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]

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.

Effect of Gravity on Liquid Plug Transport Through an Airway Bifurcation Model

2005 ◽  
Vol 127 (5) ◽  
pp. 798-806 ◽  
Author(s):  
Y. Zheng ◽  
J. C. Anderson ◽  
V. Suresh ◽  
J. B. Grotberg
Keyword(s):  
Capillary Number ◽  
Axial Direction ◽  
Bond Number ◽  
Liquid Volume ◽  
Liquid Plug ◽  
Splitting Ratio ◽  
Wide Range ◽  
Critical Capillary Number ◽  
Airway Bifurcation ◽  
Parent Tube

Many medical therapies require liquid plugs to be instilled into and delivered throughout the pulmonary airways. Improving these treatments requires a better understanding of how liquid distributes throughout these airways. In this study, gravitational and surface mechanisms determining the distribution of instilled liquids are examined experimentally using a bench-top model of a symmetrically bifurcating airway. A liquid plug was instilled into the parent tube and driven through the bifurcation by a syringe pump. The effect of gravity was adjusted by changing the roll angle (ϕ) and pitch angle (γ) of the bifurcation (ϕ=γ=0deg was isogravitational). ϕ determines the relative gravitational orientation of the two daughter tubes: when ϕ≠0deg, one daughter tube was lower (gravitationally favored) compared to the other. γ determines the component of gravity acting along the axial direction of the parent tube: when γ≠0deg, a nonzero component of gravity acts along the axial direction of the parent tube. A splitting ratio Rs, is defined as the ratio of the liquid volume in the upper daughter to the lower just after plug splitting. We measured the splitting ratio, Rs, as a function of: the parent-tube capillary number (Cap); the Bond number (Bo); ϕ; γ; and the presence of pre-existing plugs initially blocking either daughter tube. A critical capillary number (Cac) was found to exist below which no liquid entered the upper daughter (Rs=0), and above which Rs increased and leveled off with Cap. Cac increased while Rs decreased with increasing ϕ, γ, and Bo for blocked and unblocked cases at a given Cap>Cac. Compared to the nonblockage cases, Rs decreased (increased) at a given Cap while Cac increased (decreased) with an upper (lower) liquid blockage. More liquid entered the unblocked daughter with a blockage in one daughter tube, and this effect was larger with larger gravity effect. A simple theoretical model that predicts Rs and Cac is in qualitative agreement with the experiments over a wide range of parameters.

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.

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.

Subharmonic Oscillations in an Arbitrary Tank Resulting From Axial Excitation

1968 ◽  
Vol 35 (1) ◽  
pp. 148-154 ◽  
Author(s):  
Wen-Hwa Chu
Keyword(s):  
Theoretical Result ◽  
Order Theory ◽  
Computational Effort ◽  
Characteristic Functions ◽  
Third Order ◽  
Axial Excitation ◽  
First Approximation ◽  
Rectangular Tank ◽  
Simple Geometry ◽  
Good Agreement

The problem of subharmonic liquid response in a container subjected to vertical (axial) excitation has been solved to the first approximation by the method of perturbation, employing characteristic functions. In principle, the tank can be arbitrary. However, the computational effort required to construct the characteristic functions and their derivatives may limit the application to tanks of relatively simple geometry such as a compartmented axisymmetric tank. As a check of the theoretical result, the simplest example for a rectangular tank is given, and the results are in good agreement with experiments and a third-order theory by Yarymovych.

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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