Dilatational Spherical Wave Propagations of Multiple Energy Sources in Viscous Fluid-Saturated Elastic Porous Media

2012 ◽  
Author(s):  
Lu Han ◽  
Liming Dai
Keyword(s):  
Porous Media ◽  
Viscous Fluid ◽  
Spherical Wave ◽  
Elastic Solid ◽  
Stress Waves ◽  
Fluid Viscosity ◽  
Fundamental Theory ◽  
Compressible Viscous Fluid ◽  
Dissipation Term ◽  
Representative Model

Biot developed a representative model for the propagation of stress waves in a porous elastic solid containing a compressible viscous fluid, which is the fundamental theory about wave propagation in porous media. The solution proposed in that work has the same form under the model with or without fluid viscosity, though it is conflicted with the energy dissipation when the viscosity of flow is involved. In this study, the solution under the viscosity model has been modified with the exponential time dissipation term introduced to different forms under light and heavy viscosity, which complies with Biot’s oscillation form when there is no damping caused by fluid viscosity, and makes more sense as less oscillatory when the viscosity becomes large, as the energy will be dissipated in that case.

The forced vibration of the system consisting of an elastic plate, compressible viscous fluid and rigid wall

2015 ◽  
Vol 23 (11) ◽  
pp. 1809-1827 ◽  
Author(s):  
Surkay D Akbarov ◽  
Meftun I Ismailov
Keyword(s):  
Viscous Fluid ◽  
Elastic Plate ◽  
Forced Vibration ◽  
Stokes Equations ◽  
Excitation Frequency ◽  
Rigid Wall ◽  
Navier Stokes ◽  
Fluid Viscosity ◽  
Compressible Viscous Fluid ◽  
Plane Flow

The forced vibration of the system consisting of a pre-stressed elastic plate, barotropic compressible Newtonian viscous fluid and rigid wall is considered. The space between the plate and rigid wall is filled by the fluid. It is assumed that the forced vibration is caused by the lineally-located time-harmonic force acting on the free face plane of the plate. The motion of the plate is written by utilizing the exact equations of elastodynamics, but the motion of the compressible viscous fluid is described by the linearized Navier-Stokes equations. Moreover, it is assumed that the velocities and stresses of the constituents are continuous on the contact plane between the plate and fluid, and that the impermeability conditions on the rigid wall are satisfied. The dimensionless parameters which characterize the compressibility and viscosity of the fluid as well as the elasticity constants of the plate are introduced. Plane strain state in the plate and two-dimensional plane flow of the fluid are considered. Numerical results on the interface normal stress and velocities are presented. The influence of the problem parameters is also discussed, including the fluid viscosity and compressibility, thickness of the plate and fluid depth as well as the excitation frequency. In this discussion the focus is on the influence of the fluid depth on the studied quantities. This is the parameter through which the main difference arises between the present and previous works by the authors.

Experiments and mechanistic modeling of viscosity effect on a multistage ESP performance under viscous fluid flow

2021 ◽  
pp. 095765092110149
Author(s):  
Yi Shi ◽  
Jianjun Zhu ◽  
Haoyu Wang ◽  
Haiwen Zhu ◽  
Jiecheng Zhang ◽  
...  
Keyword(s):  
Fluid Flow ◽  
Viscous Fluid ◽  
Prediction Error ◽  
Flow Direction ◽  
Fluid Viscosity ◽  
Oil Viscosity ◽  
Viscous Fluid Flow ◽  
Viscosity Effect ◽  
High Production Rate ◽  
Pump Head

Assembled in series with multistage, Electrical Submersible Pumps (ESP) are widely used in offshore petroleum production due to the high production rate and efficiency. The hydraulic performance of ESPs is subjected to the fluid viscosity. High oil viscosity leads to the degradation of ESP boosting pressure compared to the catalog curves under water flow. In this paper, the influence of fluid viscosity on the performance of a 14-stage radial-type ESP under varying operational conditions, e.g. rotational speeds 1800–3500 r/min, viscosities 25–520 cP, was investigated. Numerical simulations were conducted on the same ESP model using a commercial Computational Fluid Dynamics (CFD) software. The simulated average pump head is comparable to the corresponding experimental data under different viscosities and rotational speeds with less than ±20% prediction error. A mechanistic model accounting for the viscosity effect on ESP boosting pressure is proposed based on the Euler head in a centrifugal pump. A conceptual best-match flowrate QBM is introduced, at which the impeller outlet flow direction matches the designed flow direction. The recirculation losses caused by the mismatch of velocity triangles and other head losses resulted from the flow direction change, friction loss and leakage flow etc., are included in the model. The comparison of model predicted pump head versus experimental measurements under viscous fluid flow conditions demonstrates good agreement. The overall prediction error is less than ±10%.

