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TheAnalysisofFloodedSubmarineMotionStateVaryingFromDifferent.pdf
The Analysis of Flooded Submarine Motion State Varying From Different
Attack Angle Under Blowing Ballast Tank
LIU Hui, PU Jin-yun, LI Qi-xiu, WU Xiang-jun
College of Power Engineering, Naval Univ. Of Engineering
Wuhan, China
Keywords: Recovery maneuver; Large angle of attack; Hydrodynamics; Forecast.
Abstract. The paper establishes emergency recovery maneuver model of six degree of freedom and
blowing ballast compartment model of high pressure air. Based on standard maneuver equation,
considering the influence of large angle of attack to hydrodynamics coefficient, correct the standard
equation through supplementing hydrodynamics items. Applying large and small angle of attack
system to simulate and calculate state parameters, and find the occasion of large of attack, the
influence of initialization velocity and depth to change of angle of attack. The results prove that large
angle of attack system is significant to forecast the state parameters.
Introduction
Submarine as one of the most important deterrent of modern navy, how to improve the safety and
mobility are an important direction of development of countries in the Navy. In the course of the
navigation and fighting, when submarine damage caused by collision or attack by enemy
anti-submarine weapons, the submarine would be a negative buoyancy and trim moment. If you do
not take or do not actively take proper control measures, under the negative buoyancy of the hull,
hydrodynamic of the hull and the propeller thrust effect, the submarine will be beyond the limits of
depth of the submarine in a very short period of time, and the submarine pressure hull caused by the
pressure loss, or the submarine hit bottom in shallow water [1,2].
Based on submarine standard motion equation [3]
delivered by ITTC,through data regress of the
results of ship model experiment, the paper acquires the added hydrodynamic items caused by the
motion state of high angle of attack, and modify the space motion equation. Combining the added
force model, the paper established the high pressure air
blowing main ballast tank model and emergency recovery
maneuver model. Compared to the difference of small attack
angle and high attack angle, the paper summarizes the
influence of the various parameters to emergency floating
maneuver and analyzes the motion characteristic of submarine
during emergency maneuver.
Emergency Retrieve Maneuvering Model of Submarine
Coordinate System. To research the maneuvering motion law of submarine and fix the position and
pose of a moving submarine [4]
, the absolute coordinate system ξηζ−E and relative coordinate
system xyzO− attaching to the submarine are established , which are shown as Fig.1.
In Fig.1, X , Y and Z represents axis force, side force and vertical force on the submarine
respectively; and K , M and N represents heeling moment, trim moment and drifting moment of the
submarine respectively.
x y
z
XY
Z K
M
N
)G(O
E ξ
η
ζ
Fig.1. Coordinate system
Applied Mechanics and Materials Vols. 336-338 (2013) pp 442-445 Online available since 2013/Jul/15 at www.scientific.net © (2013) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/AMM.336-338.442
All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of TTP, www.ttp.net. (ID: 165.215.209.15, ProQuest-16/10/13,01:52:59)
Submarine Space Motion Equation. This paper choose the submarine space motion model with six
degree of freedom released by DTNSRDC in 1967 as the basic model [5]
.
The motion Equation of Large Angle of Attack . Emergency recovery motion equation of flooded
compartment is different from normal maneuvering motion,and it belongs to maneuvering of high
angle of attack.When submarine maneuvers in small angle of attack, mainly affected by the fluid
viscous resistance, but when submarine maneuvers in the high attack angle, except for viscous
resistance, the inertial component of resistance will be significantly enhanced.Especially when the
attack angle of submarine is greater than 50°,submarine expresses highly nonlinear characteristics.
According to ship model hydrodynamics experiment of large angle of attack and different propeller
load, the paper analyzes the hydrodynamic coefficient, and acquires additional hydrodynamic items of
six motion direction, which mainly represents fluid inertia resistance items [6]
.Combining the basic
maneuvering equation, established motion equation of high angle of attack.Due to space limitations,
the paper don’t specifically describe in the text.
Hydrodynamic Coefficients. The hydrodynamic coefficient applied in this paper is obtained from
limited ship model hydrodynamics experiment of large angle of attack and different propeller
load [6]
.Two sets of hydrodynamic coefficient are obtained from the experiment:the first is under the
situation of low angle of attack(angle of attack ]12,12[ °°−∈α ); the second is under the situation of high
angle of attack(angle of attack ]50,50[ °°−∈α ).
