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Numerical Modelling of a Planing Craft
with a V-Shaped Spray Interceptor
Arrangement in Calm Water
Mikloš LAKATOŠ a,1, Kristjan TABRI a, Abbas DASHTIMANESH a
and Henrik ANDREASSON b
a
Tallinn University of Technology, Estonia
b
Flow Naval Architects AB, Sweden
Abstract. V-shaped spray interceptors are a novel concept of spray deflection on
planing craft. Conventional spray rails are positioned longitudinally on the bottom
of the hull and detach the spray from hull deflecting it towards the sides or slightly
down and aftward. The V-shaped spray interceptors, on the other hand, are located
in the spray area forward of the stagnation line such that they would deflect the
oncoming spray down and aftward, thereby producing a reaction force that reduces
the total resistance. An experimental study reported that the V-shaped spray
interceptors to reduce the total resistance at low planing speed by up to 4%. This
paper features a numerical comparison of two planing craft, one equipped with a
conventional setup of longitudinal spray rails and the other with a V-shaped spray
interceptor. Both configurations were simulated in calm water conditions and were
free to pitch and heave in a speed range of ܨݎ
ఇ
= 1.776 to 3.108. The numerical
model was analyzed for grid sensitivity and numerical results were compared with
experimental results. The two concepts were compared in terms of total resistance,
lift, running position and wetted surface area. Conventional spray rails were shown
to account for up to 5.6% of total lift and up to 6.5% of total resistance. The V-
shaped spray interceptor was shown to reduce the total resistance by up to 8%. Since
the V-shaped spray interceptor was located in the spray area forward of the
stagnation line, it deflected the oncoming spray thereby producing a horizontal
reaction force (-1.5% of ܴ
்ெ
) in the direction of the craft’s motion. The rest of
differences in the total resistance of the hulls equipped with the conventional spray
rails and the V-shaped spray rails was due to absence of the resistance of the absent
spray rails.
Keywords. Planing craft, spray rails, CFD, model tests data
1. Introduction
Whisker spray is the area of wetted bottom forward of the stagnation line of a planing
craft. The direction of the fluid in the spray area is such that the streamlines are nearly a
reflection of the free-stream about the stagnation line [1]. The resistance caused by spray
has been shown to account for 10 - 25% of total resistance (ܨݎ
ఇ
>4) by inference from
a comparison of model test data of craft with and without spray rails [2–5]. Spray
resistance is usually reduced by installing two to four longitudinal spray rails on the
1
Corresponding Author, Miklos Lakatos, Estonian Maritime Academy, Tallinn University of
Technology, Tallinna 19, 93819 Kuressaare, Estonia; E-mail: miklos.lakatos@taltech.ee
HSMV 2020
E. Begovic (Ed.)
IOS Press, 2020
© 2020 The authors and IOS Press. All rights reserved.
doi:10.3233/PMST200024
33
bottom of the hull. These rails detach the spray from the hull surface and deflect it
towards the sides or slightly down and aftward, thereby reducing the frictional resistance
by up to 18% [3].
A recent study suggests using spray deflectors that redirect the flow on the bottom
of the craft and thereby recover spray energy to reduce the total resistance by up to 30%
(compared to the bare hull) [6]. The spray deflectors are essentially a further iteration of
the stepped hull concept that has been investigated significantly more than spray rails.
Unlike the models used in [7] and [8], where the step was perpendicular to the keel, or
[9], where the step had a forward sweep, in [6] the step was swept backwards. Besides,
the step was located in the spray area forward of the stagnation such that it would deflect
the oncoming spray down and aftward. Hence it is called deflector rather than a step.
However, the study considered a hull with a constant deadrise at a fixed running position
i.e. the influence of the spray deflectors on the craft’s sinkage and pitch motion was
neglected. The spray deflectors proposed in [6] were experimentally compared with
conventional spray rails in model scale through towing tank testing in calm water and
irregular waves [10]. The study reported that while the conventional spray rail setup
reduced the total resistance by up to 9%, the spray deflectors reduced it by up to 20%.
