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International Conference on Computer Applications in Shipbuilding 2017, 2628 September 2017, Singapore
© 2016: The Royal Institution of Naval Architects
A NUMERICAL AND EXPERIMENTAL STUDY OF RESISTANCE, TRIM AND SINKAGE OF AN INLAND
SHIP MODEL IN EXTREMELY SHALLOW WATER
Q Zeng, R Hekkenberg, C Thill and E Rotteveel, Delft University of Technology, the Netherlands
SUMMARY
Inland vessels generally experience a resistance increment when the water in which they sail is extremely shallow. In
this case, resistance extrapolation from ship model to full scale becomes complicated, and the traditional approaches do
not often lead to satisfactory predictions. In this study, both numerical and experimental methods were applied to
investigate the ship resistance, trim and sinkage in extremely shallow water. In the numerical calculations, the model
initially has a trim and sinkage obtained from the model tests. The overset mesh technique was used to save the meshing
effort. A 1/30 scaled model, which is only allowed to pitch and heave, was used in the model tests. It was found that, in
extremely shallow water, the ITTC57 correlation line is not sufficient to extrapolate the resistance.
NOMENCLATURE
Molecular dynamic viscosity (m2 s1)
t
Turbulent viscosity (m2 s1)
Density of water (kg m3)
f
C
Frictional resistance coefficient
CFD Computational Fluid Dynamics
c
Air clearance (m)
EFD Experimental Fluid Dynamics
Fn
Froude number
h
Fn
Depth Froude number
GCI The grid convergence index
h
Water depth (m)
I
The turbulent intensity
L
Length of ship model (m)
f
R
Frictional resistance (N)
S
Wetted surface at zero speed (m2)
ave
U
Reynolds averaged velocity (m s1)
x
u
Velocities of flow in x direction (m s1)
y
u
Velocities of flow in y direction (m s1)
'u
The rootmeansquare of the turbulent
velocity fluctuations (m s1)
ukc underkeel clearance (m)
V
Velocity of ship (m s1)
W
Width of the towing tank (m)
1. INTRODUCTION
Model tests are the most common way of predicting the
resistance of ships. A correlation line [1] with a constant
form factor [2] are used to build a relationship between
the resistance of the ship and its scaled model. The
definition of frictional resistance coefficient (Cf) in
model tests is as follows:
2
0.5 f
f
R
CVS
, (1)
where
f
R
is the drag force,
V
the ship speed and
S
the
wetted surface when the ship speed is zero.
When the water becomes extremely shallow
(
/ 2.0hT
), however, the correlation line may not be
valid, and the assumption of a constant form factor
becomes false. This is probably due to the backflow
and/or a different wetted surface. Therefore, the
traditional way might cause avoidable errors in the
resistance prediction in shallow water.
To fix this, Toxopeus [3] proposed a modified form
factor for shallow water using doublebody simulations.
Raven [4] suggested considering the scale effect into the
viscous resistance calculation in the extrapolation. But
the different trim and sinkage, which belongs to the
important features of shallow water, are ignored.
Likewise, shallow water effects specific on frictional
resistance were not well discussed.
Alternatively, ship researchers, like Schlichting [5],
Lackenby [6] and Jiang [7], built empirical formulas
trying to predict ship resistance in shallow water based
on the results from deep water tests. Their methods are
physically reasonable and practically useful, but they are
often limited by the ship types they used, and the graphs
they offered still need to be validated for a different ship
type.
Computational Fluid Dynamics (CFD) is another option
to do ship research in shallow water [810]. Compared
with model tests, the physics around the model can be
better understood and forces on the ship surface can be
easier achieved.
Therefore, this study applied CFD method especially to
reveal the changes of friction on the model surface in
shallow water. A number of model tests were also used
to validate the simulations and investigate ship behave
ours in shallow water. It was confirmed that the resis
tance, trim and sinkage were significantly affected by the
water depth and showed nonlinear changes. The discre
pancies between the calculated friction and the ITTC57
line were explained, and a piecewise function is probably
needed for a shallow water correlation line.
