study of sloshing effects, in cylindrical tanks ali sarreshtehdari in the name of allah
TRANSCRIPT
Study ofStudy of
Sloshing Effects, In Cylindrical Sloshing Effects, In Cylindrical TanksTanks
Ali Sarreshtehdari
In The Name Of ALLAH
Project GoalsProject Goals
Finding Effects of Sloshing on Cylindrical Tanks
Avoid from Critical ConditionsFind the Procedure of Baffles Design Modified Present Tanks to other
Missions Designing Safe & Better Tanks, for
Each Condition *
IntroductionIntroduction
Sloshing is the Periodic Motion of the Free Surface of a Liquid in a Partially Filled Tank or Container Can be Caused by Several Factors
Sloshing Viewed in Many Industry Applications
Sloshing Study in Two Domain of Science :
1. Hydrodynamic
2. Hydroelasticity *
IntroductionIntroduction (Cont...)(Cont...)
In Freely Slosh , it Can Produce Forces That Cause Instability , Rollover and Failure or Damage in Tank or Container in Some Cases
Sloshing Magnitude and Hence its Effects Depends on Known Parameters
Baffles Used as Sloshing Suppression Devices *
History History
1952 RODRIGUEZ , GRAHAM & ABRAMSON (Tests in Airplane & Missile Control)
1989 BRYSON (Tests in Airplane & Missile Control)
1992 ARMENIO (Marine Transport) SANKAR & PATANKAR (liquid Carriers)
1997 VENUGOPAL & BERNSTEIN (Big Tanks Like Dams) , FEDDEMA , … (Maximum Velocity to Transfer) *
Chaptures ReviewChaptures Review
Chap. 1 IntroductionChap. 2 General Study
of Analytic Solution Chap. 3 Analytic
Solution of Slosh in Cylindrical Tanks & Application relations *
Chaptures ReviewChaptures Review (Cont...)(Cont...)
Chap. 4Dynamic Simulation of Slosh Phenomena
Chap. 5Methods of Test & Dimentionless
Analysis Chap. 6
Conclusion & Solve an Example *
Analysis Methods Analysis Methods
Analytical Methods
- Mathematics Based With Boundary Conditions & Some Assumptions
- Dynamic Modelling (1. Theoritical)Experimental Methods
- Dynamic Modeling (2. Exprimental)
- Dimensionless Groups Numerical Methods
- CFD Codes , ...*
Analytical MethodAnalytical Method
AssumptionsMathematics Modeling -
Differential Eqations - Boundary Conditions
Solve EquationObtain Unknown & Desired Parameters -
Natural Frequency - Pressure, Forces & Moments *
AssumptionsAssumptions
Rigid TankNon Viscose FluidIncompressible FluidSmall Movement, Melocity & Change for
Free Surface Irrotational Flow With no Source or Sink Homogenous Flow *
Diff. EquationDiff. Equation
Irrotational Flow : V= (x,y,z,t) Which : V=u i+ v j+ w k u = /x v = /y w = /z *
Boundary ConditionsBoundary Conditions
Bottom of Tank
Vertical Tank Wall
Free Surface
01 z
01 r
*0121
2
zg
t
Solve Equation Solve Equation
)()()()(),,,(1 zZGrRtTtzr
*)/()/(
)]//([),,,( 1
11 arJ
ahCosh
ahazCoshCoseatzr n
n
n
n
tin
n
With Sepration of Variables Method :
Obtained Equation :
Desired Parameters Desired Parameters
)/tanh(2 aha
gnnn
12
1
122
2
02
)1)((
)/(
)(
2),,,(
n nn
n
n
ti
J
arJ
a
rCosaextzrP
*)/(
)]//([gz
ahCosh
ahazCosh
n
n
: Natural Frequency
: Pressure Distribution
Desired ParametersDesired Parameters (Cont...)(Cont...)
2
0
0 2
0
2201
2
0
0 2
0 0
221
2
0
0
1
2
0 1
0
)2/(
)2/(
h
a
y
h
a
x
hy
hx
drdCosrPdzdCoszhapM
drdSinrPdzdSinzhapM
dzdSinaPF
dzdCosaPF
Note :
p1= Press. On Wall & p2= Press. On Bottom *
Desired Parameters Desired Parameters ((Cont…)Cont…)
1222
22
03
1222
2
22
)1)/(
2(
/
2)/tanh(
)/1)(1(
)/(
4
)/1)(1(
)/tanh()/(2
n nnn
nnny
n nnn
nnx
ahCoshahah
h
axhaM
ahahxaF
*0 xy MF
Dynamic SimulationDynamic Simulation
With Mass-Spring System
With Mass-Spring-Dashpod System
With Pendulum System *
Mass-Spring SystemMass-Spring System
Mass Spring Sys.Mass Spring Sys. Equations Equations
2
1
200
2000 2
1
2
1)(
2
1n
nnn VmIhxmT
*2/1]sin)cos1([)cos1( 200000 nnnnn xkxhgmghmU
Kinematic Energy :
Potensial Energy :
Mass Spring Sys.Mass Spring Sys. Equations Equations (Cont...)(Cont...)
L=T-U
*)]()([ 000000
00
Fhxxmhxmdt
d
Fx
L
x
L
dt
d
nnn
Equation of Motion From Lagrange Method :
Mass Spring Sys.Mass Spring Sys. Equations Equations (Cont...)(Cont...)
