Proceedings of ASME 28th International Conference on Ocean, Offshore and Arctic Engineering
OMAE2009
May 31-June 5, 2009, Honolulu, Hawai
OMAE2009-79587
TIME DOMAIN ANALYSIS FOR DP SIMULATIONS
Jorrit-Jan Serraris
MARIN
Offshore Department
P.O. Box 28, 6700 AA Wagenigen
The Netherlands
Email: j.j.serraris@marin.nl
ABSTRACT
As the offshore industry is developing into deeper and
deeper waters Dynamic Positioning (DP) techniques are
becoming more important to the industry. MARIN’s new
multibody time domain simulation program aNySIM is recently
extended with a module to simulate DP applications. The
model is 6 degrees of freedom and includes a Kalman filter,
PID controller and a Lagrange optimized allocation algorithm.
Thruster interaction effects are taken into account in the model.
The present paper focuses on the methods used in the
numerical DP model. A typical case for a DP operated
monohull drillship is presented and will be discussed in
comparison with model test results.
INTRODUCTION
Operations in the offshore industry are getting more and
more complex and are growing more and more together:
moored FPSOs are offloaded by dynamic positioning (DP)
controlled shuttle tankers, supply vessels use dynamic tracking
(DT) to follow the motions of a sailing vessel and FPSO’s
switch in case of heavy environmental conditions from a
mooring configuration with a submerged turret loading system
(STL) to dynamic positioning mode.
Previously at MARIN the different aspects in the offshore
industry were simulated individual by different simulation
programs. However, the developments in the offshore industry
showed the need for a more integrated simulation package in
which the different aspects of the offshore industry are
combined. To provide clients with an up to date simulation
program MARIN developed the modular multi-body time
domain simulation program aNySIM. In aNySIM the different
specialized simulations tools which have been developed and
validated through the years at MARIN are combined around
the central multi-body time domain simulation module.
Applications of the program are: multi-body side-by-side
studies see for instance Ref. 1, mooring simulations and multibody lifting operations. Recently the functionality of MARIN’s
time domain DP simulation program DPSIM has been
integrated as a module into aNySIM.
The aim of the present paper is to outline the different
components of the DP system and the techniques included in
the numerical model and to show its applications in relation to
model tests.
The present paper starts with a description of the multibody time domain core of the computer program and how
environmental forces are accounted for. Next the methods of
the different components of the DP module will be described. A
typical case for a DP operated monohull drillship is presented
and will be discussed in comparison with model test results.
NOMENCLATURE
length between perpendiculars
[m]
LPP
T
vessel draft
[m]
frontal wind area
[m2]
Af
Al
lateral wind area
[m2]
AC
current area = LPP x T
[m2]
M
mass matrix of a body
[t, tm2]
a, A
added mass matrix of a body
[t, tm2]
b
damping matrix
[kNs/m, kNms/rad]
B
matrix of retardation functions
[kN/m, kNm/rad]
c, C
hydrostatic restoring forces matrix [kN/m, kNm/rad]
F
external force in the k-th mode
[kN]
t
time
[s]
k,j
hydrodynamic response in the k-mode
due to motion in the j-mode
[-]
water density
[kg/m3]
ρw
ρa
air density
[kg/m3]
1
Copyright © 2009 by ASME
CC
CW
FC,MC
FW,MW
VC
VW
N
T
D
β
n
ct
current coefficients
[-]
wind coefficients
[-]
current force / moment
[kN, kNm]
wind force / moment
[kN, kNm]
current velocity
[m/s2]
wind velocity
[m/s2]
number of thrusters
[-]
thrust
[kN]
propeller diameter
[m]
hydrodynamic pitch angle
[deg]
propeller rate of turn
[rev/s]
thrust coefficient
[-]
torque coefficient
[-]
Cq
η TH
thruster-hull efficiency
[-]
P
proportional gain PID controller [kN/m, kNm/rad]
D
damping PID controller
[kNs/m, KNms/rad]
R
horizontal offset
[m]
natural period
[s]
TP
w
penalty weight factor
[-]
x,y,ψ
surge, sway and yaw position
[m, deg]
[m/s, deg/s]
x& , y& , ψ& surge, sway and yaw velocity
x& T , y& T Velocity at the thruster
x& S , y& S Vessel velocity at CoG
Vessel rate of turn
ψ& S
RT
Horizontal distance of thruster to CoG
αT
Thruster position wrt CoG
γC
Current direction
Vessel heading
Thruster azimuth
Advance speed
μ
α
Va
+ a kj )&x& j + b ki x& j + c kj x j = Fk
for k = 1,2...6
∑
(Mkj + A kj )&x& j +
j=1
∫B
kj ( t
− τ)x& j ( τ)dτ + Ckj x j = Fk ( t )
−∞
for k = 1,2...6
(2)
The coefficients A, B and C in the Eq. 2 are respectively the
added mass matrix, the matrix of retardation function and the
matrix of hydrostatic restoring forces based on the geometry of
the floating object. The coefficients A and B can be determined
as worked out in Ref. 4 by comparing the solution of Eq. 2 for
a harmonic oscillation with unit amplitude, described by
x=1.0cos(ωt), with the analytical frequency domain solution
for this motion. The analysis results in definition of the matrix
of added mass and the retardation function:
∞
A kj = a kj ( ω) +
1
B kj ( τ) sin(ωt )dτ
ω
∫
0
(3)
2
B kj ( t ) =
b kj ( ω) cos( ωt )dω
π
∫
0
6
kj
t
6
∞
[m/s]
[m/s]
[deg/s]
[m]
[deg]
[deg]
[deg]
[deg]
[m/s]
TIME DOMAIN SIMULATIONS
The various modules of the simulation program are
clustered around the central time domain multi-body core of the
program. At each time step the equation of motion is solved
taking non-linear vessel responses and interaction effects
between bodies into account. This section describes briefly how
the classical static equation of motion of a floating object is
implemented in the simulation program to make analysis in the
time domain possible.
