International Journal

on Marine Navigation

and Safety of Sea Transportation

Volume 6

Number 1

March 2012

1 INTRODUCTION

For a long time ship manoeuvring characteristics

were considered to be of marginal importance. Nev-

ertheless, from the operational point of view of in-

land vessels, manoeuvring characteristics play a

crucial role. Operating in restricted waterways sub-

stantially increases the risk of accidents and disasters

as a result of manoeuvring errors. To increase level

of safety on the waterways, it is important to ensure

that vessels have appropriate manoeuvring charac-

teristics. For this purpose it is necessary to develop

research methods for determining the manoeuvring

properties of inland ships.

Currently, one of the more commonly used re-

search methods in ship hydrodynamics are numeri-

cal methods. With improvements in computing pow-

er and increasingly more accurate CFD methods it is

possible to simulate more complicated cases. This

paper presents a numerical method for prediction of

ship manoeuvrability. It is based on a mathematical

model of the ship equations of motion, described in

section 3. This model requires knowledge of the co-

efficients of the hydrodynamic forces acting on the

ship. In section 4 there is presented a method for de-

termining the hydrodynamic coefficients using CFD.

On inland waters the most restrictive rules are

described in Rhine Regulations. The severity of the

Rhine Regulations is the result of difficult conditions

on the Rhine: a strong current and high traffic inten-

sity. Vessels that fulfil these requirements are al-

lowed to operate on other waterways in Europe.

These regulations specify requirements for: a mini-

mum speed of the vessel, the ability to stop, the abil-

ity to move backwards and turning manoeuvrability.

In addition, there is specified an additional manoeu-

vre - "evasive action" , which is analogous to zig-

zag test and is a specific requirement for inland wa-

ters. The main characteristic of this evasive action

[1] is the moment of switching the rudder to the op-

posite side, which occurs when the ship reaches the

desired angular velocity.

2 MATHEMATICAL MODEL OF SHIP

MOTION

Motion simulation is based on two coordinate sys-

tems. The first one is the global, stationary coordi-

nate system. The ship position and orientation is de-

termined in the global coordinate system. The

second one is the local coordinate system. The cen-

tre of the local coordinate system is located at the

centre of gravity of the ship. Equations of motion of

the ship are written in the local coordinate system.

Figure 1 shows the two coordinate systems used in

the paper. It also shows the velocity components of

the vessel.

Application of CFD Methods for the

Assessment of Ship Manoeuvrability in Shallow

Water

T. Górnicz & J. Kulczyk

Wrocław University of Technology, Poland

ABSTRACT: Safety in water transport plays a significant role. One way to increase safety in the waterways is

to ensure that ships have proper manoeuvrability. Evaluation of manoeuvring properties performed at an early

stage of design can detect problems that later would be difficult to solve. To make such an analysis the nu-

merical methods can be used. In the paper the nu

merical method to evaluate the ship manoeuvrability on the

shallow water is presented. Additionally author shows the procedure of determining hydrodynamic coeffi-

cients on a basis of CFD calculation. The simulation results of inland ship was compared with experimental

data.

Figure 1. Coordinate systems and velocity components of the

vessel.

The movement of the ship is considered to be

planar motion (limited to three degrees of freedom).

This study only analysed small velocities at

which sinkage and trimming of the ship is minimal.

Therefore, these phenomena are not considered in

the research..

Interaction between the hull, rudder and propel-

lers are only simulated by appropriate coefficients.

In inland vessels the centre of gravity is far lower

than in marine ships. In addition, the centre of gravi-

ty is located near the centre of buoyancy. As a result

of this , the roll of the vessel is relatively small and

could also be neglected.

Wavelength on inland waterways is relatively

small in proportion to the length of the vessel. In the

study the influence of waves on the trajectory of the

ship was not taken into consideration.

The equations of motion (1) were written for the

centre of gravity of the ship. The left side of equa-

tions describes the ship as a rigid body. On the right

side of equations there are hydrodynamic external

forces (X, Y) and the hydrodynamic moment (N)

acting on the vessel.

mu mvr X

mv mur Y

Ir N

−=



(1)

where:

m – vessel mass; u –longitudinal velocity; v –

transversal velocity; r – yaw rate; ˙- dot, the deriva-

tive of a variable over time; I

– moment of inertia

of the vessel; X,Y,N – hydrodynamic force and mo-

ment acting on the vessel according to the axes of

local coordinate system. Detailed information about

model can be found in [2].

External hydrodynamic forces and the hydrody-

namic moment acting on the ship were written like

in the MMG model [3], as a sum of the compo-

nents.

HPR

XX X X

YY Y

NN N N

= ++

= +

= ++

(2)

where:

, Y

, N

– hydrodynamic forces and moment act-

ing on the bare hull; X

, N

- force and moment in-

duced by the operation of propellers, X

, Y

, N

–

forces and moment induced by flow around the rud-

der.

