study of sloshing effects, in cylindrical tanks ali sarreshtehdari in the name of allah

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