scholarly journals IV. On double refraction in a viscous fluid in motion

1874 ◽  
Vol 22 (148-155) ◽  
pp. 46-47 ◽  
Keyword(s):  
Internal Friction ◽  
Viscous Fluid ◽  
Polarized Light ◽  
Elastic Solid ◽  
The State ◽  
Solid Cylinder ◽  
Annular Space ◽  
Double Refraction ◽  
Fresh Start ◽  
The Moment

According to Poisson’s theory of the internal friction of fluids, a viscous fluid behaves as an elastic solid would do if it were periodically liquefied for an instant and solidified again, so that at each fresh start it becomes for the moment like an elastic solid free from strain. The state of strain of certain transparent bodies may be investigated by means of their action on polarized light. This action was observed by Brewster, and was shown by Fresnel to be an instance of double refraction. In 1866 I made some attempts to ascertain whether the state of strain in a viscous fluid in motion could be detected by its action on polarized light. I had a cylindrical box with a glass bottom. Within this box a solid cylinder could be made to rotate. The fluid to be examined was placed in the annular space between this cylinder and the sides of the box. Polarized light was thrown up through the fluid parallel to the axis, and the inner cylinder was then made to rotate. I was unable to obtain any result with solution of gum or sirup of sugar, though I observed an effect on polarized light when I compressed some Canada balsam which had become very thick and almost solid in a bottle.

Influence of fluid viscosity and flow transition over non-linear filtration through porous media

2021 ◽  
Vol 130 (4) ◽  
Author(s):  
Ashes Banerjee ◽  
Srinivas Pasupuleti ◽  
Mritunjay Kumar Singh ◽  
Dandu Jagan Mohan
Keyword(s):  
Porous Media ◽  
Fluid Viscosity ◽  
Flow Transition ◽  
Non Linear ◽  
Linear Filtration

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 Steady MHD Flow of Viscous Fluid between Two Parallel Porous Plates with Heat Transfer in an Inclined Magnetic Field

2015 ◽  
Vol 7 (3) ◽  
pp. 21-31 ◽  
Author(s):  
D. R. Kuiry ◽  
S. Bahadur
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Viscous Fluid ◽  
Pressure Gradient ◽  
Reverse Flow ◽  
Flow Behavior ◽  
Fluid Pressure ◽  
Mhd Flow ◽  
Fluid Viscosity ◽  
Temperature Dependent Viscosity

The steady flow behavior of a viscous, incompressible and electrically conducting fluid between two parallel infinite insulated horizontal porous plates with heat transfer is investigated along with the effect of an external uniform transverse magnetic field, the action of inflow normal to the plates, the pressure gradient on the flow and temperature. The fluid viscosity is supposed to vary exponentially with the temperature. A numerical solution for the governing equations for both the momentum transfer and energy transfer has been developed using the finite difference method. The velocity and temperature distribution graphs have been presented under the influence of different values of magnetic inclination, fluid pressure gradient, inflow acting perpendicularly on the plates, temperature dependent viscosity and the Hartmann number. In our study viscosity is shown to affect the velocity graph. The flow parameters such as viscosity, pressure and injection of fluid normal to the plate can cause reverse flow. For highly viscous fluid, reverse flow is observed. The effect of magnetic force helps to restrain this reverse flow.

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.

The Effects of Vibrations on Particle Motion in a Viscous Fluid Cell

2008 ◽  
Vol 75 (3) ◽  
Author(s):  
Samer Hassan ◽  
Masahiro Kawaji
Keyword(s):  
Viscous Fluid ◽  
Drag Force ◽  
Particle Motion ◽  
Fluid Model ◽  
Resonance Phenomenon ◽  
Fluid Viscosity ◽  
Mass Force ◽  
Amplitude Data ◽  
Viscous Fluid Model ◽  
Fluid Cell

The effects of small vibrations on particle motion in a viscous fluid cell have been investigated experimentally and theoretically. A steel particle was suspended by a thin wire at the center of a fluid cell, and the cell was vibrated horizontally using an electromagnetic actuator and an air bearing stage. The vibration-induced particle amplitude measurements were performed for different fluid viscosities (58.0cP and 945cP), and cell vibration amplitudes and frequencies. A viscous fluid model was also developed to predict the vibration-induced particle motion. This model shows the effect of fluid viscosity compared to the inviscid model, which was presented earlier by Hassan et al. (2004, “The Effects of Vibrations on Particle Motion in an Infinite Fluid Cell,” ASME J. Appl. Mech., 73(1), pp. 72–78) and validated using data obtained for water. The viscous model with modified drag coefficients is shown to predict well the particle amplitude data for the fluid viscosities of 58.5cP and 945cP. While there is a resonance frequency corresponding to the particle peak amplitude for oil (58.0cP), this phenomenon disappeared for glycerol (945cP). This disappearance of resonance phenomenon is explained by referring to the theory of mechanical vibrations of a mass-spring-damper system. For the sinusoidal particle motion in a viscous fluid, the effective drag force has been obtained, which includes the virtual mass force, drag force proportional to the velocity, and the Basset or history force terms.

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