585
1 INTRODUCTION
The increasing trend of using underwater manned or
unmanned vehicles to perform risky missions is
visible. The risks are relate to limited spaces or
fairways, ensuring sufficient movement speed and safe
handling. The conditions that unite these risk factors
are maneuverability of underwater apparatus near the
free surface. It is fact, that when moving close to the
free water surface or bottom, the body interacts with
them and exerts a suction force on it. The pressure field
around the body affects the nearby free surface and
generates waves that subsequently change the pressure
distribution over the body. In these modes, the free
surface significantly influences on the hull
hydrodynamic forces and moments. The wave system
that is "fed" with energy by the forces acting on the
body, adds wave resistance component and everything
else. It causes unwanted vertical lift “Z” and possible
pitch moment “M” (Fig. 1) (Renilson at al., 2011)[1],
(Zemlyak at al., 2020)[2].
Good example of this phenomenon is the detailed
numerical study of Torunski (2018)[3]. However, it
considers the realistic case of an upright submarine
close to the free surface, which is experimentally
impossible to realize due to the influence of the HPMM
with two struts.
In a previous study was determined the influence of
the free surface on course stability, but only at low drift
angles (Efremov and Milanov, 2019)[4]. In the present,
as an extension of the abovementioned, the
maneuvering forces of the DARPA SUBOFF are
investigated at high drift angles at 6 up to 12 degrees.
The reason for that is the practical cases of carry out
rapid maneuvers in limited fairways. But the well-
Investigation of Darpa Suboff on the “Suction”
Influence to the Maneuvering Forces at High Drift
Angles and Shallowly Immersion Conditions
D. Efremov
1,2
, A. Vasileva
1,2
& E. Milanov
1,2
1
Bulgarian Ship Hydrodynamics Centre (BSHC), Varna, Bulgaria
2
Bulgarian Academy of Sciences (BAS), Varna, Bulgaria
ABSTRACT: The increasing trend of using underwater manned and unmanned vehicles to perform risky
missions is visible. The risks are relate to limited spaces or fairways, ensuring sufficient movement speed and safe
handling. The conditions that unite these risk factors are maneuverability of underwater apparatus near the free
surface. The pressure field around the body affects the nearby free surface and generates waves that subsequently
change the pressure distribution over the body. In these modes, the free surface significantly influences the hull
hydrodynamic forces and moments. The known suction force in shallow immersion can changes its character
radically at angles of attack. It is possible, at high drift angles to become into a force of repulsion from the free
surface. The scope of work consists of captive model experiments to analyses the suction phenomenon (Z)
influence to the axial resistance (X) and lateral force (Y) for a submarine operating close to the free surface at high-
drift-angle. Could be summarize that the forces considered regarding maneuverability in the horizontal plane
near the free water surface should not be considered in isolation from those acting in the vertical plane. They are
permanently interacting.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 20
Number 3
September 2026
DOI: 10.12716/1001.20.03.06
586
known mathematical prediction models for the
maneuvering motion of submarines, are relied on the
linear derivatives of the hydrodynamic coefficients
determined in deep water (H/D>6) (Vasileva and
Kyulevcheliev, 2018)[5], (Öztürk at al., 2023)[6], (Jong-
Yong Park at al., 2017)[7].
Figure 1. Coordinate system
In calm water and straight ahead, the surface
suction is due to reduced volume above the submarine,
compared to below it, which results in higher flow
velocity, and hence lower pressure. Also, the known
suction force in shallow immersion, changes its
character radically at high angles. The pressure is
reduced when the vessel is at an angle to the flow. This
is due to increased velocity over top and bottom of the
vehicle, caused by the transverse component of the
flow around the hull, when it is at drift angle (Fig. 2). It
is possible at these angles to become into a repulsion