Starting point is the response function of a floating
structure to waves in the frequency domain, described by:
∑ (M
Cummins-equation into account Eq. 1 and following the
approach of Ref. 3 results in:
(1)
j=1
The linear frequency domain approach does not allow taking
variations in time into account nor non-linear motion response
effects. In Ref. 2 a method is described to make Eq. 1 suitable
for analysis in the time domain by a normalization of the
potential Φ. This method is described in Ref. 3. Taking the
The derived retardation function and added mass matrix give
the relation between the motion components in the frequency
and in the time domain. This relationship makes it possible to
use the linear results of a diffraction analysis to determine the
added mass and damping of a floating object in the time
domain.
The derived equation allows taking into account arbitrary
in time varying loads, such as wave excited forces, current
forces and non-linear mooring or thruster forces, into the
equation of motion at the right hand side of Eq. 2.
The simulation program allows analysis of combinations of
multiple coupled bodies. The coupled motion response is not
described in the present study. The coupled motion response
and a practical application are described in Ref. 1.
The fourth order Runge Kutta method is used to determine
the positions and velocities of the body at the following time
step. Form the known motions at time t the positions and
velocities are estimated in a small intermediate time step t+Δt’.
At time t+Δt’ the accelerations are calculated taking the
external forces into account and solving Eq. 2 for the
accelerations only. The positions and velocities derived from
the accelerations at t+Δt’ by integration are compared with the
estimated values. When the difference is acceptable the
computation continues for the next time step Δt’. The positions
and velocities at time t+Δt are the weighted average of the
positions and velocities of the body at the time steps Δt’.
2
Copyright © 2009 by ASME
ENVIRONMENTAL LOADS
Wave forces The first and second order wave forces are
calculated based on the first and second order frequency
transfer functions obtained by diffraction analysis and a user
defined wave spectral density function or time series. Various
types of wave spectral density functions can be specified by the
user.
Wind Loads The wind forces acting on the body are
calculated in 6 dof prior to each time step. A constant or a
varying wind velocity and direction can be simulated. Various
types of wind spectra are available within the model.
Alternatively a user defined timetrace can be applied. The
following OCIMF formulas, see Ref. 6, are applied to calculate
the wind forces:
2
FWX = 0.5ρaC WFX VW
Af
2
FWY = 0.5ρaC WFY VW
Al
2
FWZ = 0.5ρaC WFZ VW
Al
2
MWX = 0.5ρaC WMX VW
A lLPP
(4)
2
MWY = 0.5ρaC WMY VW
A f LPP
2
MWZ = 0.5ρaC WMZ VW
A lLPP
The wind coefficients are to be defined by the user and can for
example be obtained by wind tunnel tests.
Current loads The current forces acting on the body are
calculated in 6 dof at each time step. If required Wichers
damping might be applied, see Ref. 7. Current can be specified
in multiple layers. The current in each layer can either be
uniform or time-varying. The current forces on the vessel are
calculated according to OCIMF definition, see Ref. 6. The
following formulas are used:
FC = 0.5ρ w CC VC2 A C
MC = 0.5ρ w CC VC2 A CLPP
• PID Controller
• Thrust allocation algorithm
The actuators of the vessel can be considered as the hardware
components of the DP system. The effective thrust delivered by
the actuators forces the Control Point (CP) of the vessel to
move its Reference Point (RP). The RP is the required position
and heading of the vessel in the earth fixed coordinate system.