Model of Blowing Ballast Tank System
Model of Blowing Ballast Compartment. In the process of blowing ballast compartment, the
pressure F P declines rapidly in the air cylinder, in which the gas flow can be considered isentropic
because of its slow heat exchange. In the ballast compartment the accumulated gas flow can be seen as
isentropic expansion. This paper gained the model of blowing ballast compartment by dint of Laval
nozzle model, combining the instance of actual submarine.
Gas Flux in High-pressure Air Cylinder.
1
1
1 ) 1
2 (,)
1
2 ( −
+
−
+ =
+ ≤ k
k
F
Ft F
k
k
F
B
k k
RT
CpA m
kp
p �
(1)
))()(( 1
2 ,1)
1
2 (
12
1 k
k
F
Bk
F
B FFtF
F
Bk
k
p
p
p
p
k
k pCAm
p
p
k
+
− − −
=≤≤ +
ρρρρ� (2)
Pressure in Ballast Compartment.
B
B BB
B
B
V
dt
dV pRT
dt
dm
dt
dp −
= (3)
Discharged Water Flux in Ballast Compartment.
) )(2
(∑∑∑ −
=== i
WBi Hihi
i
hihihi
i
Bi
pp ACvACqQ
ρρρρ (4)
F m and
B m represents the mass of gas in air flask and in ballast compartment respectively;
t A is
the area of Laval nozzle ;C is valve coefficient（ 10 ≤≤ C ）;k is isentropic coefficient, 4.1=k ; R is Gas
Constant 287.1J/(kg·K ）； Q is discharged water flux; W p is the pressure of environment;
h C is
coefficient of losses, in this paper 7.0= h C ;i is the serial number of the ballast compartment.
Applied Mechanics and Materials Vols. 336-338 443
The Simulation and Analysis of Submarine Emergency Recovery
Recovery Maneuvering Simulation System. The simulation system consists of initialization state
setting module, damage setting module, recovery scheme setting module and real-time display
module. After simulation, firstly setting submarine’s initialization state and damage situation. If
blowing ballast compartment, the simulation system will record the time of blowing automatically.
The simulation system can choose calculation system through judging submarine’s angle of attack,
also can set in advance. The system solve the non-linear differential equation with Runge-Kutta of
four steps in fixed pace, and the fixed step is 1/10 second. The submarine’s state parameters will
refurbish each second and are displayed in real-time. When simulation finish, the system can output
the recovery scheme and submarine’s real-time parameters in whole simulation stage. The simulation
flow is as following Fig.2.
Analysis of Simulation Results. When compartment broken in submarine’s bow and amidships,
before the advent of high angle of attack, the results of simulation and calculation is approximation by
the large angle of attack and the small angle system under the same conditions, and the reasons is the
nonlinear items caused by large angle of attack does not work. But when large angle of attack appears,
the calculation results show that state parameters of the submarine is obviously different calculated by
different computing system from the results, after the big angle of attack angle, the results using large
angle of attack system is more consistent with the actual situation.
When compartment broken in submarine’s bow and
midship,compared to variety of measures ,the submarine
will most likely appear motion state of large angle of attack
under taking "not manipulating rudder, not blowing ballast
tanks” and "not manipulating rudder, not blowing ballast
tanks”. The reasons are that the submarine’s pose cannot be
controlled when not manipulating rudder, and the
submarine will appear large angle of attack. In order to
avoid the emergence of motion state of large angle of
attack, it is necessary to recovery submarine by measures of
manipulating rudder and increase the speed of the
submarine during recovery course.
When compartment broken in submarine’s stern, the
submarine will lose power, if taking measures of "stopping
deceleration, blowing ballast tanks " and using small angle
of attack system to recovery the submarine, submarine will
appear divergent, mutation and so on. When calculating the
motion state using of large angle of attack system, because
the equations of motion correction attached, the calculation
results were amended, does not appear above situation, and
the calculated results closer to the actual situation.
According to compartment broken in submarine’s stern, the submarine is usually the motion state of
large angle of attack, so it will play a key role to accurately forecast submarine’s motion state by
taking large angle of attack simulation model.
Numerical Example. This paper chooses the representative condition that the IV compartment is
flooded with initial depth being 200m, initial speed being 4 knots, diameter of crevasse being 100mm.
