Research on Motion Law of Submarine Emergency Floating Under
High-Pressure Blowing
Hui Liu, Zhi-hui Li, Dong Guan and Xiang-jun Wu
Naval University of Engineering, Wuhan, China
Keywords: High-Pressure Air, Submarine, Blowing, Emergency, Recovery.
Abstract: The use of high-pressure air to blow out the ballast tank to obtain positive buoyancy and enable the submarine
to quickly rise to the surface of the water is an important measure for emergency recovery of the submarine
in the event of damage and water ingress accidents. However, during the emergency ascent process of
submarines, especially in the later stage of recovery, attitude control is very difficult due to the rapid increase
of positive buoyancy. Dangerous trim and heeling are highly likely to lead to the failure of submarine recovery.
This article constructs a mathematical model for the blowing of ballast water tanks to accurately control the
blowing timing, blowing position, and blowing time during the emergency recovery process of submarines.
It optimizes and adjusts the motion posture of submarines in real time to ensure the safety of submarines
during emergency recovery. The simulation results indicate that the constructed mathematical model can
effectively predict the motion law of submarine emergency buoyancy.
1 INTRODUCTION
When submarine is navigating underwater or
maneuvering in battle as a strategic weapon, if
accidents such as rudder jamming, grounding and
collision cause damage to the pressure hull and water
ingress, damage to the sea pipeline and water ingress,
sudden change of seawater density, mechanical
failure and manipulation error occur, the
maneuvering state of the submarine will change
dramatically, which is very likely to cause accidents
due to large trim and exceeding the limit depth.
In order to study the maneuver characteristics and
motion laws of submarine during emergency ascent,
it is necessary to calculate the force changes during
emergency ascent in real time, control the space
attitude of submarine during emergency recovery,
and prevent the submarine from rolling and rolling
due to dangerous pitch and roll. Literature (LIU H,
2013) established the mathematical model of gas
parameters and drainage flow in the ballast tank
during gas purging through thermodynamic analysis
of the process of gas purging ballast tank. Literature
(YANG S, 2009) established a mathematical model
of the ballast tank purging process, and carried out a
small-scale experiment on the principle of the
submarine emergency gas purging system model,
which effectively verified the mathematical model
established. The results of literature (LIU R J, 2014)
show that the process of gas release from the high-
pressure gas cylinder can be considered as an
adiabatic process, the gas and water in the ballast
water tank have the same temperature, and the gas
expansion process in the ballast water tank is
considered as a constant temperature process. The
above literature research methods are similar. A
mathematical and physical model for purging is
established by analyzing the change characteristics of
the gas in the high-pressure gas purging ballast water
tank. Combined with the submarine emergency
operation model, the attitude change of the submarine
during the floating process is studied
(ZHANG J H,
LIU C B).
Due to the change of the gas in the ballast tank
with the submarine depth will cause the change of the
force and attitude of the submarine, it is necessary to
study the high pressure blow off time and the time to
release the pressure in the submarine recovery
process. Based on the construction of high-pressure
air blowing model and pressure relief model,
combined with the submarine emergency buoyancy
control model developed by the research group
(WU
W Y, 2015), this paper studies the submarine
buoyancy movement law and attitude control strategy
during the emergency recovery of high-pressure air
blowing ballast tank.
328
Liu, H., Li, Z., Guan, D. and Wu, X.
Research on Motion Law of Submarine Emergency Floating Under High-Pressure Blowing.
DOI: 10.5220/0012282800003807
Paper published under CC license (CC BY-NC-ND 4.0)
In Proceedings of the 2nd International Seminar on Artificial Intelligence, Networking and Information Technology (ANIT 2023), pages 328-332
ISBN: 978-989-758-677-4
Proceedings Copyright © 2024 by SCITEPRESS – Science and Technology Publications, Lda.
2 MODELOF HIGH-PRESSURE
AIR BLOWING BALLAST
TANK BASED ON
COMPRESSIBLE ISENTROPIC
FLOW THEORY
In order to facilitate the research, the pressure
cylinder used for purging on the submarine is
equivalent to a high-pressure air shunt box, which is
used to control high-pressure air blowing into each
main ballast water tank. According to the one-
dimensional isotropic compressible flow theory, the
maximum flow velocity at the high-pressure gas
blowing outlet is sound velocity (WU W Y, 2015)
.
The experiment shows that when the pressure ratio on
both sides of the outlet is lower than the critical value
lj
T
, the release velocity of high-pressure gas at the
outlet is sound velocity.
1
2
()
1
k
k
lj
T
k
(1)
Assuming that the high-pressure gas flow is
isotropic flow during the process of high-pressure gas
blowing off the ballast tank.
1
2
1
()
k
F
F
dt
C
dt
,
2
1
0
1
0
k
F
F
t
dt
d
C
(2)
1
C
is a negative constant, which only depends on
the capacity of the high-pressure gas cylinder and the
diameter of the nozzle. By integrating the above
equation, the isotropic model of high-pressure gas
purging can be obtained.
2
1
2
1
(1 )
2
F
F
k
(t )
k
Ct
,
00
2
1
012
00
F
F
F
F
k
F
m
t
dt
dm
t
dt
d
CC
(3)
0
2
1
2
1
(1 )
2
F
F
k
k
P
P (t )
k
Ct
,
(4)
The mass of high-pressure gas entering the
simulated ballast water tank at each quasi-static
calculation time point is as flowing.
00
22
11
22
[]
11
[1 ( 1)] (1 )
22
FF
F
kk
mm
mt
kk
C t C t


