Free surface due to a flow driven by a rotating disk inside a vertical cylindrical tank: Axisymmetric configuration

2014 ◽  
Vol 26 (7) ◽  
pp. 072105 ◽  
Author(s):  
L. Kahouadji ◽  
L. Martin Witkowski
Keyword(s):  
Free Surface ◽  
Rotating Disk ◽  
Cylindrical Tank ◽  
Axisymmetric Configuration

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.

Depletion and Retention of Fluid on a Rotating Disk

1983 ◽  
Vol 105 (4) ◽  
pp. 625-629 ◽  
Author(s):  
Yih-O Tu
Keyword(s):  
Contact Angle ◽  
Free Surface ◽  
Fluid Pressure ◽  
Rotating Disk ◽  
Rotating Speed ◽  
Radial Gradient ◽  
Flat Disk ◽  
Laplace Formula ◽  
Solid Phases ◽  
Liquid And Solid Phases

Assuming that a dry circular center is present at which the contact angle between the liquid and solid phases remains constant at all times, the axisymmetric free surface of liquid on a flat disk is determined from the Laplace formula in which the radial gradient of the fluid pressure balances the centrifugal force. The depletion of a thin layer of fluid from a rotating finite disk is described quasi-statically. A remnant of residual fluid is determined to remain on the disk. For moderate rotating speed, this remnant fluid volume is retained on the disk without loss.

Experimental Analysis and Flow Visualization of a Thin Liquid Film on a Stationary and Rotating Disk

1991 ◽  
Vol 113 (1) ◽  
pp. 73-80 ◽  
Author(s):  
S. Thomas ◽  
A. Faghri ◽  
W. Hankey
Keyword(s):  
Free Surface ◽  
Film Thickness ◽  
Liquid Film ◽  
Flow Visualization ◽  
Thin Liquid Film ◽  
Rotating Disk ◽  
Radial Spreading ◽  
Frictional Forces ◽  
The Mean ◽  
The Waves

The mean thickness of a thin liquid film of deionized water with a free surface on a stationary and rotating horizontal disk has been measured with a nonobtrusive capacitance technique. The measurements were taken when the rotational speed ranged from 0–300 rpm and the flow rate varied from 7.0–15.0 lpm. A flow visualization study of the thin film was also performed to determine the characteristics of the waves on the free surface. When the disk was stationary, a circular hydraulic jump was present on the disk. Upstream from the jump, the film thickness was determined by the inertial and frictional forces on the fluid, and the radial spreading of the film. The surface tension at the edge of the disk affected the film thickness downstream from the jump. For the rotating disk, the film thickness was dependent upon the inertial and frictional forces near the center of the disk and the centrifugal forces near the edge of the disk.

Structure of Flows in Viscoplastic Fluids Mixing

2002 ◽  
Author(s):  
Fre´de´ric Savreux ◽  
Pascal Jay ◽  
Albert Magnin ◽  
Jean-Michel Piau
Keyword(s):  
Numerical Simulation ◽  
Free Surface ◽  
Finite Elements ◽  
Constitutive Equation ◽  
Power Consumption ◽  
Viscoplastic Fluid ◽  
Two Dimensional ◽  
Cylindrical Tank ◽  
Stream Lines ◽  
Isothermal Mixing

The laminar isothermal mixing of a viscoplastic fluid is considered in the absence of any free surface and when the material can be modelled using a Bingham constitutive equation. The material is mixed by a rotating cylindrical tank and a fixed anchor impeller. A two-dimensional numerical simulation is performed with a finite elements method. The effects of viscoplasticity and inertia are related to an Oldroyd (Od) and to a Reynolds (Re) number. Stream lines, vortices, yield surfaces and power consumption are shown and analysed depending on the value of Od and Re parameters.

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.

Axisymmetric rotating flow with free surface in a cylindrical tank

2018 ◽  
Vol 861 ◽  
pp. 796-814 ◽  
Author(s):  
Wen Yang ◽  
Ivan Delbende ◽  
Yann Fraigneau ◽  
Laurent Martin Witkowski
Keyword(s):  
Reynolds Number ◽  
Free Surface ◽  
Surface Deformation ◽  
Fluid Layer ◽  
Three Dimensional ◽  
Azimuthal Velocity ◽  
Meridional Plane ◽  
Cylindrical Tank ◽  
Aspect Ratios ◽  
Steady Solutions

The flow induced by a disk rotating at the bottom of a cylindrical tank is characterised using numerical techniques – computation of steady solutions or time-averaged two-dimensional and three-dimensional direct simulations – as well as laser-Doppler velocimetry measurements. Axisymmetric steady solutions reveal the structure of the toroidal flow located at the periphery of the central solid body rotation region. When viewed in a meridional plane, this flow cell is found to be bordered by four layers, two at the solid boundaries, one at the free surface and one located at the edge of the central region, which possesses a sinuous shape. The cell intensity and geometry are determined for several fluid-layer aspect ratios; the flow is shown to depend very weakly on Froude number (associated with surface deformation) or on Reynolds number if sufficiently large. The paper then focuses on the high Reynolds number regime for which the flow has become unsteady and three-dimensional while the surface is still almost flat. Direct numerical simulations show that the averaged flow shares many similarities with the above steady axisymmetric solutions. Experimental measurements corroborate most of the numerical results and also allow for the spatio-temporal characterisation of the fluctuations, in particular the azimuthal structure and frequency spectrum. Mean azimuthal velocity profiles obtained in this transitional regime are eventually compared to existing theoretical models.

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