1. SIMULATION OF SHIP HANDLING

1. Model tests for design and training

Model tests are widely used for the assessment of hydrodynamic characteristics of ships. Ship resistance, powering, seakeeping and manoeuvring characteristics are typical ship properties that are assessed using model tests. Model tests are performed in specially constructed towing tanks or as in case of manoeuvrability, sometimes in open water areas - ponds and lakes, because of the need to have rather wide water areas.

In case of manoeuvrability models are used in the design stage of a ship in order to predict manoeuvring characteristics of the ship to be built. Models are also used for training purposes.

In the first case models could be used for the estimation of hydrodynamic coefficients describing forces in manoeuvring motion; the models are tested then in towing tanks - they are usually smaller (3 to 6m long) - towed under so called planar motion mechanism (PMM). Models could be also used for the estimation of manoeuvring characteristics of ships, such as turning circle, stopping distance, dynamic stability on straight courese etc., and then they are somehow larger, remote controlled or manned, and tested in open water areas.

In the second case, when models are used for training purposes, they are much larger (8 to 15 m long), manned and manoeuvring exercises are performed in wide open water areas.

In order to achieve good prediction of manoeuvring characteristics based on model tests as well as a realistic representation of various maneouvres during the training, the models must properly represent the behaviour of real ships. They have to be constructed and operated according to requirements of simulation laws. This applies to the geometrical characteristics of the model itself as well as to kinematic and dynamic charcterics of the motion.

1.2. Scaling down the ship's geometry

First of all, the geometric similitude criteria must be satisfied. It means that the ratio of all linear dimensions of the full-scale vessel to the corresponding dimensions of the model must be the same and equal to the model scale - λ (fig, 1-1):

Fig. 1-1

Although the dimensions of the model are reduced, it is seen from the above figure that the corresponding angles for the model and the full- scale vessel have the same value.

Of interest will be also the knowledge of the relationship between any surface for a model and a ship. For example, a full-scale vessel rudder area is:
and a model rudder area is:
(fig. 1-2).

Fig. 1-2: Comparison of rudder areas for a ship and a model

From the geometric similitude criteria, we have:
and
.

Hence the following ratio of ship and model rudder areas:

All other corresponding areas of the full-scale vessel and the model are also proportional to the model scale squared, i.e.:

Corresponding volumes of the full-scale ship and the model are proportional to the model scale in the power 3:

because:

Ship volumetric displacement is:

Model volumetric displacement is:

Then we can write:

The same procedure can be extended over the calculation of corresponding mass (ship displacement)

Where:

Assuming that
(because of the geometric criteria- the same form of hulls for a full-scale ship and a model) and neglecting the differences in salt water and fresh water densities we get:

1.3. Flow pattern around ship body and forces acting

A ship moving through the water generates a characteristic flow pattern. This flow pattern consists of the system of surface waves moving with the ship, the boundary layer along the ship hull and the ship wake (the fluid volume with fluid motion induced by the moving ship).

It is obvious that for good reproduction of ship's behaviour, the flow patterns for a model and a full-scale vessel must be similar. The similitude laws assure the similarity.

The wave system moving with the ship is caused by the gravity forces. Around the moving ship the pressures are different in different areas. Around the bow and also around and little behind the stern there are high pressure areas, while along the majority of the ship body there is a low pressure area. Pressure differences materialize in the differences of water level (fig.1.3). Then there is a bow wave corresponding to the high pressure area at the bow (bow cushion) and a stern wave corresponding to the high pressure area at the stern.

Fig. 1-3 Pressure distribution along the moving hull

Along the ship body the water level drops down. This is called a primary wave formation. Water particles raised by the moving ship fall down and initiate oscillatory motion creating a wave train. This is called a secondary wave formation (fig.1.4).

Fig. 1-4 The secondary wave formation

Behind the stern of the ship the bow wave system interferes with the stern wave system creating a complex wave system that is observed in reality. Apart from transverse waves shown in fig 1-4, there are also observed short oblique waves as shown in fig. 1-5.

Fig. 1-5 The secondary wave system

In order to generate waves on the water surface, some energy must be transferred from the moving ship. This energy is proportional to the wave amplitude squared, and is equal to the work of the wave resistance force:

Where: r₀² is wave amplitude squared; g is the acceleration due to gravity.