International Conference on Computer Applications in Shipbuilding 2017, 2628 September 2017, Singapore
© 2016: The Royal Institution of Naval Architects
2. CFD METHOD
Figure 1: Computational domain
CFD was applied to solve the timeaveraged Navier
Stokes equations. All simulations were completed on a
commercial package ANSYS Fluent (Version 18.1). In
the simulations, ship model had an initial trim and an
initial sinkage, and those values were obtained from the
model tests. Making the model fixed to its final situation
can make it easier to converge and also, to avoid groun
ding while the algorithm is seeking for the applicable
equilibrium situation.
2.1 THE COMPUTATIONAL DOMAIN
The computational domain is shown in Figure 1. It
stretches
L
(the length of the ship) in front of the ship
and 2
L
in the back. The width (
W
) is set comparable to
the width of the towing tank. The water depth (
h
) is a
variable and depends on the position of the water bottom.
The air clearance (
c
) is set to a constant (10 meters).
Due the symmetry of the domain, half of the model was
used.
In the simulations, Case 0 simulates a deep water situa
tion for comparison, as shown in Table 1.
T
is the draft
of the ship and
h
the water depth. Two other cases of
shallow water (
/ 2.01hT
and 1.20) were chosen for the
shallow water study. The Froude number (
Fn
) was from
0.0566 to 0.2074, and the corresponding water depth
Froude number (
h
Fn
) was varied from 0.0857 to 0.9386.
Table 1: Cases in the simulations
Cases
h/T
Fn
Fnh
0(deep)
10.71
0.0566
0.0857
0.1320
0.1999
0.2074
0.3142
1
2.01
0.0566
0.1983
0.1320
0.4627
0.2074
0.7271
2
1.20
0.0566
0.2560
0.1320
0.5973
0.2074
0.9386
Since shallow water conditions are mostly observed in
inland waterways, fresh water at 15℃ was used as the
upstream flow. For all calculations, the technique of
“Open Channel Flow” was implemented to simulate
the twophase flow. The SST kω model was chosen as
the turbulence model. The scheme of the Pressure
Velocity Coupling was “Coupled”, and the accuracy was
second order for all items in the spatial discretization.
2.2 MESH
Because the trim and sinkage are different for different
cases, it would cost huge effort to build one set of mesh
for each case. To avoid this, a function in ANSYS
Fluent, overset mesh, was applied. The mesh around the
ship and that in the background does not necessarily
match, as shown in Figure 2.
Figure 2: Overset meshing around the ship
Data are interpolated in the overlapping area, which has a
larger datatransfer zone than the nonoverlapping hybrid
mesh. Therefore, a calculation with overset mesh could
be faster than a nonoverlapping hybrid mesh when they
have a similar accuracy. Overset meshing of each part in
the domain can be built separately without considering
the conformation of each part’s grids [11]. Consequently,
the trim and sinkage can be realized by rotating and mo
ving the mesh around the ship, and the different water
depth can also be easily realized by changing the back
ground mesh only.
2.3 BOUNDARY CONDITIONS
The boundary conditions are illustrated in Figure 3.
Figure 3: Boundary conditions
International Conference on Computer Applications in Shipbuilding 2017, 2628 September 2017, Singapore
© 2016: The Royal Institution of Naval Architects
2.3 (a) The Inlet And Outlet Boundaries
The flow entering the domain was undisturbed and
incompressible. Dirichlet conditions (2) and (3) were
applied at the inlet boundary and conditions (3) for the
outlet boundary:
x
uU
,
0
y
u
; (2)
'5%
ave
u
IU
,
10
t
. (3)
In equations (2) and (3),
x
u
and
y
u
are the velocities of
upstream flow in x and y direction, respectively. I is the
turbulent intensity,
'u
the rootmeansquare of the
turbulent velocity fluctuations,
ave
U
the Reynolds ave
raged velocity,
t
the turbulent viscosity, and
the
molecular dynamic viscosity. Free surface level and
bottom level were specified at both the inlet and outlet
boundaries.
