On the Sloshing of Liquid in a Flexible Tank

1958 ◽  
Vol 25 (2) ◽  
pp. 277-283
Author(s):  
J. W. Miles
Keyword(s):  
Free Surface ◽  
Incompressible Fluid ◽  
Liquid Surface ◽  
Frequency Equation ◽  
Cylindrical Tank ◽  
Cantilever Bending ◽  
Free Bending ◽  
Kinetic And Potential Energies ◽  
Tank Diameter

Abstract The kinetic and potential energies of an incompressible fluid having a free surface in a cylindrical tank subjected to translation, rotation, and simple bending are derived in the forms 1 2 ∑ i ∑ j m i j q . i q . j and 1 2 ∑ i ∑ j k i j q i q j where the qi (t) are generalized co-ordinates. The results are illustrated by a calculation of the frequency equation for coupled bending and free-surface motions. It is found that if the mass of the empty tank is small compared with that of the liquid and the depth of the liquid is equal to the tank diameter the presence of the free surface increases the bending frequency (relative to that calculated with a plane cap that coincides with the liquid surface and is normal to the axis of the cylinder) by about 5 per cent for cantilever bending oscillations and 27 per cent for free-free bending oscillations.

Response of Liquid in Cylindrical Tank with Rigid Annual Baffle Considering Damping Effect

2011 ◽  
Vol 255-260 ◽  
pp. 3687-3691 ◽  
Author(s):  
Jia Dong Wang ◽  
Ding Zhou ◽  
Wei Qing Liu
Keyword(s):  
Free Surface ◽  
Dynamic Response ◽  
Potential Function ◽  
Natural Frequencies ◽  
Damping Ratio ◽  
Cylindrical Tank ◽  
Generalized Coordinates ◽  
Damping Effect ◽  
Total Potential ◽  
Free Surface Wave

Sloshing response of liquid in a rigid cylindrical tank with a rigid annual baffle under horizontal sinusoidal loads was studied. The effect of the damping was considered in the analysis. Natural frequencies and modes of the system have been calculated by using the Sub-domain method. The total potential function under horizontal loads is assumed to be the sum of the tank potential function and the liquid perturbed function. The expression of the liquid perturbed function is obtained by introducing the generalized coordinates. Substituting potential functions into the free surface wave conditions, the dynamic response equations including the damping effect are established. The damping ratio is calculated by Maleki method. The liquid potential are obtained by solving the dynamic response equations of the system.

Sloshing in Rectangular and Cylindrical Tanks

2002 ◽  
Vol 46 (03) ◽  
pp. 186-200 ◽  
Author(s):  
Pierre C. Sames ◽  
Delphine Marcouly ◽  
Thomas E. Schellin
Keyword(s):  
Free Surface ◽  
Finite Volume ◽  
Temporal Evolution ◽  
Numerical Study ◽  
Computational Method ◽  
Test Cases ◽  
Grid Refinement ◽  
Cylindrical Tank ◽  
Excitation Period ◽  
Cylindrical Tanks

To validate an existing finite volume computational method, featuring a novel scheme to capture the temporal evolution of the free surface, fluid motions in partially filled tanks were simulated. The purpose was to compare computational and experimental results for test cases where measurements were available. Investigations comprised sloshing in a rectangular tank with a baffle at 60% filling level and in a cylindrical tank at 50% filling level. The numerical study started with examining effects of systematic grid refinement and concluded with examining effects of three-dimensionality and effects of variation of excitation period and amplitude. Predicted time traces of pressures and forces compared favorably with measurements.

scholarly journals On a new method for the determination of atmospheric carbon dioxide, based on the rate of its absorption by a free surface of a solution of caustic alkali

1905 ◽  
Vol 76 (507) ◽  
pp. 112-117 ◽  
Keyword(s):  
Carbon Dioxide ◽  
Free Surface ◽  
Partial Pressure ◽  
Atmospheric Carbon Dioxide ◽  
Liquid Surface ◽  
Caustic Alkali ◽  
Optimal Velocity ◽  
Rate Of Absorption ◽  
A Current

In an appendix to a paper on the static diffusion of gases, communicated to the Society in 1900, it was shown that when a current of air containing a constant proportion of carbon dioxide is caused to move in a turbulent stream over the free surface of a solution of caustic alkali, the rate of absorption of that gas increases with the velocity of the air-current up to a certain optimal speed, beyond which no further increase in the speed of the current influences the rate of absorption. It was further shown that when the optimal velocity of the air-current has been reached, and the temperature is maintained practically constant, the rate of absorption then varies directly as the partial pressure of the carbon dioxide in the air. In other words, if under the above conditions the rate of absorption per unit of area of the liquid surface is a for a partial pressure of carbon dioxide represented by and is for a partial pressure of p' , then at similar temperatures, a / p = a' / p' . A suggestion was also made that this principle might be found applicable to a determination of the carbon dioxide in air, and that if the method were found to be a practical one it would have the manifest advantage of not requiring any measurement of the air from which the gas was absorbed.

Centrifugal waves

1960 ◽  
Vol 7 (3) ◽  
pp. 340-352 ◽  
Author(s):  
O. M. Phillips
Keyword(s):  
Free Surface ◽  
Angular Velocity ◽  
Circular Cylinder ◽  
Rigid Body ◽  
Water Depth ◽  
Frequency Equation ◽  
Rigid Rotation ◽  
Body Motion ◽  
Small Perturbations ◽  
The Stability

When a hollow circular cylinder with its axis horizontal is partially filled with water and rotated rapidly about its axis, an almost rigid-body motion results with an interior free surface. The emotion is analysed assuming small perturbations to a rigid rotation, and a criterion is found for the stability of the motion. This is confirmed experimentally under varying conditions of water depth and angular velocity of the cylinder. The modes of oscillation (centrifugal waves) of the free surface are examined and a frequency equation deduced. Two particular modes are considered in detail, and satisfactory agreement is found with the frequencies observed.

The formation of a dip on the surface of a liquid draining from a tank

1967 ◽  
Vol 29 (2) ◽  
pp. 385-390 ◽  
Author(s):  
Barry T. Lubin ◽  
George S. Springer
Keyword(s):  
Experimental Data ◽  
Liquid Surface ◽  
Cylindrical Tank ◽  
Simple Analytical Expression ◽  
Analytical Expression ◽  
Stationary Liquid ◽  
Circular Orifice ◽  
Good Agreement

Experiments were performed studying the formation of a dip on the surface of an initially stationary liquid draining from a cylindrical tank through an axisym-metrically placed circular orifice. Based upon the information obtained from the experiments, a simple analytical expression was derived predicting the height of the liquid surface in the tank at which this dip forms. A comparison was made between the experimental data and the results of the analysis and good agreement was found between theory and data.

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