to the manoeuvrability of trailing suction hopper dredgers in restricted water, a research project was initiated by IHC, Ballast HAM (now Van Oord), Boskalis and MARIN. The title of this joint industry project (JIP) is: �HOppers in Shallow WAter� or HOSWA. Within this research project the primary aim was to increase the knowledge on squat behaviour, course keeping ability and manoeuvring ability of trailing suction hopper dredgers, how to optimise the design and how to increase safety. Therefore a series of full scale and model scale tests were conducted together with an intensive CFD study.

2. OBJECTIVES

The project was to give designers and operators knowledge with which the course keeping, manoeuvring and squat behaviour of modern trailing suction hopper dredgers on shallow water could be explained and subsequently could be predicted. Furthermore the helmsman-ship interaction had to be investigated. From the safety point of view, the response of the vessels in shallow water should be clarified, identified, deviations from expected

excursions identified and if possible quantified. For the operator, the project was to yield information on how exactly the vessel was performing compared to his expectations.

Validation of existing knowledge on shallow water effects and extension of the knowledge by means of full scale and model scale test exercises were conducted. The ship response on shallow water needs better understanding and design tools are needed to better implement the ship behaviour on shallow water in the design process to optimise new designs for increased safety on shallow water.

The derived knowledge from the HOSWA JIP makes it possible to: - validate design tools like RANS solvers to

enhance the design process. - develop manoeuvring simulation tools to validate

new designs and to train ship crew on existing and newly developed vessels.

- produce a safety envelope for each trailing suction hopper dredgers to give ship crew insight in the behaviour of their vessel in shallow water conditions.

- develop advanced autopilots which automatically control some do�s and don�ts on shallow water.

- provide guidance to designers regarding the behaviour of the ship in shallow water.

3. TRAILING SUCTION HOPPER DREDGERS

It has to be mentioned that in general trailing suction hopper dredgers are twin screw vessels with a rather high block coefficient, sailing both in deep water and at very restricted water depths. This type of vessel experiences different loading conditions during its

operation which makes the design of any trailing suction hopper dredger a challenge. The length and draught of the vessel are minimised to enlarge the navigational freedom. Latest designs push the limits of fullness even further as can be seen in Fig.1.

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Fig.1 Time line of the shift of global design

coefficients.

These shifts in fullness, length-beam and beam-draught ratios influence the course keeping and course checking ability. Fig.2 presents the 1st overshoot zig zag results from a selection of modern trailing suction hopper dredgers.

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Fig.2 Zig zag 10°/10° 1st overshoot angle from 35 modern trailing suction hopper dredgers.

The trailing suction hopper dredgers which were investigated in the HOSWA JIP are presented in Fig.3 through Fig.5. Table 1 presents the non-dimensional main particular ratios and coefficients of the studied trailing suction hopper dredger designs.

Table 1 Main dimensions of the investigated trailing suction hopper dredgers.

hull 1 hull 2 hull 3Length-Breadth ratio Lpp/B 4.97 3.66 4.72Breadth-Draught ratio B/TM 2.56 3.71 2.73Length-Draught ratio Lpp/TM 12.72 13.56 12.88Block coefficient Cb 0.86 0.84 0.87

The three selected trailing suction hopper dredgers have different propulsion configurations, hull 1 has a stern with exposed shafthoses and an integrated skeg, hull 2 has a twin gondola stern with flat skeg and both sterns are equipped with streamline bodies towards the propellers with integrated nozzles. Hull 3 has a pram type stern with pods. The fore body and bulb designs of the three selected trailing suction hopper dredgers show many differences. The hull 2 design has a relatively large breadth.

Fig.3 Body plan of hull 1.

Fig.4 Body plan of hull 2.

Fig.5 Body plan of hull 3.

