Fluid Pressure Waves Research Articles

Analysis of layered solid-fluid media using a discrete wavenumber and normal-mode superposition method

Layered solid-fluid media were analyzed using a discrete wavenumber and normal-mode superposition method, in which normal modes were obtained by finite-element method. A scalar wave equation for fluid pressure was employed in the formulation to introduce the effects of fluid layer. The scalar wave equation for fluid pressure and elastic wave equation for solid displacement were coupled using solid-fluid interaction equations. Green's function in the time domain was represented in terms of normal modes for layered solid-fluid media. A comparison was made between the solutions of the present method and those obtained from Biot's (1952) characteristic equation as well as by Pekeris and Lifson (1957) so as to examine the effects of a fluid layer.

An explicit numerical time domain formulation to simulate pulsed pressure waves in viscous fluids exhibiting arbitrary frequency power law attenuation

An explicit time domain algorithm is developed which is capable of numerically simulating pulsed pressure waves propagating through media whose attenuation increases with frequency according to a power law dependency. Because of possible noninteger exponents in the power law formulation, standard temporal differential operators cannot be defined and traditional finite difference approximations are therefore inappropriate. We derive a method that is consistent with the fact that the complex wavenumber often must include a nonlinear phase if system causality is to be ensured. This phase is derived from the power law attenuation and, due to their interdependency, the two terms in the wave equation corresponding to attenuation and phase can be combined into a single factor. This so-called dispersion wave equation is mapped into complex discrete-time frequency. In this domain, noninteger exponents can be eliminated via a power series expansion, and the resulting equations transform naturally to discrete time operators. The algorithm is tested by comparing numerically evaluated attenuation with the exact power law form, and the issues of stability in relation to the convergence of the power series and the accuracy of the mapping are investigated.

A FE-BE METHOD IN TIME DOMAIN FOR DYNAMIC RESPONSE ANALYSIS OF DAM-FOUNDATION-RESERVOIR SYSTEMS

A FE-BE method in time domain adaptable to dynamic interaction analysis of a dam-foundation-reservoir system is developed. In order to formulate the method, FEM is applied to the dam and the part of reservoir near the dam, and BEM is applied to the foundation and the part of reservoir away from the dam. The role of BEM is to satisfy the radiation conditions of waves which include elastic waves traveling from the dam to the foundation and fluid pressure waves generated at the interface of dam and reservoir. Basic equations in time domain of each region; that is dam, foundation and reservoir, is coupled by a method of weighted residuals, and an algorithm similar to the Newmark's beta method is obtained.An advantage of this algorithm is the capability of taking into account all the effects of dam-foundation interaction, dam-reservoir interaction, and reservoir-foundation interaction.

Wave propagation in solid and fluid structures using finite element transfer matrices

A numerical technique for the analysis of the transmission of pressure waves in elastic rods, tubes and fluids is presented. In this finite element method a new fluid element is used. The properties of the eigenvalues of the transfer matrices generated from the analysis provide the characteristic propagating wave modes, and their associated phase velocities and attenuation constants.

A hydrophone vertical seismic profiling experiment

To reduce the cost of VSP data acquisition, it is necessary to record the VSP signal from a vertical array of geophones for a single operation of the source. Until a vertical array of clamped three‐component geophones is available, it seems logical to evaluate the capabilities of a vertical array of hydrophones, which is much easier to fabricate. It is well known that elastic waves in the solid couple to pressure waves in the borehole fluid. It is also well known that this coupling excites in the borehole fluid energy known as tube‐wave noise that dominates the borehole pressure signal after the first arrival. (The borehole acts as a waveguide.) In this paper we test the effectiveness of velocity filtering of the borehole pressure signal to attenuate the slowly propagating tube‐wave noise and enhance the faster propagating body‐wave signals. Our initial test satisfactorily extracted from the hydrophone array data a strong reflected event that was also observed in the conventional clamped geophone VSP taken in the same borehole. We were not as successful in recovering subsequent weaker reflected signals from the hydrophone data, because of the strong incoherent ambient tube‐wave noise. This incoherency resulted from instrumental limitations that allowed us to record, for each shot, only three of the twelve hydrophone channels available in the vertical array.