The CP is the point on and the heading of the vessel, coinciding
with the RP in ideal cases. The difference between the position
of the RP and the CP is the position error. Based on the
calculated position error of the vessel the control components
determine the azimuth and thrust to be delivered by each
individual thruster of the DP system. An schematic overview of
the DP control loop is given in Figure 1. Figure 1 shows the
following components of the DP system, the functionality of
these components will be explained in more detail in the
following Sections:
• Actuators: Numerical model of the vessel and its actuators.
The actuators deliver thrust to move the CP of the vessel to
the specified RP. The effective thrust delivered by the
thrusters is forwarded to the Time Domain Solver.
• The Time Domain Solver calculates a new position of the
vessel. This position is forwarded to the Kalman Filter.
• The Kalman Filter determines the low frequency motions
and velocities of the vessel and passes these through to the
Controller.
• The estimated low frequency position and velocity are
compared to the required position and velocity. The
position error is forwarded to the Controller.
• Controller: Based on the horizontal offset from the RP and
the velocity of the vessel the controller determines the total
amount of thrust and moment to be delivered.
• The Allocation Algorithm divides the total required thrust
over the individual thrusters.
(5)
The current coefficients are to be defined by the user and can
be obtained by wind tunnel or basin model tests. The current
velocity is defined as the relative velocity between the current
and the vessel.
DP MODULE
Description of the module In analogy with a DP system
on board of a DP operated vessel the components of the DP
system integrated in the simulation program might be divided
in software and hardware components, although of course all
aspects of the simulation program are software modules. The
components in the control loop of the DP system that can be
considered as software components are:
• Extended Kalman Filter
Figure 1: Schematic overview of DP control system in the
simulation program
The actuators are to deliver the required thrust to move the
vessels CP to the RP. However, thrust degradation effects might
3
Copyright © 2009 by ASME
occur due to the relative motions of the vessel as well as due to
the presence of the hull and other thrusters. The following
thrust degradation effects are implemented in the simulation
program for the different types of thrusters:
• Azimuthing thrusters
- Thruster – Current interaction
- Thruster – Hull interaction
- Thruster – Thruster interaction
• Main propellers
- Main propeller – Current interaction
- Wake correction
- Main propeller – Hull interaction
- Main propeller – Stern tunnel thruster interaction
- Main propeller – Rudder interaction
•
Bow Tunnel thrusters
- Thruster – Current interaction
- Thruster – Hull interaction
• Stern Tunnel thrusters
- Thruster – Current interaction
- Thruster – Hull interaction
The set of equations in Eq. 6 is described in Ref. 7. The
presence of the coupling terms y& ψ& and x&ψ& makes the system
non-linear. The so-called Munk moment −(a22 − a11 ) x&y& and
the term −a62 x&ψ& are neglected. Two sets of forces are
considered in the EKF:
• FTX, FTY and MTZ are known momentary propulsion (and, if
applied, mooring) forces, which follow from the allocation
algorithm (and the sum of the mooring line loads).
The functionality of the software components of the control
loop and the azimuthing thruster interaction effects are
described below. For more details in the components of the
control system see Refs. 8 and 9.
FEXT = Fprop + Fmoor − Fwind + Fwind
Extended Kalman Filter (EKF) The calculated vessel
motions in the simulation program are a combination of low
(LF) and high frequency (HF) motions. The low frequency
motions originate from wave drift forces, current and wind
loads, the high frequency motions from the first order wave
forces. Due to the response time of the thrusters the DP system
can not compensate for the HF motions. Moreover, the
propulsion system would suffer from high wear and tear and
the fuel consumption would increase. Typically a Kalman Filter
is implemented in the DP system to determine the LF position
and drift velocity from the vessel’s surge, sway and yaw
motions. Benefit of the Kalman Filter above a cauasal filter is
that it gives minimum phase lag.
Since non-linearities might occur in the time series of the
motions of the bodies the Extended Kalman Filter (EKF) is
implemented. The EKF linearizes the non-linear signal about
the mean and covariance by means of a Taylor series
expansion. A detailed description of the EKF is given in Refs.
10 and 11. The EKF estimates the vessel’s position by solving
a set of equations of motions, using the known mass of the
vessel and the LF excitation forces. The following set of
equations is analyzed to describe the motions of the vessel in
the horizontal plane:
(M + a11)&x& = (M + a22 )y& ψ& + FX + FTX
&& = −(M + a11)x& ψ& + FY + FTY
(M + a22 )&y& + a26ψ
&& = MZ + MTZ
a62&y& + (I6 + a66 )ψ
•
FxEXT , FyEXT and MzEXT are unknown averaged
environmental forces.
