Dynamic Response of Soft Poroelastic Bed to Nonlinear Water Wave—Boundary Layer Correction Approach

When an oscillatory water wave propagates over a soft poroelastic bed, a boundary layer exists within the porous bed and near the homogeneous water∕porous bed interface. Owing to the effect of the boundary layer, the conventional evaluation of the second kind of longitudinal wave inside the soft poroelastic bed by one parameter, ε1 = k0a, is very inaccurate so that a boundary layer correction approach for a soft poroelastic bed is proposed to solve the nonlinear water wave problem. Hence a perturbation expansion for the boundary layer correction approach based on two small parameters, ε1 and ε2 = k0∕k2, is proposed and then solved. The solutions carried out to the first three terms are valid for the first kind and the third kind of waves throughout the whole domain. The second kind of wave is solved systematically inside the boundary layer, whereas it disappears outside the boundary layer. The result is compared with the linear wave solution of Huang and Song in order to show the nonlinearity effect. The present study is very helpful to formulate a simplified boundary-value problem in numerical computation for soft poroelastic medium with irregular geometry.     

Theory of Seepage into an Auger Hole in a Confined Aquifer Overlying a Gravel Substratum

An analytical solution is presented to the problem of steady groundwater flow seeping into a pumped cylindrical hole partially penetrating a homogeneous and anisotropic confined aquifer overlying a gravel substratum. Solutions are obtained for two general cases of the problem: (1) when the level of the pumped hole is below the confining layer; (2) when it is above it. The validity of the proposed theory is tested by comparing analytical predictions obtained for a few flow situations with corresponding results obtained by numerical means. The theory presented here can be utilized to convert the rate of rise of water in a pumped auger hole into directional conductivities of soil, in areas where water is found to be in a confined state overlying a gravel substratum. The study shows that the conductivity values calculated by neglecting the confining pressure of an artesian aquifer with a gravel base [i.e., by applying the existing (Boast and Kirkham in 1971), auger hole seepage theory for a phreatic aquifer with a gravel base to confined situations] may result in serious error; hence, the artesian head of an aquifer must be accounted for while computing the conductivity values. Further, it is observed that the area contributing flow to a pumped auger hole/well with a gravel base is mostly restricted to a short radial distance from the center of the hole, particularly for situations where the gravel substratum is located close to the bottom of the hole. This is in contrast to auger hole flow situations overlying an impervious substratum, where the domain contributing flow is mostly spread out to a considerable distance from the center of the hole.     

Theory of Seepage into an Auger Hole in a Confined Aquifer

A steady-state theory is presented for predicting flow into an auger hole partially penetrating a homogeneous and anisotropic confined aquifer that is underlain by an impermeable layer. The developed equations can be directly applied (i.e., without resorting to a coordinate transformation) to translate the rate of rise of the water in a pumped auger hole into directional conductivities of soil. The study shows that the conductivity values calculated by neglecting the confining pressure of an artesian aquifer (i.e., by applying the existing unconfined auger-hole seepage theories to experimental auger data obtained from a confined aquifer) may lead to serious error; hence, the confining head of an aquifer must be considered while the conductivity values are computed. Further, the distance of the outer layer also plays an important role in determining the flow to an auger hole penetrating a confined aquifer, and this parameter must therefore be included in the theoretical analysis of the problem. The validity of the proposed theory is checked by comparing a few results obtained from the theory with corresponding results obtained from numerical and analytical works. The developed theory is an addition to already existing auger-hole seepage theories for water-table aquifers; together with the available theories, the proposed solution is expected to cover the most commonly encountered auger hole experimental flow situations in the field.     

Numerical investigation of the interface in a continuous steel casting mold water model

In this study, the steady-state Navier-Stokes equations are solved on a curvilinear nonorthogonal grid, following the finite volume approximation, with a pressure prediction-correction method, for the case of a flow in a model steel casting mold. The steel flow is simulated by water flow and the slag layer by an oil film, following conditions of previous experimental studies. The simulation aims at the understanding of the free wave and the interface surface wave behavior and the mechanism that leads to the breakup of the steel-slag interface, and thus induction of impurities inside the final steel product. Boundary conditions are set on the free and the interface surfaces, and an adaptive grid mechanism is used in order to update the grid’s shape so as to follow the wave formation. Several cases have been considered with the inlet velocity parameter, and results concerning the velocity field and the generated waves are reported. It is shown that a critical casting speed exists that leads to wave instability, which may be associated with emulsification phenomena.     