Coma associated with flaccidity produced by fluid-percussion concussion in the cat. I: Is it due to depression of activity within the brainstem reticular formation?

This study is the first attempt to characterize neurological and behavioural consequences of fluid-percussion concussive head injury in the cat. Both animals initially anaesthetized by N2O as well as unanaesthetized, chronically prepared animals were subjected to injury. Injury with a fluid-pressure wave of 1.9-2.5 atm (duration 21-24 ms) produced a brief generalized areflexia. Following this initial response, injury greater than 2.1 atm frequently produced a period associated with hypotonia of postural muscles and suppression of postural motor responses (flaccidity). A close association between flaccidity and other indices of coma such as absence of eye-opening responses was noted. These consequences of injury can occur without fatal apnoae, circulatory collapse or overt intraparenchymal haemorrhages. This result suggests that mechanical stress predominantly restricted to the brain stem in fluid percussion may be sufficient, at least in the cat, to produce coma associated with flaccidity which has been previously documented for acceleration concussion. There was no evidence that fluid percussion produced EEG depression similar to the effects of lesions in the mesencephalic reticular activating system (RAS). Thus, depression of general levels of brain activity including those within the RAS seems not be necessary for production of this form of reversible coma.

Cerebral perfusion pressure, intracranial pressure, and head elevation.

Previous investigations have suggested that intracranial pressure waves may be induced by reduction of cerebral perfusion pressure (CPP). Since pressure waves were noted to be more common in patients with their head elevated at a standard 20 degrees to 30 degrees, CPP was studied as a function of head position and its effect upon intracranial pressure (ICP). In 18 patients with varying degrees of intracranial hypertension, systemic arterial blood pressure (SABP) was monitored at the level of both the head and the heart. Intracranial pressure and central venous pressure were assessed at every 10 degrees of head elevation from 0 degree to 50 degrees. For every 10 degrees of head elevation, the average ICP decreased by 1 mm Hg associated with a reduction of 2 to 3 mm Hg CPP. The CPP was not beneficially affected by any degree of head elevation. Maximal CPP (73 +/- 3.4 mm Hg (mean +/- standard error of the mean] always occurred with the head in a horizontal position. Cerebrospinal fluid pressure waves occurred in four of the 18 patients studied as a function of reduced CPP caused by head elevation alone. Thus, elevation of the head of the bed was associated with the development of CPP decrements in all cases, and it precipitated pressure waves in some. In 15 of the 18 patients, CPP was maintained by spontaneous 10- to 20-mm Hg increases in SABP, and pressure waves did not occur if CPP was maintained at 70 to 75 mm Hg or above. It is concluded that 0 degree head elevation maximizes CPP and reduces the severity and frequency of pressure-wave occurrence. If the head of the bed is to be elevated, then adequate hydration and avoidance of pharmacological agents that reduce SABP or prevent its rise are required to maximize CPP.

Application of generalized ray methods to studying the interaction of a thin inelastic shell with a planar staggered pressure wave in a fluid

Application of generalized ray methods to studying the interaction of a thin inelastic shell with a planar staggered pressure wave in a fluid

Hydrocephalus, cervical cord lesions, and spinal deformity.

Twenty-six children (4-16 years) had hydrocephalus and spinal deformity; 22 children had scoliosis over 50 degrees, and five children had kyphosis over 100 degrees. Twenty-one children had metrizamide enhanced cord CT scans, and 12 had additional head scans. Two children died, and one was autopsied. Three children had intracranial pressures monitored during spinal surgery. All children had Type I and II Arnold-Chiari malformations, 58% had cord cavitation (syringo/hydromyelia), 67% had cord tethering. The anatomic study showed extensive fibrosis and scarring of the upper cord and brain stem, but intraoperative studies showed that there is free transmission of fluid pressure wave from the cord across the foramen magnum with a consequent rise in intracranial pressure. This study documents frequent coexistence of spinal deformity and central nervous system lesions (hydrocephalus, Arnold-Chiari malformation, cord tethering with atresia, and cord cavitation). It supports the theory that the Arnold-Chiari malformation is a primary developmental deformity and that cord cavitation noted in these patients is primarily syringomyelia formed on the basis of ischemic necrosis within the cord. The free transmission of a fluid pressure wave from the cord to the lateral ventricle supports the Williams theory of propagation of syringomyelic cavities once they have developed. It is conjectural but likely that the CNS lesions cause spinal deformity by disrupting coordinating control of spinal musculature by the normal postural reflex mechanisms. Hydrocephalic patients who develop spinal deformity require thorough investigation for CNS lesions with head scans, CT scans, and metrizamide enhanced CT scans. NMR technology, however, may supplant techniques currently employed.