The unknown environmental forces are estimated based on the
known forces and taken into account in the EKF to improve the
position estimate. The unknown environmental forces are
estimated by:
FEXT = Fprop + Fmoor = Fcurr + Fwave + Fwind
(7)
Or when the optional Wind Feed Forward function is applied:
Where
(8)
denotes the moving average over a user defined time
interval and in which FWIND is the time averaged wind force
and FWIND is estimated instantaneous from the wind
measurements. With the known and estimated forces within the
EKF the position and drift velocity of the vessel are determined
from Eq. 6. The predicted position and drift velocity are next
forwarded to the controller of the DP system.
PID Controller The estimated position of the vessel by the
EKF is a low frequency signal that is used as input signal for
the controller of the DP system. The controller of the DP
system reacts like a spring and damper combination on the
filtered low pass signal of the motions of the body and
determines the total thrust in the horizontal plane (3 dof: TxREQ,
TyREQ, MzREQ) required by the propulsion system to correct for
position errors in surge, sway and yaw.
The controller implemented in the simulation program is a
PID controller. The stiffness of the DP system is represented by
the P-coefficient, the damping is represented by the Dcoefficient. The integration coefficient I might be added to
compensate for a mean offset value. The required thrust of the
propellers is calculated by, see Ref. 5:
Tx REQ = PX Δx + D X x& + IX
∫ Δxdt
ΔT
Ty REQ = Py Δy + D y y& + Iy
(6)
∫ Δydt
(9)
ΔT
MzREQ = Pψ Δψ + Dψ ψ& + Iψ
∫ Δψdt
ΔT
4
Copyright © 2009 by ASME
the thruster layout is given in Figure 8. The same sets of PID
coefficients are applied during the model tests and the
simulations. Added mass and damping are added to the body’s
matrices a and b in Eq. 1 to tune the results of the numerical
model to the model test results.
Figure 2 presents the motions of the vessels Control Point
(CP) around the Reference Point (RP) as well as the openwater
thrust delivered by the DP system. Note that non-dimensional
values are presented. The response time is non-dimensionalized
by the natural period TP, defined by:
TP = 2π
M+a
P
(12)
The motions are non-dimensionalized by the offset amplitudes
XO, YO and ΨO, the total thrust is divided by the total openwater
thrust NTOW.
1.5
1.5
Model Test
Model Test
Simulation
Simulation
1
X/X0 [-]
Tx/Txow [-]
1
0.5
0.5
0
0
0
0.5
1
-0.5
1.5
0
0.5
T/Tp [-]
1
1.5
T/Tp [-]
1.5
1.5
Model Test
Model Test
Simulation
Simulation
1
Ty/Tyow [-]
1
Y/Y0 [-]
Selection of control coefficients The control settings have to
generate stable positioning and make effective use of the
possibilities of the thrusters. The following aspects have to be
considered while determining a set of control coefficients:
• Severity of the environmental conditions: severe
conditions require larger control values (more stiff) than
relatively calm conditions. In mild environmental
conditions optimization of the control coefficients might
improve positioning accuracy and reduce thruster loading.
In severe environmental conditions the optimization of the
control coefficients might be of vital importance: too low
control coefficients might increase thruster saturation and
result in drift off of the vessel.
• Especially in conditions in which the DP system is taxed to
the limits heading control is very important. The values of
the yaw control coefficients Pψ and Dψ can be chosen
relatively high compared to the surge and sway stiffness
and damping in order to give priority to heading control.
• Due to the inertia of the propulsion system too high
frequent azimuth variations have to be avoided, since those
may result in destabilisation, wear and tear of the
propulsion system and an increase of the fuel consumption.
A typical time to rotate 360° is 30 seconds.
• Rules of thumb for the selection of an initial set of control
coefficients are based on experience. The following rules
of thumb can be applied:
P) Set the proportional gain P to deliver the maximum
available thrust at 50%-70% of the allowable horizontal
excursion:
N.Tmax
P=
(10)
50 − 70%Rmax
0.5
0.5
0
D) The damping is set to 50-70% of the critical damping:
DDP = 50 − 70%Dcrit
Dcrit = 2 (M + a)P
0
0
0.5
1
-0.5
1.5
0
0.5
T/Tp [-]
(11)
0
Decay tests The stiffness P and damping D of the DP system
can be analyzed in calm water DP decay tests. Figure 2 shows a
comparison of the results of surge, sway and yaw decay tests
between model tests and numerical simulations. The tests are
performed for a 100,000 tonnes deepwater DP drillship with six
azimuthing thrusters. A schematic overview of the vessel and
Model Test
Simulation
Simulation
0
Mz/Mz ow [-]
Ψ/Ψ0 [-]
1.5
0.5
Model Test
-0.5
I) In model tests the integrator coefficient in the PID
controller is often set to zero. Experience shows that
instability of the system might occur. The integrator term
reduces the mean positioning error between the Reference
Point (RP) and the Control Point (CP), which is not
important from a positioning accuracy point of view, since
in terms of station keeping accuracy one is often interested
in the wave frequency vessel motions around the mean
position.
