[PROPULSION] - MARIN · PDF file[PROPULSION] Page 3 of 25 D:\Projects\aNySim\trunk\Docs\[PROPULSION].doc The maximum thrust is limited by the available power. This power may be given

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D:\Projects\aNySim\trunk\Docs\[PROPULSION].doc

1 General

2 Thrust and torque

2.1 Propeller characteristics

2.2 Saturation

2.3 Advance speed

2.4 Propulsion load

3 Thruster – current interaction

4 Thruster – thruster interaction

4.1 Azimuthing thruster – azimuthing thruster interaction

4.2 Main propeller – stern tunnel interaction

5 Thruster – hull interaction

5.1 Azimuthing thruster – hull interaction

5.2 Main propeller – hull interaction

5.3 Tunnel thruster – hull interaction

6 Rudders

6.1 Rudder forces

6.2 Main propeller – rudder interaction

6.3 Rudder – hull interaction

1. General

The Propulsion module contains 3 types of thrusters:

Azimuthing thrusters;

Main propellers;

Tunnel thrusters.

Furthermore, the module contains also rudders.

The number of thrusters per body is unlimited, with the exception of main propellers: the

maximum per body is 2. When a body is equipped with rudders the number of rudders must

be equal to the number of main propellers.

It must be noted that all calculations are done in still water. Therefore, phenomena like

emersion of tunnel thrusters, main propellers or rudders and vertical velocitiy components

due to vessel motions are not accounted for.

The following interactions can be disabled / enabled by the user:

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Switch Control

ApplyThrusterCurrentInteract All thrusters: current speed added to advance speed.

Tunnel thrusters:

power correction;

add longitudinal hull force;

correction induced transverse hull force;

correction induced hull yaw moment;

correction impeller force.

ApplyThrusterHullInteract Tunnel thrusters: add induced transverse hull force.

Azimuthing thrusters: apply thrust deduction.

Main propellers:

add hull longitudinal and transverse force and yaw moment;

if stern tunnel thrusters are present: correction of hull forces.

ApplyUserDefHullInteract Azimuthing thrusters: apply user defined thrust deduction

factors, vary with azimuth angle.

ApplyThrusterThrusterInteract Azimuthing thrusters: addition of jet stream velocities of

upstream azimuthing thrusters to advance speed of

downstream azimuthing thrusters.

If combination main propellers - stern tunnel thrusters is

present:

correction of main propeller thrust and impeller force of stern tunnel thruster.

if hull interaction is applied: correction of hull forces induced by main propellers.

ApplyJet90_JJS Azimuthing thrusters: apply simplified jet stream model.

ApplyThrusterRudderInteract Main propellers:

correction of wake (advance speed);

add hull longitudinal and transverse force and yaw moment;

correction of thrust;

correction of power.

ApplyRudderHullInteract Rudders:

correction of inflow angle and speed;

correction of rudder forces;

add hull longitudinal and transverse force and yaw moment if main propellers don’t give thrust.

Table 1 Controllable interactions

To simulate the inertia of the propulsion system response times can be defined for RPM’s cq

pitches, azimuthing and rudder angles. The response times limit the change of these

quantities per timestep.

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The maximum thrust is limited by the available power. This power may be given as input or it

is derived from the given maximum thrust. In case the maximum thrust is exceeded the

RPM’s are reduced so that the consumed power doesn’t exceed the available power.

2. Thrust and torque

2.1 Propeller characteristics

For each thruster a propeller can be selected from the propeller database (PropDBase.ini).

The following propellers are available:

Name Nr of

blades

AeAo P/D Variable pitch

possible

Ka_4_70_Nozzle19A_4Q

Ka_4_70_Nozzle37_4Q

B_3_65_4Q

B_4_40_4Q

B_4_55_4Q

B_4_70_4Q

B_4_85_4Q

B_4_100_4Q

B_5_75_4Q

B_6_80_4Q

B_7_85_4Q

4

4

3

4

4

4

4

4

5

6

7

0.70

0.70

0.65

0.40

0.55

0.70

0.85

1.00

0.75

0.80

0.85

0.0 – 1.4

0.0 – 1.4

1.0

1.0

1.0

0.0 – 1.4

1.0

1.0

1.0

1.0

1.0

Yes

Yes

No

No

No

Yes

No

No

No

No

No

Table 1 Available propellers

The phrase “4Q” in the name of the propellers indicates that the thrust and torque coefficients

are described in 4 quadrant diagrams. Therefore the coefficients are denoted CT and CQ

resp., rather than KT and KQ as used in 1 quadrant diagrams. With the 4 quadrant diagrams

all combinations of RPM’s and advance speed are covered:

1st quadrant: RPM’s > 0 advance speed > 0

2nd

quadrant: RPM’s < 0 advance speed > 0

3th quadrant RPM’s < 0 advance speed < 0

4th quadrant RPM’s > 0 advance speed < 0

AeAo is the ratio of expanded blade area Ae and the area of the propeller plane A0. P/D is the

ratio of the pitch at 0.7R and the diameter.

For three propellers there are a range of pitches available in the database. The user may

select any value in the given ranges, the CT and CQ coefficients are determined by linear

interpolation.

It is possible with these three propellers to control the thrust with the pitch: in that case the

fixed RPM’s must be given.

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The propeller diagrams were taken from the PSP program, version 5.0. This program is

based on the data from Ref. [1].

The CT and CQ coefficients are given as function of the undisturbed inflow angle , which is

also known as the hydrodynamic pitch angle. This angle is defined as:

aV arctan

0.7 n D [rad]

in which: Va advance speed [m/s]

n revolutions [s-1

]

D diameter [m]

The thrust and torque follow from:

2 2

T r

1

2 4T = C V D [kN]

2 3

Q r

1

2 4Q = C V D [kNm]

in which: water density [ton/m3]

Vr incoming velocity [m/s]

The incoming velocity Vr is:

2 2

r aV = V +(0.7 n D) [m/s]

The consumed power follows from the torque:

P = 2 Q n [kW]

The user may give either the maximum thrust or the maximum power of a thruster. If the

maximum thrust is given the corresponding revolutions are calculated using the CT coefficient

for = 00. With these revolutions and the CQ coefficient for = 0

o the torque is found and

hence the (required) available power.

If the maximum power is given the maximum thrust is determined likewise with the CT and CQ

coefficients for = 0o.

For tunnel thrusters an extra provision for the maximum thrust has been made. Due to the

presence of the propeller drive inside the tunnel the maximum thrust to one side of the vessel

is different than to other side. To account for this asymmetry the user can define to which

side the tunnel thruster delivers its maximum thrust ( = 00).

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2.2 Saturation

The power is used to check whether a thruster is saturated. This is the case when the

consumed power exceeds the available power. The revolutions are then reduced in an

iterative procedure. As the power is approximately proportional to n3 (when Va = 0) a new

value for the revolutions is estimated with:

13

maxi+1 i

cons,i

Pn = n

P

With the new value of the revolutions ni+1 the hydrodynamic pitch angle is recalculated ( i+1),

new values of CT and CQ are retrieved with i+1 and the consumed power is recalculated

(Pcons,i+1). When the consumed power Pcons,i+1 is less than the maximum available power, or

when the maximum number of iteration steps is exceeded (10), the iteration procedure stops.

The same procedure applies to variable pitch thrusters. The pitch setting follows from the

required thrust. When the required torque is too high with this pitch the RPM’s are reduced,

as described above, until the consumed power matches the maximum available power.

2.3 Advance speed

The advance speed Va depends on the ship velocity, the thruster position and the current

speed and direction. As the current model of aNySim allows for multiple current layers the

current depends on the draft of the thruster.

The user may disable the thruster – current interactions to see the effect of the current on the

thrust. It must be noted that the advance speed is always dependent on the vessel velocity:

this dependency cannot be disabled.

For each type of thruster the advance speed is resolved in a longitudinal and a transverse

component and calculated as follows:

T S S T TX = X - R sin( ) [m/s]

) T S S T TY = Y + R cos( [m/s]

with: TX longitudinal relative velocity at thruster in ship local s.o.c. [m/s]

TY transverse relative velocity at thruster in ship local s.o.c. [m/s]

SX longitudinal ship velocity in it’s local s.o.c. [m/s]

SY transverse ship velocity in it’s local s.o.c. [m/s]

S

ship rate of turn [rad/s]

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RT distance ship CoG – thruster position [m]

T direction of line thru CoG and thruster position [rad]

In case thruster – current interactions are to be accounted for the ship velocities in the above

equations are replaced by the relative ship velocities:

'

S S C CX = X - V cos( - ) [m/s]

