A Mechanical Model for Low-Gravity Sloshing in an Axisymmetric Tank

2004 ◽  
Vol 71 (5) ◽  
pp. 724-730 ◽  
Author(s):  
M. Utsumi
Keyword(s):  
Mechanical Model ◽  
Bond Number ◽  
Characteristic Functions ◽  
Tank Wall ◽  
Efficient Computation ◽  
Analysis Method ◽  
Low Gravity ◽  
Frequency Responses ◽  
Cost Efficient ◽  
Lateral Excitation

A mechanical model for low-gravity sloshing in an axisymmetric tank is developed using a newly developed slosh analysis method. In this method, spherical coordinates, whose origin is at the top of the cone that is tangent to the tank at the contact line of the meniscus with the tank wall, are used to analytically determine the characteristic functions for an arbitrary axisymmetric tank for which it is customary to resort to numerical methods. By this means, fast and cost-efficient computation can be conducted. Parameters of the mechanical model are determined such that the frequency responses of the resultant force and moment to lateral excitation coincide with those of the actual sloshing system. Influences of the Bond number and the liquid-filling level on the parameters of the mechanical model are examined.

Experimental and Theoretical Studies of Liquid Sloshing at Simulated Low Gravity

1967 ◽  
Vol 34 (3) ◽  
pp. 555-562 ◽  
Author(s):  
F. T. Dodge ◽  
L. R. Garza
Keyword(s):  
Natural Frequency ◽  
Mechanical Model ◽  
Small Diameter ◽  
Bond Number ◽  
Liquid Sloshing ◽  
Theoretical Studies ◽  
Low Gravity ◽  
Equivalent Mechanical Model ◽  
Experimental And Theoretical Studies ◽  
Experimental Comparisons

Analyses and experimental comparisons are given for liquid sloshing in a rigid cylindrical tank under conditions of moderately small axial accelerations; in particular, the theory is valid for Bond numbers larger than 10. The analytical results are put in the form of an equivalent mechanical model, and it is shown that the sloshing mass and the natural frequency of the first mode, for a liquid having a 0 deg contact angle at the tank walls, are smaller than for high-g conditions. The experimental data, obtained by using several small-diameter tanks and three different liquids, are compared to the predictions of the mechanical model; good correlation is found in most cases for the sloshing forces and natural frequency as a function of Bond number.

Low-Gravity Sloshing in an Axisymmetrical Container Excited in the Axial Direction

2000 ◽  
Vol 67 (2) ◽  
pp. 344-354 ◽  
Author(s):  
M. Utsumi
Keyword(s):  
Liquid Surface ◽  
Characteristic Root ◽  
Axial Direction ◽  
Bond Number ◽  
Characteristic Functions ◽  
Surface Oscillation ◽  
Low Gravity ◽  
The Past ◽  
Axial Excitation ◽  
Modal Equation

The response of low-gravity propellant sloshing is analyzed for the case where an axisymmetrical container is exposed to axial excitation. Spherical coordinates are used to analytically derive the characteristic functions for an arbitrary axisymmetrical convex container, for which time-consuming and expensive numerical methods have been used in the past. Numerical results show that neglecting the surface tension results in the underestimation of the magnitude of the liquid surface oscillation. The reason for this is explained by the influences of the Bond number and the liquid filling level on the critical value of the coefficient of the excitation term in the modal equation, above which the oscillation is destabilized, and on the characteristic root of the destabilized system. [S0021-8936(00)01502-6]

scholarly journals Low-Gravity Fuel Sloshing in an Arbitrary Axisymmetric Rigid Tank

1970 ◽  
Vol 37 (3) ◽  
pp. 828-837 ◽  
Author(s):  
Wen-Hwa Chu
Keyword(s):  
Bond Number ◽  
Forced Oscillations ◽  
Low Gravity ◽  
Mass System ◽  
Numerical Examples ◽  
Galerkin Procedure

Solutions to free and forced oscillations have been found in terms of an auxiliary set of eigenfunctions through the use of a modified Galerkin procedure. The slosh force and moment for an arbitrary axisymmetric rigid tank at arbitrary Bond number have been derived for both pitching and translation, and expressed in terms of characteristics of an equivalent spring-mass system. Numerical examples have been constructed which which compare favorably with available theories and experiments.