2.1 Hull

To determine the hydrodynamic forces induced by

flow around the hull the following mathematical

model was used [3]:

() ( )

()

H x T vv vr y

rr vvvv

H y v r x vvv vvr

vrr rrr

H zz v r vvv vvr

vrr rrr

X m u R u X v X m vr

Xr X v

Y mv Yv Y mu r Y v Y v r

Y vr Y r

N jrNvNrNv Nvr

N vr N r

−− + + + +

=− ++− + + +

=−+++ + +



(3)

where:

, m

– added mass coefficients, in x and y direc-

tion; j

– added inertia coefficient; R

(u) – hull re-

sistance; X

, X

,..., Y

, Y

,... - coefficient of hydro-

dynamic forces acting on the hull; N

, N

, ... –

coefficients of hydrodynamic moment acting on the

hull.

2.2 Rudders

Hydrodynamic forces induced by rudder laying can

be calculated on the basis of equations (4). The

model was taken from[4].

(1 ) sin

(1 ) cos

( ) cos

R RN

R HN

R R HH N

X tF

Y aF

N x ax F

=−−

=−+

(4)

where:

- coefficient of additional drag; a

- ratio of addi-

tional lateral force; x

– x-coordinate of application

point of F

; x

- x-coordinate of application point of

additional lateral force; δ rudder angle; F

– normal

hydrodynamic force acting on the rudder.

The value of normal force F

was determined

on the basis of model (5).

( )

0, 5·

1 (1 · ( ))

2 (2 )·

()

0.6

cos

1 (1 )

2·

N RN R

F ACU

U w Cg s

K ss

gs K

s wU

α δ γβ

ββ

=−+

−−

−

=−−

′

= −

′ ′′

= −

(5)

where:

ρ – water density; A

– rudder area; C

– normal

force coefficient; U

- effective rudder inflow ve-

locity; C – coefficient, dependent on ruder angle

sense (C≈1.0); D – propeller diameter; h

– height of

rudder; w

- wake fraction at propeller location; w

wake fraction at rudder location; w

- effective

wake fraction at rudder location, in straight ahead

ship motion; U – total velocity of vessel; β – drift

angle; n – rotational speed of propeller; P – propeller

pitch; x’

– non-dimensional x-coordinate of appli-

cation point of F

; r’ – non-dimensional yaw rate.

2.3 Propellers

This paper uses a mathematical model of hydrody-

namic forces generated by two propellers.

(1 )( )

X tT T

N tT Td

=−+

=−−

(6)

where:

t - thrust deduction factor; T

– thrust generated

by propellers; d- distance from the axis of propeller

to symmetry plane of the vessel, in y direction.

Propeller thrust was determined on the basis of

the relation (6).

1 22

cos

·exp( 4.0 )

()

(

)

T nDK J

K J a aJ

ββ

−

′′

−

=++

(7)

where:

T – propeller thrust; J - advance coefficient; a

, a

– K

polynomial coefficients; w

- effective

wake fraction in straight ahead ship motion; x’

–

non-dimensional x-coordinate of propeller..

Values of thrust coefficients used in the calcula-

tions were derived from experimental research.

3 DETERMINING OF HYDRODYNAMIC

COEFFICIENTS

3.1 The coefficients of the hydrodynamic forces

acting on the hull

The model of the hydrodynamic forces described in

section 2.1 requires knowledge of the values of hy-

drodynamic coefficients: X

, X

,..., Y

, Y

,..., N

, .... The literature, including [5], describes the

empirical formulas derived for marine ships. Due to

the complicated nature of these forces, the results

can be insufficiently accurate. For this reason, pref-

erence is given to other, more accurate method to

determine the coefficients of hydrodynamic forces.

One of these methods is the CFD calculation. In ad-

dition to the providing accurate results, numerical

calculations enable the model to take into account

specific operational conditions of the inland ship, for

example, that the impact of shallow water on the hy-

drodynamic forces acting on the hull.

o determine the coefficients of hydrodynamic in-

teractions it is necessary to have a database con-

taining the values of the hydrodynamic forces and

the corresponding to them values of velocity (u,v,r)

and the acceleration (

,,uvr



) of the ship. One way to

obtain such a database is to simulate with help of

CFD software the series of tests (manoeuvres): yaw ,

yaw with drift, sway test. Figure (2) shows the tra-

jectory of a ship during these manoeuvres.

The values of the added mass (m

,) coeffi-

cients , added inertia (j

) coefficient and the ship

resistance (R

(u)) can be obtained on the basis of

empirical methods or CFD calculations.

