SPECIAL GREENTECH | Operational Optimisation
Efficient adjustment
of propulsion power
Trim optimisation In the last ten years, Denmark-based FORCE Technology has done extensive research and development on trim optimisation. The work has been documented in various
projects, and the latest study has resulted in some interesting findings on the factors causing
the change in propulsive power and the weight of these factors. The study has also shown
which methods are the most precise in finding optimum trim.
T
he trim study was described more thoroughly in Ship&Offshore’s GreenTech
supplement in 2011; the following article focuses on the study’s results.
Much of the trim research performed by
FORCE Technology has been centred on
possible savings, the results of the research
being used for trim guidance. However, the
physical effects that reduce the propulsive
power have not been investigated thoroughly. It has been claimed that the gain
is a result of changed flow around the bulbous bow. This is correct, but changes in
the propulsive coefficients could also be a
part of the performance change.
32 Ship & Offshore | GreenTech | 2012
Findings in short
The physics behind changed propulsive
power when trimming a vessel have been
analysed in order to detect the origin of the
changes. An example has been investigated
for a large cargo vessel at a partly loaded
draught and reduced speed. For this draught,
the propulsive power can be reduced by
more than 10% with a forward trim seen
relative to even keel. Approximately 80% of
the reduction is caused by changes in the
residual resistance coefficient, i.e. changes
in the flow around the bulbous bow. The
remaining 20% is from improved propulsive efficiency at the trimmed condition.
The performance has been investigated
with model tests, RANS CFD and potential theory CFD. Where the model tests
were carried out as self-propulsion, the
CFD was limited to calculation of the
hull resistance in order to keep the calculation time at a reasonable level. Trim
guidance with RANS CFD was found to
be in line with the result from the model
test. However, this was not the case for
the potential theory CFD calculations,
which were found to underpredict the
change in performance when trimming.
The basis for these findings is explained
in detail below.
Again, the aim is to reduce all values in order to gain from the trim.
The allowance coefficient (CA) is normally
kept constant except for vessels with a large
variation in the draught, e.g. a VLCC in
loaded/unloaded condition. Change in the
friction resistance coefficient (CF) is, according to the ITTC standards, related to the Reynolds number for the flow along the hull:
0.075
CF = ______________
(log10(Re) - 2)2
Where Re is the Reynolds number defined by:
V ∙ Lwl
Re = ________
v
Figure 1: Sketch of the vessel centreline
and water level at the three conditions
Trimming effects
In general, the physical effects that reduce
the propulsive power (PD) when a ship is
trimmed can relate to the hull resistance
(RT) or the total propulsive efficiency (ŋT )
as shown in the formula
The kinematic viscosity of sea water (v) is
constant for the same temperature. From
(4) and (5) it can be derived that the frictional resistance coefficient is a function of
the waterline length (Lwl), and that they are
inversely proportional (Figure 2).
The large reduction in water line length
fromeven keel to forward trim is when the
bulbous bow submerges.
RT ∙ v
PD = _____
ŋ
Trim
-2.0m
0.0m
2.0m
-2.5%
0.0%
1.8%
The speed (v) is kept constant.
It is obvious that the aim is to reduce the
resistance and/or increase the efficiency in
order to gain from trimming.
In the following, the hull resistance and propulsive efficiency are investigated. The effects are treated individually although they
might be connected. The findings are based
on model tests unless otherwise stated.
An example is made with reference in
the -2.0m and 2.0m trimmed conditions
seen relative to the even keel condition, a
Froude number of 0.128. These trims have
been chosen due to the waterline variation
around the bulbous bow (Figure 1).
At forward trim (-2.0m) the bulbous bow
is submerged, at even keel it is at the water
level, and at aft trim it is above the water
level. Changes in the stern region are modest – the waterline moves a bit up and down
the stern. Within those trims, the change in
propulsive power is:
Re [-]
1.91E+09
1.95E+09
2.00E+09
CF [-]
1.415E-03
1.412E-03
1.407E-03
0.2%
0.0%
-0.3%
ΔLWL [%]
T
Trim
-2.0m
0.0m
2.0m
ΔPD [%]
-11.3%
0.0%
20.7%
ΔPD Lwl [%]
ual resistance coefficient (CR), also called the
wave resistance coefficient, is often said to be
the effect most affected by trim (Figure 3).