'

S S C CY = Y - V sin( - ) [m/s]

with: '

SX longitudinal relative ship velocity [m/s]

'

SY transverse relative ship velocity [m/s]

VC current velocity at thruster draft [m/s]

C current direction in global s.o.c. at thruster draft [rad]

ship heading in global s.o.c. [rad]

Figure 1 Relative velocity at thruster

CoG

RT

TX

SX SY

VC

C

S

S RT

TY

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So, for main propellers the advance speed is TX and for tunnel thrusters

TY . For azimuthing

thrusters the azimuth angle must be accounted for:

a T TV = X cos( ) + Y sin( ) [m/s]

with: azimuth angle [rad]

see figure below:

Figure 2 Advance speed azimuthing thruster

2.4 Propulsion load

When the thrusts of all thrusters have been established they are summed to obtain the total

propulsion load on the ship.

This propulsion load includes also a heel and trim moment. The arm of these moments

consists of the vertical distance between the thruster shaft and half the draft of the vessel:

TX

TY

Va

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Figure 3 Arm of heel moment

TP,x = Tx,i [kN]

TP,y = Ty,i [kN]

TP, Ty,i ZT,i ) [kNm]

TP, -Tx,i ZT,i ) [kNm]

TP, = ( -Tx,i YT,i + TY,i XT,i ) [kNm]

with: TP,x longitudinal propulsion force [kN]

TP,y transverse propulsion force [kN]

TP, propulsion heel moment [kNm]

TP, propulsion trim moment [kNm]

TP, propulsion yaw moment [kNm]

Tx,i longitudinal thrust component thruster i [kN]

Ty,i transverse thrust component thruster i [kN]

XT,i longitudinal position thruster i relative to CoG [m]

YT,i transverse position thruster i relative to CoG [m]

ZT,i vertical distance half the draft - shaft thruster i [m]

3 Thruster – current interaction

The thruster – current interactions are accounted for by adding the current vector to the

relative velocity vector at the thruster positions, see section 2.3.

The reported open water thrust includes relative velocity (without current) at the thrusters, the

reported total thrust includes current velocity and all interactions.

For tunnel thrusters model tests have been done with four different vessel types:

thrust

reaction force

force

½ draft

Heel arm

arm

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supply vessel;

ferry;

container ship;

hopper dredger.

These models were equipped with one bow tunnel and towed at various speeds and drift

angles. The body plans of the supply vessel, ferry and container ship can be found in Ref. [8],

Figures 1 thru 3.

From the model tests correction factors were derived for consumed power, impeller force, hull

induced transverse force and yaw moment. Moreover, the model tests showed that there

were significant longitudinal forces acting on the hull. These forces are also accounted for by

taking a fraction of the transverse induced hull force.

The correction factors are found by quadratic interpolation in one of the four databases

(BOWSUP, BOWFER, BOWCON, BOWHOP) with the relative current angle, the jet velocity

ratio and the advance ratio as arguments.

The jet velocity ratio is taken as (Ref. [8], page 9):

a

2

VVVJ =

4 T

D

and the advance ratio:

aVJ =

n D

where: Va sum of transverse vessel velocity at the tunnel position and the current

component perpendicular to the hull

T total thrust = impeller force + hull induced force

The five afore mentioned properties: consumed power, impeller force, hull induced transverse

and longitudinal force and yaw moment, are also corrected for the ratio waterdepth : draft.

The correction factors are found by quadratic interpolation in the BOWFHT database, where

these factors are given for, amongst others, two waterdepth : draft ratios: 1.25 and 2.50. For

the interpolation it is assumed that for waterdepth : draft ratios of 4 and higher the factors are

1.

Other arguments for the interpolation are the relative current angle and the jet velocity ratio,

as given above.

4 Thruster – thruster interaction

4.1 Azimuthing thruster – azimuthing thruster interaction

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When thruster – thruster interactions are to be accounted for the advance speed is increased

with the vectorial sum of the jetstreams of all upstream azimuthing thrusters. There are no

interactions between azimuthing thrusters and main propellers or between azimuthing

thrusters and tunnel thrusters.

A jetstream of an upstream azimuthing thruster is added to the advance speed of a

downstream thruster when the latter is in the downwash sector of the former. The boundary

of a downwash sector is defined as:

[deg]

where: downwash sector [deg]

L distance between upstream and downstream thruster [m]

D diameter of upstream thruster [m]

There are two routines in aNySim which calculate the velocities within a jetstream: Jet90 and

Jet90_JJS. Both routines are based on modeltests and empirical relations from Ref. [3].