A recent experimental study [11] compared a V-shaped spray interceptor (VSI) with
conventional spray rails in calm water at ܨݎ
ఇ
=1.74…3.26. Although the VSI works
essentially the same way as the spray deflectors do, there is a major difference between
the two concepts. While the spray deflectors are in principle steps of a hull i.e. they are
integral parts of the hull, the V-shaped spray interceptors are strips welded to the hull i.e.
they are more like spray rails. The study reported that in planing regime the VSI reduced
the total resistance of the craft by up to 4%, while conventional spray rails reduced it by
up to 2%. The V-shaped spray interceptor was located in the spray area forward of the
stagnation line such that it deflected the oncoming spray down, thereby producing a
reaction force that reduced the total resistance, which confirmed the claims made in [6].
This study aims to further investigate the influence of the V-shaped spray
interceptors [11] on the hydrodynamic characteristics of a planing craft in calm water
and compare it with that of conventional spray rails. The numerical simulation allows
analyzing phenomena (pressure distribution and wetted area) that are difficult to evaluate
under experimental conditions. Finally, the numerical results of simulations of both hulls
are compared with experimental data.
1.1. Test case
The object of this study is a test case vessel that has been designed the Small Craft
Competence Centre (SCC) in Kuressaare, Estonia to compare conventional and novel
spray rail configurations. The main particulars (Table 1) of the hull design are common
for a high-speed patrol, search and rescue (SAR) vessel or a larger pleasure boat. The
craft was designed to operate at a ܨݎ = 1.355 and ܨݎ
ఇ
= 3.108, equivalent to the
displacement of 40 t and speed of 35 knots in full scale.
The conventional spray rails arrangement (Figure 1a) was modelled with triangular
8x3mm profile (Figure 1b), with the deflection surface being horizontal. The V-shape
arrangement (Figure 1c) was modelled with a triangular profile (Figure 1d) with the
deflection surface perpendicular to the hull. The V-shaped spray interceptor was
designed for ܨݎ = 1.355 and ܨݎ
ఇ
= 3.108, equivalent to 40 t and 35 knots in full-
scale.
M. Lakatoš et al. / Numerical Modelling of a Planing Craft34
Table 1. Main Dimensions of the test case hull.
Parameter
Model Scale 10
Length overall
ை
1.921 m
Length between perpendiculars
1.800 m
Length waterline
ௐ
1.703 m
Beam overall
ை
0.581 m
Beam waterline
ௐ
0.581 m
Draugh
t
0.108 m
Displacement mass ∆
40 kg
Displacement volume 0.040 m3
Longitudinal Centre of Gravity
ீ
0.669 m
Vertical Centre of Gravity 0.200 m
Figure 1. Spray rail configurations and their profiles: a) conventional spray rails (SR), b) 8x3 mm spray rail
c) V-shaped spray interceptor (VSI), d) triangular 5x5mm interceptor.
2. Numerical model
The hydrodynamics of the planing hull was modelled using a commercial software Star-
CCM+ v.15.02.007. An implicit unsteady solver was selected implementing RANS
equations with k–ε turbulence model. The multiphase flow involving air and water is
solved using the Volume of Fluid (VOF) approach that tracks the free surface boundary.
The dynamic fluid-body interaction (DFBI) model was used for the evaluation of pitch
and heave of the vessel. Main particulars of the numerical setup and the computational
domain are shown in Table 2 and Figure 2 respectively.
The mesh is made of hexahedral control volumes and prism layer meshes are used
for solving the flow in the boundary layer. The computational domain is divided into two
regions: a stationary far-field region designated as “Tank” (Figure 3a) and a moving
region designated as “Overset” (Figure 3b). The far-field region has three types of
boundaries: Velocity Inlet, Pressure Outlet and Symmetry. The moving overset region
has on the other hand: Wall, Symmetry and Overset. Since the model uses the overset
grid and reference frame approach, the flow velocity is defined under reference frame
and set to 0 in the Velocity Inlet boundary condition. The numerical model uses wave-
damping for preventing wave reflection from the Inlet, outlet and side boundaries, with
the wave damping length set to constant of 2.5 m from the boundary.