During the yaw manoeuvre the ship transverse

velocity v and acceleration



are zero. The equa-

tions of the hydrodynamic forces acting on the hull

can be simplified to the following form:

()

H x T rr

H x r rrr

H zz r rrr

X mu R X r

Y murYrYr

N jr N N r

=−− +

=− ++

=−+ +



(7)

In the results of CFD simulation of the yaw ma-

noeuvre the relation between hydrodynamic forces

and moment (X

, Y

, N

) and velocity u, r, and ac-

celeration



is obtained. The least squares method

can be used on the results from yaw simulation to

approximate the following coefficients: X

, Y

rrr

, N

rrr

During the sway manoeuvre the speed r and the

acceleration

,ru



are zero. The equations of hydro-

dynamic forces acting on the hull can be simplified

to the following form:

()

H T vv vvvv

H y v vvv

H v vvv

X R Xv X v

Y mvYvYv

N Nv

=−++

=− ++

= +



(8)

When simulating the sway manoeuvre using CFD

the data showing the relation between hydrodynam-

ic forces acting on the hull (X

, Y

, N

) and veloci-

ties u and v is obtained. The least squares method is

used on the results from sway simulation to approx-

imate the following coefficients: X

, X

vvvv

, Y

vvv

, N

vvv

The CFD simulation of the yaw with drift ma-

noeuvre provides the calculations for the rest of hy-

drodynamic coefficients: X

, Y

vvr

, Y

vrr

, N

vvr

, N

vrr

More information about determining hydrody-

namic coefficients can be found[6]

Figure 2. The manoeuvres for determining the hydrodynamic

coefficients: A) yaw manoeuvre B) yaw with drift, C) sway

manoeuvre.

3.2 Rudder characteristic.

A mathematical model of hydrodynamic forces act-

ing on the rudders, described in section 2.2, requires

knowledge of the normal force coefficient (C

) . The

characteristics of isolated rudders have been de-

scribed in many sources, for example [7]. Working

conditions of rudders installed under the hull of the

inland vessels may be significantly different than

these from a single rudder. This is due to the pres-

ence of wake and propeller streams as well as the

impact of the limited depth of the waterway. In order

to determine the correct characteristics of the rudder,

more accurate methods should be used.

In studies to determine the characteristics of the

rudders CFD methods were used. The calculations

were carried out in two ways. Firstly, the approach

shown in Figure 3, was based on calculations of a

rudder located in the propeller stream. The geometry

of propeller was replaced by the disk with a pres-

sure jump. The value of the pressure jump was

equivalent to propeller thrust. Restriction of flow

around a rudder at the top and bottom edge was

simulated by two flat plates. The symbols c and d on

the scheme denotes distance between rudder and

plates. The main advantage of this approach is the

low complexity of the discrete model, which signifi-

cantly accelerates the calculations.

The second method used in the study was to build

a full geometric model of the entire hull with propel-

lers and rudders. This solution required the usage of

discrete models with a much larger number of ele-

ments. CFD calculations of the entire hull give more

accurate results but require large computing power.

Figure 4 shows an example of a discrete model of

the stern of the ship with the rudders and simplified

models of propellers.

Additional information on the rudder force nu-

merical calculations can be found in [8].

Figure 3. Scheme of model for rudder force calculations.

Figure 4. Example of discrete model of the stern of the ship

with propellers and rudders.

4 CFD METHODS

In the studies the Ansys Fluent commercial CFD

software was used. It is based on a finite volume

method. To solve the three-dimensional turbulent

flow the RANS method was used. The turbulence

model k-ε-Realizable was used. The boundary layer

was calculated using the Enhanced Wall Treatment

model. The result of research presented in [9]

shows that this model works best for flows with

large pressure gradients and a separation phenome-

non.

The calculations mainly used a structured mesh

with hexagonal elements. Unstructured (tetragonal)

grids were only used in the calculation of the hull

with rudders and propellers, due to the complicated

geometries involved.

To simulate the yaw, yaw with drift, sway ma-

noeuvre the moving mesh technology was tech-

nique was utilised. Parameters of mesh motion were

defined in an additional batch program (UDF) to the

system Ansys Fluent (UDF). The program is written

in C language.

5 RESULTS

Numerical calculations were performed for a model

of inland transport vessel (ship A). The scale model

was λ = 21.81.

For the same scale a physical model was created

and tests in the towing tank were performed. All

tests were performed in the shallow water. In this

paper the results for h/T=1.89 are presented. Table 1

contains the main parameters of the ship A.