Jet90 was the first implementation by Nienhuis (1984).

The Jet90 routine was taken from the PROPINT program. The calculation method of this

program is described in detail in Ref. [2].

It appeared that the Jet90 routine deviated significantly from the modeltests and calculations

in Ref. [2] and it failed to give solutions in some (unpredictable) cases. Therefore the new

routine Jet90_JJS was written: this is now the default routine used by aNySim. It is simplified

w.r.t. the Jet90 routine in so far that it doesn’t account for a “wall” above the thrusters, like a

flat keel of a vessel, and it neglects the velocity of the surrounding water, which may bend the

jetstream flow.

When the old routine is to be used the key “ApplyJet90_JJS” in the input file should be set

false.

A detailed description of the Jet90_JJS jetstream model is given in Ref. [7].

Below an example is given of the differences in results of the old and the new routine (from

Ref. [7]):

500

L 20D

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Figure 4 Thrust reduction vs. thruster distance – Jet90

Figure 5 Thrust reduction vs. thruster distance – Jet90_JJS

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The two routines have different criteria whether the jetstream is to be calculated. They both

check whether a thruster is in the downwash sector of an upstream thruster. Apart from that

the Jet90 routine uses a velocity UJ as criterion:

2 2

J a,up t,upU > 1.1 V + V [m/s]

with: Va,up advance speed upstream thruster [m/s]

Vt,up transverse speed upstream thruster [m/s]

UJ is defined as:

UJ = Va,up + {Wor - ½ Va,up sign( Va,up )} sign( Tup )

with: sign( ) function which returns the sign of the argument

up2

or a,up2

up

TW = ½ V +

D4

[m/s]

with: Tup thrust upstream thruster [kN]

Dup diameter upstream thruster [m]

The Jet90_JJS uses the distance between two interacting thrusters as criterion. If the

dimensionless distance x/D > 26, where D is the diameter of the upstream thruster, the

jetstream is not calculated.

During a simulation the azimuth angles may change such that at one moment a downstream

thruster is just outside a downwash sector and the next moment within. This can cause

sudden jumps in the advance speed and thus in the thrust of the downstream thruster.

Because these jumps are not realistic (jetstreams need time to built-up) the jetstream

velocities are filtered to obtain a more gradual change of thrust. The amount of filtering

depends on the thrust of the upstream thruster and on the distance between the two

interacting thrusters. The filter is implemented as follows:

jet,i x,mean,i

x,mean,i+1 x,mean,i

V - VV V

1 [m/s]

with: Vx,mean jetstream velocity at downstream thruster [m/s]

Vjet jetstream velocity as calculated by Jet90 cq Jet90_JJS [m/s]

filter time constant [-] i timestep index [-]

The time constant depends on the distance, the maximum jetstream velocity at the

downstream thruster and the simulation timestep:

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dp

d

v Δt [-]

with: d distance between interacting thrusters [m]

Vdp maximum jetstream velocity at downstream thruster [m/s]

t simulation timestep [s]

The maximum jetstream velocity Vdp at the downstream thruster is calculated with:

dp up b

up

aV = V

d

D

[m/s]

with: Vup jetstream velocity at upstream thruster [m/s]

Dup diameter of upstream thruster [m]

a, b curve fit coefficients [-]

This formula describes the decrease of the jetstream velocity as function of the

dimensionless distance between the two thrusters. It was taken from Ref.[3], Eq. 3.17, page

58. There are two sets of curve fit coefficients a and b for two advance ratios of the upstream

thruster. For J = 0 they are:

a = 0.805

b = 0.389

Finally, the jetstream velocity at the upstream thruster is found with its maximum thrust and

diameter (Ref [3], Eq. 3.18, page 59, with Vs = 0 en km = 1):

up

up

up

2 TV =

A [m/s]

with: Tup maximum thrust upstream thruster [kN]

water density [ton/m3]

Aup propeller disc area upstream thruster [m2]

4.2 Main propeller – stern tunnel thruster interaction

The main propeller – stern tunnel thruster interaction is accounted for in two ways: the thrusts

of the main propellers and stern tunnel thrusters are corrected and the hull forces, induced by

the main propellers, are corrected.