scholarly journals Synchronization and Stability of Elasticity Coupling Two Homodromy Rotors in a Vibration System

2016 ◽  
Vol 2016 ◽  
pp. 1-10
Author(s):  
Yongjun Hou ◽  
Mingjun Du ◽  
Pan Fang ◽  
Yuwen Wang ◽  
Liping Zhang
Keyword(s):  
Theoretical Analysis ◽  
Computer Simulations ◽  
Stability Criterion ◽  
Mechanical Model ◽  
Induction Motors ◽  
Simplified Model ◽  
Vibration System ◽  
Analysis Method ◽  
Lagrange Equations ◽  
Synchronous State

The mechanical model of an elasticity coupling 1-DOF system is proposed to implement synchronization; the simplified model is composed of a rigid body, two induction motors, and a connecting spring. Based on the Lagrange equations, the dynamic equation of the system is established. Moreover, a typical analysis method, the Poincare method, is applied to study the synchronization characteristics, and the balanced equations and stability criterion of the system are obtained. Obviously, it can be seen that many parameters affect the synchronous state of the system, especially the stiffness of the support spring, the stiffness of the connecting spring, and the installation location of the motors. Meanwhile, choose a suitable stiffness of the connecting spring (k), which would play a significant role in engineering. Finally, computer simulations are used to verify the correctness of the theoretical analysis.

Dynamics of Liquid Sloshing in Upright and Inverted Bladdered Tanks

1987 ◽  
Vol 109 (1) ◽  
pp. 58-63 ◽  
Author(s):  
F. T. Dodge ◽  
D. D. Kana
Keyword(s):  
Structural Dynamics ◽  
Mechanical Model ◽  
The Body ◽  
Liquid Sloshing ◽  
Model Parameters ◽  
Test Results ◽  
Governing Equations ◽  
Low Gravity ◽  
Equivalent Mechanical Model ◽  
Mechanical Models

The sloshing of liquids in tanks that use a flexible, inextensible bladder to contain the liquid is investigated experimentally and theoretically. The bladder affects both the configuration of the liquid in the tank and the sloshing frequencies and motion. The governing equations of liquid sloshing coupled to the structural dynamics of the bladder are formulated and examined to determine the interaction between the body forces of the liquid and the stiffness of the bladder and to show that the slosh dynamics can be represented by equivalent mechanical models. Tests are conducted to establish such mechanical models for normal and low-gravity conditions. For an inverted tank (liquid above the bladder), the sloshing is sufficiently different from conventional sloshing that the form of the equivalent mechanical model as well as the numerical values of the model parameters must be derived from the test results.

Free-Surface Vibrations of a Magnetic Liquid

1972 ◽  
Vol 94 (1) ◽  
pp. 103-108 ◽  
Author(s):  
F. T. Dodge ◽  
L. R. Garza
Keyword(s):  
Magnetic Field ◽  
Free Surface ◽  
Magnetic Fluid ◽  
Magnetic Interaction ◽  
Surface Tension Force ◽  
Bond Number ◽  
Low Gravity ◽  
Fluid Sloshing ◽  
Apparent Reduction ◽  
Surface Vibrations

A theory of magnetic fluid sloshing in a solenoidal magnetic field is developed herein. It shows that (a) the free-surface waves on a magnetic fluid are dynamically similar to the waves on an ordinary liquid in a reduced gravity field, and (b) the apparent reduction in gravity depends on the strength of the applied magnetic field. But, a deviation from true low-gravity behavior occurs whenever the Bond number (ratio of effective gravitational force to surface tension force) is much smaller than 1.0. The deviation is caused by a magnetic interaction that induces a jump in pressure across the free surface. To verify the conclusions of the theory and to evaluate the usefulness of magnetic sloshing as a low-gravity sloshing simulation, an exploratory series of tests was conducted using a magnetic-colloid liquid and a large solenoidal electromagnet. Measured slosh natural frequencies agreed well with theory, but the measured slosh damping was larger than predicted by existing correlation equations.

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