4. PROJECT ACTIVITIES

The project activities were focused on knowledge development as well as on tool development. The following activities are conducted within the framework of the project: - Literature study - Full scale trials - SurSim validation - Flow investigation - Model tests, captive static and captive dynamic - Tool development - Safety study

After a literature study on squat and shallow water effects, a series of full scale trials were conducted. With the full scale trials the behaviour of the actual ships was monitored. This provided insight in relevant manoeuvres, loading conditions and nautical procedures.

The main objective of the full scale trials was gathering knowledge of the shallow water effects on full scale, verification of existing squat prediction methods, verify model test predictions against the full scale results and generating benchmark data for the simulation software.

With the available full-scale trial results an extensive validation of the MARIN SurSim manoeuvring simulation software has been conducted. With this study the omissions in the SurSim software to predict the manoeuvring behaviour of trailing suction hopper dredgers are identified.

Flow investigations using measured wake fields and CFD calculations, both with potential flow (RAPID) and viscous flow (PARNASSOS), were performed to get qualitative insight in the flow around a trailing suction hopper dredger in close proximity to the bottom. The investigation focused on the following three main topics: - The relation between the flow in the fore ship, the

wave elevation and the dynamic trim and sinkage. - Study of the flow in the aft-ship at the propeller

location as a function of water depth, hull form and loading condition.

- Study of the flow around a hull under drift angle at deep and shallow water.

Based on the full scale trial results relevant conditions were isolated. The isolated conditions formed the basis for the model testing program with hull 1 and hull 2 which focused on the speed-power-squat relation and the manoeuvring forces as function of hull form variation and water depth. The captive static and dynamic tests were conducted in a modular way to isolate the contributions of the hull, propellers, nozzles, rudders, bilge keels and their interactions.

From the tests the forces acting on the ship, rudders and propellers at various speeds, water depths, drift angles, yaw rates of turn, propeller loadings and loading conditions were determined in order to: - Obtain data to determine the hydrodynamic

derivatives and to generate data to create the mathematical model, i.e. SurSim for TSHD.

- Investigate the directional stability of the ships. - Observe the dynamic trim and sinkage response

on the applied motions

A simulation model SurSim for TSHD, based on the existent SurSim program, was developed based on the full and model scale results. The model was validated with the full scale trial data. With the model

the influence on squat, course keeping, manoeuvring and navigational safety of variations in ship dimensions and hull form can be investigated. The limitations of the simulation model in the design optimisation process were identified.

The safety study provided insight in the behaviour of the vessels on shallow water conditions. Based on the simulations and full scale trials a list of do�s and don�ts can be derived resulting in a safety envelope.

5. TESTS

For the generation of knowledge on the use of trailing suction hopper dredgers and hydrodynamic effects occurring while sailing on shallow water full scale as well as model scale tests are conducted.

5.1 Full scale

Full scale tests are the most expensive method of investigating the behaviour of ships. Recording al influences during the trails, mapping the results to the conditions and derive conclusions from these is complex. However, it has the great advantage that no idealized situation is used; all additional influences are taken into account, no scale effects.

Within the framework of the HOSWA JIP four full scale trial series were conducted. During the trials all relevant characteristics were recorded included water depth, dynamic trim and sinkage and loading condition. The trials conducted provide insight in the nautical procedures, realistic loading conditions, relevant manoeuvres and dynamic sinkage and trim.

Fig.6 presents the height of the instability loop from the reverse spiral and the observed yaw rate of turn (r) when a rudder angle (δ) of 35° is applied, as measured during the full scale trials with the hull 2 vessel. Fig.7 presents the ratio between the yaw rate of turn at δ = 0° and δ = 35° respectively. If the ratio is one, the vessel would turn as fast with 0° rudder angle as with 35° rudder angle. The ratio shows a strong variation with water depth primarily a result of the dynamic trim and sinkage and the change of the flow around the hull due to the presence of the bottom. The large variation in response makes the vessel�s behaviour unpredictable for the helmsman.

5.2 Speed-power-squat measurements

A series of tests on deep as well as on shallow water are performed to validate the MARIN standard extrapolation methods to scale propulsion predictions on shallow water to full scale and compare the squatting behaviour on model scale with full scale. The tests on restricted water depths underlined the necessity to correct for the effects of blockage.