When the ship is moving in a viscous fluid like water, then around the ship hull a boundary layer is created. In the boundary layer water particles close to the ship's skin stick to the skin due to the friction and their relative velocity with respect to the ship is zero. Particles farther from the skin have a higher relative velocity and eventually at some distance from the hull their relative velocity is equal to the ship speed, i.e. their absolute velocity is equal zero. The boundary layer is thin, at a stern of a 200 m long ship moving at 20 knots its thickness is equal to about 1m. Within the boundary layer the absolute velocities of water particles change from zero on the outside the boundary to the velocity equal the ship speed close to the skin, and relative velocities change from zero close to the ship skin to the ship speed at the outside of the boundary (fig. 1-6).

At the stern of the ship at a certain point a separation of the flow occurs, behind this point vortices are created and the flow is highly turbulent (fig.1-6)

Fig. 1-6.

The viscosity of water causes that between the hull skin and the surrounding water a tension (friction) is created. Summation of the elementary tensions over the hull surface gives the total viscous (frictional) force acting on the ship opposite to the direction of motion. This force is viscous or frictional resistance.

If the ship is moving over the water at a constant speed on a straight course, the total force opposing this motion, or the ship total resistance is composed of two components:

• pressure resistance (wave making resistance, form resistance - hull curvature and transom form influence)

• viscous (frictional) resistance

If one wants to accelerate or to slow down the ship, then additional force must act on the ship, and the value of the additional force is almost equal to the acceleration times the mass of the ship:

The same happens with the water particle moving along a curved hull surface: the velocity vector of the particle changes its direction thus there is acceleration, so the force must act on the particle. Therefore the particle will exert a force on the ship's hull, ant this kind of force will be called the inertia force as well. These inertia forces are caused by the change of the water particles speed or the direction of particles motion (ultimately they are “seen” on the hull surface as pressure forces).

In order to properly simulate the behaviour of the model in comparison to a full-scale ship all forces must be properly scaled down. It is clear that three kind of forces act on the manoeuvring ship:

• Viscosity forces

• Gravity forces

• Inertia forces

Different laws of dynamic similitude govern scaling (or modelling) of different forces categories.

The laws of dynamic similitude serve two purposes:

1. determining the conditions of the tests (e.g., velocity, pressure, temperature),

2. determining the method of scaling the measured quantities from model to full-scale ship.

Gravity forces are proportional to the mass of the ship (or the mass of particle) and the acceleration.

The wave resistance that is caused by the gravity forces is equal to:

where: S_w is wetted surface

C_W is a non-dimensional wave resistance coefficient that is a function of the non-dimensional parameter called Froude's number, so C_W = f (Froude number)

The governing law for the wave resistance is FROUDE'S law of similitude

FROUDE'S law of similitude says that: if one wants to obtain the same scaled (coefficients C_W) wave resistance (pressure) forces, then the Froude's numbers for the ship and its model must be equal:

where g is the acceleration due to gravity.

Viscous (frictional) forces are proportional to the velocity squared, wetted surface and the friction coefficient.

Viscous (frictional) resistance is equal to:

where: C_f is a non-dimensional viscous resistance coefficient (friction coefficient) that is function of the non-dimensional parameter called Reynolds number, so C_f = C_f (Reynolds number).

The governing law for the viscous resistance is REYNOLDS law of similitude.

REYNOLD'S law of similitude says that if one wants to obtain the same scaled (coefficients C_f) viscous resistance (frictional) forces, then the Reynolds numbers for the ship and its model must be equal:

where: ν_S and ν_M are kinematic viscosity coefficients for sea and fresh water

V_S and V_M is velocity of a ship and a model

Inertia forces are proportional to the mass of ship and acceleration. To inertia forces the general law of dynamic similitude applies.

1.4. Conditions of similitude for model tests and work with models

The REYNOLDS law and the Froude's law provide different dynamic conditions for the model tests and the work with models. From the Reynolds law we have:

and from there it is possible to calculate the model velocity:

Neglecting the difference between the kinematic viscosity coefficients for sea water and fresh water, and bearing in mind that
(model scale), we have:

With a model scale equal to 24 as in IÅ‚awa centre, the model speed should be equal to 24xV_S, and it means that for the 10 knots ship speed, the model speed should be 24x10knots=240 knots. This obviously is impossible.