force from the free surface. It should be noted that, in
constant depth, at low Froude numbers, the suction is
upward, while at high Froude numbers the suction is
downward (Renilson, 2015)[8], (Bridges at al., 2004)[9].
In free surface, at shallowly immersion conditions and
drift angle, the force along the Z-axis interact with the
pair forces X – axial, Y - lateral (Fig. 3).
Figure 2 Pressure over the length of a maneuvering
submarine in deep water (Seil and Anderson, 2013)[10]
The numerical studies of Renilson at al. (2011)[1]
and Ling at al. (2022)[11] clearly shows how the values
of the coefficients of hull forces and moments vary
under the influence of immersion depth and drift
angle. The generally accepted suction when
approaching a free surface or bottom has its boundary
conditions, after which it can turn into repulsion.
Amiri at al. (2018)[12] conducts an interesting study
on the influence of the free surface to the
hydrodynamics of a submarine, but also pays attention
to its influence on the experimental setup and
corresponding results. The leading struts in deep water
have negligible influence, but in shallow submergence,
they distort the hull-generated wave profile, and have
little effect on the transverse force “Y” and pitch
moment “M” (Renilson, 2015)[8]. Rozhdestvensky
(1970)[13] confirmed the unstable nature of the motion
parameters of an underwater vehicle close to the free
water surface, also. At low drift angles, by different
approaches of the numerical hydrodynamics, Vaz at al.
(2010)[14] presents homogeneous increase of the forces
and moments in the horizontal plane, with
corresponding increase of the drift angle. Therefore,
further numerical study of the cases would help to
analyze the behavior of the submarine, because when
the speed in shallow submersion vary, the trend of
increasing hull forces and moments is non-linear.
The work scope consists of captive model
experiments to analyze the suction phenomenon (Z)
influence to the axial resistance (X) and lateral force (Y)
for a submarine operating close to the free surface at
high-drift-angle (Fig. 3).
Figure 3, Interaction between Z-force and the pair forces X, Y
2 OBJECT OF RESEARCH
Object of the investigation is axisymmetric streamlined
elongated reference body, developed for the Defense
Advanced Research Projects Agency (DARPA)
SUBOFF Project. Based on the submarine geometry
(Groves at al., 1989)[15], the 3D vehicle model is
generated and physical plastic model was
manufactured (Fig. 4).
Figure 4 BSHC DARPA Suboff model (yellow) mount to
HPMM (blue)
The hull and control surfaces data of the
underwater vehicle (DTRC MODEL 5470) are given in
Table 1. The propeller model is INSEAN E1619 (The
INSEAN E1619 Propeller Dataset, 2016)[16].
Table 1 Main particular of the hull and appendages
Hull data
Values
Length overall, m
4,356
Diameter moulded, m
0,508
Volume of displacement, m
3
0,718
Wetted surface, m
2
6,338
Number propellers
1
Number rudders
4
Coordinate system origin, m
2,016
Control surfaces data
Values
Rudder area, m
2
0,0814
Rudder height, m
0,17
Rudder mean chord, m
0,184
Aspect ratio
0,72
Rudder profile
NACA 0020
587
3 EXPERIMENTAL TEST PROGRAM AND RANS
SET-UP CASES
The experiments are propulsive static PMM tests and
resistance numerical cases in configuration - fully
appended hull. The results present the influence of the
shallow submergence relative to the free water surface,
on the maneuvering characteristics of the "DARPA
SUBOFF" underwater vehicle in the horizontal plane.
Experiment
The tests are carry out in the BSHC’s deep-water
towing tank (200m length x 16m breadth x 6.5m depth).
Measurements are conduct at one steady forward
speed, self-propulsion point, range submergence
depths and drift angles. The self-propulsion points are
determined for every depth, in zero drift angle (Table
2).
To meet requirements of submerged body tank
testing, a project for the modernization of the existing
Horizontal Planar Motion Mechanism was implement.
Specially developed telescopic struts are connect
rigidly to the two pair of two-component (X-Y) load
cells with strain gages (Fig. 5). This creates possibility
to carry out captive maneuvering tests in the horizontal
plane of submerged objects.
2 2 2 2
''
0,5 0,5
XY
XY
V L V L