Theory of nonstationary interaction between pressure waves in a fluid and unclosed surfaces

Problems of nonstationary scattering of incident waves by unclosed surfaces have been solved in the general formulation under the usual assumptions of the linear mechanics of ideal compressible fluids. Such problems are encountered in a number of important hydrodynanic applications. In this case the nonstationary wave field must be known at any distance from the scatterer, and in particular in its immediate vicinity. The known methods of stationary diffraction cannot be used in nonstationary problems, when it is not possible to obtain exact expressions for the Fourier transforms of the unknown solutions and hence guarantee the unique recovery of the inverse transforms. However, the direct solution of the nonstationary problem is possible only in very simple situations: scattering of pressure waves by a plate, diffraction at the edge of a half-plane or at a slit in a flat screen, etc. These circumstances make it necessary to develop special approaches to the solution of the problem of the nonstationary scattering of pressure waves in a fluid by arbitrary unclosed surfaces. This paper outlines a method which leads to the construction of the Laplace transforms of the unknown solutions and is based on a unique means of satisfying the boundary conditions with the subsequent obtaining of exact expressions for the coefficients (densities) of the expansions employed. The class of problems solvable by this method is confined to those for which it is possible to obtain corresponding solutions by expansion in series or integrals over the complete orthogonal system of eigenfunctions on the assumption that the surface of the obstacle is closed. The Laplace transforms of the solutions can be inverted by any approximate method. The solutions constructed in accordance with the formalism developed are in satisfactory agreement with the experimental data and coincide with the classical results.

Response of poroelastic layers to moving loads

This paper presents a study of the response of layers of fluid-filled porous elastic (poroelastic) materials to surface tractions moving at constant speed.Solutions are obtained to Biot's equations for poroelastic materials using a Fourier Transform Method. Although physical domain behavior is found using a Fast Fourier transform for numerical inversion, it is shown that the distribution of fluid flow, pressure, stress and displacement may be determined directly in the transform domain without recourse to inversion.Layer response to a moving porous indenter and to a moving fluid pressure wave is determined. The flow, pressure and stress distributions for the two cases are found to be markedly different.

Significance of the ventricular fluid pressure wave form in the diagnosis of cerebral circulatory arrest and brain death.

The fluctuations in the absolute value of the ventricular fluid pressure (VFP) with simultaneous changes in the amplitude and frequency of the oscillations of the ventricular fluid wave form are described in seven patients who developed brain death following either a head injury or a cerebrovascular accident, and are compared with those observed in nineteen patients who survived similar brain pathology. The findings in the two groups were significantly different. It is suggested that VFP monitoring does provide reliable evidence of brain death even while the patient is on artificial respiration.

Transients in tubes containing liquids

An experimental investigation of the elastic and fluid pressure waves produced by the longitudinal impact of steel strikers on 25.4 mm (1.0 in.) dia. tubes filled with water was performed by means of a modified Hopkinson pressure bar technique. The tubes employed consisted of aluminum and acrylic plastic with three different wall thicknesses. Spherical strikers with diameters up to 12.7 mm (0.5 in.) were fired from pneumatic guns; larger steel balls were utilized in a pendulum configuration so as to achieve a variety of pulse amplitudes and durations. Longitudinal and hoop strain histories were measured on the surfaces of the tubes both in the unfilled and filled conditions; fluid pressure records were obtained along the tube axis by means of piezoelectric transducers. The experimentally-determined wave velocities in the two components of the system were compared with those predicted by the original and an extended version of the classical theory of water hammer, based on measured Young's moduli and Poisson's ratios determined from Hopkinson bar tests on solid circular rods. Excellent correspondence between observed and predicted values was obtained. While some slight dispersion was found for the empty aluminum and acrylic tubes, significant attenuation occurred only in tests with the latter substance, indicative of strong viscoelastic effects. The introduction of fluid into the aluminum specimen did not produce any substantial changes but, for the acrylic tubes, slightly increased the pulse velocity in the container and the attenuation of the peak. High-frequency vibrations observed on some of the records are associated with breathing action of the tube, an effect derivable from theoretical models only by inclusion of radial inertia.