(5)
In the above formula,
F
P
,
F
m
and
F
respectively represent the gas pressure, gas mass and
density in the high-pressure cylinder group.
2
C
is the
purging constant of high-pressure gas, which may
vary from - 0.1 to -0.01, mainly depending on the
nozzle diameter and the high-pressure gas storage
capacity in the cylinder.
F
m
is the high pressure
gas flow, and
t
is the calculation time step at every
two calculation time points.
k
is the isotropic
constant.
3 RELIEVING PRESSURE
MODEL OF HIGH PRESSURE
AIR BLOWING MAIN
BALLAST TANK
3.1 The Basic Assumption of
Combining Model
When stopping to blow the main ballast water tank
after a period of time with high-pressure gas blowing,
the gas status parameters in the high-pressure gas
cylinder remain unchanged, and the gas flow of the
main ballast water tank system with high-pressure gas
blowing is 0. When the submarine rises to a certain
depth, due to the decrease of environmental pressure,
the gas in the main ballast water tank continues to
expand, and the displacement of the ballast water tank
continues to increase. At this time, the attitude of the
submarine is difficult to control. If no measures are
taken, the submarine will rush out of the water at a
high speed, and form a large heel, which poses a
threat to the submarine (LIU H, 2019). Therefore, in
the process of emergency buoyancy of the submarine,
it is necessary to choose an appropriate time to relieve
the pressure in the main ballast tank. If the pressure is
relieved too early, the submarine may sink again due
to insufficient buoyancy. If the air pressure is released
too late, the submarine may not be able to control
because of the fast floating speed.
In the process of relieving the air pressure, on the
one hand, the gas in the main ballast tank continues
to expand. On the other hand, the gas in the main
ballast tank is discharged through the vent valve. In
order to establish the main ballast tank pressure relief
model, the following assumptions are made
(JIN T,
2010).
1) The gas expansion in the main ballast tank is
adiabatic expansion.
2) The outflow process of gas from the main
ballast tank through the vent valve is isentropic flow,
and can be simulated as Laval nozzle.
Research on Motion Law of Submarine Emergency Floating Under High-Pressure Blowing
329
3) The gas in the main ballast tank is in stagnation
state.
4) The status parameters at the vent valve outlet
are
k
P
,
k
T
,
k
,
0k
P
.The outlet area is
k
A
, and valve
coefficient is
k
C
.
3.2 Relieving Pressure Model of Main
Ballast Tank
When the high-pressure gas stops blowing to relieve
the pressure, part of the high-pressure gas in the
ballast water tank continues to expand and part of it
flows out through the vent valve. According to the
Laval nozzle model, the outlet flow
B
m
of the vent
valve can be obtained, and the gas change law in the
ballast water tank can be obtained.
1)
1
0
1
2
k
k
B
k
kP
P
,
the air flow at the vent valve outlet
is sonic, and the outlet gas pressure is critical
pressure.
1
1
2
1
k
k
k k B
B
B
A C P
mk
k
RT