==
where X and Y – axial and lateral force, respectively
[N]; ρ – water density [kg/m
3
]; V – carriage speed [m/s];
L - Length overall [m];
Figure 5. Model installed on the HPMM via struts & load cells
The set-up allows to be varied the body immersion
and by towing carriage – the linear motion speed.
Assuming the dominant role of the hull forces, without
considering the wave resistance and wave pattern, the
suboff model is inverted. It is avoids the influence of
the struts – the set-up of sail between two struts. In
view of previous studies, on the influence of the free
surface to the submarine behavior in horizontal plane,
are used results from deep immersion where there is
no such effect (Roddy, 1990)[22]. The selected
experimental shallowest depth are up to a relative
submersion related to the influence of shallow water,
corresponding to critical Froude number, FrH 1
(Renilson at al., 2011)[1].
/.
H
Fr V g H=
where: V – carriage speed [m/s]; g - gravitational
acceleration [m/s
2
]; H - submergence depth of model
centerline axis to the free-surface [m];
The BSHC experimental investigation is performed
at three depth shallow immersions of the vehicle
model.
Table 2.
H 3
H 2
H 1
H
m
0,508
1,016
1,27
H/D
[-]
1
2
2,5
Rn
10
6
8,95
8,98
9,03
FrH
[-]
1,035
0,732
0,655
Fr
[-]
0,353
0,353
0,353
Table 3. The tank test matrix in towing static mode.
STATIC TESTS
Test Mode
Speed
U [m/s]
Immersion
Drift angle
[deg]
Static drift
2,31
H1, H2, H3
-2, 0; 2; 4; 6; 8;
10; 12
CFD
The two-component sensors measure the loads only
in the horizontal X-Y plane. It is insufficient to prove
the interaction between the pair of X-Y forces and the
suction along Z. A more detailed study of the
phenomenon was conduct by numerical experiments
based on the Navier-Stokes equations, using Star
CCM+ software. The simulation is defines as a transient
turbulent multiphase. The phase interface between
water and air to solve the deformation of the free
surface. The present setting considers a viscous and
incompressible fluid, turbulent flow and solves the
Reynolds equations (Reynolds-averaged Navier-
Stokes equations - RANS).
The numerical method for solving the RANS
equations in Star CCM+ is the Finite Volume Method
(FVM). The volume of fluid (VOF) model was use to
capture the interface between water and air (free
surface) (STAR CCM+ 11, 2016)[17]. For the model
fluid flow, the current CFD simulations impose a finite
volume method, which uses the integral form of the
conservation equations and divides the computational
domain into finite number of joined control volumes.
The set turbulent model for the experiments is k-Ɛ,
which is a standard model extensively used in
industrial applications. The chosen time step satisfy
t=0.005~0.01L/V=0.0188, recommended by ITTC (ITTC
– Recommended Procedures and Guidelines, 2011)[18]
for standard resistance computations.
Were followed the best practice guidelines for
generating the computational domain size. The grids
for all different cases were generate with Star CCM+.
Fig. 6 displays the volume mesh that was generate. The
y+ value is present in Fig. 7.
588
Figure 6. Generated volume mesh
Figure 7. Wall y+ value for medium mesh
The uncertainty analysis of the grid is did by the
Grid Convergence Method (GCI) (Celik at al.,
2008)[19]. The analysis of the meshes was conduct here
by three solutions with different meshes. The base size
of the mesh was adjust to generate a different mesh
with the same topological structure. The different
meshes were define as total numbers of cells as fine,
medium, and coarse mesh - N1, N2 and N3,
respectively. Table 4 displays the discretization error
results. For variable φ, the chosen value of the
resistance force is from the simulations with different
meshes.
The Grid Convergence Index (GCI) is define as:
21
21
21
1.25
1
a
fine
p
e
GCI
r
=
−
(1)
The approximate (2) and extrapolated (3) errors as:
21
12
1
a
e