Table 1. The main parameters of the ship A

______________________________________________

Parameter unit ship value

______________________________________________

LPP m 85.50 3.920

B m 11.45 0.525

T m 2.65 0.122

CB - 0.0853

LCB m 43.71 2.004

Number of propellers - 2

Number of rudders - 2

______________________________________________

Parameters of the propeller (model)

_____________

Parameter unit value

______________________________________________

D m 0.08

P/D - 1.1102

- 0.7474

Z - 4

______________________________________________

Parameters of the rudder (model)

_____________

Parameter unit value

m 0.092

0.0103

Profile - N

ACA0012

______________________________________________

5.1 Direct Comparison

CFD calculations are characterized by a number of

restrictions and simplifying assumptions. In the nu-

merical calculations of yaw, yaw with drift and

sway test, which are necessary for determining the

value of hydrodynamic coefficients, a problem with

calculation stability occurred . After disabling two-

phase flow (air-water) the problem disappeared.

Therefore, the calculation of coefficients of hydro-

dynamic forces acting on the hull X

, Y

, and N

does not include the impact of the free surface. This

problem didn't appear in the calculation of the re-

sistance of the ship. In the subsequent research only

situations with low ship speed (Fr = 0.12) were ana-

lysed. When the ship speed is relatively low the in-

fluence of free surface on the hydrodynamic force is

negligible.

The figures 5,6,7 shows a comparison of results

obtained from CFD calculations and the experi-

mental test performed in the towing tank. The charts

show the course of the hydrodynamic forces X

, Y

and hydrodynamic moment N

during the yaw and

sway test. During the tests in towing tank the PMM

mechanism was used. The worst comparison be-

tween CFD and experiment is for X

. This force is

relatively small and it is very susceptible for differ-

ent factors and disturbances. The comparison for

hydrodynamic moment N

is much better. The hy-

drodynamic moment depends mainly on huge differ-

ence of pressure on both sides of a hull. And the

pressure field was accurately predicted by CFD cal-

culations.

Figure 5. Comparison of the results of the experiment and CFD

calculations for the characteristic of X

forces obtained during

yaw test.

Figure 6. Comparison of the results of the experiment and CFD

calculations for calculations for

force obtained during yaw

test.

Figure 7. Comparison of the results of the experiment and CFD

calculations for the N

moment obtained during the sway test.

5.2 Indirect Comparison

In the towing tank the model tests of ship A were

performed. The following tests were performed:

yaw, yaw with drift and sway. On the basis of the

experimental results the coefficients of hydrody-

namic forces were calculated. Similarly, on the basis

of the CFD calculations the results of a second set

of hydrodynamic forces coefficients was deter-

mined. For both sets of coefficients the simulation of

standard manoeuvres was performed.

The manoeuvre results were obtained from the

author's program to simulate the motion of the ship.

The following figures show the comparison of the

results obtained from experimental tests and com-

puter simulation. The figures 8,9,10 illustrate the

characteristic charts for the turning circle manoeu-

vre, evasive action and spiral test.

Figure 8. Comparison of trajectory for turning circle manoeu-

vre, rudder δ = 35 °.

Figure 9. The comparison of characteristic chart of the eva-

sive action.

Figure 10. The comparison of characteristic chart of the spi-

ral test.

6 SUMMARY

The paper presents a numerical method for evaluat-

ing manoeuvring characteristics. Research on a

model of the inland vessel showed good agreement

between numerical calculations and experimental re-

sults.

Due to problems with the stability of the CFD

code only the mono-fluid calculations were per-

formed. Further studies will be carried out to calcu-

late the free surface effects, and taking into account

phenomena such as sinkage and trim.

BIBLIOGRAPHY

[1] COMMISSION DIRECTIVE 2008/126/EC European Par-

liament and of the Council laying down technical require-

ments for inland waterway vessels, Official Journal of the

European Union L 32/1.

[2] Właściwości manewrowe statku śródlądowego na wodzie

ograniczonej, Tabaczek T., Górnicz T., Kulczyk J., Zawi-

ślak M, Raporty Instytutu Konstrukcji i Eksploatacji Ma-

szyn, SPR, Politechnika Wrocławska, 2010.

[3] The Specialist Committee on Esso Osaka Final Report and

Recommendations, Conference Proceedings of the 23rd

ITTC, Volume II, Venice, 2002.

[4] Kijima, K., Tanaka, S., Furukawa, Y., Hori, T.On predic-

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[5] The Manoeuvring Committee Final Report and Recom-

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Volume II, Venice, 2002

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and Stephen R. Turnock, Elsevier, 2007.

[7] Metoda oceny właściwości manewrowych statku śródlądo-

wego. Górnicz T, Raporty Instytutu Konstrukcji i Eksploat-

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Kulczyk Jan, Tabaczek Tomasz, XXV. Plavebné dni, 2008,

[9] Computional Fluid Dynamics A practical Approach, Jiyuan

Tu, Guan Heng Yeoch and Chaoqun Liu, Elsevier, 2008