Oscillation of the water level in a well connected to a confined aquifer

The water in a well, which is connected to a confined aquifer, will oscillate if it is displaced and then released. The motion of the water is composed of a periodic and an aperiodic part. The damping of the periodic part is allways subcritical. The frequency of the periodic part increases with the damping and the inertia of the water in the aquifer. The motion is effectively characterized by two parameters: a non-dimensional transmissivity and the storativity. The inertia of the water in the aquifer has a small influence on the frequency, but negligible influence on the damping.     

A Pressure Field in an Acoustic Medium Containing a Cylindrical Solid and a Sphere Oscillating in a Predetermined Manner

A problem on the interaction of a spherical body oscillating in a predetermined fashion and a rigid cylinder is formulated. The bodies do not intersect, are immersed into an ideal compressible liquid, and their centers are in one plane. The solution is based on the possibility of representing the partial solution of the Helmholtz equation, written in cylindrical coordinates, in terms of partial solutions in spherical coordinates, and vice versa. An infinite system of linear algebraic equations is obtained by satisfying the boundary conditions on the sphere and cylinder surfaces. The system is intended for determining the coefficients of the expansion of the velocity potential into a series in terms of spherical and trigonometric functions. The system obtained is solved by the reduction method. The appropriateness of this method is substantiated. The hydrodynamic characteristics of the liquid surrounding the spherical and cylindrical bodies are determined. A comparison is made with the problem on a sphere oscillating in an infinite incompressible liquid that contains also a cylinder and in a compressible liquid that contains nothing more. Two types of motion of the sphere — pulsation and oscillation — are considered     

Motion of a slender body made of magnetizable composite in a traveling magnetic field

The motion of a slender body made of magnetizable composite in a channel, along which coils producing a heterogeneous “traveling” magnetic field are mounted, is investigated. The coil axes are vertical and lie in the same plane. A mathematical model of a slender body made of viscoelastic magnetizable material is proposed. The magnetic force is calculated from a formula used in ferrohydrodynamics of magnetic fluids with equilibrium magnetization. The problem of the motion of this body in a channel in a vertical plane under the action of the magnetic field produced in an experimental setup is numerically solved. The dependence of the body velocity on the coil switching frequency is calculated and the effect of different problem parameters on the form of this dependence is studied. The theoretical results are compared with the experimental data.     

Reduction in drag and vortex shedding frequency through porous sheath around a circular cylinder

A numerical study on the laminar vortex shedding and wake flow due to a porous‐wrapped solid circular cylinder has been made in this paper. The cylinder is horizontally placed, and is subjected to a uniform cross flow. The aim is to control the vortex shedding and drag force through a thin porous wrapper around a solid cylinder. The flow field is investigated for a wide range of Reynolds number in the laminar regime. The flow in the porous zone is governed by the Darcy–Brinkman–Forchheimer extended model and the Navier–Stokes equations in the fluid region. A control volume approach is adopted for computation of the governing equations along with a second‐order upwind scheme, which is used to discretize the convective terms inside the fluid region. The inclusion of a thin porous wrapper produces a significant reduction in drag and damps the oscillation compared with a solid cylinder. Dependence of Strouhal number and drag coefficient on porous layer thickness at different Reynolds number is analyzed. The dependence of Strouhal number and drag on the permeability of the medium is also examined. Copyright © 2009 John Wiley & Sons, Ltd.     

Note on the reflexion of water waves at a nearly vertical cliff in the presence of surface tension

In this note the two-dimensional problem of incoming surface waves against an approximately vertical wall or cliff in water of infinite depth is examined, using velocity potential formulation and linearized boundary-value problem theory for time-harmonic motion. The cliff has arbitrary profile but for simplicity is taken to be vertical at the free surface. The approximate first-order solution is determined subject to a dynamical edge condition apposite to the presence of surface tension, and contains partially reflected outgoing waves. The solution is obtained by perturbation theory in a form involving known unperturbed and first-order correction potentials that is applicable also to water of finite constant depth. The motivation for the note is to point out a correction in principle to the results of a recent investigation for a specific profile, in which reflexion is ignored and another error made in obtaining a first-order solution by a method that is restricted to infinite depth.     