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5.3 Force measurements

Captive static and captive dynamic model tests on the hull 1 and hull 2 models were conducted: to obtain data to determine the hydrodynamic derivatives, to generate data to create the mathematical model, to investigate the directional stability of the ship as function of the water depth, speed and loading condition and to observe the dynamic trim and sinkage response in the applied motions.

The test program comprised tests with the ship models equipped with and without propellers, nozzles and rudders. Four configurations were tested being: the bare hull, bare hull with bilge keels, appended without rudders and fully appended. With these configurations a series of water depths, speeds, drift angles, yaw rates of turn, propeller loadings and loading conditions were tested.

The forces and moments measured on the whole ship and on the appendages form the basis for the mathematical modelling with which safety studies on trailing suction hopper dredgers can be conducted.

Fig.8 presents the measured transverse hull forces and moments as a function of drift angle for five water depths.

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6. MATHEMATICAL MODEL

The mathematical model on one hand is based on theoretical relations; on the other hand frequent use is made of the empirical information from the model tests. Combinations of the series of model tests and theoretical prediction methods, along with proof-tested interaction relationships are the basis for the modelling.

The mathematical model as described in the following paragraphs describes the acting forces and moments on the hull and appendages in a modular way. In the model the effects of hull, rudder (s), propeller(s), nozzle(s), etc are separated. The complex interaction effects with hull, propeller, rudder and nozzle are separately identified in this model. The utility, however, will be fantastic, allowing easy, quick, and inexpensive trade-offs among rudder, hull form, and propeller alternatives in improving ship design and derive ship handling procedures.

The mathematical model consists of the following parts: - coefficients describing the straight ahead motion:

resistance, wake: sailing straight ahead, wake: while drifting and turning, propeller thrust, thrust

deduction, nozzle thrust, rudder to propeller interaction due to presence of a rudder, rudder to propeller interaction due to rudder deflection

- forces due to rudder inflow angles: inflow angle, inflow velocity, rudder forces, rudder to hull interaction, coefficients describing the flow-straightening

- linear hull forces - non-linear hull forces - forces on the nozzle - trim and sinkage relations

6.1 Resistance

The change of the slope of the resistance curve due to the change of the water depth showed for all tested vessels a relation with the ship breadth water depth and ship draught. With these three parameters a generic description of the water depth influence on the ship resistance is made. The effect of shallow water on ship speed is assumed to be composed of two parts: a �back-flow� component arising from the restricted water depth and a component due to the distortion of the wave system. The effect of the back-flow is incorporated in the formulation by the relation between the vessels draught, the beam and the water depth, describing the amount of blocking. The distortion of the wave system is described by the water depth.

6.2 Wake

Due to the change in pressure distribution over the hull as a result of the variation in water depth, the development of the boundary layer will be different compared to deep water. The strong pressure gradient along the fore ship can, on shallow water, extend the shift to a turbulent flow. The boundary layer development will be suppressed more than on deep water. This in combination with the higher flow velocities in the outer stream lead to higher frictional resistance. At the aft ship the higher pressure gradients increase the risk of flow separation. Both the dimensions of the separation area as the pressures are influenced by the blockage, resulting in an increase of the viscous pressure resistance. This will have an effect on the wake field. The nominal wake w is a function of the wave contribution ww, the displacement contribution wd and the friction contribution wf. All the components change as a function of water depth. The amplification of the primary wave system and the change of the wave length of the secondary wave system will influence ww. For large blockage the displacement wake will change significantly. It is even possible that for extreme full ships like the vessels under consideration, wd will be negative due to the backflow. The frictional part of the wake depends strongly on the boundary layer development. Therefore a strong influence of the blockage and the speed on the wf is found.

Strong hull form dependence can be expected in the water depth dependence of the wake. It is observed that the wake, while sailing straight ahead increases 60% for hull 1 and 40% on hull 2 when going from deep to shallow water..

