1. Study of Sloshing Effects, In Cylindrical Tanks
In The Name Of ALLAH
Study of Sloshing Effects, In Cylindrical Tanks
Ali Sarreshtehdari

2. Project Goals Finding Effects of Sloshing on Cylindrical Tanks
Avoid from Critical Conditions
Find the Procedure of Baffles Design
Modified Present Tanks to other Missions
Designing Safe & Better Tanks, for Each Condition *

3. Introduction
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 *

4. Introduction (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 *

5. 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) *

6. Chaptures Review Chap. 1 Introduction
Chap General Study of Analytic Solution
Chap Analytic Solution of Slosh in Cylindrical Tanks & Application relations *

7. Chaptures Review (Cont...)
Chap Dynamic Simulation of Slosh Phenomena
Chap Methods of Test & Dimentionless Analysis
Chap Conclusion & Solve an Example *

8. 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 , ...*

9. Analytical Method Assumptions
Mathematics Modeling - Differential Eqations - Boundary Conditions
Solve Equation
Obtain Unknown & Desired Parameters - Natural Frequency Pressure, Forces & Moments *

10. Assumptions Rigid Tank Non Viscose Fluid Incompressible Fluid
Small Movement, Melocity & Change for Free Surface
Irrotational Flow With no Source or Sink
Homogenous Flow *

11. Diff. Equation
Irrotational Flow : V= (x,y,z,t) Which : V=u i+ v j+ w k u = /x v = /y w = /z *

12. Boundary Conditions
Bottom of Tank
Vertical Tank Wall
Free Surface

13. Solve Equation With Sepration of Variables Method :
Obtained Equation :

14. : Pressure Distribution
Desired Parameters
: Natural Frequency
: Pressure Distribution

15. Desired Parameters (Cont...)
Note :
p1= Press. On Wall & p2= Press. On Bottom *

16. Desired Parameters (Cont…)

17. Dynamic Simulation With Mass-Spring System
With Mass-Spring-Dashpod System
With Pendulum System *

18. Mass-Spring System

19. Mass Spring Sys. Equations
Kinematic Energy :
Potensial Energy :

20. Mass Spring Sys. Equations (Cont...)
L=T-U
Equation of Motion From Lagrange Method :

21. Mass Spring Sys. Equations (Cont...)

22. Mass Spring Sys. Solution

23. Mass Spring Sys. Results

24. Pendulum Sys.

25. Pendulum Sys. Equations

26. Mass Spring Sys. Simplified Eq.

27. Ex. Of Mechanical Models

28. Mass Spring Sys. Simplified Eq. (cont...)

29. 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 *

30. Dimensionless Analysis (Cont...)
Effective parameters (Continue...) 7. Liquid density
8. Excitation period
Physical parameters length Time Force *

31. Dimensionless Analysis (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 *

32. Dimensionless Analysis (Cont...)
n-m=8-3=5
Therefor We Have Five Dimentionless Groups :
There Are
Euler , Weber & Reynolds Dimentionless Groups
In Above Relation . *

33. Dimensionless Analysis (Cont...)

34. CFD Codes

35. 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 *

36. 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 *

37. Thank You For Attention
***

38. Sloshing Caused Factors
Path form & properties of motion
Wind gusts during powered flight
Programmed changes in vehicle attitude
Attitude-stabilization control pulses
Separating impulses
Elastic deformation of the vehicle
Maneuver conditions *

39. Applications
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) *

40. Effective Parameters Tank Geometry Propellant Properties
Effective Damping
Height of Propellant In The Tank
Acceleration Field
Perturbing Motion of The Tank *

41. Acceleration Fields Low Gravity Field High Gravity Field 
Defined With Bond Number :

42. Some Of Baffles Configuration

43. Some Of Baffles Configuration