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The thrust correction factors are found by interpolation in the PRPINT.DAT database. The

contents of this database are based on the modeltests as reported in Ref. [5]. It has been

implemented in the STERNT and DPSIM programmes.

In Ref. [4], where the STERNT programme is described, there is an explicit warning in the

introduction that the interaction effects are large and in some cases unpredictable.

The interpolation arguments are:

the ratio of relative ship velocity and jet velocity of the main propellers Qmain:

S mainSmain

J PS SB

V D VQ = =

V 2 T + T

the ratio of relative ship velocity and jet velocity of the stern tunnel thrusters Qstern (same formula as used for Qmain, the diameter is the average diameter of the tunnel thrusters);

the relative ship velocity;

the combination of RPM’s of the main propellers.

The correction factors for the hull forces, induced by the main propellers in combination with

stern tunnel thrusters, are found by interpolation in the HULINT.DAT database. This database

is also the result of the modeltests as reported in Ref. [5] and has the same interpolation

arguments as the PRPINT.DAT database.

5 Thruster – hull interaction

5.1 Azimuthing thruster – hull interaction

For azimuthing thrusters the thruster – hull interactions may be accounted for in two ways.

Either the default thrust deduction fraction is applied, which is 0.04 for all azimuth angles, or

user defined thrust deduction factors are applied, which may vary with the azimuth angles.

During a simulation the factors are linearly interpolated to the momentary azimuth angles and

multiplied with the thrusts.

5.2 Main propeller – hull interaction

Before the thrust and torque are calculated the wake flow is determined. The wake depends

on whether rudders are present and when they are, the combination of positive and negative

RPM’s of the two main propellers.

When rudders are not present the wake is found by quadratic interpolation in results of

modeltests (Ref. [4], page 7). These modeltests concerned a twin screw supply vessel

without rudders, see Ref. [5] for model drawings.

The argument for interpolation is the direction of the relative ship velocity thru the water:

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S

S

S

Y = arctan +

X [rad]

As mentioned earlier, the ship velocities SX and

SY include current when the user has

choosen to apply thruster-current interactions.

When rudders are present and both main propellers don’t rotate the wake fraction from the

input is corrected as follows (Ref. [6], Appendix I). First the relative velocity and direction at

the rudders is determined:

2

2

SR S S S rudV = X + Y + X [m/s]

SR

S S rud

S

Y + X = -arctan

X [rad]

If SR < 0 its sign is changed to positive and the calculation continues as if the other main

propeller is the subject.

When SR > 900 a velocity correction CV is applied, which depends on the subject main

propeller (port side or starboard), see Fig. I.1 of Ref. [6], Appendix I. When SR < 900 a

correction CS is applied to the inflow direction, see same reference. The inflow velocity and

direction at the rudder follow from:

2

SR- 4

rud SR VU = V C 1 - w e [m/s]

rud = CS SR [rad]

with: CV velocity correction = f( SR) [-]

w inputted wake fraction [-]

CS direction correction = f( SR) [-]

and finally the wake:

rud rud*

S

U cos w = 1 -

V [-]

Note that when the wake fraction w is not given by the user a default value is calculated with

the vessel’s block coefficient:

w = 2 CB5 (1 – CB) + 0.1 [-]

When rudders are present and at least one main propeller delivers thrust the wake is found

by interpolation in the database VADAT.DAT. The contents of this database are based on

modeltests (Ref. [6]) and were first implemented in the RUDFOR program.

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In VADAT.DAT the wake is given for 4 different combinations of RPM’s (see Table 2), for 7

inflow directions, ranging from 00 thru 180

0 with a step of 30

0, and for 4 advance ratios, from

0 thru 0.489.

Ncomb

RPMPS > 0 - RPMSB > 0 2

RPMPS > 0 - RPMSB < 0 3

RPMPS < 0 - RPMSB > 0 4

RPMPS < 0 - RPMSB < 0 5

Table 3 RPM combinations for rudder interactions

The definition of the advance ratio used in combination with this database is:

S0

PS SB

2 V (1 - w)J =

n + n D [-]

with: 2 2

S S SV = X + Y [m/s]

w wake fraction [-]

nPS revolutions port side propeller [s-1

]

nSB revolutions starboard propeller [s-1

]

D diameter [m]

From the interpolated value of the wake (aV ) the final wake follows from:

a

S

V n D 1w = 1 -

5.2947 V [-]

Note that the dimensions of the term aV n D

5.2947 are not m/s but (m/s)

2 (denominator only),

but it is unknown which physical quantities are put in the constant 5.2947.