Fig.9 and Fig.10 presents at deep and shallow water for the hull 1 and hull 2 the non-dimensional axial velocity component. It can be observed that for the hull 1 the wake more or less uniformly increases. On the hull 2 the wake not only increases, but the distribution of the wake field changes as well. The change of the wake distribution on hull 2 is most probably a result of the large beam and the presence of the gondola.

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Fig.9 Axial velocity component; hull 1.

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When the vessel is in a drift or turning motion the wake field will change from the straight ahead condition. The hull form which is not parallel to the flow will in some areas accelerate the flow and decelerate or even block the flow in others. Flow

lines which were attached to the hull in the straight ahead motion can separate when the vessel is at an angle of attack with the flow.

Fig.11 for deep water and Fig.12 for shallow water present the calculation results of the axial velocity field in the aft ship on hull 3. The calculations were conducted using MARIN�s in-house viscous flow solver Parnassos [2]. Comparing the conditions on deep and shallow water, a somewhat thinner boundary layer is present on shallow water. The wake in the aft ship however is much more pronounced in shallow water than in deep water. The windward bilge vortex is not as separated from the hull in shallow water compared to deep water, due to the stronger cross-flow.

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This change of flow field in the aft ship will have its effect on thepropeller and rudder inflow velocity and angle and hence on the manoeuvring behaviour of the vessel. The behaviour of the flow on the leeward (LEE) and weather (LUFF) side is substantially different resulting in a separate formulation for the leeward and weather area to describe the change from the straight ahead wake due to a cross flow.

On hull 1 the wake on the weather side drops to 50% of the straight ahead wake. On the leeward side the wake increases with 50%. On hull 2 the weather side wake is independent of the inflow angle. On the leeward side the wake drops to 50% of the straight ahead wake.

6.3 Thrust

The amplification of the propeller hull interaction by shallow water also affects the thrust deduction. On shallow water, the normally smaller changes due to

the flow from the propeller can be amplified by the backflow. Additional dynamic sinkage and dynamic trim, resulting in an increase of the blockage, result in a significant increase of the backflow velocity, which again affects the dynamic trim and sinkage. The thrust deduction will normally increase as the depth of water decreases.

6.4 Rudder

A rudder on a ship performs its function in a highly complicated medium. Hydrodynamic flow phenomena such as stall, ventilation, cavitation, and aeration exist which place definite limits on maximum achieved rudder performance. The presence of the rudder will affect the flow in the aft ship, which results in the so called rudder-to-hull and rudder-to-propeller interaction.

In the following, an overview is presented of the mathematical descriptions in a modular fashion. A distinction is made between calculation of the flow velocity and orientation in the rudder plane and the calculation of the forces on the rudder blade in this flow.

Inflow angle For both vessels it can be observed that the change of neutral angle due to the variation in water depth is small. In extreme shallow water a sudden increase in neutral angle can be observed on hull 2. The larger variation of the inflow angle on shallow water of the hull 2 can partly be explained by the nominal wake field, see §6.2, which shows a blockage of the flow between the gondolas at extreme shallow water. The effect of the shift of the neutral angle from deep to shallow water is implemented in the mathematical model in the form of a cross flow in the propeller plane.

Inflow velocity For the determination of the local longitudinal and lateral flow velocity, respectively uR and vR and the flow orientation, δH, in the rudder plane, see Fig.13, two conditions are determined: the trailing edge inward condition and the trailing edge outward condition.

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Fig.13 Schematic decomposition of the total force

In these two flow field conditions the rudder works in two different environments. In the trailing edge outward it is more in the free stream as for the trailing edge inward condition it is more in the wake from the hull and close to the skeg, especially for the hull 2 where it is operating between the gondolas. The difference between the two conditions increases when moving to more shallow water.

