5. INTERACTION EFFECTS
5.1. Continuity law and Bernoulli's law
In order to understand the interaction effects between solid bank /wall, bottom or other ships on the behaviour of a ship moving along, it is necessary to study the pressure distribution around the ship's hull and the relevant basic laws governing flow phenomena.
The pressure distribution around a moving ship is shown in fig 5-1. There is a high pressure area around the ship's bow, called bow cushion, and a similar, but weaker, high pressure area near the stern, called stern cushion. Along the most of the ship's length there is a low pressure area.
Fig. 5-1
The relations between velocities and pressures in the flow are governed by two basic physical laws: the continuity law and the Bernouilli law. They are explained below on the example of a flow through a canal with varying cross-section (Fig.5-1)
Continuity law: Velocity x cross section area along the canal= const
V1 x S1 = V2 x S2 = const.
Consequence: if the cross section area decreases, the velocity increases and vice versa
Bernoulli's law: fluid pressure + static pressure + dynamic pressure along the canal = const.
static pressure = atmospheric pressure + head of water
dynamic pressure = C x velocity squared
Consequence: if the fluid velocity increases, then the dynamic pressure increases and the sum of fluid pressure and static pressure decreases, and vice versa.
Using these two basic laws it is easy to understand and explain the interaction effects.
5.2. Wall effect. Suction force
When the ship is moving close to a solid wall or bank then there is a reduction of the flow cross section area between the ship and the bank (from S1 to S2, fig.5-2) . Considering this case in a way that the ship is at rest and the water flows against it with a speed equal to the ship's speed, then in the space between the ship and the bank (S2) the water velocity increases, because of the reduced cross-section area. On the other side of the ship the flow cross-section area is not reduced and the water velocity does not change (when comparing to the open-water situation). If the water velocity increases, then according to the Bernouilli's law the dynamic pressure increases and the fluid and static pressure decrease. The difference of pressures on both ship sides creates a force that is directed from the higher static pressure area towards the lower static pressure area. This is the suction force drawing the ship closer to the bank. (Fig.5-2)
Fig. 5-2
The suction force is proportional to the speed of the ship squared and inversely proportional to the distance from the bank. Suction forces calculated for an example ship are shown below:
Fig. 5-3 |
|
||
|
Suction force (Tanker 148000 tdw) |
||
|
Distance a [m] |
Speed [kn] |
Force [Ton] |
|
50 |
5 10 |
21 83 |
|
30 |
5 10 |
31.6 124.5 |
|
5 |
5 10 |
63 250 |
|
|
|
|
Fig. 5-4
The suction force developing on the ship's side together with the bow cushion effect make the ship bow to yaw outward the wall and the stern to move closer to the bank. The rudder is to be used to counter this effect by providing force acting against the suction force and providing moment turning the bow toward the bank.
Fig. 5-5
If the rudder is not used in time or if the rudder force is insufficient, then the ship takes a sheer and - because of the bank proximity - the suction force action point moves closer to the stern. As a result the suction effect becomes stronger and this might turn into a dangerous situation.
Using suction force to the advantage
Two examples how to use the suction force to the advantage are shown below:
1. Sailing in a bend canal
Fig. 5-6
2. Passing through a narrow passage
Fig. 5-7
Entering the passage closer to the portside bank the suction force helps turning to starboard as needed (Fig.5-7). If the ship is entering closer to the starboard island, the suction develops on the wrong quarters (starboard aft) and opposes the intended turning to starboard.
5.3. Interaction between two ships
When two ships are close together, either on the same course or in the opposite course, there is a restricted space between them. In this space there is an accelerated flow and in consequence the fluid and static pressure drop. Suction forces tend to bring the ships closer, but the bow cushions have the tendency to push the bows apart (moving on the same course). This is shown diagrammatically in fig. 5-8.
The lower part of the figure shows the case when a small ship overtakes much larger ship while passing very close to the latter. The interaction effect on the larger ship is nil, because of high inertia. But the small ship experiences suction and rejection forces depending on its positions relatively to the large ship.
Fig. 5-8
Some rules for interaction
Maintain a sensible speed. Excessive speed magnifies the interaction.
If possible, recognize and anticipate the interaction. It is much preferable to avoid sheer than to try steer out of it.
Interaction effects are greater in shallow water.
When coming alongside other ship the area of the safest approach is near the middle of the ship. The greatest interaction effects occur near the bow or the stern of another ship.
5.4. Interaction between the ship and the bottom. Squat
Definition
A certain pattern of pressure distribution develops around a moving ship (see Chapter 2). Along the most of the ship's length there is a low pressure region and consequently a certain drop of the water level. Lower pressure acting on the ship's bottom means a decrease of the buoyancy force. To compensate for the partial loss of the buoyancy force the ship must sink with regard to the initial position which will increase back the pressure acting on the ships bottom, thus leading again to the balance of the ship's weight and the buoyancy force.
In a shallow water or in a fairway with restricted cross-section the cross-section area of the flow below the keel is reduced and that, in turn, causes an acceleration of the flow and reduction of fluid pressure. Because of that a suction force is created, similarly as in case of a ship sailing along a bank, but now the suction force is acting downward. This suction force pulls the ship towards the bottom and reduces the clearance between the keel and the bottom of the fairway. (fig. 5.9). This clearance reduction is called squat.