It can be seen in the figure that residual resistance is more than five times larger at aft
trim compared with forward trim.
Trim
-2.0m
0.0m
2.0m
CR [-]
6.80E-05
2.34E-04
5.41E-04
ΔCR [-]
70.9%
0.0%
131.7%
ΔPD CR [%]
-8.8%
0.0%
16.4%
Table 3: Change in power due to residual
resistance coefficient at Fn=0.128
It can be concluded by comparing the savings in Table 4 with Table 1 that the major
part of the reduction in propulsive power is
caused by changes in the residual resistance
coefficient. By analysing the centrelines and
water levels shown in Figure 2, it is easy to
see that the variations relate to the changed
flow around the bulbous bow. For the -2.0m
trim, the bulbous bow is slightly submerged
and should be working properly. The opposite is the case for the 2.0m trim condition
in which the bulbous bow is above the water level and working more as an unconventional elongation of the waterline.
Summing up the contributions from the
resistance parts to the savings in propulsive
power gives the following result:
Trim
-2.0m
0.0m
2.0m
Table 2: Change in power due to waterline length at Fn=0.128
ΔPD S [%]
-0.3%
0.0%
0.1%
ΔPD Lwl [%]
0.2%
0.0%
-0.3%
At -2.0m trim, the waterline length has decreased by 2.5% compared with the even
keel condition. However, since inverse proportionality is present, the result is an increase in the propulsive power of only 0.2%.
The effect compared with the overall savings
is minimal. The form factor (1+k) is often
kept constant at each draught in order to
save time in the towing tank. Due to limited
form factor data for the vessel in trimmed
conditions, it is kept constant for now and
set at 1.13 throughout this article. The resid-
ΔPD CR [%]
-8.8%
0.0%
16.4%
ΔPD RT [%]
-8.9%
0.0%
-16.2%
Table 4: Change in propulsive power due
to hull resistance at Fn=0.128
By comparison with Table 1, it can be concluded that changes in the hull resistance
(caused by the residual resistance coefficient)
result in most of possible savings by trimming the vessel. The change from the hull resistance is 78 to 82% of the total change. 
Table 1: Change in propulsive power due
to trim at Fn=0.128
The residual resistance coefficient
The total resistance coefficient can be described by the following formula:
CT = CR + (1 + k) ∙ CF + CA
Figure 2: Waterline length as a function
of trim
Figure 5: Residual resistance coefficient
as a function of trim at Fn=0.128
Ship & Offshore | GreenTech | 2012 33
SPECIAL GREENTECH | Operational Optimisation
Improved propulsive efficiency
The hull efficiency is a function of the thrust
deduction (t) and the wake fraction (w).
1–t
ŋH = _____
1–w
From (8) it can be concluded that the
thrust deduction should decrease and the
wake fraction increase in order to gain
from trimming.
The thrust deduction is a function of the
propeller thrust (T) and the hull resistance.
Trim
-2.0m
0.0m
2.0m
w [-]
0.209
0.181
0.17
Δw [-]
15.5%
0.0%
-6.1%
ΔPD w [%]
-3.5%
0.0%
1.3%
Table 6: Change in power due to wake
fraction at Fn=0.128
T – RT
t = ______
T
It has already been shown that the hull
resistance changes when the vessel is
trimmed. Naturally, the propeller thrust
will also change as the speed is kept constant. However, the relation is not necessarily constant (Figure 4).
The thrust deduction changes with both
speed and trim. Most interesting is the peak
for Fn=0.128 around -2.0m trim. This is
when the propeller submergence decreases
to a critical level. For the two higher speeds,
the peak will come later due to increased
dynamic sinkage and stern wave.
Trim
As the vessel speed is kept constant, changes in the wake fraction can only relate to
the propeller inflow velocity (Figure 5).
As for the thrust deduction, there is a peak
around -2.0m trim. However, here it is
present for all three speeds.
-2.0m
0.0m
2.0m
t [-]
0.166
0.145
0.147
Δt [-]
14.9%
0.0%
1.7%
ΔPD t [%]
2.5%
0.0%
0.3%
Table 5: Change in power due to thrust
deduction at Fn=0.128
As seen in the table, the changes in thrust
deduction result in significant changes in
the propulsive power. However, due to (8),
changes in the thrust deduction must be
seen relative to changes in the wake.