The propeller inflow velocity can be calculated based on the undisturbed velocity corrected for the wake which depends on the water depth and the local drift angle. With the propeller characteristics the propeller impulse can be calculated and hence the propeller outflow velocity. The flow between the propeller and rudder decelerates depending on the ratio between the propeller outflow and the surrounding flow velocity. Based on mass conservation the diameter of the flow from the propeller in the rudder plane can be determined, see Fig.14.

self propulsion point

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Fig.14 Propeller rudder configuration (hatched

rudder area valid for self-propulsion point condition)

The average longitudinal flow velocity over the rudder uR is defined as a weighted average of the flow from the propeller and the surrounding flow. The transverse flow component at the rudder depends on the neutral inflow angle and the local side velocity due to a combination of a rotating and drifting motion of the vessel.

Rudder forces From Fig.15 and Fig.16 it can be observed that the non-dimensional transverse force on the rudder as a function of rudder deflection angle from the hull 2 design is significantly larger compared to the hull 1 design. The largest differences in the characteristics of the two rudders are the geometric aspect ratio λR which is 1.0 for the hull 2 and 1.6 for the hull 1 and the thickness ratio t/c which is 21% for the hull 2 and 13% for the hull 1. The rudder design of the hull 2 has a larger lift coefficient and higher stall point, but is more sensitive for variations in water depth and propeller loadings this could be a direct result of the differences in thickness and aspect ratios but also due to hull-rudder interaction. The hull 2 rudder design can produce more steering force but the available steering force will change more as a function of the environment, making it less predictable for the helmsman.

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Fig.16 Non dimensional rudder side force (Y�) on

hull 2, h/T = 1.4, 1.7, 2.0, 2.5 for under, over and self propulsion point conditions

Rudder to hull interaction The rudder effectiveness is defined by the transverse force that is generated at a given rudder angle δ. It is observed that at a given angle a transverse force Y(δ) is generated which is larger than a transverse force generated on the rudder only, see Fig.17.

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Fig.17 Forces excited on the rudder and the hull

due to rudder deflection.

In certain cases the rudder can influence the flow around the hull. The flow forces on the hull are influenced by this effect.

Fig.18 and Fig.19 present the measured hull force versus the sum of the rudder forces sailing at zero drift angle for a series of rudder deflection angles. The slope of the corresponding points presents the rudder to hull interaction. The interaction is complex and is dependent of the water depth, ship speed, propeller loading and rudder deflection angle. For hull 2 the rudder to hull interaction, as presented in Fig.19, shows for small rudder angles a large interaction force of the opposite sign than the rudder forces.

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Fig.19 Rudder to hull interaction (YH�) on hull 2,

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Flow �straightening The effective inflow angle δe that is used to calculate the rudder force is determined based on the actual steering angle δ and the average predicted flow orientation at the rudder location. The average flow orientation is commonly predicted using so-called flow-straightening. The flow-straightening can be determined by comparing the calculated lateral and longitudinal rudder force due to the variation of the angle of attack of the rudder to the measured lateral and longitudinal force attributed due to the variation of the angle of attack of the vessel. The rudder angles of incidence are calculated with which the description of the rudder calculates the measured rudder forces at the tested drift angle (β). The calculated rudder angles are rated against the angle of attack, which gives the flow-straightening coefficient Cdb. If Cdb is one the flow angle is equal to the drift angle. If Cdb is zero the flow orientates parallel to the ship centre line.

Fig.20 presents the derived coefficients for the LEE condition and Fig.21 for the LUFF condition for the hull 1 and hull 2 design.

Both hull forms show an opposite trend in flow-straightening. Focussing on the LUFF side when moving from deep to shallow water a decreasing trend is observed for the hull 2 design. A dependence on the propeller loading is observed. The hull 1 shows an increasing trend with large variations in the flow-straightening.

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Rudder to propeller interaction The presence of a rudder downstream of the propeller will have an effect on the propeller performance. For the modelling two effects are isolated. The first part being the interaction due to the presence of the rudder will effect the propeller thrust. The second part describes the effect of rudder deflection. When the rudder is moved trailing edge outward the effect is small. But when the rudder is moved trailing edge inwards the effect on the thrust is significant. The interaction is dependent of the rudder inflow velocity (uR) en the propeller inflow velocity (up).

