Comparison of different methods of measurement of pressure of underwater shock waves generated by electrical discharge

Different methods for measurement of strong underwater shock waves pressure pulses with peak pressures of up to 200 MPa and rise time of tens to hundreds of nanoseconds are described and compared. The experimental techniques include direct methods of pressure measurement using various electromechanical gauges such as quartz, carbon-based, and commercially available PCB gauges, and nondirect methods based on measurement of the velocity of the shock wave such as time-of-flight and fast-streak photography. Advantages and disadvantages of the used gauges and methods are discussed. The shock waves were produced by underwater electrical discharge (discharge current amplitude ≤100 kA, pulse duration ≤5 μs) initiated by an exploding wire. A good correspondence between the pressure amplitudes measured by the various gauges and methods was observed. The obtained dependence of the shock wave pressure on the distance from the discharge channel was found to be best fitted by a r ^−0.7 law. It is also shown that none of these methods can be used to determine the time evolution of the pressure behind the front of the shock wave.     

A low frequency torsional rheometer

Summary An instrument has been developed for measuring the viscoelastic behaviour of polymer melts at low frequencies, in the range 10^–3 to 50 Hz. The sample is contained between a cone and a fixed plate, or between parallel plates. The moving member is driven in torsional oscillation through a torsion wire. The amplitude of the resulting oscillation is compared in amplitude and phase with the driven end of the torsion wire. The amplitudes are measured digitally using optical diffraction gratings, and either an oscilloscope or a high-speed ultra-violet recorder is used to determine the phase angle between the two signals. The moving member is supported on an air bearing, which provides a very low friction support with a high degree of positional control thus giving a well defined sample geometry. The torsion wire is driven using a vibrator with a d.c. drive amplifier fed from a very low frequency oscillator. The sample temperature is controlled to better than 0.01 °C, with temperature gradients across the sample of a similar order of magnitude. The temperature range of the instrument is from –50 °C to +200 °C.The angular resolution of the measuring system is 3 × 10^–5 radius, so that an accuracy of better than ±1% in the amplitude measurements can be obtained with the amplitude of shear in the sample kept sufficiently low that a linear stress-strain relation is maintained.With 3 figures     

Mesh effects on the computation of small amplitude water waves

Computational difficulties arise in the non-linear free-surface problem for water waves both at large amplitudes when the crest becomes nearly singular and at small amplitudes when the wave is very close to the alternative uniform flow solution. Since the limiting wavelengths for small amplitude waves are known from the Stokes linearized theory, these are used in checking results for finite-amplitude programs. When Southwell and Vaisey¹ first tried this, their methods gave an unexplained overestimate, by 6 per cent, of the limiting wavelength. This paper shows how coarse mesh effects can create such an overestimate, gives very accurate solutions at small amplitudes and considers accuracy in relation to the mesh for short and long waves.     

考虑非稳态风荷载斜拉索风雨激振响应分析

为研究自然风荷载对斜拉桥拉索风雨激振的影响,将数值模拟的非稳态风荷载作用到拉索振动微分方程中,对拉索振动响应进行了详细分析。首先,针对水线初始位置,使用最小二乘法拟合得到水线初始位置方程;接着,采用四阶Runge-Kutta法求解拉索振动响应。通过比较在非稳态风和稳态平均风作用下的拉索响应,发现在非稳态风荷载下拉索最大振幅的变化趋势并没有发生较大改变,皆是随着风速的增大先增大后减小;但拉索的整个振动过程发生了变化,伴随着节拍改变,其最大振幅也出现在不同振动周期内。此外,从风速-振幅曲线知,对频率为1 Hz,2 Hz和3 Hz的拉索,在一定风速范围内,考虑非稳态风荷载的拉索振幅反而更大,而且此时的风速范围也更大。     

Spectral method for solving the equal width equation based on Chebyshev polynomials

A spectral solution of the equal width (EW) equation based on the collocation method using Chebyshev polynomials as a basis for the approximate solution has been studied. Test problems, including the migration of a single solitary wave with different amplitudes are used to validate this algorithm which is found to be accurate and efficient. The three invariants of the motion are evaluated to determine the conservation properties of the algorithm. The interaction of two solitary waves is seen to cause the creation of a source for solitary waves. Usually these are of small magnitude, but when the amplitudes of the two interacting waves are opposite, the source produces trains of solitary waves whose amplitudes are of the same order as those of the initial waves. The three invariants of the motion of the interaction of the three positive solitary waves are computed to determine the conservation properties of the system. The temporal evaluation of a Maxwellian initial pulse is then studied. Comparisons are made with the most recent results both for the error norms and the invariant values.     