1
T/Tp [-]
-1
-0.5
-1
-1.5
0
0.5
1
1.5
T/Tp [-]
2
2.5
-1.5
0
0.5
1
1.5
T/Tp [-]
2
2.5
Figure 2: Comparison of DP decay tests for surge (top), sway
(mid) and yaw (bottom) between model tests (solid line) and
simulation (dashed line): motions (left), thrust (right).
Figure 2 shows a good agreement between the model tests and
the simulations for the decay motion and the delivered thrust in
surge and sway directions. For the yaw decay motion the
agreement between the model test and the simulation is less
good due to induced surge and sway motions during this
manoeuvre in the model tests.
5
Copyright © 2009 by ASME
Allocation Algorithm The total required force determined
by the controller is allocated over the individual propellers by
an allocation algorithm. The allocation algorithm determines
for each thruster in the configuration which amount of thrust
has to be delivered as well as the azimuth of the azimuthing
thrusters. A generic thruster allocation algorithm is developed
that allocates main thrusters, azimuthing thrusters, tunnel
thrusters and rudders. An allocation algorithm based on the
Lagrange multiplier method with penalty functions is
implemented to minimize the sum of the total squared thrust
ratio’s. The following function is minimized:
r
F( x ) =
N
∑
i=1
Ti
Tmax
2
N
+
∑
i =1
⎛⎛ T
w i ⎜⎜ ⎜⎜ i
T
⎝ ⎝ max
2
⎞
⎞
⎟ − 1⎟
⎟
⎟
⎠
⎠
2
• Thruster – Hull interaction
• Thruster – Thruster interaction
A description of how these three interaction effects are taken
into account in the simulation program is given below.
Thruster – Current interaction During DP operations the
azimuthing thrusters will experience a relative axial inflow
velocity or advance speed Va due to current and vessel motions.
The advance velocity is a function of the relative velocity at the
thruster in the vessels coordinate system. Figure 3 shows a
schematic overview of a moving vessel with azimuthing
thrusters in current. The velocity components and the applied
coordinate system and directions are defined in the figure.
(13)
r
In which x is the vector of unknowns. The last summation is
the penalty function that adds to the function when thruster
saturation occurs i.e. Ti > Tmax.
The thrusters have to be allocated such that the required xforce, the y-forces and the yaw-moment are delivered by the
thrusters.
The allocation algorithm allows forbidden zones of
azimuthing thrusters to be taken into account. When forbidden
zones are applied the procedure is as follow:
1) The algorithm is solved without forbidden zones.
2) It is checked if azimuth angles of any of the thrusters are
orientated within the forbidden zones. If none, the
configuration is applied.
3) If one or more azimuth angles are orientated within a
forbidden zone, the azimuth angle is fixed to its nearest
boundary.
4) Step 1 (including the fixed azimuth settings) to 3 are
repeated until none of the azimuthing thrusters have
azimuth angles within a forbidden zone.
Thruster failure options are available in the simulation
program. Thruster failure can either or not be taken into
account by the allocation procedure. If taken into account the
allocation is solved without the failed thruster, if not taken into
account the allocation is not aware of the thruster failure and
determines the optimum configuration as if the failed thruster
would be functional.
Azimuthing Thrusters performance Most of the recent
dynamically positioned vessels in the offshore industry are
equipped with azimuthing thrusters. Thrust degradation might
occur due the positioning of the thrusters underneath the vessel,
often in close proximity of each other, and the relative motions
between the vessel and the water. Three azimuthing thruster
interaction effects are identified and taken into account in the
simulation program:
• Thruster – Current interaction
Figure 3: Schematic overview of the coordinate system and
sign conventions for a DP operated vessel with azimuthing
thrusters in current.
The relative velocities at the thruster are calculated based on
the velocity of the vessel and the position and orientation of the
thrusters:
& SRT sin( α T ) − VC cos( γ C − μ )
x& T = x& S − ψ
y& T = y& S + ψ& SRT cos( α T ) − VC sin( γ C − μ )
(14)
In the first two terms the relative vessel velocity at the thruster
is calculated. In the last term the presence of current is taken
into account. The axial inflow velocity is calculated taking the
azimuth angle into account:
Va = x& T cos(α ) + y& T sin( α )
(15)
The hydrodynamic pitch angle is calculated based on the
advance speed:
⎛
Va ⎞
⎟⎟
⎝ 0.7πnD ⎠
β = arctan⎜⎜
6
(16)
Copyright © 2009 by ASME
In Figure 4 a typical four quadrant (4Q) propeller diagram is
presented for a ducted azimuthing thruster. The hydrodynamic
pitch angle is on the horizontal axis and is used to lookup the
thrust and torque coefficients ct and cq. Databases with a variety
of 4Q-diagrams are available within the program and in
addition can be added by the user.