Laminar transient flow in pipes

AbstractThe effects of fluid viscosity, pipe length, radius and pressure wave celerity are examined by solving the equations of fluid motion numerically for impulsively started flows. Velocities are obtained in terms of axial and radial positions and time. Pressures are obtained as a function of axial position and time using an averaging process. The dimensionless group \documentclass{article}\pagestyle{empty}\begin{document}$\frac{{\rho a{\rm R}^2}}{{\mu {\rm L}}}$\end{document} is shown to determine the development of these profiles.At low values of this group, a significant axial variation in the velocity profiles occurs. The pressure fluctuations accompanying startup however are progressiveely more damped as this group decreases. Such fluctuations are shown theoretically and experimentally to disappear when the aforementioned group falls to about 1.6. The numerical method used is capable of being applied to other transient pipe flows.

Continuous pressure monitoring in experimental obstructive hydrocephalus. II. The origin of undulating ventricular waves and periodic respirations.

Mayer waves and undulating ventricular waves were produced in hydrocephalic and nonhydrocephalic animals. Carotid sinus stimulation resulted in an increase in both wave forms, whereas carotid sinus denervation resulted in their diminution. The reflex pathway involved in the production of the waves constitutes a feedback mechanism between carotid sinus, the peripheral proprioceptor, and medullary vasomotor center. The ventricular fluid pressure wave forms are the intracranial manifestations of passively transmitted changes occurring in the systemic circulation secondary to dysfunction of the brain stem.

New method for measuring lag time between human uterine contraction and the effect on fetal heart rate

Two types of fetal heart rate dips, commonly referred to as Types I and II dips, may occur under abnormal conditions during labor. The purpose of this paper is to describe a new method for analyzing the time relation between Type II dips and the corresponding amnictic fluid pressure wave. Instead of using only one point corresponding to the minimum of fetal heart rate plus one point from the peak of amniotic fluid pressure and taking the difference, this method comprehensively includes many points from each wave form. This circumvents large lag-time errors as illustrated by analysis of 16 wave-form pairs.

Plane Waves in Layered Media

This paper describes how to couple equations describing pressure and shear waves of elastic materials with equations describing pressure waves in fluids. The media treated are homogeneous and occupy doubly infinite slabs of finite thickness. As a result, the transmission and reflection coefficients for a baffle composed of a finite number of slabs of elastic and fluid materials are obtained. These concepts are useful in the determination of transmission and reflection of sonar baffles, ocean bottom, etc. Limits can be taken, letting the thickness of a fluid layer go to zero, to see the effects of lubricated boundaries in baffles, etc.

Uterine contractions in spontaneous labor: A quantitative study

A statistical study was made of the amniotic fluid pressure wave form for each centimeter of cervical dilatation in 12 multiparous patients during spontaneous labor which produced mature term-sized infants. It was found that tonus, intensity, and frequency of contractions as well as uterine activity increase as labor progresses. No significant differences were found between average values obtained before and after rupture. The duration of contractions was found to remain fairly constant throughout labor. The regularity of the rhythm of contractions increased as labor progressed.

On spherical near fields and far fields in elastic and visco-elastic solids

Like divergent fluid pressure waves or electromagnetic radiations, divergent spherical stress waves produced by periodic excitation in infinite elastic and linearly visco-elastic homogeneous isotropic solids can exhibit near fields dominated by stationary vibrations decaying with r −3 and far fields dominated by progressive waves decaying with r −1, if r is the radial distance from the centre of the source. On a divergent motion the zone of transition between these fields, where the length of a peripheral line is of the order of the wave lengths, acts like a high-pass filter in preferentially attenuating the lower frequencies, whereas a convergent motion would have its lower frequencies reinforced preferentially. Due to phase changes in the stresses, the maximum shear stress in the transitional region is no longer half the arithmetical but half the time-vector difference between the principal, radial and circumferential stresses. If a source of excitation with a boundary in the transitional region is compared in its effect with one having its boundary in the near or far field, a damped resonance-like phenomenon is evident which increases in intensity with Poisson's ratio. In materials of high Poisson's ratios, a stress transition giving rise to such a resonance can be distinguished from a subsequent strain transition without resonance. A source of given size and pressure amplitude radiates a maximum of energy into the solid at frequencies that place the boundary in the transitional zone. A superimposed static state of stress does not alter the vibrational phenomena. A weak viscous effect does not influence the stress distribution and amplitudes in the near field but reduces the resonant amplitudes in the zone of transition and causes the known exponential decay in the far field.