Techniques of ray averaging

Ray methods are used in coastal and harbour wave disturbance investigations where the area to be modelled is large compared to the wavelength. The interpretation of forward-plotted ray diagrams, once obtained, has always been a difficult problem. The technique described in this paper calculates wave amplitudes during the ray plotting process and requires only minor modifications to existing ray plotting programs. The idea is to superimpose a grid of square elements over the entire sea area under study, and to perform a spatial averaging of the rays crossing each square element. This ‘square-averaging’ technique has a number of advantages. It smooths the rapid amplitude variations near caustics, calculates the interference of several wave trains, and generates amplitudes automatically in a square array covering the whole studied sea area. Two types of sensitivity tests are carried out. These tests are designed to determine the accuracy of the predicted wave amplitudes with respect to: (1) the square size per wavelength, and (2) the ray density. These two factors largely determine the computing storage, time and cost of a ray model. An upper limit on the square size per wavelength and a lower limit on the ray density are obtained.     

Theoretical analysis of the spatial variability in tillage forces for fatigue analysis of tillage machines

This paper presents a new theoretical model to describe the spatial variability in tillage forces for the purpose of fatigue analysis of tillage machines. The proposed model took into account both the variability in tillage system parameters (soil engineering properties, tool design parameters and operational conditions) and the cyclic effects of mechanical behavior of the soil during failure ahead of tillage tools on the spatial variability in tillage forces. The stress-based fatigue life approach was used to determine the life time of tillage machines, based on the fact that the applied stress on tillage machines is primarily within the elastic range of the material. Stress cycles with their mean values and amplitudes were determined by the rainflow algorithm. The damage friction caused by each cycle of stress was computed according to the Soderberg criterion and the total damage was calculated by the Miner’s law. The proposed model was applied to determine the spatial variability in tillage forces on the shank of a chisel plough. The equivalent stress history resulted from these forces were calculated by means of a finite element model and the Von misses criterion. The histograms of mean stress and stress amplitude obtained by the rainflow algorithm showed significant dispersions. Although the equivalent stress is smaller than the yield stress of the material, the failure by fatigue will occur after a certain travel distance. The expected distance to failure was found to be d_f = 0.825 × 10⁶ km. It is concluded that the spatial variability in tillage forces has significant effect on the life time of tillage machines and should be considered in the design analysis of tillage machines to predict the life time. Further investigations are required to correlate the results achieved by the proposed model with field tests and to validate the proposed assumptions to model the spatial variability in tillage forces.     

Influence of a combustion-driven oscillation on global mixing in the flame from a refinery flare

An assessment of the influence of strong combustion-driven oscillations on mixing rates and visible radiation in the flame from a full-scale refinery flare is reported. Importantly, the oscillations were generated naturally, with no external forcing, and at a high Reynolds number of 4 × 10⁶. These conditions differentiate this study from those of previous investigations, which all involved some external forcing and were at a Re too low to ensure fully turbulent flow within the flame. A frame-by-frame analysis of video footage, providing good resolution of the instantaneous edge of each flame, was used to assess flame dimensions, and so to determine a global residence time. Since the flames are in the fast-chemistry regime, the visual imagers can be used to determine a global mixing rate. The analysis reveals a consistent picture that the combustion-driven oscillations do not result in a significant change to the global mixing rate, but do increase the visible radiation. This is in contrast to previous investigations, using externally forced jets, where forcing at the preferred mode has been found to increase mixing rates and reduce radiation.     