Scattered-light photoelastic stress analysis of a solid-propellant rocket motor

Scattered-light photoelasticity, a nondestructive technique, is used to determine the stress distribution in a three-dimensional, solid-propellant rocket motor. The model is a case-bonded solid propellant with a stargrain internal boundary. Stresses are induced by internal pressure. The pressure load simulates part of the stresses developed in firing a rocket. The model material is polyurethane rubber which is similar to the binder material in actual rockets. The model construction and data analysis are discussed in detail, and the results are presented in graphical form.     

AN ARTIFICIAL DISSIPATION FORMULATION FOR A SEMI-IMPLICIT,PRESSURE BASED SOLUTION SCHEME FOR VISCOUS AND INVISCID FLOWS

The formulation of artificial dissipation terms for a semi-implicit, pressure based flow solver, similar to SIMPLE type formulations, is presented and is applied to both the Euler and the Navier-Stokes equations. The formulation uses generalized coordinates and a non-staggered grid. This formulation is compared to some SIMPLE and time marching formulations. The relationship between SIMPLE and time marching formulations is discussed briefly. The artificial dissipation inherent in some commonly used semi-implicit formulations, e.g. upwind differencing, powerlaw, QUICK and pressure weighting, is investigated. The scheme used here includes these dissipation terms directly, but retains the ability to mimic previous schemes. The potential for errors introduced by the simultaneous use of artificial dissipation in the continuity equation and central differencing of convective terms, is revealed. The effect of the amount of dissipation on the accuracy of the solution and the convergence rate is quantitatively demonstrated for two-dimensional inviscid flow in a mildly curved duct, three-dimensional laminar flow in a square cross section elbow with strong secondary flows, and two-dimensional turbulent flow through a turbine nozzle. The spurious effects of artificial dissipation, particularly second order dissipation, inherent in some commonly used algorithms, is clearly shown. The effect of artificial dissipation on the convergence rate is also demonstrated. The main conclusion drawn from the results is that the minimum amount of artificial dissipation that gives the required accuracy, but also an adequate convergence rate for a particular case, has to be used. This amount of dissipation is case dependent. The direct inclusion of artificial dissipation terms provides control over the amount of dissipation used.     

On the implementation of a multi-surface kinematic hardening plasticity and its applications

This paper is concerned with an application of the multi-surface plasticity in solid mechanics and geotechnical problems. The model is of a von-Mises type with associated flow rule, originally proposed by Montans. The Mroz translation rule is implemented to the movements of the yield surfaces and the fully implicit scheme with radial mapping method is applied in numerical computations. Algorithmic consistent tangent modulus with numerical integration algorithm of constitutive equations is extracted. The model is developed in the class of kinematic hardening models, so the ‘Masing’ rule is preserved. The model is able to consider the plastic strain accumulation in constant axial stress state, such as ratcheting. The implementation is validated by means of a simple deformation path of combined extension and compression test, a pure shear test with pseudo-random loading, a test which demonstrates the capabilities of the model in simulation of cyclic loading and ratcheting, a cyclic shear test in saturated undrained sand and finally, the analysis of a plate with holes, which presents the shear band using the multi-surface plasticity model.     

Asymptotic response of a two DOF elastoplastic system under harmonic excitation. Internal resonance case

The study of a two DOF elastoplastic system is formulated in a suitable phase space, velocity and force, in which an originally multi-valued restoring force is represented by a proper function. The asymptotic response can thus be studied using the Poincaré map concept and avoiding approximate analytical techniques. On account of the peculiarity of this hysteretic system, which has a well-defined yielding point, its dynamics is studied in a reduced dimension phase space using an efficient numerical algorithm. It is shown that the asymptotic response is always periodic with the period of the driven frequency and is always stable. Thus the response of the oscillator is described by its frequency response curves at various intensities of the excitation. The results presented refer to a system with two linear frequencies in a ratio of 1 : 3. The response is highly complex with numerous peaks corresponding to higher harmonics. The effect of coupling in conditions of internal resonance is a strong modification of the frequency response curves and of the oscillation shape of the structure.     

The effect of longitudinal vibration on poiseuille flow in a non-circular pipe

The effect is discussed of a superposed longitudinal sinusoidal vibration on the flow, under a constant pressure gradient, of a slightly non-Newtonian fluid in a straight pipe of non-circular cross-section. It is found that a flow in transverse planes is produced. This is the superposition of steady and sinusoidal flows. The stream-function corresponding to the steady flow is obtained in the case when the pipe has a rectangular cross-section. The discussion is based on a Rivlin-Ericksen constitutive equation in which only“second-order” non-Newtonian terms are present.     