The wake fraction is a function of the vessel
speed and the propeller inflow velocity (VA).
It can be seen in Table 6 and Table 7 that
for the forward trim the thrust deduction
and wake effect balance each other, and the
result is a gain of 1.0% in total.
Propeller efficiency
The propeller efficiency can be identified in
the open water curve. The curve is a nondimensionalised result of a propeller test
in open water, i.e. not in the wake of a vessel (Figure 6).
The open water curve is plotted as a function of the advance ratio , where (n) is the
propeller revolution and (D) is the propeller diameter.
VA
J = ______
n∙D
It has already been concluded that the
propeller inflow velocity was affected by
the trim. The same goes for the resistance
resulting in changed thrust and required
revolutions since it is a fixed pitch propeller.
Even minor changes in the advance ratio
result in a changed propulsive power since
the open water curve for the propeller efficiency is inclined for the actual advance
ratio.
Relative rotative efficiency
The relative rotative efficiency is defined as
the ratio between the moment on the propeller in open water (Qow) and moment
behind the ship (Qship).
Qow
ŋrr = _____
Qship
The moment measured on the ship/model
differs from the moment in open water
due to non-uniform flow and the level of
turbulence (Figure 7)
As for the thrust deduction and wake fraction, it is clearly visible when the propeller
is affected by limited submergence due to
forward trim.
Trim
ŋRR [-]
ΔŋRR [-]
ΔPD ŋRR [%]
-2.0m
0.0m
2.0m
1.005
0.988
0.982
1.7%
0.0%
-0,6%
-1.7%
0.0%
0.6%
Table 8: Change in power due to relative
rotative efficiency at Fn=0.128
Also, the relative rotative efficiency results
in significant power savings.
Summing up the contributions from the
propulsive effects to the savings in propulsive power gives the following result:
Trim
-2.0m
0.0m
2.0m
-2.0m
0.0m
2.0m
ΔPD t [%]
2.5%
0.0%
0.3%
J [-]
0.751
0.752
0.729
ΔPD w [%]
-3.5%
0.0%
1.3%
ŋ0 [-]
Δŋ 0 [-]
0.638
0.639
0.629
ΔPD ŋ0 [%]
0.1%
0.0%
1.5%
-0.1%
0.0%
-1.5%
ΔPD ŋRR [%]
-1.7%
0.0%
0.6%
0.1%
0.0%
1.5%
ΔPD ŋT [%]
-2.7%
0.0%
3.7%
Trim
ΔPD ŋ0 [%]
V – VA
w = ______
V
Table 7: Change in power due to propeller efficiency at Fn=0.128
Table 9: Change in power due to propulsive effects at Fn=0.128
Figure 4: Thrust deduction as function of
trim
Figure 5: Wake fraction as a function of
trim
Figure 6: Open water curve is plotted as
a function of the advanced ratio
34 Ship & Offshore | GreenTech | 2012
The change from the propulsive efficiency
is 18-24% of the total change.
Adding up the savings from changes in
hull resistance and propulsive coefficients
should give a result equal or close to the
reference (Table 1):
Trim
-2.0m
0.0m
2.0m
ΔPD RT [%]
8.9%
0.0%
16.2%
ΔPD ŋT [%]
-2.7%
0.0%
3.7%
ΔPD [%]
-11.5%
0.0%
19.9%
Ref [%]
-11.3%
0.0%
20.7%
Diff [%]
-0.3%
0.0%
-0.7%
Table 10: Change in propulsive power
due to trim at Fn=0.128
It is seen that the difference is less than
1% when compared with the reference.
The difference originates in the correlation
between the different effects and is not included in this analysis.
It is concluded that the residual resistance
coefficient is the factor most affected by
trim. However, the propulsion affects the
results at a level detectable in model tests
and should not be neglected.