The time step ∆t is controlled by a field function ∆ ∆/
ு௨
0.25/
ு௨
, where ∆x is the cell size (25% of the base size) the first level of
refinement of the overset region and
ு௨
the velocity of the hull. Hence, the field
function defines the time step ∆ such that the CFL=0.5 on the outer boundary and
CFL=1 in the first level of refinement of the overset region. Hence, for the base size BS
= 0.06m and
ఇ
= 1.776 to 3.108 the respective time steps are ∆ 0.008
/
ு௨
,
a) b) c) d)
M. Lakatoš et al. / Numerical Modelling of a Planing Craft 35
which satisfies the ITTC recommendation [12] ∆ 0.01 ~ 0.005 / , where l is
characteristic length (in this case
) and
ு௨
is the hull velocity.
A mesh sensitivity study was done to identify the minimum base size of the
computational domain. Since the running trim of a planing craft is known to be extremely
sensitive to generated lift, the grid sensitivity study was done on a craft with a fixed
running position. Figure 4 shows that as the cell count increases, after base size
0.06 (1.9 million cells) the differences in total resistance were below 0.01%. Therefore,
a base size 0.06 was selected for the rest of the simulations, resulting in 209,478
cells in the far-field region and 1,828,934 and 1,696,801 cells in the overset regions of
the hulls equipped with spray rails and the V-shaped spray interceptors respectively.
Figure 5 shows the distribution of wall y+ on the respective hulls.
Table 2. Solver settings
Item
Description
Convection Term 2
nd
orde
r
Temporal Discretization 1
st
order
Time-step [s] Function of velocity and mesh size
Inner iterations per time step 5
Turbulence model Realizable k-ε
Overset interpolation scheme Linear
Iterations of 6-DOF solver per inner iteration 3
Wall treatment Two-Layer All y+
Figure 2. Dimensions of the simulation domain.
a)
b
)
Figure 3. Boundary conditions of the Tank (left) and Overset (right) regions.
Pressure
Outlet
Symmetry plane
Velocity
Inlet Overset
Wall
W
all
Symmetry plane
Overset
M. Lakatoš et al. / Numerical Modelling of a Planing Craft36
Figure 4. Grid sensitivity of total resistance.
Figure 5. Wall Y+ on the hulls with spray rails (left) and the V-shaped spray interceptor (right)
at ܨݎ
ఇ
=3.108.
3. Results and discussion
Figure 6 compares the vertical component of the lift ܮ
acting on the hull with
conventional spray rails (SR) to that of the hull with the V-shaped spray interceptor (VSI).
The differences in the lift were below 0.1% throughout the whole speed range, hence
they were considered negligible.
When comparing the distribution of the vertical lift component on the individual hull
parts at the top speed of ܨݎ
ఇ
= 3.108 (Figure 7), the spray rails were seen to account for
a much larger lift than the V-shaped spray rail did. The spray rails produced 22N of
vertical lift accounting for 6% of total lift, while the V-shaped spray interceptor only
produced 1N of lift accounting for 0.3% of the latter. However, this difference in the lift
on the spray rails and V-shaped spray interceptor was compensated by that of the bottom.
The bottom of the hull equipped with V-shaped spray interceptor produced 19N more
lift than the hull equipped with spray rails did. As for the chine, deck, keel, side and
transom, no significant differences in the lift were observed.
Figure 8 compares the numerical and experimental values of the non-dimensional
total resistance ܴ
்ெ
/∆ of the hull equipped with spray rails (SR) to those of the hull
equipped and the V-shaped spray interceptor (VSI). Compared to model test results, the
total resistance of the hull with spray rails (SR) was underestimated by 3% to 9%, while
that of the hull with the VSI was underestimated by 6% to 8%. The most likely reason
for the difference in resistance between the numerical and experimental results is the
absence of the trimming moment due to towing force [13]. In the simulation the hull is
moving relative to the background using reference frame method and the only forces
acting on it are gravity and the hydrodynamic and hydrostatic forces that result in
resistance and lift. In the experimental setup, on the other hand, besides the lift and drag,
a towing force is acting at the towing point (x=0.36 m from the transom and z= 0.09 m
from the baseline).
