Nonsteady motion of solid sphere in compressible viscous fluid under the action of a pulse

1987 ◽  
Vol 23 (6) ◽  
pp. 602-605
Author(s):  
A. S. Basmat
Keyword(s):  
Viscous Fluid ◽  
Solid Sphere ◽  
Compressible Viscous Fluid ◽  
Nonsteady Motion

Wave Motion of a Compressible Viscous Fluid Contained in a Cylindrical Shell

1993 ◽  
Vol 115 (3) ◽  
pp. 302-312 ◽  
Author(s):  
J. H. Terhune ◽  
K. Karim-Panahi
Keyword(s):  
Velocity Field ◽  
Viscous Fluid ◽  
Imaginary Part ◽  
Fluid Velocity ◽  
Wave Number ◽  
Mode Shapes ◽  
Infinite Length ◽  
Complex Frequency ◽  
Compressible Viscous Fluid ◽  
Fluid Velocity Field

The free vibration of cylindrical shells filled with a compressible viscous fluid has been studied by numerous workers using the linearized Navier-Stokes equations, the fluid continuity equation, and Flu¨gge ’s equations of motion for thin shells. It happens that solutions can be obtained for which the interface conditions at the shell surface are satisfied. Formally, a characteristic equation for the system eigenvalues can be written down, and solutions are usually obtained numerically providing some insight into the physical mechanisms. In this paper, we modify the usual approach to this problem, use a more rigorous mathematical solution and limit the discussion to a single thin shell of infinite length and finite radius, totally filled with a viscous, compressible fluid. It is shown that separable solutions are obtained only in a particular gage, defined by the divergence of the fluid velocity vector potential, and the solutions are unique to that gage. The complex frequency dependence for the transverse component of the fluid velocity field is shown to be a result of surface interaction between the compressional and vortex motions in the fluid and that this motion is confined to the boundary layer near the surface. Numerical results are obtained for the first few wave modes of a large shell, which illustrate the general approach to the solution. The axial wave number is complex for wave propagation, the imaginary part being the spatial attenuation coefficient. The frequency is also complex, the imaginary part of which is the temporal damping coefficient. The wave phase velocity is related to the real part of the axial wave number and turns out to be independent of frequency, with numerical value lying between the sonic velocities in the fluid and the shell. The frequency dependencies of these parameters and fluid velocity field mode shapes are computed for a typical case and displayed in non-dimensional graphs.

scholarly journals Analytical Expressions of Hydro-Seismic Forces on Dams

2018 ◽  
Author(s):  
Abdelmadjid Tadjadit ◽  
Boualem Tiliouine
Keyword(s):  
Viscous Fluid ◽  
Linear Combination ◽  
Upstream Face ◽  
Compressible Viscous Fluid ◽  
Natural Modes ◽  
Boundary Method ◽  
Complete Sets ◽  
Seismic Forces ◽  
Analytical Expressions

Analytical expressions for the determination of hydro-seismic forces acting on a rigid dam with irregular upstream face geometry in presence of a compressible viscous fluid are derived through a linear combination of the natural modes of water in the reservoir based on a boundary method making use of complete sets of complex T-functions.Analytical expressions for the determination of hydro-seismic forces acting on a rigid dam with irregular upstream face geometry in presence of a compressible viscous fluid are derived through a linear combination of the natural modes of water in the reservoir based on a boundary method making use of complete sets of complex T-functions. The formulas obtained for distributions of both shear forces and overturning moments are simple, computationally effective and useful for the preliminary design of dams. They show clearly the separate and combined effects of compressibility and viscosity of water. They also have the advantage of being able to cover a wide range of excitation frequencies even beyond the cut-off frequencies of the natural modes of the reservoir. Key results obtained using the proposed analytical expressions of the hydrodynamic forces are validated using numerical and experimental solutions published for some particular cases available in the specialized literature.

On the Torsional Oscillations of a Solid Sphere in a Viscous Fluid

1956 ◽  
Vol 23 (4) ◽  
pp. 601-605
Author(s):  
G. F. Carrier ◽  
R. C. Di Prima
Keyword(s):  
Velocity Field ◽  
Viscous Fluid ◽  
Angular Displacement ◽  
Solid Sphere ◽  
Circumferential Velocity ◽  
Torsional Oscillations ◽  
Viscosity Measurements ◽  
First Approximation ◽  
Viscous Torque ◽  
Solid Bodies

Abstract Most treatments of the torsional oscillations of solid bodies assume that the velocity field is circumferential. In this paper the motion in planes containing the axis of oscillation is also considered. An expansion in terms of the angular displacement ϵ (assumed small) is made. The first approximation to the circumferential velocity is computed, and then used in computing the first approximation to the pumping motion. This is used to compute the correction to the circumferential velocity and, in particular, the correction to the viscous torque. For the range of parameters considered it is found that the correction to the torque is of the order of 0.04ϵ2|N0|, where N0 is the classical viscous torque. This problem is of interest in practical viscosity measurements.

Sign in / Sign up

Export Citation Format

Share Document