Stability analysis of a polymer film casting problem

The polymer cast film process consists of stretching a molten polymer film between a flat die and a drawing roll. Drawing instabilities are often encountered and represent a drastic limitation to the process. Newtonian fluid film stretching stability is investigated using two numerical strategies. The first one is a ‘tracking’ method, which consists of solving Stokes equations in the whole fluid area (extrusion die and stretching path) by finite elements. The interface is determined to satisfy a kinematic equation. A domain decomposition meshing technique is used in order to account for a flow singularity resulting from the change in the boundary conditions between the die flow region and the stretching path region. A linear stability method is then applied to this transient kinematic equation in order to investigate the stability of the stationary solution. The second method is a direct finite element simulation in an extended area including the fluid and the surrounding air. The time‐dependent interface is captured by solving an appropriate level‐set function. The agreement between the two methods is fair. The influence of the stretching parameters (Draw ratio and drawing length) is investigated. For a long stretching distance, a critical Draw ratio around 20 delimitating stable and unstable drawing conditions is obtained, and this agrees well with the standard membrane models, which have been developed 40 years ago. When decreasing the stretching distance, the membrane model is no longer valid. The 2D models presented here point out a significant increase of the critical Draw ratio, and this is consistent with experimental results. Copyright © 2015 John Wiley & Sons, Ltd.     

Energy harvesting from a magnetic levitation system

Numerical and experimental studies of a magnetic levitation harvester are presented in the paper. The idea is based on the motion of permanent cylinder magnet in a coil exploited for energy harvesting. The novel model is based on a new definition of the coupling coefficient (inductive coefficient) which relates mechanical and an electrical components. The performed static and dynamics experimental tests show that this coefficient is a nonlinear function of the magnet position, and highly depends on the magnet coordinate in the coil, in such a way that the maximum energy is obtained in a coil ends. The comparison between classical – fixed value model – and novel nonlinear model of the inductive coefficient is presented for selected cases. The most essential differences are presented.     

Identification of Nonlinear Oscillator with Parametric White Noise Excitation

An identification technique is proposed for a nonlinear oscillator excited by response-dependent white noise. Stiffness, damping and excitation are estimated from records of the stationary stochastic response. The estimation of the stiffness is based on a nonparametric procedure in which the potential energy at the displacement extremes is obtained from the kinetic energy at the previous mean-level-crossing. A nonparametric estimate is obtained by an iterative averaging, in which the increased knowledge of the potential energy in each step is used to avoid bias. The second step in the procedure is to estimate the stationary probability potential in a nonparametric form from a histogram of the kinetic energy at mean-level-crossings. The damping is also estimated in a nonparametric way from approximate expressions of the covariance functions of a set of modified phase plane variables at a given energy level. Finally, the excitation is estimated from a relation between the stationary probability potential, the damping and the excitation. The separation of damping and excitation requires a parametric representation. The system identification technique is investigated by application to response records obtained by stochastic simulation. The stiffness estimation generally gives excellent results, while the damping and excitation estimation tend to be slightly biased for systems with strongly nonlinear stiffness.     

A reusable biaxial strain transducer

This paper describles a transducer which is, in effect, a reusable strain-gage rosette. The sensitive member of the instrument is a flat element shaped in the form of a hollow equilateral triangle. At the corners of the triangle are styli mounted perpendicular to the plane of the triangular element. On each side of each arm, an electric-resistance strain gage is centrally mounted parallel to the edges of the arm. The two gages on an arm form a temperature-compensated pair. In operation, the styli are pressed into the test surface, and subsequent straining of the surface induces bending and twisting strains in the arms of the element. The bending strain in an arm is detected by the strain gages mounted thereon and is proportional to the strain in the test surface in the direction parallel to the arm. The bending strain in a particular arm is unaffected by the forces in the other two arms. The theory of the transducer is discussed and experimental evidence which supports the theory is provided.     

The dynamics of a droplet in a capillary constriction underwave excitation

The frequency dependence of the amplitude of the wave excitation mobilizing a droplet trapped in a capillary constriction is determined. The effect of droplet viscosity is analyzed. The problem of free longitudinal oscillations of a viscous-fluid droplet in a capillary constriction is considered. The influence of the surface tension, the droplet volume, and the constriction shape on the natural frequency of droplet longitudinal oscillations is studied. A formula for calculating the droplet natural frequency in the conical constriction is obtained and analyzed.     