2.3 (b) Other Boundary Conditions
The Side and the Bottom conditions were set to the non
slip “moving wall”, which with the same speed as the
upcoming flow. The velocity and all derivatives in y
direction on these boundaries were set to zero, and the
speed in x direction relative to these moving walls was
also set to zero.
Dirichlet conditions were set for the ship surface, which
was a stationary, nonslip wall. The velocities were zero
at both x and y directions. Symmetry conditions were set
for the Top and Symmetry boundary. The velocities and
all the derivatives of the flow at y direction were set to
zero.
2.4 VERIFICATION
In this part, the numerical uncertainties are given after a
mesh refinement study. Basically, the numerical error is
the difference between a numerical result and its exact
solution. According to Roache [12], the numerical error
has three components: the roundoff error, the iterative
error and the discretization error.
The roundoff error comes from the limited precision of
the computers, but using double precision can usually
keep this error negligible[13]. The iterative error results
from the nonlinearity of the mathematical equations.
Using doubleprecision scheme and sufficient number of
iterations can normally keep this error to the level of
roundoff error. In this study, the convergence criteria of
all residuals are set to 107 (local scaling). However, for a
simulation with free surface (like this study), this strict
convergence criteria were probably never met. Alterna
tively, we considered the residuals of some important
physical parameters, like resistance coefficients and the
position of the centre of gravity of the ship. When these
values become stable or change periodically during the
calculation, the iterative error is considered negligible.
The discretization error is generated when transforming
the partial differential equations into algebraic equations,
and usually occupies the majority of the numerical error.
Therefore, in this article, only the discretization error is
considered.
Roache [12] recommended a grid refinement study for
verification, which is commonly accepted as a good way
to estimate the numerical uncertainty [14, 15]. In this
study, three geometrically similar grids (Grid1 was the
finest) were generated for the deep water case. The
number of nodes in x, y and z directions had a refinement
ratio of 1.25, as shown in Table 2.
Table 2: Number of nodes in x, y and z directions for the
deep water case
Background part
Ship part
Nxb
Nyb
Nzb
Nxs
Nys
Nzs
Grid 1
327
86
152
444
90
136
Grid 2
263
66
120
344
70
108
Grid 3
207
54
96
276
54
92
The procedure of the numerical uncertainty analysis
proposed by Roache [12] is shown as follows:
1) The observed order of accuracy p (1fine, 2medium,
3coarse)
23
12
ln( )
ln( )
21
pr
;
2) The error estimates
12
21
1
e
;
3) The grid convergence index (GCI)
21
21
21
r1
s
fine p
Fe
GCI
.
The
i
is the result from grid i and the r21 the grid refine
ment factor. The Fs is a safety factor. When 0.5 ≤ p ≤ 2.1,
Fs = 1.25; otherwise, Fs = 3.
Following the above procedure, the uncertainties of the
total and frictional resistance for the finest grid (G1) are
shown in Table 3.
Table 3 The GCI of total and frictional resistance for the
finest grid (G1)
Total resistance (N)
Frictional resistance(N)
Grid 1
5.9630
3.5402
Grid 2
6.0684
3.5552
Grid 3
6.4160
3.6884
p
5.3476
9.7865
GCI(G1)
2.31%
0.16%
International Conference on Computer Applications in Shipbuilding 2017, 2628 September 2017, Singapore
© 2016: The Royal Institution of Naval Architects
The values of GCI are small (less than 3%), which
indicates that the results are within the asymptotic region.
Since the results of Grid 3 has acceptable accuracy for
this study and consumes less computation efforts, this set
of grid is used for further calculations.
3. EXPERIMENTS
3.1 SHIP MODEL
A fullloaded inland vessel was used in this study, and its
1/30 scaled model is shown in Figure 4. The detailed
parameters of the vessel and its model are shown in
Table 4.