(6)
2)
1
0
1
2
1
k
k
B
k
kP
P
， the air flow at the vent
valve outlet is subsonic, and
0kk
PP
.
k
B
B
k
k
k
P
P
，
21
21
1
k
kk
kk
B
B t t
BB
B
PP
P
k
m AC
k P P
RT





(7)
3)
Bk
PP
0
，the air flow is zero.
0
B
m
(8)
For the gas in the main ballast tank, according to
the gas adiabatic expansion state equation.
B
BBB
V
qP
dt
dP
,
dt
dV
q
B
B
，
B
BBB
B
B
V
qPRT
dt
dm
dt
dP
(9)
According to the isotropic flow calculation
formula and equation of state
k
BB
PC

,
BBBB
RTmVP
,
2
12
BB
B
PV
k
C
k
,
1
BB
B
B
dT T
km
dt m

(10)
3.3 Drainage Rate for the Water of
Main Ballast Tank
1)
0 ghPP
whB
gh
PP
V
w
hB
h
2
2
,
gh
PP
ACAVCq
dt
dV
w
hB
hhhhhB
B
2
2
(11)
2)
0 ghPP
whB
gh
PP
V
w
Bh
h
2
2
,
gh
PP
ACAVCq
dt
dV
w
Bh
hhhhhB
B
2
2
(12)
In the above formula,
B
P
,
B
T
,
B
V
and
B
respectively represent the gas pressure, gas
temperature, gas volume and density.
h
P
,
h
V
,
h
A
and
w
respectively represent submarine depth, drainage
velocity, drainage valve area and water density.
h
C
is
drainage coefficient, and equal to 0.45.
k
is
isentropic constant, and equal to 1.4.
R
is gas
constant.
4 THE RESULTS AND ANALYSIS
OF SIMULATION
EXPERIMENT
Through the mathematical model of submarine
emergency manoeuvring movement established by
the research group, combined with the high-pressure
air blow off ballast tank and pressure relief model
established in this paper, the simulation experiment
was carried out for the emergency recovery of a
submarine with high-pressure blow off ballast tank
after the damage of the sea opening pipeline in the
bow I cabin caused the cabin water ingress accident.
The motion characteristics of submarine recovery
process under three conditions of normal pressure
relief, no pressure relief and early pressure relief
during high-pressure gas blowing are compared and
analyzed, which provides a theoretical basis for
accurate control under accident conditions.
Table 1. Emergency recovery plan under submarine
accident state.
Depth
Speed
Diameter of
broken hole
Recovery plan
Remarks
100m
4kn
150
pk
mm
20ts
,
increase speed,
20 5
sb
,

30ts
,
blow head main ballast
tanks
60ts
,stop blowing
115ts
, release pressure,
25
sb
,

Normal
release
pressure
20ts
, increase speed,
20 5
sb
,

30ts
,blow head main ballast
tanks
60ts
, stop blowing
Don’t
release
pressure
ANIT 2023 - The International Seminar on Artificial Intelligence, Networking and Information Technology
330
20ts
, increase speed ,
20 5
sb
,