In Figure 4 the red lines show the database values, the blue dots
show the values returned by the program while current
direction and delivered thrust were varied.
submersibles when the slipstream of the thruster on one
pontoon is directed towards the opposite pontoon, but also
at the stern of a monohull vessel when the slipstream is
directed towards a skeg.
An effective method to determine thruster-hull interaction
coefficients for a specific vessel is by model tests. A typical
setup is to mount a model of the vessel to a 6-component force
transducer frame. The thrusters are activated and the forces on
the component frame are measured for a range of azimuth
angles. Thruster-hull interaction tests can either be performed
for the individual thrusters as well as for the vessel as a whole
with all thrusters active. The thruster-hull efficiency is defined
by:
ηTHWOC =
Ftot
NTOW
(17)
Note that the method and formula described above apply for
thruster-hull interaction without current. Thruster-hull
interaction coefficients on current can be defined by:
η THWC =
Figure 4: Typical four quadrant (4Q) propeller diagram.
Thruster – Hull interaction The inflow field as well as the
slipstream of a thruster will be influenced by the presence of an
object in the vicinity of the thruster. Thrust degradation might
occur due to the position of a thruster underneath a vessel.
Thruster-hull interaction is accounted for in the simulation
program by a thrust degradation factor, which might either be
the default thrust reduction of 4% of the effective openwater
thrust or a user defined set of thrust efficiency coefficients. The
thrust efficiency coefficients can be defined for each
azimuthing thruster as a function of azimuth angles.
Thruster-hull interaction can be caused by a number of
different effects. For a description see fore instance Refs 12, 13
and 14. Important interaction effects are:
• The flow of the slipstream along the hull results in friction
on the hull. The thrust degradation depends on the length
of the flow along the hull. Degradation will be maximum
when a thruster is directed along the length of the vessel.
• When a thruster is orientated in transverse direction
Coanda effects might occur. The slipstream of the thruster
deflects upwards from the bilge of the vessel. The extend
of the deflection of the slipstream depends on the bildge
radius and the length of the flow underneath the hull.
• Blockage of the slipstream due to presence of the hull
occurs when a slipstream is orientated towards the hull.
Blockage effects might especially occur on semi
Ftot − FC
NTOW
(18)
In which the open water thrust TOW is corrected for the axial
inflow velocity of the propellers.
Thruster – Thruster interaction Thruster-thruster interaction is
the effect on the performance of a thruster influenced by
another thruster in close proximity. Thrust degradation occurs
when the slipstream of an upstream thruster is directed towards
the inflow side of a downstream thruster. Thruster – Thruster
interaction effects are investigated and described in Ref. 12 and
15. Figure 5 shows a downstream thruster operating in the
velocity field of an upstream thruster. The velocity field of the
upstream thruster is visualized by the blue vertical lines, the
positions of maximum velocity by the red vertical lines.
The calculation procedure in the simulation program to
calculate Thruster – Thruster interaction effects is developed by
Nienhuis, as described in Ref. 12. The effectiveness of the
downstream thruster is calculated within the simulation
program based on the azimuth of both thrusters and the
distance between the two thrusters defined as the nondimensional distance x/D. The method worked out by Nienhuis
in Ref. 12 is restricted to x/D < 14, the implemented method is
extrapolated to be applicable for larger values.
7
Copyright © 2009 by ASME
T
T
Figure 7: Thruster efficiency of a downstream thruster as
function of the azimuth angle of an upstream thruster.
UPSTREAM
THRUSTER
DOWNSTREAM
THRUSTER
Figure 5: Downstream thruster (right) operating in the velocity
field (blue lines) of an upstream thruster(left).
DP APPLICATION
Results of station keeping accuracy calculated with the
simulation program are compared to results of model tests
recently performed at MARIN on a mononhull deepwater DP
drillship. The vessel is equipped with six azimuthing thrusters.
The thruster configuration of the drillship is shown in Figure 8.
Figure 6 and 7 show the effectiveness of a downstream thruster
as presented in Ref. 12 (askeris and red straight line) and as
calculated with the simulation program (blue straight line,
DP_JET90new). In Figure 6 the efficiency is shown as function
of the non-dimensional distance between the thrusters for the
aligned configuration.
Figure 8: Schematic overview of the vessel and thruster
configuration.
The results of the simulation program and the model tests are
compared for two environmental conditions: a mild Normal
Drilling Condition (NDC) and a medium severe Standby
Condition (SBC). The environmental conditions are listed in
Table 1.