6.5 Linear hull forces

The linear hull forces are described by the slenderbody method. The Slenderbody method has the advantage that it is universal. Slenderbody uses a strip wise approach. For each strip the transverse force is calculated. Integration over the ship length results in the total hull forces and moments. The Slenderbody method determines the linear reaction forces and moments in a 3-stage manner: 1. Virtual hull calculation

Adopts the boundery layer sheet. 2. Calculation of the added mass distribution based

on the virtual hull frames. mYY = in sway direction due to a sway motion. mRY = in sway direction due to a yaw motion.

3. Incorporating trailing vortices and trailing edges.

The virtual hull represents the steel hull plus the boudery layer sheet. For the boundery layer sheet formulation a distinction between three different sections in made: the positive pressure gradient (Foreship), the zero pressure gradient (Midship) and the negative pressure gradient (Aftship), see Fig.22. The development of the boundery layer is dependent on the water depth draught ratio.

Phase III Phase II Phase I(aft ship, negative pressure gradient) midship, zero pressure gradient fore ship, positive pressure gradient

line represents a typical displacement thickness over the length Fig.22 Different stages in the boundary layer along

a ship and the related calculations

The added mass distribution based on the virtual hull as a function of water depth and dynamic loading conditions are calculated with linear potential strip-theory.

Vortices trail sternwards after being shed around the tip (keel plane) of the hull, skeg, sonar dome or gondola etc. Based on RANS calculations and PIV observations it is observed that vortices already are significant at small drift angles (5 degrees). The exact influence of the trailing vortices on the forces are still unknown, however it is expected that the vortices influence the linear coefficients as derived from the model tests.

The hypothesis that the linear coefficients are influenced by the trailing vortices is supported by the correlation of the measurements with the Slenderbody theory.

To study the trailing vortex system around a manoeuvring vessel it is of importance to distinguish different vortex sub-systems: - Bow vortex

Shed around deep V sections (e.g. sharp stem with or without bulbous bow) or a sonar dome.

- Bilge vortex Shed around the bilge of the vessel. May be dependent of the presence of bilge keels.

- Skeg/gondola vortex.

Clarke [1] presented a method to incorporate the effect of bilge vortices in the slender body method. The bilge vortex system he included in his theory represented the vortex system existing in the

straight-ahead condition for the vessel he studied. A correlation study for this revised study did not proof the method to be successful. Based on the segmented model tests conducted at MARIN and other experiments available, a kind of memory effect is observed in the fore ship.

A similar observation was made analysing segmented model tests of a frigate. However here the effect is not only to be contributed to trailing vortices. It can be derived from the measurements that the linear force over the foremost segment is similar to the maximum sectional added mass mYY for this segment. The hypothesis is that the sonar dome can be attributed to be a separate body with a trailing edge (similar to a dagger board on a sailing boat). Forces acting on such a body will not dissipate like the initial theory suggested. The forces on this separate body can be determined using the mYY value on the trailing edge of this body. The trailing vortices will also exist on these separate bodies (appendages). The same approach can be applied on the forces as generated by a skeg or gondola body or other separate appendages.

Fig.23 presents the added mass distribution at ω→0 on hull 1 along the ship length together with the calculated Yuv distribution and linear derivative Yuv which is plotted as a fat black marker at the frame 0 for one water depth and four speeds.

Yuvn

-1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21-1.0e+5

0

1.0e+5

2.0e+5

3.0e+5

4.0e+5

5.0e+5

6.0e+5

7.0e+5

xpos

myy

Water depth: 23, Vs=1Water depth: 23, Vs=6Water depth: 23, Vs=11Water depth: 23, Vs=16

Fig.23 Slenderbody calculation of Yuv from mYY

distribution for hull 1

Fig.24 presents a comparison of the linear derivative N�β versus the draught water depth ratio. The effect of speed is neglected in this comparison. A good correlation is found between the slenderbody calculations and the model test results. On extreme shallow water a misprediction is observed. In this condition the flow is extremely instationaire.