New laboratory tests to measure rheological properties of paper coatings in transient and steady-state flows

The paper describes pertinent laboratory tests to characterize the rheological properties of paper coatings with regard to blade coating over a very wide range of shear rates in both transient and steady-state shear flows. Shear rates as high as 10⁶ s^–1 can be reached by means of a gas-driven capillary rheometer. Examples for the evaluation of end effects, wall effects, and coating thixotropy are given. A stiff and fast Couette rheometer is used to determine flow curves and the shear stress overshoot in step shear rate tests. The primary normal stress difference can be measured up to 10⁴ s^–1 by means of a high shear cone-plate rheometer with piezo transducer. A correct evaluation of the measurements has to take into account inertia contributions to the normal force. First results using a sinusoidal modulation of the shear rate are presented.Paper presented at: International Symposium on Pigment Coating Structure and Rheology, Helsinki, Febr. 8–9, 1989     

Template-free synthesis and characterization of K-phillipsite for use in potassium extraction from seawater

Kbphillipsite was prepared using a hydrothermal method. Soluble glass and sodium aluminate were used as raw materials in the absence of an organic template. Investigations regarding the K＋ ions were con- ducted at room temperature to determine the ion-exchange capacity in the seawater sample and the selectivity coefficient of the mixed K＋-Na~ solution. The sample was characterized by X-ray diffraction （XRD）, scanning electron microscopy （SEM）, and energy dispersion spectroscopy （EDS）. The K＋ ion- exchange capacity is 51 mg/g in seawater and the selectivity coefficient is 75.1 in the mixed K＋-Na＋ solution. The sample has a selectivity preference for K＋, and therefore can be used to selectively extract potassium from seawater. The sample composed of Si, Al, K, Na, and O exhibits a cross-like shape and is a typical K-phillipsite structure.     

Use of natural instabilities for generation of streamwise vortices in a laminar channel flow

An analysis of pressure-gradient-driven flows in channels with walls modified by transverse ribs has been carried out. The ribs have been introduced intentionally in order to generate streamwise vortices through centrifugally driven instabilities. The cost of their introduction, i.e. the additional pressure losses, have been determined. Linear stability theory has been used to determine conditions required for the formation of the vortices. It has been demonstrated that there exists a finite range of rib wave numbers capable of creating vortices. Within this range, there exists an optimal wave number which results in the minimum critical Reynolds number for the specified rib amplitude. The optimal wave numbers marginally depend on the rib positions and amplitudes. As the formation of the vortices can be interfered with by viscosity-driven instabilities, the critical conditions for the onset of such instabilities have also been determined. The rib geometries which result in the vortex formation with the smallest drag penalty and without interference from the viscosity-driven instabilities have been identified.     

VORTEX-EXCITED VIBRATIONS IN BUNDLED CONDUCTORS: A MATHEMATICAL MODEL

Wind-excited vibrations generated by vortex shedding are very common in high-voltage overhead transmission lines. Although such vibrations are barely perceptible due to their low amplitudes (less than a conductor diameter), they are, however, extremely important since they may lead to conductor fatigue. Mathematical models are therefore necessary for the computation of these vibrations, in order to evaluate the risk of potential damage to the line as well as for studying the efficiency of damping measures. For single conductor lines, the so-called energy-balance method gives good results in estimating the vibration amplitudes. However, the problem becomes more involved for bundled conductors with spacer dampers, commonly used in high-power transmission in many countries, and a modified form of the energy-balance method is presented here. Singular perturbation methods are employed, along with the energetically equivalent standing wave amplitudes obtained from the modified energy-balance methods, to determine the bending strains at critical points. This gives an estimate for the maximum strain levels in a conductor, which can be very useful in the design of transmission lines and for the optimization of the corresponding damping devices.     

Yield behavior of photoplastic materials

A mixture of flexible and rigid polyester resins has been used previously by Morris and Riley¹⁶ and by Zachary and Riley⁹ to model plastic deformations. The last of these papers furnished mechanical and optical properties under uniaxial tension and compression for several different mixture ratios of the polyester resins and also presents some results under multiaxial-stress conditions from thin cylinders under internal pressure. In a recent paper, Burger, Gomide and Scott¹⁴ used the rigid polyester resin at elevated temperature to model plastic deformations in upset rings; the behavior of the rigid polyester was verified with diametrically compressed disks and uniaxial-compression specimens. A very important similitude requirement for model to prototype scaling in photoplasticity work is that the macroscopic yield behavior of model and prototype materials must be the same. Thus, not only uniaxial tension and compression properties must be examined, but also yield properties under multiaxial-stress states have to be determined. The purpose of this paper is to provide additional information on the yield behavior of polyester mixtures which appear suitable for model studies of manufacturing methods such as rolling and extruding. For these processes, mixture ratio, test temperature and strain rate can be used to control the shape of the stress-strain curve and the yield behavior. The experimental procedure used to determine the initial yield locus of the photoplastic materials employed a new specimen geometry proposed by Arcan, Hashin and Voloshin¹⁸ which produces uniform biaxial-stress fields of opposite sign in one section of the specimen. Both polycarbonate and polyester materials were evaluated using this procedure and results are compared with those available in the technical literature.     