Simulation of compressibility of entrapped air in an incompressible free surface flow using a pressure-based method for unified equations

A pressure-based method is developed to solve the unified conservation laws for incompressible and compressible fluids. A polytropic law is used to model the compressibility of a gas and decouple the energy equation. The pressure field is calculated by solving a single-pressure Poisson equation for the entire flow domain. The effects of the compressibility of the gas are reflected in the source term of the Poisson equation. The continuities of pressure and normal velocity across a material interface are achieved without any additional treatment along the interface. To validate the developed method, the oscillation of a water column in a closed tube due to the compression and expansion of air in the tube is simulated. The computed time history of the pressure at the end wall of the tube is in good agreement with other computational results. The free drop of a water column in a closed tank is simulated. The time history of the pressure at the center of the bottom of the tank shows good agreement with other reported results. The developed code is applied to simulate the air cushion effect of entrapped air in a dam break flow. The computed result is in good agreement with other experimental and computational results until the air is entrapped. As the entrapped air pocket undergoes rapid pulsation, the pressure field of water around the air pocket oscillates synchronously.     

Steady sliding frictional contact problem for a 2d elastic half-space with a discontinuous friction coefficient and related stress singularities

The steady sliding frictional contact problem between a moving rigid indentor of arbitrary shape and an isotropic homogeneous elastic half-space in plane strain is extensively analysed. The case where the friction coefficient is a step function (with respect to the space variable), that is, where there are jumps in the friction coefficient, is considered. The problem is put under the form of a variational inequality which is proved to always have a solution which, in addition, is unique in some cases. The solutions exhibit different kinds of universal singularities that are explicitly given. In particular, it is shown that the nature of the universal stress singularity at a jump of the friction coefficient is different depending on the sign of the jump.     

Stress-Sensitive Permeability: Application to Fault Integrity During Gas Production

The objective is to propose a simple theoretical approach and the associated numerical algorithm to capture the permeability evolution within a fractured region in response to a stress perturbation. The stress range of interest is typical of a reversible deformation such that the fractures have varying apertures but constant lengths and densities. It is the permeability evolution from a negligible value characteristic of flows on geological times to values more relevant for gas production which is important for the structural integrity of the fractured region. A simple 1D application related to the sealing capacity of a fault bounding a producing gas reservoir is proposed to illustrate the theory. The stress change on the two sides of the faults is obtained with a 2D finite-element simulation based on the theory of poro-elasticity and considering the fault as a material discontinuity. The 1D flow simulation is done in a second step, and the flux is assumed to occur through the fault thickness from the non-depleted (minus side) to the depleted (plus side) regions. It is shown how the depletion results in the fractures opening in the fault damaged zone close to the minus side and the fracture closure next to the plus side. This evolution could be non-monotonic in time because of the development and the thinning of a boundary layer in the fluid pressure at the plus side. The simulations end once a Coulomb criterion is reached, typically at the minus side of the fault. The presence of a low-permeability core in the fault center does not change these conclusions although a positive effective normal stress is detected in the damaged zone on the minus side of the core prior to the Coulomb criterion activation.     

Unsteady pressure in the annular flow between two concentric cylinders,one of which is oscillating: Experiment and theory

The first objective of this paper is to present a series of accurate experimental measurements of the unsteady pressure in the annulus between two concentric cylinders, the outer one of which executes a harmonic planar motion, either transverse translational or rocking motion about a hinge, with and without annular flow. The second objective is the solution of the unsteady Navier–Stokes and continuity equations for the same annular geometry under the same boundary conditions for an incompressible fluid in the laminar regime. The solutions are obtained with a three-time-level implicit integration method in a fixed computational domain by assuming small amplitudes of oscillation of the outer cylinder. A pseudo-time integration method with artificial compressibility is used to advance the solution between consecutive real time levels. The finite difference method is used for spatial discretization on a stretched staggered grid. The problem is reduced to a scalar tridiagonal system, solved by a decoupling procedure which is based on a factored Alternating Direction Implicit (ADI) scheme with lagged nonlinearities. The third objective is the comparison of the experimental results with the theoretical ones. This comparison shows that the two are in good agreement in the case of translational motion, and in excellent agreement in the case of rocking motion. The experimental and theoretical work presented in this paper is useful for fluid–structure interaction and flow-induced vibration analyses in such geometries.