With the corrected wake and the relative velocity at the main propeller the hydrodynamic

pitch angle is determined and consequently the thrust and consumed power (see Section

2.1).

The hull forces which originate from the main propellers (without rudders) are expressed as

fractions of the thrust of each main propeller. In case there is only one main propeller its

thrust is equally divided over two equivalent propellers.

The fractions are found by interpolation in the HULCOEF.DAT database. The contents of this

database are derived from modeltests as reported in Ref. [5]. These modeltests were done

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with the same model of a supply vessel as used in the “Passieve manoeuvreerhulpmiddelen”

project, but without the rudders.

The interpolation arguments are the same as with the PRHDAT.DAT database, except for the

rudder angles.

In the HULCOEF.DAT database the directions of the relative velocity range from 00 thru 360

0,

with a step of 450 and the velocity ratios from 0 thru 2.5. The RPM combinations include also

combinations with zero RPM’s.

Furthermore, thrust deduction fractions are derived for each main propeller separately. In

case of positive thrust the fraction is 0.04. In case of negative thrust the fraction depends on

the block coefficient and the number of main propellers:

single screw: t = 0.058 + 0.188 CB [-]

twin screw: t = 0.058 + 0.121 CB [-]

5.3 Tunnel thruster – hull interaction

The total thrust of a tunnel thruster is split-up in an impeller force (open water thrust, without

tunnel and hull) and a hull induced force (due to the pressure differences at the hull sides).

The ratio of these forces is either given by the user or calculated with a detailed tunnel model.

This model is based on modeltests (Ref. [8]) and was first implemented in the BOTHRUS

program. It accounts for the tunnel grid properties, length, height from keel, drive position,

entrance orientation and entrance fairing.

The limitations of the tunnel model are:

tunnel tunnel

1 L D L

3;

vertical distance keel to shaft D;

entrance corner radius < 0.2 D;

angle between entrance plane and local waterline < 300;

angle between entrance plane and local frame < 300.

When for example the force ratio is 4 the impeller force is 80% of the total thrust and the hull

force is 20%. If the thruster-hull interactions are switched off with the input flag

“ApplyThrusterHullInteract” the hull induced force is set to 0. So, with the above ratio example

the remaining total thrust will be 80%.

This switch can be set for each vessel separately.

Dit hoort bij main propeller – stern tunnel interactions, dus nog verplaatsen:

The interaction effects of the main propellers are accounted for by:

a correction of the impeller force, dependent on the relative vessel velocity, the main propellers RPM combination (both ahead, one ahead and one astern, both stopped, one stopped) and the thrust of the main propellers and stern tunnel thruster;

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a correction of the hull forces, this is dependent on the same properties as mentioned above for the impeller force correction.

In case there is only one main propeller a dummy second propeller is created with the same

properties as the existing one. When there is more than one stern tunnel the sum of their

thrusts is used. Also, the average of their diameters is used for the calculation of the jet

velocity.

The correction factors are found by 2-dimensional linear interpolation in the modeltest

databases with the jet velocities of main propellers and stern tunnel as arguments. The

databases contain the results of modeltests with only one vessel type: a supplier with two

main propellers and one stern tunnel (no rudders), see Figures 4 and 5 in Ref. [5].

6 Rudders

6.1 Rudder forces

The model of the rudder forces is composed of theoretical-empirical relations, based on

modeltests with a supply vessel (Ref. [6] and [9]), and of pure empirical relations (Ref. [10]).

The lift and drag coefficients of the rudders are either given by the user or they are

calculated. When they are to be calculated there are two options: use a detailed or a simple

model. The simple rudder model is the model as used by the general Lagrange allocation.

When they are to be calculated and the inflow angle relative to the rudder is smaller than the

stall angle the lift, drag and moment coefficients are calculated with the theoretical relations,

otherwise they are determined by interpolation in the results of the modeltests. The stall

angle itself is also determined with the results of the modeltests.

After the calculation of the lift, drag and moment coefficients the local rudder forces are

converted to the vessel system of axes and corrected for the interactions with the hull and the

main propellers

First, the flow velocity and angle at the rudder position are calculated. The calculation method

depends on the main propeller.