Fig. 5.9
Squat occurs even in a deep unrestricted water, but it is much more pronounced in a shallow water and, particularly, in a canal. In a canal the restriction of flow cross-section area under the keel and around the ship body is much larger, so the water is much accelerated and the water level is depressed further, causing a significant reduction of the under the keel clearance. From the point of view of safe passage it is important to predict the squat.
Simple considerations lead to the following conclusions:
*Squat is proportional to the speed of the ship squared, because dynamic pressures are proportional to the velocity squared. The dynamic pressure change is responsible for the change of the fluid pressure acting on ship's hull.
*Squat is proportional to the block coefficient, because the higher the block coefficient the larger the hull bottom area where the restriction of the flow cross-section area occurs
*Squat is proportional to the restriction of the flow cross-section, so called blockage effect equal to the ratio of the cross- section area of the ship to the fairway cross-section area.
The blockage coefficient is defined as:
Where:
- Ship cross-section
Cross-section of the fairway (fig. 5-10).
The blockage coefficient could also be defined as:
Fig. 5-10
In a wide shallow fairway the width of the fairway used for calculation of the blockage coefficient is taken as a width of influence or the effective width, that is a width of water influenced by the moving ship. According to Barrass it is equal:
and then the blockage coefficient for unrestricted width is calculated as:
Open water conditions exist if there are no restrictions within the effective width. The effective width is taken in the area shown in fig. 5.-11 depending on the multitude of ships breadths:
Fig. 5.11.
Formulae for squat assessment
There is a number of different formulae for squat calculations. The simplest formulae are formulae proposed by Barrass (fig.5-12):
Fig. 5-12
Formulae by Barrass:
Ship in shallow water: Squat
Ship in the canal: Squat
Where: S - squat in meters
V - ship speed in knots
AS - cross-section of the ship in m2
AC - cross- section of the canal in m2
h - depth of water in meters
T - draft of the ship in meters
Note: these formulae provide approximate values of squat for the ship in even keel
More recently Barrass developed universal formula valid for open water as well as for canal navigation, where the blockage coefficient for open water is used:
where: C1 = 20 for ship in a canal
C1 = 30 for ship in open water
Formula by Tuck (1967):
The above formula could be simplified taking:
and then:
in the above formulae FR is the Froude's Number
Formula by Watt:
Squat:
Diagrams developed by the British National Physical Laboratory (BMT)
On the basis of systematic model tests of squat the BMT developed the diagram allowing to calculate the squat in shallow water for tankers. The squat is a function of ship length, water depth, ship speed and ship's trim (see fig.5.13).
Fig. 5.13 - BMT diagram for ship squat
All formulae for the calculation of squat are approximate and for a particular case the squat calculated could be different. Fig. 5.14 shows a comparison of squat values calculated by Barrass, Tuck and BMT methods for the tanker of LCC size (full scale) sailing in a shallow water of the depth 18 and 25 m with different speeds. As it is seen the differences obtained using different methods are rather high.
Interesting comparison of squat values calculated using Tuck formula with those obtained in full-scale measurements for a ship sailing in lower river Elbe is shown in fig. 5-15. Although in particular measurements the discrepancies are rather high, the mean line for the measurement points shows a good correlation with Tuck formula.
Fig. 5-15
Effect of heeling, trim and turning on squat
Effect of heeling:
Fig. 5-16 |
|
|
|
ïª [deg] |
ï„T [m] |
|
1 |
0.41 |
|
2 |
0.85 |
|
3 |
1.26 |
|
4 |
1.67 |
|
5 |
2.09 |
|
|
|
|
||
Sinkage when turning
Fig. 5-17
Effect of trim
Fig. 5-18 |
|
Entering or leaving shallow bank
When the ship is entering a shallow bank then due to restricted cross-section area and a reduced pressure under the bow portion of the ship the dynamic trim to bow may occur and the ship may hit the bottom with the bow.
When the ship is leaving a shallow bank and entering a deep-water area, the opposite may occur due to the increase of the pressure under the bow, and the ship may hit the bottom with the stem.
Fig. 5-19
Chapter 5- Interaction effects 5 - 12
4
8
12
16
ship speed [knots]
water depth [m]
10
15
20
25
40
35
30
trim
1/500 to bow
1/100 to stern
stern
bow
0 trim
1/100 to stern
1/500 to bow
0 trim
0.5
1.0
1.5
2.0
2.5
3.0
3.5
squat
in m
Length of the ship [m]
100
150
200
250
300
350
! Large scale diagram available upon request
Squat
[m]
0.5
1.0
1.5
2.0
8
10
12
14
16
ship speed [knots]
Barras
Tuck
BMT
h=18m
h=25m
Fig. 5-14
Undisturbed water level
Accelerated flow
Low pressure region
Suction force
Suction force
Clearance reduced
AS
T
B
BC
h
Beff
h
AS
8 10 12 14 16
Number of ship's breadths
0.80
0.70
0.60
0.50
0.40
CB
Area of open water confditions
Area of restricted water cnditions
measurements
mean line
1
0.5
0
-0.5
Squat acc. to Tuck
Squat acc. to full scale measurements
Accelerated flow, lower pressure
Accelerated flow lower pressure
New desired heading
Wyszukiwarka