Taking blowing mid and stern ballast compartment and steering rudder to retrieve submarine. The
paper simulate the process with small angle of attack system and large angle of attack system
respectively. The real-time developing trends of submarine’s angle of attack(AOA), depth(H), roll
angle, pitch angle and axis velocity(Vx),floating velocity(Vceta) are shown as Fig.3.
Fig.2. The simulation flow of emergency recovery motion
flooded compartment of submarine
The setting of Initialization parameters
Solveing motion equation of six freedom degree
The setting of damage
Making emergency maneuver plan
Making emergency blowing plan
Whether relieveing tank's pressure
Whether discarding ballast
Reconfirm hydrodynamic coefficients
The state evaluation of real time
Whether changing recovery plan
Matching between attack angle and hydrodynamic
Yes
No
Ending the simulation process
Analyzing the motion characteristic of submarine
Yes
No
444 Industrial Instrumentation and Control Systems II
-100
-80
-60
-40
-20
0
20
40
60
80
100
0 50 100 150 200 250 300 350
t(s)
A t t a c k a n g l e ( d e g )
small angle of attack
high angle of attack
100
200
300
400
500
0 50 100 150 200 250 300 350 t(s)
D e p t h ( m )
s mall angle of attack
high angle of attack
-20
0
20
40
60
80
100
0 50 100 150 200 250 300 350
t(s)
R o l l ( d e g )
s mall angle of attack
high angle of attack
-40
-30
-20
-10
0
10
20
0 50 100 150 200 250 300 350
t(s)
P i t c h （
d e g ）
small angle of attack
high angle of attack
-6
-4
-2
0
2
4
6
8
10
0 50 100 150 200 250 300 350
t(s)
V X ( m / s )
small angle of attack
high angle of attack
-1
0
1
2
3
4
5
0 50 100 150 200 250 300 350
t(s)
V c e t a ( m / s )
small angle of attack
high angle of attack
Fig.4 . State parameters’s change of flooded compartment in submarine’s middle
The Fig.3 give the simulation results with small angle of attack system and large angle of attack
system respectively, and the conclusion is obvious that simulation results of small angle of attack are
abrupt, not constringe and far from nicety, due to submarine maneuver in large angle of attack. We
can see that the angle of attack of submarines nearly 80 degrees during recovery process, far beyond
the motion state of small angle range. The state parameters calculated by system of high angle of
attack are analyzed, and the results correspond with the actual situation. Comparing to limited ship
model experiments, the results applied hydrodynamics coefficients of large angle of attack are
accurate.
Conclusions
Based on submarine standard motion equation, considering that submarine usually maneuvers in
large angle of attack, increasing the additional inertia hydrodynamic items of motion state of large
angle of attack to amend the standard equation. According to the emergency recovery course of
flooded compartment, using the state model of small angle and large angle of attack to simulate and
calculate respectively, found that the results vary widely by using of small angle system and high
angle of attack system, and when submarine appears large angle of attack, the result simulated by
system of small angle of attack is unreasonable. So it is special significance that the accurate
hydrodynamics coefficients to forecast submarine’s maneuverability.
References
[1] SHI Shengda. Submarine Controlling , Defense Industry Press, Beijing,18-20(1995).
[2] DAI Yuliang. Motion Analysis and controlling Research of Submarine Emergency Surfacing,
Wuhan University of Technology, Wuhan,20-25( 2007).
[3] Wang W, Wang Y , Yin K . Modeling and Simulation of Six DOF Maneuvering for Submarine.
International Conference on Navigation ,Guidance and Control , Harbin Engineering University Pr,
Harbin, 428-432(2001).
[4] Joonyoung K,Kihun K.Estimation of Hydrodynamic Coefficients for an AUV Using Nonlinear
Obserbers,IEEE Journal of oceanic Engineering, 27(4),830-840(2002).
[5] Gentler. Standard equation of motion for submarine simulation,DTNSRDC Report 2510,
19-23(1967).
[6] Jin Tao, Yang Feng,Wang Jingqi.Submerged maneuverability of flooded submarine with large
angle of attack, Journal of Huazhong University of Science and Technology（Nature Science Edition
）, 36(12),79-82(2008).
Applied Mechanics and Materials Vols. 336-338 445
Industrial Instrumentation and Control Systems II 10.4028/www.scientific.net/AMM.336-338 The Analysis of Flooded Submarine Motion State Varying from Different Attack Angle under Blowing
Ballast Tank 10.4028/www.scientific.net/AMM.336-338.442
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