62.6
62.7
62.8
62.9
1.0E+06 2.0E+06 3.0E+06 4.0E+06 5.0E+06
RTM [N]
Cell Count
M. Lakatoš et al. / Numerical Modelling of a Planing Craft 37
Figure 6. The vertical component of Lift.
Figure 7. Distribution of the vertical component of the lift ܮ
on the hull at ܨݎ
ఇ
= 3.108.
Comparing numerical with experimental results, the general trends of resistance of
the two hulls were rather similar. Compared to the hull with the spray rails, the total
resistance of the hull with the V-shaped spray interceptor was significantly 7% and 8%
lower at ܨݎ
ఇ
=2.66 and ܨݎ
ఇ
=3.11 and 1% and 6% higher at ܨݎ
ఇ
=1.77 and ܨݎ
ఇ
=
2.22 respectively. However, it was observed that the differences in numerical total
resistance were nearly twice as large as of those in experimental results.
Probably the most notable difference arose from the comparison of the total
resistance of individual parts of the hull (Figure 9), in particular those of the spray rails
and the V-shaped spray interceptor. The V-shaped spray interceptor accounted only for
negative -1.3N (-1.5% of ܴ
்ெ
) resistance, while the spray rails accounted for 4.5N (6.5%
of ܴ
்ெ
) of resistance. That is because the V-shaped spray interceptor was located in the
spray area forward of the stagnation line such that it deflected the oncoming spray down,
thereby producing a reaction force that reduced the total resistance.
It is important to note that since the VSI only produced a comparatively small
reaction force (-1.5% of ܴ
்ெ
) in the direction of the hull’s motion, the rest of the 8%
difference was due to absence the of pressure and frictional resistance of the absent spray
rails. As for the chine, deck, keel, side and transom, their resistance was negligibly
smaller than that of the hull with spray rails. Figure 10 compares the pressure distribution
of the hulls with the SR with those of the hull with the VSI. It was observed that at ܨݎ
ఇ
=
1.77 and ܨݎ
ఇ
=2.22, the VSI gets in the way of the oncoming flow and causes a low-
pressure area behind itself. This explains 1% and 6% higher total resistance compared to
the hull with the spray rails.
1.0008
1.0009
1.0010
1.0011
1.0012
1.0013
1.0014
1.7 1.9 2.1 2.3 2.5 2.7 2.9 3.1 3.3
LV/ Δ
Fr
∇
SR
VSI
M. Lakatoš et al. / Numerical Modelling of a Planing Craft38
Figure 8. The total resistance of simulated configurations compared to model test results.
Figure 9. Distribution of the total resistance ܴ
்ெ
on the hull with conventional spray rails (SR) and V-
shaped spray interceptor (VSI) at ܨݎ
ఇ
= 3.108.
Figure 10. Pressure distribution of SR (left) and VSI (right) at ܨݎ
ఇ
= 1.774 to 3.108 (top to bottom).
The running position of the simulated hulls is compared with that of model tests in
terms of trim and sinkage in Figure 11 and Figure 12 respectively. While in the most
cases trim was underestimated by around 0.6 to 0.9 degrees (13% to 16%), in the case of
the hull equipped with the V-shaped spray interceptor (VSI) at ܨݎ
ఇ
=2.22 the trim was
underestimated by 1.4 degrees (25%). This outlier was also seen in the comparison of
0.13
0.14
0.15
0.16
0.17
0.18
0.19
1.7 1.9 2.1 2.3 2.5 2.7 2.9 3.1 3.3
RTM / Δ
Fr
∇
SR-EXP VSI-EXP
SR-CFD VSI-CFD
M. Lakatoš et al. / Numerical Modelling of a Planing Craft 39
sinkage. While in most cases sinkage was underestimated by 3mm to 6mm (9% to 12%),
in the case of the hull with the VSI at ܨݎ
ఇ
=2.22 sinkage was underestimated by 20mm
(70%). Based on experimental data, the hull with the VSI was expected to have similar
trim to that of the hull with spray rails (SR). Besides the absent moment due to towing
force, a likely reason for that outlier is numerical ventilation observed in Figure 15.
Figure 11. Trim of simulated configurations compared to model test results.