Table 1: Environmental conditions in simulations and model
tests.
Seastate
Current
Figure 6: Thruster efficiency of a downstream thruster
operating in the slipstream of an upstream thruster in aligned
configuration.
Figure 7 shows the thruster efficiency as function of the
azimuth of the upstream propeller for x/D = 3 and x/D = 6.
The results of the calculations presented in Ref. 12 and of the
implemented model show small variations. Both sets of results
show an underestimate of the effective thrust in case the
azimuth of the upstream thruster is rotated.
Wind
Hs
Tp
Type
Vel.
Type
Vel.
Type
[m]
[s]
[m/s]
[m/s]
NDC
SBC
4.6
9.6
PM
0.37
uniform
23.2
uniform
7.3
12.0
PM
0.46
uniform
28.9
Uniform
In both conditions waves, uniform wind and uniform current
were applied parallel opposite to the vessel heading of 0°.
Model Test setup
DP control system During the model test the real time DP
control system RUNSIM developed at MARIN was used, see
Refs. 8 and 16. This control program contains software DP
8
Copyright © 2009 by ASME
control components identical to the simulation program. The
following components are implemented:
• Extended Kalman Filter
• PID controller
• Lagrange allocation algorithm
In addition to the software control components the system is
equipped with the following hardware:
• Position measurement system.
• Azimuthing thrusters
The position measurement signal is the input for the DP control
system. Output of the DP control system are the required thrust
and azimuth of each individual thruster. A schematic overview
of the hardware and software components in the test setup is
shown in Figure 9.
•
Figure 9: DP model test setup.
Results of the comparison
Presentation of the results As a measure for positioning
accuracy the standard deviation of the horizontal offset, σ(R),
from the Control Point (CP) on the vessel to the Required
Position (RP) and the standard deviation of the vessel heading,
σ(ψ) are considered. The horizontal offset is defined by:
Measurements Series of heading optimization tests were
performed in which the heading of the vessel was increased
with steps of 5° off the parallel environmental conditions. The
duration of each measurement in the heading optimization
series was 0.5 hour measurement time. In addition two 3.5 hour
measurements, of which the first 0.5 hour were excluded from
the analysis as startup time, were performed near the maximum
heading at which the vessel was able to keep station.
Simulation setup
Simulation input The input for the numerical simulations is
based on the circumstances during the model tests. The
following parameters of the model test setup are used as input
for the numerical simulations:
• Environmental conditions:
- Time series wave train from model test basin
- Applied uniform current and uniform wind
• PID and Kalman coefficients optimized in the basin
• Forbidden zones
In addition the following characteristics of the vessel are
specified as input for the simulations:
• Main dimensions
• Thruster configuration
• Diffraction model
Wind and current coefficients obtained from wind tunnel
model tests
It must be noted that although the input of the simulations is
brought as good as possible in line with the circumstances of
the model tests differences between the tests and the
simulations are present. The following differences are noted:
• Interaction effects: Complex physical phenomena like
wave-current interaction effects, viscous effects in the
wave drift forces as well as the thruster interaction effects
are automatically present in the model tests. Effort has
been made to include interaction effects in the numerical
model as good as possible. It is however considered that
the interaction effects in the simulation program remain a
simplified representation of reality.
• Thruster characteristics: In the simulations the theoretical
propeller diagram is used, while during the model tests
simplified model scale thruster were used, modelled to
deliver the required open water thrust based on the known
thrust-RPM relation.
• Wind forces and moment: For the model tests schematic
topsides were modelled to represent the superstructure.
Prior to the tests the wind forces and moment (Fx, Fy and
Mx) were calibrated based on wind tunnel model test
results for one specific heading. Differences in the wind
forces and moment might be found for different headings.
In the simulations wind forces and moments from wind
tunnel model tests are applied ranging from 0° to 360°.
R = ( XRP − XCP )2 + ( YRP − YCP )2
(19)
The mean positioning error is not considered, because it is not
important from a positioning accuracy point of view.
Figure 10 shows the time trace signals from the model tests
(blue) and the numerical simulation (red) of the horizontal
offset (top) and the heading (bottom) for the maximum heading
at which the vessel is able to keep position in the Standby
Condition. The mean and the standard deviation about the
mean are included in the Figure.
In Figure 11 the standard deviations of R and ψ are
presented as a function of setpoint heading for the two
environmental conditions.
9
Copyright © 2009 by ASME
Conclusions The following is concluded from the results
presented in Figure 11:
• The simulations overestimate the capabilities of the vessel.
For both conditions the heading found from which σ(R)
rapidly increases and drift off occurs is about 5° larger in
simulations.
• Either the thrust degradation effects or the environmental
forces are underestimated in simulations.