From the Froude's law we have:

and from this equation it is possible to calculate the model velocity:

For example with the model scale equal to 24, we have:

i.e. for 10 knots ship speed, the model velocity should be approximately 2 knots.

It is obvious that the only possibility is to run models according to the Froude's law. Reynold's law cannot be satisfied simultanously. This introduces, however, some inaccuracy called a “scale effect”, which arises from neglecting the Reynolds law of similitude, or, in other words, it results in not reproducing properly the viscous (frictional) resistance.

Viscous resistance is proportional to the friction coefficient C_f , to velocity squared and to the wetted hull surface. If the friction coefficient would be the same for the ship and the model, then there would be no scale effect. However, the friction coefficient is a function of the Reynolds number. This relation is shown in fig.1-7. From the figure it is seen that the friction coefficient for the large model is about 30 to 40 % higher than for the ship, so if the viscous resistance is about 30 % of the total resistance, then the scaled total resistance of the large model is about 10 to 15 % larger than the scaled ship resistance (both are scaled down proportionally to the model scale³). This is compensated by a slightly higher number of propeller revolutions on the model. The resulting inaccuracy in the modelled manoeuvring qualities of the ship is very small.

When the model used is small, say 2 to 3 m long, then the error is much larger, in particular in cases where the laminar flow around a hull or appendages may be present.

Fig. 1-7.

When the Froude's law of similitude is used, then the ratio of forces , including resistance, for the ship and the model is as follows:

If Froude's law is applied, then C_RS = C_RM, and knowing that V_S/V_M =
; S_WS/S_WM = λ², and neglecting the difference of densities of sea water and fresh water (lake), that is rather small, we get:

This applies also to the inertia forces. The ratio of the inertia forces for the ship and the model is:

Knowing that the ratio of the mass of the ship to the mass of the model is: m_S/m = λ³, and the ratio of accelerations is: a_S/a_M = 1, we get:

This ratio applies to all forces acting on the manoeuvring ship.

Scale coefficients applicable to other physical quantities are shown in the table 1-1.

Table 1-1: relationship between geometric and kinematic parameters for Froude identity

Item	Value of ship / model ratio
Length, Beam, Draft, Turning, Diameter, Stopping, Distance, and other linear dimensions	Scale
Windage, Rudder area, etc	scale^2
Volume, Displacement, Force	scale^3
Speed	scale^1/2
Angle	1
Rate of Turn	1/scale^1/2
Time	scale^1/2
Acceleration	1

From the table it is seen that applying the Froude's law of similitude the time scale is equal to the square root of the model scale. This is important conclusion meaning that in the model work the time is running faster than in reality. With the model scale equal to 24, the time scale is approximately equal to 5. This means that all manoeuvres are performed faster than in reality. For example, if some manoeuvre in the full scale requires one hour, then the same manoeuvre in the model scale takes about 12 minutes.

Models work in the model time, not in the real time!

This must be remembered when manoeuvring the model. It results from this that “feeling for a ship” based on correct timing can be affected by the above time scale, however trainees raise this problem very rare.

This important conclusion means that all actions that depend on time must be appropriately scaled down. On the model the times to reverse the engine, times to put the rudder from zero position to full rudder or times to operate tugs are properly adjusted - see figs. 1-8 to 1-9.

Fig. 1-8 History of rudder deflection for a ship and a model

Fig. 1-9 Reversing of engine for a ship and a corresponding model

In figure 1-10 a simple comparison of kinematic and geometric parameters of a turning trial executed with the same rudder deflection for a ship and its model is shown. One can say that dimensionless turning diameter D_T expressed in ship lengths is the same for a ship and a model (assuming that the above mentioned scale effect can be neglected). The same happens when considering stopping distances.

Fig. 1-10 Comparison of a turning manoeuvre for a ship and a reproducing model

1-12

Chapter 1- Simulation of ship handling

High pressure area

Low pressure aerea

High pressure area

Bow wave

Stern wave

•

•

Bow wave system

Stern wave system

Water particles raised

Water particle falling

Transverse waves

Oblique waves

Secondary wave system

Separation point

Boundary layer thickness

*

Separation zone

Separation point

5 6 7 8 9 10

Log Re

0.007

0.006

0.005

0.004

0.003

0.002

0.001

C_F

Turbulent flow

Laminar flow

ship

model

Small

model

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