Acoustic Character Logs and Their Applications in Formation Evaluation

Abstract Examples are presented which show that the velocity, amplitude, attenuation and apparent frequency of several acoustic waves can be recorded in the borehole. Examination of such recordings, termed "character" logs, indicates that the wave types observed include a refracted compressional wave and a wave which travels with formation shear velocity.Laboratory data are used to show that compressional and shear wave velocities are dependent on porosity, effective stress and lithology; but that the change in reciprocal velocity per unit change in porosity is larger for shear waves than for compressional waves. We, therefore, conclude that the accuracy of porosity determinations can sometimes be improved by use of shear wave velocities, provided that the shear wave amplitudes are large enough to delineate the shear arrival from the preceding compressional arrival on the character log. Borehole data are presented which show that the difference between shear wave and compressional wave reciprocal velocities can be used to predict porosities. This is a refinement which may allow the prediction of porosities from single-receiver acoustic logs without introduction of errors from borehole fluid travel-times. Laboratory and field data are presented to show that the relationship between compressional and shear wave velocities can be used to indicate lithology.An example is presented to show that fractures usually cause a greater reduction in borehole shear wave amplitudes than in compressional wave amplitudes, an effect which may offer a more reliable means of detecting fractures.The complexity of the borehole acoustic wave train can make presently available cement bond logs highly sensitive to the gate and bias settings used. The character log offers a means to circumvent possible misinterpretations by recording all amplitudes, from which the interpreter can select the appropriate data for evaluating the cement bond.Character logs may also be used as a quality control for open-hole transit-time logs when existence of small compressional wave amplitudes interferes with the proper functioning of bias-controlled timing devices.Evaluation of the potential uses of character log data is not complete; but a character log presented in a form convenient for routine use would be a desirable addition to currently available logs. To summarize, possible applications for such a log in formation evaluation include the followingquality control of transit-time logs,refinement of porosity predictions,determination of lithology,improvement of fracture detection andimprovement of cement bond evaluation. Suggestions are made regarding the requirements for a sufficient but practical character log for routine use. Introduction Acoustic logs have become a widely used porosity tool in formation evaluation. In addition, there is a growing application of acoustic logs in cement bond evaluation and fracture detection. These applications have mainly involved the use of logs of first-arrival transit times and amplitudes and have not included detailed studies of the complete signal.The purpose of this paper is to show that significant benefits in formation evaluation can be gained by a more complete use of the acoustic wave train generated in the borehole by an acoustic logging tool. We hope that this discussion will also stimulate further development of logs suitable for routine use so that these benefits may be realized.Examples of acoustic wave train logs, termed "character" logs, are presented to show that several identifiable acoustic waves are present in the borehole. The measurable characteristics of these acoustic waves and some of their relations to formation properties of interest are also discussed. The more obvious potential uses of character logs are listed, and some suggestions are made regarding the requirements for a sufficient but practical character log for routine use. CHARACTER LOGS Some 10 years ago, Vogel and Summers and Broding noted that the signals received uphole from an acoustic logging tool located in a borehole had a number of interesting characteristics. The logging tool consisted of two or more pressure transducers spaced on an acoustically insulated body (Fig. 1a). One of the pressure transducers was used as a transmitter to generate pressure waves in the borehole fluid. The other transducer served as a receiver to detect any pressure waves reaching it in the borehole. The receiver then converted these pressure waves to electrical signals which were transmitted to the surface and displayed on an oscilloscope as a record of time vs receiver-signal amplitude. Fig. 1b is a schematic representation of a typical record. JPT P. 639^