-1.5

-1.0

-0.5

0.0

0.0 0.2 0.4 0.6 0.8 1.0T/h

Nβ'

hull 1, Model testshull 2, Model testshull 1, SlenderBodyhull 2, SlenderBody

Fig.24 Linear coefficient, model test result versus slenderbody calculation

From the linear coefficients a study on the expected stability of the hull forms can be made. Without the rudders the development of the transverse velocity and yaw rate of turn after some small disturbance will depend on the following criterion. The ship will be course stable if the motions will extinguish after the disturbance is vanished. This will be the case if the stabilizing arm is larger than the destabilizing arm. The ship is course stable if the centre of application of the force due to drifting lies aft of the centre of application of the apparent force in reaction to the ship�s yaw rate of turn. The same analysis can be made for the appended ship with its propellers at its self propulsion point resulting in the stability of the total system.

Fig.25 presents the stability criterion of the hull 1 and hull 2 as a function of the water depth draught ratio for the appended and bare hull conditions for one static loading condition. The figure indicates that at deeper water, the vessels are course unstable. A large part of the stability is generated by the appendages. The hull 2 shows a large variation of the stability as a function of the water depth. The contribution from the appendages to the stability increases significantly on shallow water.

1.0

1.5

2.0

2.5

3.0

-1.0 -0.5 0.0 0.5 1.0

less stable ← NγYß-Nß(Yγ-m) → more stable

h/T

hull 1 barehull hull1 appendedhull 2 barehull hull 2 appended

Fig.25 Stability criterion

6.6 Non-linear hull forces

The non-linear forces are described by a so-called cross-flow drag method, see [2] and [4]. This strip-wise theory describes the non-linear forces distribution over the length for the instantaneous immersion of the hull.

The pure drag coefficient CD90 at deep water, the cross flow drag at a pure cross flow, is mainly dependent on the form of the ship. It is found that the water depth dependence of the cross flow drag at pure cross flow follows the relation as presented in Fig.26. To correct the CD90 for water depth the deep water CD90 is multiplied with the CD90,

hT coefficient.

0

1

2

3

4

5

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

T/h [-]

CD

90,h

T [-]

HAM 318 Yumuro, A. fit Fig.26 Water depth dependency of the drag on the

hull in a pure cross flow; CD90, Yumuro, A. [5]

The local cross flow drag coefficient CD, n for a given cross section at an arbitrary drift angle is calculated from the cross flow drag at 90° drift angle which is water depth dependent and the corrected drag coefficient which is independent of the ship�s hull form and the water depth and dependent of the longitudinal location and the local drift angle, as presented in [2] and [4]. The wave dependent non-linear part is described in a CDadd coefficient which is dependent of the water depth and ship speed.

6.7 Validation

Making the simulation program SurSim for TSHD generic valid had a high priority. The hull and propeller forces are generically described. The flow in the aft ship is described in a modular way. All effects are isolated and described in a physically correct structure.

Fig.27 presents an example of the validation results. A comparison between the measured and calculated overall transverse force due to a combination of drift and yaw motion for the fully appended hull 2 is made.

Fig.27 Transverse force (Y) vs. non dimensional

yaw rate of turn (γ) for hull 2 at h/T = 2.0. Fn=0.09: x: β = 0°, %: β = 8°, +: β = 14°, o: β = 24° Fn=0.18: >: β = 0°, <: β = 8°

As a final validation a comparison between the full scale trials and free sailing model test results and the simulation at a range of water depths results is made. The validation set consists of hull 1 and hull 2 tests for a range of loading conditions, water depths and approach speeds. Fig.28 presents the maximum non-dimensional yaw rate of turn during zig-zag manoeuvres. Considering some scatter in the full-scale trial results, a good agreement between the trials and calculations is found.