Extrusion of pastes with a piston extruder for the determination of the local solid and fluid concentration, the local porosity and saturation and displacement profiles by means of NMR imaging

 Nuclear Magnetic Resonance (NMR) was used to investigate the extrusion behaviour of PTFE pastes in a ram extruder. By means of ¹H-NMR imaging (MRI) it is possible to determine the local proton density and therefore, the local fluid concentration. The ¹⁹F-MRI provides the local solid concentration. Thus the local saturation and the local porosity can be calculated with the information of the local fluid and solid concentration. Furthermore displacement profiles can be derived from NMR images by means of correlation techniques without any preparation or marking of the pastes. Received: 8 May 2000   Accepted: 1 May 2001     

Three-dimensional nonlinear vibrations of composite beams — III. Chordwise excitations

Three nonlinear integro-differential equations of motion derived in Part I are used to investigate the forced nonlinear vibration of a symmetrically laminated graphite-epoxy composite beam. The analysis focuses on the case of primary resonance of the first in-plane flexural (chordwise) mode when its frequency is approximately twice the frequency of the first out-of-plane flexural-torsional (flapwise-torsional) mode. A combination of the fundamental-matrix method and the method of multiple scales is used to derive four first-order ordinary-differential equations describing the modulation of the amplitudes and phases of the interacting modes with damping, nonlinearity, and resonances. The eigenvalues of the Jacobian matrix of the modulation equations are used to determine the stability of their constant solutions, and Floquet theory is used to determine the stability and bifurcations of their limit-cycle solutions. Hopf bifurcations, symmetry-breaking bifurcations, period-multiplying sequences, and chaotic motions of the modulation equations are studied. The results show that the motion can be nonplanar although the input force is planar. Nonplanar responses may be periodic, periodically modulated, or chaotically modulated motions.     

Study of the membrane effect on turbulent mixing measurements in shock tubes

The effect of the thin membrane on the time evolution of the shock wave induced turbulent mixing between the two gases initially separated by it is investigated using two different sets of experiments. In the first set, in which a single-mode large-amplitude initial perturbation was studied, two gas combinations (air/SF and air/air) and two membrane thicknesses were used. The main conclusion of these experiments was that the tested membrane has a negligible effect on the evolution of the mixing zone, which evolves as predicted theoretically. In the second set, in which similar gas combinations and membrane thicknesses were used, small amplitude random-mode initial perturbation, caused by the membrane rupture, rather than the large amplitude single-mode initial perturbation used in the first set, was studied. The conclusions of these experiments were: (1) The membrane has a significant effect on the mixing zone during the initial stages of its growth. This has also been observed in the air/air experiment where theoretically no growth should exist. (2) The membrane effect on the late time evolution, where the mixing zone width has reached a relatively large-amplitude, was relatively small and in good agreement with full numerical simulations. The main conclusion from the present experiments is that the effect of the membrane is important only during the initial stages of the evolution (before the re-shock), when the perturbations have very small amplitudes, and is negligible when the perturbations reach relatively large amplitudes. Received 29 August 1998 / Accepted 25 December 1998     

基于逆向工程的三维复杂地质体精细建模及ADINA前处理在FLAC3D 建模中的应用

逆向工程技术作为一门新兴学科在复杂模型建模方面具有独特优势,并在许多领域得到了广泛的应用,在此基础上本文首次提出了基于逆向工程的三维复杂地质体精细建模技术,使得建立模型达到既“可视”又“可算”的目的。利用现行大型通用有限元仿真平台(ABAQUS,AD INA,ANSYS等)良好的网格划分功能且具有与CAD /CAM软件有着良好的接口这一优点,对模型进行网格划分,然后转换为FLAC^3D能够接受的格式,从而克服了FLAC^3D在前处理建模方面的不足。以AD INA为例对相应的接口程序开发过程进行了阐述,将上述技术方法应用于工程实例,取得了很好的效果。     

