Modeling of Stokes Flow in Axisymmetrical Fields Due to Various Boundary Velocity Distributions

Volume 1 ◽  
2004 ◽  
Author(s):  
Mohamed A. Gadalla
Keyword(s):  
Exact Solution ◽  
Stokes Flow ◽  
Hankel Transform ◽  
Incompressible Fluids ◽  
Velocity Variation ◽  
Plane Boundary ◽  
Inverse Transform ◽  
Discontinuous Boundary ◽  
Boundary Velocity ◽  
Velocity Variations

This paper aims at investigating the effect of various boundary velocity distributions on the flow field in Stokes flow of incompressible fluids flow with axisymmetry. It was reported in literature that if the velocity variation at a plane boundary is suitably prescribed, the whole field of Stokes flow in a half-plane can be identified immediately by the artifice of Laplace transform. Similarly, it can be shown that if the boundary velocity distribution is represented for an axisymmetrical half-space, the whole field of Stokes flow can be described by the use of Hankel transform. With suitable given boundary velocity variations, the exact solution can be obtained through the integration of the resulting inverse transform. In this paper several realistic, continuous and discontinuous boundary velocity variations are analyzed following an intuitive derivative of the exact solution in cylindrical coordinates. The variations of the velocities and the pressure in the fluid are obtained for several examples of particular velocity variations at the plane boundary.

Dynamic properties of reflected and head waves near the critical point

1979 ◽  
Vol 16 (7) ◽  
pp. 1388-1401 ◽  
Author(s):  
Larry W. Marks ◽  
F. Hron
Keyword(s):  
Exact Solution ◽  
High Frequency ◽  
Classical Problem ◽  
Plane Boundary ◽  
Head Wave ◽  
Disk File ◽  
Ray Theory ◽  
Computational Point ◽  
Spherical Waves ◽  
Head Waves

The classical problem of the incidence of spherical waves on a plane boundary has been reformulated from the computational point of view by providing a high frequency approximation to the exact solution applicable to any seismic body wave, regardless of the number of conversions or reflections from the bottoming interface. In our final expressions the ray amplitude of the interference reflected-head wave is cast in terms of a Weber function, the numerical values of which can be conveniently stored on a computer disk file and retrieved via direct access during an actual run. Our formulation also accounts for the increase of energy carried by multiple head waves arising during multiple reflections of the reflected wave from the bottoming interface. In this form our high frequency expression for the ray amplitude of the interference reflected-head wave can represent a complementary technique to asymptotic ray theory in the vicinity of critical regions where the latter cannot be used. Since numerical tests indicate that our method produces results very close to those obtained by the numerical integration of the exact solution, its combination with asymptotic ray theory yields a powerful technique for the speedy computation of synthetic seismograms for plane homogeneous layers.

scholarly journals Effect of centimetric freezing of the near subsurface on Rayleigh and Love wave velocity in ambient seismic noise correlations

2020 ◽  
Vol 224 (1) ◽  
pp. 626-636
Author(s):  
René Steinmann ◽  
Céline Hadziioannou ◽  
Eric Larose
Keyword(s):  
Surface Wave ◽  
Wave Velocity ◽  
Love Wave ◽  
Ambient Noise ◽  
Seismic Velocity ◽  
Environmental Parameters ◽  
Velocity Variation ◽  
Small Scale ◽  
Apparent Velocity ◽  
Velocity Variations