If the main propeller doesn't rotate then:

Ur, sr f( Va, Vsr, r )

where: Va Vsr (1 w)

2

sr s rudV ( X ) 2

s sX Y

s s rudr

Yarctan

s

X

X

w wake fraction

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sX vessel relative surge velocity in its local s.o.c.

sY vessel relative sway velocity in its local s.o.c.

s

vessel turn rate

Xrud rudder longitudinal position relative to the vessel's C.o.G.

If the main propeller rotates the advance speed Va is found by interpolation in a database

with modeltest results. The flow at the rudder depends also on the main propeller diameter,

thrust and torque coefficients, and either its RPM or pitch, whichever is controllable:

UR, sr f( Va, Vsr, , , RPM or P )

with: Va = f( Vs, w, , RPM, D )

vessel drift angle:

s

s

Yarctan +

X

D main propeller diameter

h rudder height

Kt main propeller thrust coefficient

Kq main propeller torque coefficient

RPM main propeller revolutions

P main propeller pitch

The actual inflow angle then becomes:

r sr +

where is the rudder angle. The next step is to calculate (if not given by the user) the lift,

drag and moment coefficients.

The detailed model (see Ref. [11]) is dependent on the inflow angle, whether it is smaller or

larger than the stall angle .

The stall angle is determined by interpolation in modeltest results and depends on the aspect

ratio and the thickness / mean chord ratio:

),,,,,,,,,,,(,, fcrbfrrMDL cXccc

tc

hUfCCC

where: f flap angle = 2

h rudder height

c rudder mean chord (average of upper cup and lower chord clow)

t rudder thickness

ct

)tan(

32

4.0

q

t

K

K

h

D

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tail angle parameter:

tangent angle of the rudder tail

sweep angle (angle between the quarter chord line and the vertical)

cb plan form correction factor

rudder taper (ratio lower chord / upper chord)

Xcr distance rudder axis - rudder leading edge

cf rudder flap chord

See the following figures for the definition of the various properties:

Figure 6-A Rudder properties

h

cf

quarter chord line

cup

Xcr

clow

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Figure 6-B Rudder properties

C L

f

t

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The simple rudder model, as used by the general Lagrange allocation, consists of the

following formulas (in this model CM = 0):

2 2 4

D BC 1.69 1.51C sin Cdi cos Cdy sin

2 2 2

L BC 1.69 1.51C sin cos CLd Cdy sin Cdi sin cos

where: rudder angle

CB block coefficient

Cdy = 2.3

Cdi = 2CLd

0.9 Aer

CLd = 2.25Aer

Aer6.13

Aer = 2h

c

when h

< 0.7T

=

2h h

2 - 15 - 0.7c T

when h

0.7 < 0.9582T

= h

c when

h 0.9582

T

h rudder height

c rudder mean chord

T vessel draft

After this the lift and drag forces and the moment are calculated and converted to the vessel

local s.o.c. and added to the propulsion load, including a heel and trim moment:

RL ½ Ur2 h c CL

RD ½ Ur2 h c CD

RM ½ Ur2 h c

2 CM

Fxrud = RD cos( sr) + RL sin( sr)

Fyrud = RD sin( sr) + RL cos( sr)

Mxrud = Fyrud Zrud

Myrud = Fxrud Zrud

Mzrud = RM

where the heel and trim arm Zrud is taken as the vertical distance between half the draft and

the shaft of the main propeller, see Fig. 3.

6.2 Main propeller – rudder interaction

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The main propeller – rudder interaction is accounted for in three steps. The first step is the

correction of the wake at the main propellers due to the rudders as described in the previous

section.

The second step is to apply hull forces. There are two contributions to these hull forces. The

first contribution is calculated by taking fractions of the thrust of the main propellers. The

fractions are found by interpolation in the PRHDAT.DAT database. This database originates

also from the “Passieve manoeuvreerhulpmiddelen” project. The interpolation is done using

the following quantities:

the combination of RPM’s of the main propellers (see Table 2);

the direction of the relative ship velocity S (see previous section);

the rudder angle (in case of two rudders the average angle);

the ratio of relative ship velocity and thrust jet velocity:

SSmain

J PS SB

V D VQ = =

V 2 T + T [-]

The second contribution to the hull forces is calculated by taking fractions of the rudder

forces. These fractions are found by interpolation in the RHDAT.DAT database, with the

Froude number, rudder inflow angle (incl. current and vessel motions) and rudder angle as

arguments.

