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**Study of Sloshing Effects, In Cylindrical Tanks**

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

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**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 *

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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 *

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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 *

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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) *

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**Chaptures Review Chap. 1 Introduction**

Chap General Study of Analytic Solution Chap Analytic Solution of Slosh in Cylindrical Tanks & Application relations *

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**Chaptures Review (Cont...)**

Chap Dynamic Simulation of Slosh Phenomena Chap Methods of Test & Dimentionless Analysis Chap Conclusion & Solve an Example *

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**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 , ...*

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**Analytical Method Assumptions**

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

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**Assumptions Rigid Tank Non Viscose Fluid Incompressible Fluid**

Small Movement, Melocity & Change for Free Surface Irrotational Flow With no Source or Sink Homogenous Flow *

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

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Boundary Conditions Bottom of Tank Vertical Tank Wall Free Surface

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**Solve Equation With Sepration of Variables Method :**

Obtained Equation :

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**: Pressure Distribution**

Desired Parameters : Natural Frequency : Pressure Distribution

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**Desired Parameters (Cont...)**

Note : p1= Press. On Wall & p2= Press. On Bottom *

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**Desired Parameters (Cont…)**

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**Dynamic Simulation With Mass-Spring System**

With Mass-Spring-Dashpod System With Pendulum System *

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Mass-Spring System

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**Mass Spring Sys. Equations**

Kinematic Energy : Potensial Energy :

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

L=T-U Equation of Motion From Lagrange Method :

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

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**Mass Spring Sys. Solution**

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**Mass Spring Sys. Results**

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Pendulum Sys.

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**Pendulum Sys. Equations**

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**Mass Spring Sys. Simplified Eq.**

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**Ex. Of Mechanical Models**

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

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**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 *

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**Dimensionless Analysis (Cont...)**

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

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**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 *

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**Dimensionless Analysis (Cont...)**

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

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**Dimensionless Analysis (Cont...)**

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CFD Codes

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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 *

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**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 *

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**Thank You For Attention**

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**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 *

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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) *

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**Effective Parameters Tank Geometry Propellant Properties**

Effective Damping Height of Propellant In The Tank Acceleration Field Perturbing Motion of The Tank *

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**Acceleration Fields Low Gravity Field High Gravity Field **

Defined With Bond Number :

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**Some Of Baffles Configuration**

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**Some Of Baffles Configuration**

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