SUMMARY About a decade ago, noise-based monitoring became a key tool in seismology. One of the tools is passive image interferometry (PII), which uses noise correlation functions (NCF) to retrieve seismic velocity variations. Most studies apply PII to vertical components recording oceanic low-frequent ambient noise ( < 1 Hz). In this work, PII is applied to high-frequent urban ambient noise ( > 1 Hz) on three three-component sensors. With environmental sensors inside the subsurface and in the air, we are able to connect observed velocity variations with environmental parameters. Temperatures below 0 °C correlate well with strong shear wave velocity increases. The temperature sensors inside the ground suggest that a frozen layer of less than 5 cm thickness causes apparent velocity increases above 2  % , depending on the channel pair. The observations indicate that the different velocity variation retrieved from the different channel pairs are due to different surface wave responses inherent in the channel pairs. With dispersion curve modelling in a 1-D medium we can verify that surfaces waves of several tens of metres wavelength experience a velocity increase of several percent due to a centimetres thick frozen layer. Moreover, the model verifies that Love waves show larger velocity increases than Rayleigh waves. The findings of this study provide new insights for monitoring with PII. A few days with temperature below 0 °C can already mask other potential targets (e.g. faults or storage sites). Here, we suggest to use vertical components, which is less sensitive to the frozen layer at the surface. If the target is the seasonal freezing, like in permafrost studies, we suggest to use three-component sensors in order to retrieve the Love wave response. This opens the possibility to study other small-scale processes at the shallow subsurface with surface wave responses.

The motion of particles in the Hele-Shaw cell

1994 ◽  
Vol 261 ◽  
pp. 199-222 ◽  
Author(s):  
C. Pozrikidis
Keyword(s):  
Integral Equations ◽  
Stokes Flow ◽  
Single Layer ◽  
Surface Force ◽  
Spherical Particles ◽  
Fredholm Integral Equations ◽  
Single Layer Potential ◽  
Layer Potential ◽  
Single Plane ◽  
Boundary Velocity

The force and torque on a particle that translates, rotates, or is held stationary in an incident flow within a channel with parallel-sided walls, are considered in the limit of Stokes flow. Assuming that the particle has an axisymmetric shape with axis perpendicular to the channel walls, the problem is formulated in terms of a boundary integral equation that is capable of describing arbitrary three-dimensional Stokes flow in an axisymmetric domain. The method involves: (a) representing the flow in terms of a single-layer potential that is defined over the physical boundaries of the flow as well as other external surfaces, (b) decomposing the polar cylindrical components of the velocity, boundary surface force, and single-layer potential in complex Fourier series, and (c) collecting same-order Fourier coefficients to obtain a system of one-dimensional Fredholm integral equations of the first kind for the coefficients of the surface force over the traces of the natural boundaries of the flow in an azimuthal plane. In the particular case where the polar cylindrical components of the boundary velocity exhibit a first harmonic dependence on the azimuthal angle, we obtain a reduced system of three real integral equations. A numerical method of solution that is based on a standard boundary element-collocation procedure is developed and tested. For channel flow, the effect of domain truncation on the nature of the far flow is investigated with reference to plane Hagen–Poiseuille flow past a cylindrical post. Numerical results are presented for the force and torque exerted on a family of oblate spheroids located above a single plane wall or within a parallel-sided channel. The effect of particle shape on the structure of the flow is illustrated, and some novel features of the motion are discussed. The numerical computations reveal the range of accuracy of previous asymptotic solutions for small or tightly fitting spherical particles.

scholarly journals Inspection of the residual stress on welds using laser ultrasonic supported with finite element analysis

2019 ◽  
Vol 6 ◽  
pp. 3
Author(s):  
Chong Ye ◽  
I. Charles Ume ◽  
Yuanlai Zhou ◽  
Vishnu V.B. Reddy
Keyword(s):  
Residual Stress ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Rayleigh Wave ◽  
Acoustic Waves ◽  
Velocity Variation ◽  
Element Analysis ◽  
Stress Evaluation ◽  
Longitudinal Residual Stress ◽  
Velocity Variations

Ultrasonic evaluation for residual stress measurement has been an effective method owing to its easy implementation, low cost and intrinsically being nondestructive. The velocity variations of acoustic waves in materials can be related to the stress state in the deformed medium by the acoustoelastic effects. In this study, a laser/EMAT ultrasonic method is proposed to evaluate the surface/subsurface longitudinal residual stress distribution generated by gas metal arc welding (GMAW). The velocity variation ΔV/V of Rayleigh wave, which is a surface wave, will be experimentally measured. Q-Switched Nd:YAG laser is used to generate a broadband ultrasonic wave. An electromagnetic acoustic transducer (EMAT) is attached to the welding plate for Rayleigh wave pick up. As the ultrasound receiver, the EMAT is used to measure time of flight (ToF) of the Rayleigh waves traveling along a specific path parallel to the direction of the welding seam. ToF measurements are obtained by changing Rayleigh wave path to welding zone center distance from 0 to 45 mm. A 3D thermomechanical-coupled finite element model is then developed to validate the capability of the proposed technique for welding-induced residual stress evaluation. The distributions of the normalized velocity variations from ToF experiments are compared with the distribution of the normalized longitudinal residual stresses from finite element analysis (FEA). It has been shown that there is a good correlation between these two distributions. The proposed technique provides a potential nondestructive avenue for surface/subsurface residual stress evaluation for welding parts.