Figure 7: Relative rotative efficiency as a
function of trim
Figure 8: Comparison of different trim
guidance methods
The difference in the methods
It is seen that there is good correlation between the performance change predicted
by RANS CFD, resistance and self-propulsion model test. As shown in Section 5,
the propulsive coefficients give a distinct
effect, hence the self-propulsion result deviates some. Potential theory CFD gives a
trim guidance in line with the other, with
the maximum forward trim as the optimum. However, the savings are far more
modest, and if, for example, the vessel is
constrained to -1.0m trim, no gain at all
is predicted. Potential theory CFD was
not made for 1.5m and 2.0m due to convergence problems. However, this may 
The fact that most of the changed propulsive power originates in the residual resistance coefficient makes it interesting to do
tests, or alternatively CFD calculations, for
the hull resistance alone.
The computations are performed with the
Reynolds-averaged Navier-Stokes (RANS)
solver Star-CCM+ from CD-adapco and
the potential theory CFD code SHIPFLOW
from FLOWTECH. The RANS CFD are calculated in model scale, the same as the
model tests, with 7,000,000 cells. The potential theory CFD is with 12,500 panels
(Figure 8).
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Ship & Offshore | GreenTech | 2012 35
SPECIAL GREENTECH | Operational Optimisation
Figure 9: Bow wave at -2.0m trim and Fn=0.128. Model test and
RANS CFD
be expected with the highly deformed free
surface in the bow region as indicated in
Figure 10. Common to all of the three
curves, with origin in the hull resistance, is
that they predict maximum forward trim
as the optimum, and if even more extreme
forward trim were investigated, they might
have that as the optimum. This is not the
case for self-propulsion since propeller
coefficients change to the worse for trims
more forward than -2.0m.
Figure 9 and Figure 10 show the flow
around the bulbous bow at -2.0m and
2.0m trim from both model tests and calculated with RANS CFD. It is easy to see the
increased wave generation when trimming
aft resulting in increased residual resistance
coefficient. The flow around the stern is
somewhat unchanged as Figure 2 also indicates. Hence it can be concluded that the
major contribution to the changed residual
resistance coefficient is the wave generation
around the bulbous bow.
From the RANS CFD solution it is possible
to deduct the nominal wake fraction (Figure 11).
It is obvious that there is a significant difference between the two wake curves. The
wake from the model tests is the effective
wake, i.e. measured during a self-propulsion test. The RANS CFD wake is the nominal wake, i.e. it originates directly from the
velocity of the water at the propeller plane
without the propeller present. Because the
propeller influences the boundary layer
36 Ship & Offshore | GreenTech | 2012
Figure 10: Bow wave at 2.0m trim and Fn=0.128. Model test and
RANS CFD
properties and possible separation effects,
the nominal wake fraction will normally be
larger than the effective wake fraction [4].
However, the slope of both curves is around
the same, apart from the peak at -2.0m trim
at the effective/model test curve from the
limitations in the propeller submergence,
as discussed earlier. [Anm.: ??]
Concluding remarks
It has been concluded from the analysis
of model tests that the major effect resulting in changed propulsive power when a
vessel is trimmed is the residual resistance
coefficient acting on the hull resistance.
However, the propulsive coefficients are at
a level of approximately 20% of the total
savings and cannot be disregarded totally if
accurate power at the specific condition is
needed, e.g. for performance evaluation.
If the result is to be used as trim guidance,
a rather good result can be reached only
with resistance RANS CFD calculations.
The calculation time for resistance RANS
CFD is at an acceptable level even for the
large number of speed points needed in a
trim test.
In the present study, potential theory CFD
strongly underpredicts the change in performance. The resistance varies too little
when trimming the vessel and not at all
for small forward trims. Therefore trim
guidance based on potential theory CFD
did not give practical applicable results in
this case.
Future activities
Understanding the physics of trim is an
ongoing project. The findings presented in
this paper are what have been investigated
so far. The current work focuses on:
XX Better estimation of form factor with
both model tests and various CFD calculations.
XX Thrust deduction estimation with RANS
CFD including a volume force as propulsion.
XX The correlation between nominal and
effective wake, which needs to be clarified
in order to use the nominal wake for propulsion prediction.
A trimmed ballast condition should be
tested and calculated because we have often found surprising results for this with
large trim to the aft resulting in better propulsive efficiency.
Figure 11: Wake fraction calculated with
RANS CFD and from the model tests.