Figure 4: The1/30 scaled model in the towing tank
Table 4: Parameters of the inland ship
symbol
unit
fullscale
model(1/30)
Length
L
m
86.0
2.867
Beam
B
m
11.4
0.380
Draft
T
m
3.5
0.117
Mass
M
kg
2948118
109.19
Wetted
surface
S
m2
1417.8
1.575
Block
coefficient
CB

0.8642
0.864
Horizontal
center of
gravity
CGx
m
43.726
1.458
All tests were run on the small towing tank of TU Delft
which is 85m long and 2.75m wide. Its maximum water
depth is 1.25m and the maximum carriage speed is 3m s1.
3.2 TEST TASKS
Cases with five different water depths were applied in the
tests and the smallest depthtodraught (h/T) ratio was
1.2. Positions of the bottom are qualitatively presented in
Figure 5 and some parameters in these five cases are
shown in Table 5.
Figure 5: Positions of bottom in each case
Table 5: Parameters of each case in model tests
Case
0
Case
1
Case
2
Case
3
Case
4
Depthdraft
ratio (h/T)
10.71
2.01
1.80
1.50
1.20
water depth
(m)
1.25
0.235
0.21
0.175
0.14
underkeel
clearance
(ukc) (m)
1.133
0.118
0.093
0.058
0.023
The case 0 was a deep water condition for comparison.
The velocities and the depth Froude numbers in each
case are listed in Table 6.
Table 6 Velocities and depth Froude number for each
case
V
(m/s)
1/30
model
V
(km/h)
full
scale
depth Froude number (Frh)
Case
0
Case
1
Case
2
Case
3
Case
4
0.3
5.92
0.086
0.198
0.209
0.229
0.256
0.4
7.89
0.114
0.263
0.279
0.305
0.341
0.5
9.86
0.143
0.329
0.348
0.382
0.427
0.6
11.83
0.171
0.395
0.418
0.458
0.512
0.7
13.80
0.200
0.461
0.488
0.534
0.597
0.8
15.77
0.228
0.527
0.557
0.611
0.683
0.9
17.75
0.257
0.593
0.627
0.687
0.768
1.0
19.72
0.286
0.659
0.697
0.763
0.853
1.1
21.69
0.314
0.724
0.766
0.840
0.939
The depth Froude numbers (
h
Fn
) were mostly within the
subcritical range (
1.0
h
Fn
) which was the case for
inland vessels.
4. RESULTS AND DISCUSSION
The signs of the drag force, trim and sinkage are defined
in Figure 6.
International Conference on Computer Applications in Shipbuilding 2017, 2628 September 2017, Singapore
© 2016: The Royal Institution of Naval Architects
Figure 6: Definition of the signs of the drag force, trim
and sinkage
Results of the trim and sinkage in the model tests are
shown in Figure 7 and Figure 8. To avoid grounding,
some dangerous cases (a high speed but with a small ukc)
were not involved in the tests.
Figure 7: Results of trim with the velocities in the model
tests
Figure 8: Results of sinkage with the velocities in the
model tests
Compared with deep water test (h/T=10.71), the absolute
values of trim and sinkage increase significantly in
shallow water. It should be remarked from Figure 7 that
the model first trims with the bow down, but when the
speed is fast enough, it will (or have a trend to, for
h/T=1.80) trim with the bow up.
The results of trim and sinkage were used in CFD
simulations, i.e. gave the model in CFD an initial trim
and an initial sinkage. Some simulating results of the
drag force were validated by the model tests, as shown in
Figure 9.
Figure 9: The drag force form CFD and EFD with
different velocities
In Figure 9, the results of the drag from CFD agree well
with the EFD results. After checking the total force in
vertical direction and the moment of the model, they
were both small values and can be negligible, which
means that the values of trim and sinkage were rightly
obtained from the tests.
After successfully validating the CFD calculations, in
terms of measured and calculated drag, same trim and
sinkage and thus same features of the global flow around
the ship, the frictional resistance coefficient (Cf), which
is hard to get from model tests, can be reasonably
achieved from simulations. Figure 10 compares the
results of Cf from CFD with the ITTC57 correlation line,
which were both calculated with the equation (1). The
case h/T=1.20 with Re =6.44 (V=1.1m/s) is simulated and
measured with the model fixed at the zerospeed position
(zero trim and sinkage).
