1. In The Name Of ALLAH Study ofSloshing 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 orDamage 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. 2 General Study of Analytic Solution • Chap. 3 Analytic Solution of Slosh in Cylindrical Tanks & Application relations *

7. Chaptures Review (Cont...) • Chap. 4 Dynamic Simulation of Slosh Phenomena • Chap. 5 Methods of Test & Dimentionless Analysis • Chap. 6 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. 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 1.length 2.Time 3.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