Model Test - Horizontal Offset
150
Time trace
mean = 43.9
mean +/- std, std = 32.3
R [m]
100
50
0
0
2000
4000
6000
Time [s]
8000
10000
12000
4000
6000
Time [s]
8000
10000
12000
Simulation - Horizontal Offset
150
Time trace
mean = 37.1
mean +/- std, std = 19.6
R [m]
100
50
0
0
2000
Model Test - Vessel Heading
35
Heading [deg]
Time trace
30
mean = 23.7
mean +/- std, std = 1.6
25
20
15
0
2000
4000
6000
Time [s]
8000
10000
12000
4000
6000
Time [s]
8000
10000
12000
Simulation - Vessel Heading
35
Heading [deg]
Time trace
30
mean = 25.3
mean +/- std, std = 1.9
25
20
15
0
2000
Figure 10: Time trace signals from the model tests (blue) and
the numerical simulation (red) of the horizontal offset (top) and
the heading (bottom) for the maximum heading at which the
vessel is able to keep position in the Standby Condition.
40
NDC - Model Test
NDC - 2nd order fit Model Test
NDC - Simulation
30
from Figure 10 (Top)
σ (R) [m]
NDC - 2nd order fit Simulation
20
SBC - Model Test
SBC - 2nd order fit Model Test
SBC - Simulation
10
SBC - 2nd order fit Simulation
0
-10
0
5
10
15
20
25
Setpoint Heading [deg]
30
35
40
2
from Figure 10
(Bottom)
NDC - Model Test
NDC - 2nd order fit Model Test
NDC - Simulation
1.5
σ (Ψ) [deg]
NDC - 2nd order fit Simulation
SBC - Model Test
SBC - 2nd order fit Model Test
SBC - Simulation
1
SBC - 2nd order fit Simulation
0.5
0
0
5
10
15
20
25
Setpoint Heading [deg]
30
35
CONCLUSIONS
The DP module in the time domain simulation program
aNySIM provides the possibility to investigate dynamic motion
behaviour of a DP controlled vessel in different combinations
of waves, wind and current. The time domain program includes
realistic numerical models of a Kalman Filter, a PID controller
and a Lagrange optimization allocation algorithm. Thruster
failure can be simulated for one or more thrusters. Moreover
the program includes thruster interaction effects such as
thruster-current, thruster-hull and thruster-thruster interaction.
The program offers the possibility to investigate the effects
of different PID and Kalman coefficients. Optimum sets of
control coefficients can be determined for different
environmental conditions. This is important since a poor choice
of control coefficients might decrease a vessels position
keeping accuracy dramatically.
A comparison of the results of numerical simulations with
model tests results on a monohull DP deepwater drillship
equipped with 6 azimuthing thrusters shows differences for the
heading at which drift off occurs in mild to medium
environmental conditions of about 5°.
RECOMMENDATIONS AND FURTHER WORK
To determine the accuracy of the simulations the
performance of model tests, in which complex physical
interaction phenomena are automatically taken into account, is
recommended. Based on the results of the model tests the input
for the simulation program can be optimized to increase the
accuracy of the results of the simulations. Further, detailed as
well as general, comparison of the DP functionality of the
simulation program with model test results is recommended.
The multi-body time domain simulation program offers a
variety of possibilities for numerical analysis. Detailed analysis
on the following fields of research is made possible by
integration of the DP functionality in aNySIM:
• Multi-body DP applications: dynamic tracking.
• DP assisted mooring, in which aspects of mooring and DP
are combined.
40
Figure 11: Comparison between model test results (blue Δ and
V) and numerical simulations (red * and o) for a monohull DP
deepwater drillship in a mild Normal Drilling Condition
(NDC) and medium Standby Condition (SBC).
ACKNOWLEDGMENTS
The author would like to thank Daewoo Shipbuilding &
Marine Engineering (DSME) for their cooperation and
approval of the use of data from their model test programs.
10
Copyright © 2009 by ASME
REFERENCES
1. Buchner, B., Van Dijk, A.W. and De Wilde, J.J.,
Numerical Multiple-Body Simulations of Sideby-Side Mooring
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8. Aalbers, A.B. and Merchant, A.A., The Hydrodynamic
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Walree, R., Developments in dynamic positioning systems for
offshore stationkeeping and offloading. 5th ISOPE, 1995.
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Semi Submerisbles, Glasgow, 1986.
14. Cozijn, J.L., Buchner, B. and Dijk, R.R.T. van,
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15. Lehn, E., Thruster Interaction Effects. NSFI report R102.80, Norway.
16. Wichers, J., Bultema, S. and Matten, R., Hydrodynamic
Research on and Optimizing Dynamic Positioning System of a
Deep Water Drilling Vessel. OTC paper 8854, Houston. 1998.
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Copyright © 2009 by ASME