Figure 10: Frictional resistance coefficient (Cf) with
Reynolds number in different water depths
International Conference on Computer Applications in Shipbuilding 2017, 2628 September 2017, Singapore
© 2016: The Royal Institution of Naval Architects
This figure confirms that the frictional resistance in
shallow water is larger than the ITTC57 correlation line.
Even excluding the trim and sinkage for h/T=1.20 with
Re =6.44, the friction still increases. This can be
explained by the accelerated flow under the keel, which
leads to a thinner boundary layer. And the trim and
sinkage will amplify this effect. Seen these results, the
ITTC57 correlation line is apparently underestimating
the friction in shallow water and cannot be seen suffi
cient for the extrapolation of shallow water resistance.
One may argue that the ITTC57 line can still be used
when the local speed and the exact wetted surface are
known. However, these values are difficult to measure in
a model test; even so, backflow speed and wetted surface
will both become a variable in the extrapolation process,
which makes the prediction more complicated and not
easy to use. As a result, a better way is to keep the
method of using the ship speed and the zerospeed wetted
surface unchanged, and reconsider the correlation line
together with shallow water effects.
A shallow water correlation line might be a piecewise
function. As shown in Figure 7, the values of trim are
not monotonic at the high speed range, which might have
a complex effect on the friction. Additionally, it is hard
to affirm that the results in Figure 10 are suitable for all
ship types or for all different waterways. It is the target
of ongoing research to find a restricted and easy to deter
mine set of parameters that predicts the shift of the Cf
curves independent from individual CFD calculations.
5. CONCLUSIONS
In this study, both numerical and experimental methods
were applied to investigate the resistance extrapolation of
an inland ship model in shallow water. Due to shallow
water effects, the exact frictional resistance increases,
and will be further amplified by trim and sinkage. This
will eventually lead to an unavoidable discrepancy with
the ITTC 57 line. Consequently, the correlation line be
comes insufficient in the resistance extrapolation when
the water becomes (extremely) shallow.
Therefore, the resistance extrapolation from model to full
scale should be improved specific for shallow water. And
the first step is updating the correlation line. Ship and
waterway geometry, flow acceleration, trim and sinkage
are all important factors to be considered.
6. ACKNOWLEDGEMENT
The authors cordially thank for Peter Poot, Hans v/d Hek,
Wick Hillege and Jasper den Ouden for their efforts in
the experiments in the towing tank of TU Delft.
7. REFERENCES
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8. AUTHORS BIOGRAPHY
International Conference on Computer Applications in Shipbuilding 2017, 2628 September 2017, Singapore
© 2016: The Royal Institution of Naval Architects
Qingsong Zeng holds the current position of a PhD
candidate at Delft University of Technology (DUT). His
previous experience includes CFD and ship resistance in
shallow water.
Robert Hekkenberg holds the current position of an
associate professor and Director of Studies BSc Marine
Technology at DUT. He got his PhD at DUT in 2013 on
“Inland Ships for Efficient Transport Chains”.
As researcher at DUT he was partner in many inland
shipping related EU projects such as CREATING and
MoVe IT! His research fields are design optimisation and
manoeuvring of inland ships as well as autonomous ves
sels.
Cornel Thill holds the position of the manager of the
maritime laboratories of DUT and is lecturer at the Uni
versity of DuisburgEssen in Germany, where he before
joining DUT in 2015 held the position of the head of the
hydrodynamic department of the Development Centre for
Ship technology and Transport systems (DST), one of the
most renowned research institute on inland navigating
ships. He gained further relevant experience in previous
EU projects such as CREATING, SMOOTH (coordina
tor), STREAMLINE and MoVe IT!
Erik Rotteveel holds the current position of a PhD
candidate at Delft University of Technology (DUT). His
previous experience includes CFD and inland ship stern
optimization in shallow water.