Boundary-layer receptivity due to distributed surface imperfections of a deterministic or random nature

Acoustic receptivity of a Blasius boundary layer in the presence of distributed, two-dimensional surface irregularities is investigated analytically. It is shown that, out of the entire spatial spectrum of the surface irregularities, only a narrow band of Fourier components can lead to an efficient conversion of the acoustic input at any given frequency to an unstable eigenmode of the boundary-layer flow. The location and the width of this most receptive band of wave numbers is fixed by the requirement of a relative detuning of O(R _inf1.b. ^sup–3/8 ) or less with respect to the instability wave number at the lower-branch station for the frequency under consideration. Surface imperfections in the form of discrete-mode waviness in this range of wave numbers then lead to initial instability amplitudes which are larger by a factor of O(R _inf1.b. ^sup3/8 ) than the amplitudes resulting from a single, isolated roughness element of streamwise extent comparable with the instability wavelength at the lower-branch location. In contrast, random irregularities which are spatially homogeneous in nature, and also possess a continuous spectrum in the streamwise direction, lead to instability amplitudes that are intermediate to those caused by the periodic and isolated irregularities, respectively, being, in fact, of the same order as the geometrical mean of the amplitudes in the latter two cases. A physical explanation for these asymptotic scalings is given, in addition to providing an analytical expression for the expected value of the instability amplitude for an ensemble of statistically irregular surfaces with random phase distributions. The duality between the localized and distributed receptivity analyses is also discussed.Financial support for this work was provided by the Theoretical Flow Physics Branch, Fluid Mechanics Division, NASA Langley Research Center, Hampton, VA, under contract NAS1-19299.     

Tidal Effects on Groundwater Motions

Assuming a sharp interface between freshwater and seawater within a coastal aquifer, a theory is developed to account for the piezometric head movement of steady and unsteady components in terms of large- and small-time scales. Tidal fluctuations are simulated by a series of decomposed simple harmonic motions in time. Groundwater fluctuation induced by tidal motion is perturbed to the groundwater head of large-time scale. Ghyben–Herzberg formulation is applied for solutions of large-time scale and a unified formulation for various flows of small-time scale is derived (Strack, 1989). Approximate analytical solutions for amplitudes and phase lags of tidal groundwater motions and the freshwater–seawater interface for a coastal aquifer in a circular island are obtained. The induced fluctuation amplitude generally decays in distance with a parameter consisting of hydraulic conductivity, storage coefficient, thickness of aquifer and tidal period. The present approach can be applied to confined and unconfined aquifers, with only freshwater flows or interfacial flows. The theory is verified with some experimental results (Parlange, et al., 1984; Nielson, 1990). It can also used to determine physical parameters of an aquifer by monitoring the groundwater fluctuations due to tidal motions (Carr and van der Kamp, 1969).     

Heat,Water, and Solute Transfer in Unsaturated Porous Mdeia: II -- Compacted Soil Beneath Plastic Cover

Soil surface dynamics involve coupled transferof heat, water, and solute. An experimental andtheoretical study of heat, water, and solute transferin closed compacted soil columns under surfacetemperature wave amplitudes is presented. Thetemperature wave amplitudes ranged from 17.9 to 21.0°C. Potassium chloride solution was used tomoisten Clarinda clay and Fayette silty clay loamsoils. Initial water contents of 0.403 and 0.279 andinitial solute concentrations of 0.062 and 0.052 mol kg^-1were used in Clarinda and Fayette soils,respectively. The moistened soils were packed andcompacted in PVC columns (0.075 m diameter and 0.30 mhigh). Bulk densities of the compacted Clarinda andFayette soils were 1403 and 1585 kg m^-3,respectively. The columns were buried in soil suchthat column surfaces were exposed to natural as wellas artificial radiation and thermal conditions. Thecoupled nonsteady-state balance equations of mass andenergy were solved numerically to predict soiltemperature, water content, and solute concentrationdistributions. The theoretical model described soiltemperature, water content, and solute concentrationwell as compared with the measured values. TheFickian diffusive solute flux was one or two orders ofmagnitude greater than salt-sieving and thermal-diffusion solute fluxes.