30ts
,blow head and middle
main ballast tanks
60ts
, stop blowing and release
pressure
Release
pressure in
advance
It can be seen that the motion characteristic of
submarine recovery varies greatly when high-
pressure air is used to blow off under the same
accident conditions and the air pressure is released at
different times from the simulation experiment
conditions in Table 1 and the motion characteristic
curve in the submarine emergency recovery process
in Figure 1.
(a)Change curve of submarine depth
(b)Change curve of submarine vertical velocity
(c)Change curve of displacement under
(d)Change curve of submarine axial velocity
(e)Change curve of submarine pitch
(f)Change curve of submarine heel
Figure 1. Emergency recovery history curve of submarine
high-pressure air blowing under different recovery plan.
It can be seen in Figure 1 (a) that the submarine
can recover and float to the surface if the pressure is
removed normally or not. If the pressure is removed
too early, the submarine will fail to recover. Figure 1
(b) shows the submarine vertical floating velocity. If
the air pressure is not removed, the velocities of
submarine floating to surface will more than four
meters per minute, which is very dangerous.
According to recovery success criterion, there is
failure when the floating velocity more than 3 meters
per minute. But if the air pressure is removed in
advance, the submarine cannot float to surface during
the floating force not enough. Figure1 (c) shows the
Research on Motion Law of Submarine Emergency Floating Under High-Pressure Blowing
331
displacement of the ballast water tank. If the air
pressure is not removed, the drainage of the
submarine will increase rapidly due to the rapid
expansion of the gas in the ballast water tank in the
later recovery period, which is consistent with the
result of too fast floating speed in Figure 1 (b). The
displacement and floating speed can be effectively
controlled when the air pressure is removed properly.
Figure 1 (e) shows the trim change of the submarine.
If the air pressure is not released or released in
advance, a large trim will occur due to excessive and
insufficient displacement. If the air pressure is not
released, the trim will exceed 20 degrees. If the air
pressure is released too early, the submarine will sink
to the seabed with a large trim. Figure 1 (f) shows the
change of the submarine's heel. At the initial stage of
damage and water ingress, due to the sharp increase
of the heel of the submarine under the additional
force, after taking the blowing out measures, the
additional torque decreases, and the heel decreases
significantly, basically maintaining a normal state.
5 CONCLUSION
In view of the difficulty of attitude control in
emergency recovery of submarine ballast tank by
high-pressure air blowing, this paper takes the
pressure gas in ballast tank as the research object,
builds mathematical and physical models of high-
pressure air blowing and pressure relief, and analyzes
the influence of high-pressure air release timing on
recovery results in the process of emergency recovery
of submarine high-pressure air blowing combined
with submarine accident examples.
1) When applying high-pressure air to blow out
the main ballast water tank of the submarine to
retrieve the submarine, the duration of high-pressure
air blowing out and the time to relieve the pressure in
the ballast water tank are very important, which not
only seriously affect the submarine attitude in the
recovery process, but also directly determine whether
the submarine is successfully recovered.
2) As the recovery depth of the submarine
decreases, the gas in the ballast tank expands rapidly.
If the air pressure is not relieved, the submarine will
appear serious heeling and rolling phenomenon
during floating, and the floating speed and pitch are
too large, making the submarine appear dangerous
attitude.
3) If the pressure of the ballast water tank is
released too early in the recovery process, the
submarine will have insufficient positive buoyancy at
the later stage of recovery, resulting in failure of
emergency recovery.
4) It is necessary to develop a prediction system
for submarine high-pressure air blowing emergency
recovery movement law, evaluate submarine
movement status in real time, change the time and
opportunity of high-pressure air blowing off the main
ballast tank and the time to release air pressure, and
control submarine recovery movement posture by
changing submarine speed, steering and other
dynamic anti sinking measures, so as to provide
decision-making support for submarine commanders
to formulate emergency recovery plans.
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