Ma
L
a
L
dt
d
00
)(
MgxmhhxxmIhhxmdt
dnnnnnn ])()([ 000000000
*0)( 000 gmxkhxxm nnnnnn
Mass Spring Sys.Mass Spring Sys. Solution Solution
1
22
222
001
22
22
/1
//
/1
/1
n n
nnn
T
nT
n n
n
T
nT
gh
m
mmx
m
mmF
*)/(1
)/(
)/(1
)(/2
12
22
0
1 12
2222
22
220000
n n
nnn
T
nT
n n n
nn
nnn
T
nTnn
gh
m
mym
hg
gh
m
mmhmhmIM
Mass Spring Sys.Mass Spring Sys. Results Results
*
1,)/tanh(2/
,)/2tanh()1(
)/2tanh()1(
2
1
22000
100
1002
2
nnnF
nnnn
nn
nTn
nnTn
nn
Tn
hmhmII
hmm
hdhd
hh
mmmdhh
dmm
dhh
gmk
Pendulum Sys.Pendulum Sys.
Pendulum Sys. EquationsPendulum Sys. Equations
N
j jjj
joTBi
mmmF1
22
2
)2
1.(
N
j jjj
jjjj
N
j jjj
jjooTT
Bi
Bilm
BihmhmhmM
122
122
2
)2
2.(
)2
1.(...
Mass Spring Sys.Mass Spring Sys. Simplified Eq. Simplified Eq.
0.0001
0.001
0.01
0.1
1
0
0.5 1
1.5 2
2.5 3
3.5
h/a
m1/mtm2/mtm3/mtm4/mt
Ex. Of Mechanical Models Ex. Of Mechanical Models
Mass Spring Sys.Mass Spring Sys. Simplified Eq. Simplified Eq. (cont...)(cont...)
)tanh(841.1 111
haga
)841.1tanh(4547.0 111 haahm
m
m
m
m
m 10 1
2111 mk
)920.0tanh(08.1 111 haahh
h
))((2
1 1
0
1
0
0
h
h
m
m
m
m
h
h
)841.1coth(5432.0 111 haahh
l
1111 2 mc
Dimensionless Analysis Dimensionless Analysis
Effective parameters
1. Acceleration on tank
2. Tank diameter
3. Resultant liquid force on tank wall
4. Depth of liquid in tank
5. Excitation amplitude
6. Liquid viscosity *
Dimensionless Analysis Dimensionless Analysis (Cont...)(Cont...)
Effective parameters (Continue...)7. Liquid density
8. Excitation period
Physical parameters1.length2.Time 3.Force *
Dimensionless Analysis Dimensionless Analysis (Cont...)(Cont...)
PIE BAKING HAM Theory :
(1,2,3,…,n-m) = 0
Where :
n = Number of Effective Parameters
m = Number of Base Parameter
= Combinations of Dimensionless Groups *
Dimensionless Analysis Dimensionless Analysis (Cont...)(Cont...)
])/(
,,,/
[)/).((
0223
dd
d
x
d
h
d
g
dd
F
n-m=8-3=5
Therefor We Have Five Dimentionless Groups :
There Are
Euler , Weber & Reynolds Dimentionless Groups
In Above Relation . *
Dimensionless Analysis Dimensionless Analysis (Cont...)(Cont...)
Compararison of Non Zero Th. , Model & Full-Scale Tests
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
0 1 2 3 4 5 6Frequency Parameter
Dim
en
tio
nle
ss
Fo
rce
Am
plit
ud
e
Zero Dampingh/d=0.500(Theory)
Model Test With Water ,X0/d=.00833
Model Test With METHYLENEBROMIDE , X0/d=.00417
Prototype Test , X0/d=00475
CFD CodesCFD Codes
Conclusions Conclusions
Sloshing May Be a Hazardous Phenomena In Control, Stability etc.
We Can Determine Sloshing Frequency, Force & Moment, With Various Methods
Depend of Our Sensitivity, We Can Reduce Sloshing Elevation & Change Natural Frequencies With Baffles *
Acknowledgement Acknowledgement
I wish to thanks from :
Dr. GH. ATEFI
Mr. GH. NADI
Mr. A. EGHTESADI
Mr. D. REZAEE
And All of My Friends That Help Me To Provide This Presentation *
Thank You For Attention
***
Sloshing Caused FactorsSloshing Caused Factors
Path form & properties of motionWind gusts during powered flightProgrammed changes in vehicle attitudeAttitude-stabilization control pulsesSeparating impulsesElastic deformation of the vehicleManeuver conditions *
ApplicationsApplications
Transferring The Liquids In Robotic, Metal Melting, Packaging Units & Tanker Trucks
Airplane Fuel Storage Tanks Missiles With Liquid Tanks Satellites
(Sloshing in Low Gravity Fields Applications) *
Effective Parameters Effective Parameters
Tank Geometry Propellant PropertiesEffective Damping Height of Propellant In The Tank Acceleration FieldPerturbing Motion of The Tank *
Acceleration Fields Acceleration Fields
Low Gravity Field High Gravity Field
Defined With Bond Number :
ForcestensionSurface
ForcenalGravitatiogaBo
2
*Re10
10010
1
quiredIsEffectGravityLowOfionConsideratB
ceSignificanbeMayEffectsGravityLowOfionConsideratB
NeglectedbeCanEffectstensionSurfaceB
o
o
o
Some OfSome Of Baffles Baffles ConfigurationConfiguration
Some OfSome Of Baffles Baffles ConfigurationConfiguration