Figure 12. Non-dimensional sinkage of simulated configurations compared to model test results.
The wetted hull area underway ܵ
ௐுா
of the two simulated crafts was divided into
the wetted bottom area ܵ
ௐ
and area wetted by the spray ܵ
ௐௌ
. ܵ
ௐ
was defined as the
wetted area below the still water level (ݖ<0) while ܵ
ௐௌ
was defined as wetted are above
still water level (ݖ > 0) as shown in Figure 13 and Figure 14.
Figure 13. The wetted bottom area ܵ
ௐ
, area wetted by spray ܵ
ௐௌ
and wetted hull area underway ܵ
ௐுா
.
While the hull with the V-shaped spray interceptor was expected to significantly
reduce the area wetted by spray, the numerical results show the opposite. No significant
differences were observed in either ܵ
ௐ
or ܵ
ௐௌ
, except in the case of the hull with the
VSI at ܨݎ
ఇ
=2.22, where ܵ
ௐ
was lower and ܵ
ௐௌ
was higher those of the hull with the
3.5
4.0
4.5
5.0
5.5
1.7 1.9 2.1 2.3 2.5 2.7 2.9 3.1 3.3
τ [deg]
Fr
∇
SR-EXP VSI-EXP
SR-CFD VSI-CFD
0.02
0.07
0.12
1.7 1.9 2.1 2.3 2.5 2.7 2.9 3.1 3.3
zV,CG / ∇1/3
Fr
∇
SR-EXP VSI-EXP
SR-CFD VSI-CFD
0.0
0.2
0.4
0.6
0.8
1.0
1.7 1.9 2.1 2.3 2.5 2.7 2.9 3.1 3.3
SW[m2]
Fr
∇
SWB SR
SWS SR
SWHE SR
SWB VSI
SWS VSI
SWHE VSI
M. Lakatoš et al. / Numerical Modelling of a Planing Craft40
SR. That is most likely due to the smaller than expected trim of hull with the VSI
compared to the hull with the SR. Nevertheless, the differences in wetted hull area
underway ܵ
ௐுா
=ܵ
ௐ
+ܵ
ௐௌ
were between 1% and 4% through the whole speed range,
hence marginal.
Figure 14. The wetted bottom area ܵ
ௐ
and area wetted by spray ܵ
ௐௌ
on SR (left) and VSI (right) at ܨݎ
ఇ
=
1.774 to 3.108 (top to bottom).
Figure 15. Volume Fraction of Air on SR (left) and VSI (right) at ܨݎ
ఇ
= 1.774 to 3.108 (top to bottom).
4. Conclusions
This paper presents a numerical analysis of two planing hulls in calm water, a hull
equipped with conventional spray rails (SR) and one equipped with a novel V-shaped
spray interceptor (VSI). The numerical results were compared with model test results
and showed relatively good agreement. The main reason for the difference between
numerical and experimental results was the absence of a moment due to the towing force
in the numerical setup. Conventional spray rails were shown to account for up to 5.6%
M. Lakatoš et al. / Numerical Modelling of a Planing Craft 41
of total lift and up to 6.5% of the total resistance in a speed range of ܨݎ
ఇ
=
1.774 … 3.108. The V-shaped spray interceptor was shown to reduce the total resistance
by up to 8%, compared to the hull with conventional spray rails. Since the VSI was
located in the spray area slightly forward of the stagnation line such that it deflected the
oncoming spray thereby producing a horizontal reaction force (-1.5% of ܴ
்ெ
) in the
direction of the hull’s motion. The rest of 8% differences in resistance of the hulls
equipped with the SR and the VSI was due to absence the of resistance of the absent
spray rails.
Future studies will investigate the influence of the width ܾ
ௌோ
and the bottom angle δ
of the spray rail as well as that of the V-shaped spray rail and chine interceptors on the
hydrodynamics characteristics of the craft in calm water and waves. Furthermore, future
studies will investigate the application of the Adaptive Mesh Refinement (AMR), a fairly
new feature in the STAR-CCM+ software. AMR is particularly interesting since the
perspective of achieving a high-resolution solution of the free surface and spray with a
smaller number of cells is rather appealing.
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