However, this second contribution is only applied when the main propellers don’t deliver

thrust.

Apart from a longitudinal hull force, there is also a transverse force and a yawing moment.

The latter two are set to zero in case both main propellers give positive or negative thrust

(Table 2: Ncomb = 2 or 5), the (average) rudder angle is zero and the direction of the relative

velocity is either 00 or 180

0.

Finally, the third step is to correct the thrust and consumed power. The correction factors are

also found by interpolation in a database: RPDAT.DAT, also originating from the “Passieve

manoeuvreerhulpmiddelen” project.

The arguments to interpolate with are the same as with the PRHDAT.DAT database, except

that the used rudder angle is the actual angle and not the averaged one.

Note that the modeltests of the “Passieve manoeuvreerhulpmiddelen” project, the basis for all

main propeller – rudder – hull interaction calculations, were done with a model of a supply

vessel which had twin screws without nozzles and two rudders.

6.3 Rudder – hull interaction

The rudder – hull interactions depend on whether the main propeller RPM’s are zero or not.

[PROPULSION]

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In case they are zero the induced hull forces are fractions of the rudder forces, where the

fractions are found by linear interpolation in the HRDAT.DAT database. Interpolation

arguments are:

Froude number, in which the velocity is the relative velocity at the rudder position;

relative flow angle at the rudder position;

rudder angle.

In case the main propeller RPM’s are not zero the HPRDAT.DAT is used and the fractions

are found by linear interpolation with the following arguments:

main propeller(s) jet stream ratio Qmain, see previous section;

relative flow angle at the rudder position;

rudder angle.

In both cases the relative flow must be known. This is calculated with the method as given in

Appendix I of Ref. [6]. The basis for the method is the semi-empirical method of Hirano,

which describes the flow field around a main propeller with rudder, extended for twin screw

vessels and for current directions other than head currents (1500 – 210

0).

The calculation of the relative flow at a rudder uses the following input:

relative current angle at the rudder position, incl. vessel velocities;

main propeller RPM’s and pitch;

ratio propeller diameter : rudder height;

if the RPM’s > 0: propeller thrust and torque coefficients.

The HRDAT.DAT and HPRDAT.DAT databases are created with results of model tests (Ref.

[9]), in which a spade rudder was used with an aspect ratio of 2.58, with and without a

propeller in front. Tests were done with a propeller with and without a nozzle: it appeared that

the nozzle had little influence on the rudder characteristics.

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REFERENCES

1. The Wageningen propeller series. G. Kuiper.

MARIN Publication 92-001, May 1992.

2. Beschrijving programma PROPINT. U. Nienhuis

MARIN Report 45476-5-RD, Februari 1984.

CMO Project 83 B.2.5.

3. Analysis of thruster effectivity for dynamic positioning and low speed manoeuvring. U. Nienhuis.

Phd. thesis, T.U. Delft, October 1992.

4 Beschrijving programma STERNT. U. Nienhuis, F. van Walree

MARIN Report 49156-6-RD, December 1985.

5 Interactie hekbuis-hoofdvoortstuwers: modelproeven. U. Nienhuis

MARIN Report 49156-2-RD, March 1985.

6 Passieve manoeuvreerhulpmiddelen Modelonderzoek aan romp-schroef-roer kombinatie.

F. van Walree

MARIN Report 49194-2-RD, May 1989.

7 Validation of the DP module of aNySim. J.W. Serraris

M.Sc. thesis, T.U. Delft, 2007

8 Manoeuvreren met boegschroeven – Modelproeven. F. van Walree

MARIN Report 49182-1-RD, April 1986

9 Passieve manoeuvreerhulpmiddelen: open water proeven met roer.

U. Nienhuis

MARIN Report 49194-1-HT, June 1987

10 Passieve manoeuvreerhulpmiddelen: een literatuurstudie.

U. Nienhuis

MARIN Report 49156-1-RD, November 1984

11 Computer program RUDFOR. Theory and user’s manual.

F. van Walree, A. de Wit

1989 - 1993

Documents

[PROPULSION] - MARIN · PDF file[PROPULSION] Page 3 of 25 D:\Projects\aNySim\trunk\Docs\[PROPULSION].doc The maximum thrust is limited by the available power. This power may be given