Fig.28 Maximum non dimensional yaw rate of turn

Calculated (prediction) vs. free-sailing test results (experiments) %: model scale, x: full scale

7. SAFETY ENVELOPE

The worse and less predictable the behaviour of the ship on items like course keeping ability, manoeuvrability and squat, the smaller the error margin for the helmsman. Combined with operations in confined shallow waters with high traffic density there is a necessity for focus on safety. Actions like training of the helmsman can increase the safety. A better knowledge of the influence of design variations on the sailing characteristics of the vessel can increase the safety envelope. Knowledge on the response of the vessel as a function of water depth, loading condition and bottom bathymetry are essential and can help to increase the safety margin.

If you want to reduce the number of accidents like groundings the key is to not focus on the groundings, or minor accidents. Instead, concentrate on the fundamentals that eliminate the behaviour that cause the near misses and move us up the Heinrich triangle, Fig.29. In general the primary cause of manoeuvring accidents is operator error. However poor

manoeuvring characteristics minimise the room for error and less predictable behaviour of the ship reduces the chance of a correct response.

MajorInjury

MinorInjuries

No-injuryAccidents

Unsafe PracticesUnsafe Conditions

AccidentSeverity

Reliability ofReporting

Fig.29 Heinrich�s triangle

In shallow water hydrodynamic conditions exist which may cause the ship to behave in an apparently anomalous and unpredictable manner. If these conditions are more clearly understood by those concerned with the operation of the trailing suction hopper dredgers a reduction of accidents can be expected leading to greater safety at sea.

8. CONCLUSIONS

The behaviour of trailing suction hopper dredgers on shallow water was measured. Squat, manoeuvring, course keeping and speed/ power relations were then correlated with model test results. A mathematical model describing the manoeuvring characteristics and squat response is developed and validated against the full scale and model scale data. An extensive CFD study has been conducted to gain insight in the physics behind the shallow water effects on trailing suction hopper dredgers. The investigations show that the manoeuvring and squat behaviour is sensitive for design details. The purpose of the HOSWA JIP was to improve understanding of these processes, to increase the safety of navigation with trailing suction hopper dredgers on shallow waters and to improve the mathematical modelling. The dimensions of new trailing suction hopper dredgers designs are slowly pushing to the boundaries. The knowledge gained in the HOSWA JIP can help keeping the new trailing suction hopper dredgers safe.

REFERENCES

[1] Clark, D. and Horn, J.R. �The Effect of Trailing Vortices and stern Design on Ship Manoeuvring�, The 6th International Marine Design Conference Vol. 1 Proceedings, June 1997 [2] Hoekstra, M. �Numerical Simulation of Ship

Stern Flows with a Space-Marching Navier-Stokes Method.�, PhD thesis, Delft University of Technology, Faculty of Mechanical Engineering and Marine Technology, October 1999. [3] Hooft, J.P. �The cross-flow drag on a manoeuvring ship�, Ocean engineering, 1994. [4] Hooft, J.P. and Quadvlieg, F.H.H.A. �Non-linear hydrodynamic hull forces derived from segmented model tests�, MARSIM, 1996 [5] Yumuro, A. �A consideration on Nonlinear component of maneuvring hydrodynamic force from segmented model test results �Effect of shallow water-�, J. Kansai Soc. N.A., Japan No. 237, March 2002

AUTHOR�S BIOGRAPHY

Albert J. Jurgens has studied Naval architecture and science in control engineering and works at MARIN since nine years presently as a project manager at the ships-manoeuvring department. He is responsible for projects related to the manoeuvring and course keeping of cruise vessels, tugboats, hopper dredgers, naval vessels and submarines.

Arie de Jager holds a Bsc. degree in shipbuilding from the Technical High School at Dordrecht and works at IHC HOLLAND Dredgers B.V. the dredgers design & construction company, since 1988. His current occupation as Senior Engineer for ship hydrostatics and hydrodynamics is divided into 50% Drawing office, 30% Research & Development (Involved in several EU research projects) and 20% Design.