−
=
(2),
12
21
1
12
ext
ext
ext
e

−
=
(3)
The extrapolated value
21
ext
, from:
( )
( )
12
21
21
21
1
p
ext
p
r
r

−
=
−
And apparent order p:
( )
( )
32 21
21
1
ln /
ln
p q p
r

=+
,
Where:
( )
21
32
ln
p
p
rs
qp
rs

−
=


−

( )
32 21
1. /s sgn

=
32 3 2
=−
21 2 1
=−
Table 4. Calculations of discretization error.
N1, N2, N3
1763785; 934213; 375133
r21
1,4
r32
1,667
φ1
60,715
φ2
60,739
φ3
63,762
p
2,739
21
ext
60,699
e
21
a
0,04%
e
21
ext
0,03%
GCI
21
fine
0,03%
The grid convergence analyses for current CFD
calculations leads to selection of the meshes with a
medium mesh for all tested cases.
H2
Figure 8. β=6°
Figure 9. β=8°
589
Figure 10. β=12°
H3
Figure 11. β=6°
Figure 12. β=8°
Figure 13. β=12°
4 RESULTS
For standard static PMM tests of a ship or submerged
body in deep water, the derivatives of the
hydrodynamic coefficients are with linear
characteristic, generally. However, in the cases of
shallow water or shallow submergence, the
characteristics of the derivatives becomes non-linear
(Fig. 14), (Ling at al., 2022)[11], Rozhdestvensky
(1970)[13], (Kyulevcheliev at al., 2004)[20], (Joubert,
2004)[21].
In the present study, the experimental results for the
bow (Y1) and stern (Y2) sensors along the Y direction
have a different character (Fig. 15). The first has classic
linear character regardless of the immersion depth and
drift angle. The second, however, with decreasing
immersion and increasing drift angle, reaches an
almost quadratic function character. The behavior of
the transverse force in the stern area (Y2) can be
considered in two ranges. Low drift angles – from -2°
up to 4° and high angles – from 6° up to 12°.
Figure 14. Experimental total Y force and Yaw moment in
low and high drift angles
Figure 15. Experimental Y forces – fwd (Y1), astern (Y2) and
CFD Z force in low and high drift angles
Could be saw that in the area of high angles and
small immersion depths – H1, H2, the stern force Y2
does not increase, which affects to the total Y force. The
increase in the total Y force, despite increasing the drift
angle, becomes slower. This phenomenon becomes
particularly strong at the critical depth H3. The values
of the stern force Y2, despite the increase in the drift
angle, decrease until they reach very low values. It is
interesting that the values of Y2 from the low and high
angle periods are close, and the loss of load in the Y2
location is compensate by the bow Y1.
A possible reason for this phenomenon is the well-
known suction effect at critically shallow submergence
and the corresponding Froude number. This can also
cause an additional effect known as the sail effect.
590
For detail analyze of the experimental results
described above, is carried out additional CFD study.
The case is fully appended hull with a sail upward, at
the same experimental depths and FrH. Attention is pay
to the range of high drift angles, where the nonlinear
character of the hydrodynamic coefficients is observe
clearly. To determine the critical draft at which the
"suction" effect is observed, three immersions at 0° drift
angle are tested. The case FrH=0,62 – lowest Fr, is the
deepest by DTMB, (Roddy, 1990)[22]. From the results,
it is saw that at the shallowest, i.e. largest FrH, the
"suction" is generated (Fig. 16).
Figure 16. CFD Z - force (suction/repulsion) vs experimental
- FrH=0,62 (Roddy, 1990)[22], in zero drift and varied
immersion
As the drift angle increases, however, the suction
force is observe to reverse its direction and become into
repulsion (Fig. 17). This is more clearly noticeable
when entering the range of high angles - over 6°. Here
the flow condition is complex because the influence of
the FrH which continues to act. It is saw an interaction
between FrH and high drift angles (Fig. 15, Fig. 18).
Considering the experimental results, could be
expect that the suction/repulsion does not act
uniformly over the entire hull. It is could be induced a
pitch moment M because of them (Roddy, 1990)[22]. Its
action, due to change in the direction of the force along
Z, would cause the bow to sink or rise. The CFD results
confirm that expectation (Fig. 8 - Fig. 13). In shallow
conditions the pressure on the top of hull, which is
closer to the free surface, is smaller than on the bottom
of hull. Also with increasing the drift angle, the
pressure at the bow is bigger than at the stern.
Figure 17. CFD Z - force (suction/repulsion) vs experimental
- FrH=0,62 (Roddy, 1990)[22], in varied immersion and drift
Figure 18. CFD Z - force (suction/repulsion) vs experimental
- FrH=0,62 (Roddy, 1990)[22], in varied immersion and drift
It is seen that the pitch M changes its direction when
pass from the range of low angles to that of high ones.
This phenomenon is only at the highest FrH - shallowest
immersion. A reason for its generation is due
additional effect observed only in high drift angles
(Fig. 19).
Figure 19. CFD M – pitch (suction/repulsion) vs experimental
- FrH=0,62 (Roddy, 1990)[22], in varied immersion and drift
When a submarine is in steady drift condition, both
the sail and the hull generate vortices. There will be a
strong tip-vortex from the sail, and an opposing
circulation induced by its image in the hull. This will
modify the vortices shed by the top and the bottom of
the hull, resulting in a force and moment in the vertical
plane as discussed by Seil and Anderson (2013)[10].
This will normally result in a downward force over the
stern of the submarine. Seil and Anderson (2013)[10]
show that the primary reason is due to the effect of sail
on the hull-vortices, and hence the force and moment
on the hull, rather than the force and moment on the
sail itself (Renilson, 2015)[8]. This effect is significantly
intensify under the influence of decreasing immersion
depth.
5 CONCLUSION
It is evident from the results that the character of the
hydrodynamic coefficients is non-traditional like in
deep water. At low drift angles, it is expectedly linear,
but at high angles, it is highly nonlinear. This refers to
the forces acting in the stern area. Of course, the main
influence here is the suction force. It is interesting that
can be observe experimentally this phenomenon by the
classical HPMM type only - with two struts,
respectively at two measurement points. Modern ones
with one strut do not provide such an opportunity.
It is reasonable to assume that tight curvilinear
maneuvers, such as turning, which are usually
591
associated with a high drift angle, can change the
suction force character. This can cause a pitch moment
M much earlier than in straight motion. The most
critical condition is FrH ≈ 1 (H3), it is could turns the
suction into repulsion from the water surface. The
reason for this is the influence of the vortices released
by the sail at a high angle of attack - known as sail
effect. In the range of low angles the bow sinks, and at
high angles it raises (Fig. 19).
It confirmed that the forces regarding
maneuverability in the horizontal plane, near the free
water surface, should be not investigate separately
from those acting in the vertical plane. They are
permanently interacting.
ACKNOWLEDGEMENT & FUNDING
This study is co-financed by the MASRI – Infrastructure for
Sustainable Development of Marine Research including the
Participation of Bulgaria in the European Infrastructure
Euro-Argo, an object of the National Roadmap for Scientific
Infrastructure (2017-2023 and 2020-2027) of Republic of
Bulgaria.
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