scholarly journals Quasi-steady Stokes flow of multiphase fluids with shear-dependent viscosity

2007 ◽  
Vol 18 (4) ◽  
pp. 417-434 ◽  
Author(s):  
CARSTEN EBMEYER ◽  
JOSÉ MIGUEL URBANO
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Stokes Flow ◽  
Incompressible Fluids ◽  
Existence Results ◽  
Renormalized Solutions ◽  
Shear Dependent Viscosity ◽  
Multiphase Fluids ◽  
Dependent Viscosity ◽  
Compactness Arguments

The quasi-steady power-law Stokes flow of a mixture of incompressible fluids with shear-dependent viscosity is studied. The fluids are immiscible and have constant densities. Existence results are presented for both the no-slip and the no-stick boundary value conditions. Use is made of Schauder's fixed-point theorem, compactness arguments, and DiPerna–Lions renormalized solutions.

On steady Stokes flow in a trihedral rectangular corner

2003 ◽  
Vol 476 ◽  
pp. 159-177 ◽  
Author(s):  
A. M. GOMILKO ◽  
V. S. MALYUGA ◽  
V. V. MELESHKO
Keyword(s):  
Velocity Field ◽  
Stokes Flow ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Stagnation Line ◽  
Stagnation Points ◽  
Boundary Velocity ◽  
Different Types ◽  
Spiral Shape ◽  
Induced Flow

Motivated by the recent paper of Hills & Moffatt (2000), we investigate the Stokes flow in a trihedral corner formed by three mutually orthogonal planes, induced by a non-zero velocity distribution over one of the walls of the corner. It is shown that the local behaviour of the velocity field near the edges of the corner, where a discontinuity of the boundary velocity is assumed, coincides with the Goodier–Taylor solution for a two-dimensional wedge. Analysis of the streamline patterns confirms the existence of eddies near the stationary edge in the flow, induced either by uniform translation of one of the walls of the corner in the direction perpendicular to its bisectrix or by uniform rotation of a side about the vertex of the corner. These flows are shown to be quasi-two-dimensional. If the wall rotates about a centre displaced from the vertex, the induced flow is essentially three-dimensional. In the antisymmetric velocity field, a stagnation line appears composed of stagnation points of different types. Otherwise the three-dimensionality manifests itself in a non-closed spiral shape of the streamlines.

scholarly journals On the Steady Flow of a Second-Grade Fluid between Two Coaxial Porous Cylinders

2007 ◽  
Vol 2007 ◽  
pp. 1-11 ◽  
Author(s):  
M. Emin Erdoğan ◽  
C. Erdem İmrak
Keyword(s):  
Exact Solution ◽  
Reynolds Number ◽  
Steady Flow ◽  
Newtonian Fluid ◽  
Velocity Variation ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Grade Fluid ◽  
The Cross ◽  
Porous Cylinders

An exact solution of an incompressible second-grade fluid for flow between two coaxial porous cylinders is given. The velocity profiles for various values of the cross-Reynolds number and the elastic number are plotted. It is found that for large values of the cross-Reynolds number, the velocity variation near boundaries shows a different behaviour than that of the Newtonian fluid.

Stokes flow due to fundamental singularities before a plane boundary

2004 ◽  
Vol 25 (7) ◽  
pp. 799-805 ◽  
Author(s):  
N. Aktar ◽  
F. Rahman ◽  
S. K. Sen
Keyword(s):  
Stokes Flow ◽  
Plane Boundary
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