Shallow Water Wave Propagation in Convectively Accelerating Open-Channel Flow Induced by the Tailwater Effect

Propagation of shallow water waves in viscous open-channel flows that are convectively accelerating or decelerating under gradually varying water surface profiles is theoretically investigated. Issues related to the hydrodynamics of wave propagation in a rectangular open channel are studied: the effect of viscosity in terms of the Manning coefficient; the effect of gravity in terms of the Froude number; wave translation and attenuation characteristics; nonlinearity and wave shock; the role of tailwater in wave propagation; and free surface instability. A uniformly valid nonlinear solution to describe the unsteady gradually varying flow throughout the complete wave propagation domain at and away from the kinematic wave shock as well as near the downstream boundary that exhibits the tailwater effect is derived by employing the matched asymptotic method. Different scenarios of hydraulically spatially varying surface profiles such as M1, M2, and S1 type profiles are discussed. Results from the nonlinear wave analysis are further interpreted and the influence of the tailwater effect is identified. In addition to the nonlinear wave analysis, a linear stability analysis is introduced to quantify the impact from such water surface profiles on the free surface instability. It is shown that the asymptotic flow structure is composed of three distinct regions: an outer region that is driven by gravity and channel resistance; a near wave shock region dominated by the convective inertia, pressure gradient, gravity and channel resistance; and a downstream boundary impact region where the convective inertia, pressure gradient, gravity and channel resistance terms are of importance. The tailwater effect is demonstrated influential to the flow structure, free surface stability, wave transmission mechanism, and hydrostatic pressure gradient in flow.     

Lagrangian Modeling of Weakly Nonlinear Nonhydrostatic Shallow Water Waves in Open Channels

A Lagrangian, nonhydrostatic, Boussinesq model for weakly nonlinear and weakly dispersive flow is presented. The model is an extension of the hydrostatic model—dynamic river model. The model uses a second-order, staggered grid, predictor-corrector scheme with a fractional step method for the computation of the nonhydrostatic pressure. Numerical results for solitary waves and undular bores are compared with Korteweg-de Vries analytical solutions and published numerical, laboratory, and theoretical results. The model reproduced well known features of solitary waves, such as wave speed, wave height, balance between nonlinear steepening and wave dispersion, nonlinear interactions, and phase shifting when waves interact. It is shown that the Lagrangian moving grid is dynamically adaptive in that it ensures a compression of the grid size under the wave to provide higher resolution in this region. Also the model successfully reproduced a train of undular waves (short waves) from a long wave such that the predicted amplitude of the leading wave in the train agreed well with published numerical and experimental results. For prismatic channels, the method has no numerical diffusion and it is demonstrated that a simple second-order scheme suffices to provide an efficient and economical solution for predicting nonhydrostatic shallow water flows.     

Laminar Poroelastic Media Flow

The continuity and momentum equations of laminar flow through poroelastic media and the sufficient boundary conditions are found in the present paper. The land subsidence equation, Brinkman equation, Darcy's law, and so forth, can be recovered by the simplified governing equations of the present model. A water wave passing over a poroelastic bed is taken as an example of application of this laminar poroelastic media flow model. It is found from the example that, besides the two kinds of longitudinal waves and one kind of transverse wave inside the porous media that the conventional poroelastic model can provide, a second kind of transverse wave is obtained by this model. It is also found that the tangential stress and flow velocity inside the porous bed, according to the laminar poroelastic media flow model, are very different from those obtained by the conventional potential poroelastic media flow model. Finally, the limiting rigid bed solution of the application example, which is useful for the experimental verifications, is also given in this study.     

Estimation of left ventricular end-diastolic pressure with the difference in pulmonary venous and mitral A durations is limited when mitral E and A waves are overlapped

Previous studies showed that difference in pulmonary venous and mitral A-wave durations can be used for the estimation of left ventricular end-diastolic pressure, which is based on the assumption that the pulmonary venous A wave and mitral A wave start with the beginning of left atrial contraction. It is also assumed that the mitral A wave ends with the end of left atrial contraction. These assumptions may not be correct if left atrial contraction occurs before the early left ventricular filling is completed. Adequate Doppler mitral inflow and pulmonary venous flow signals were obtained simultaneously with left ventricular pressures at the cardiac catheterization laboratory in 50 patients who showed separated E and A waves in mitral inflow. After heart rate was increased by right atrial pacing to make the mitral E and A waves overlap, Doppler and hemodynamic measurements were repeated. When E and A waves are separated, pulmonary A-wave duration exceeding mitral A-wave duration has a sensitivity of 67% and specificity of 85% in the prediction of elevated left ventricular end-diastolic pressure (>/=20 mm Hg), whereas the pulmonary A wave ending later than mitral A wave has a sensitivity of 83% and a specificity of 45%. When the mitral E and A waves are overlapped, the pulmonary A wave ending later than mitral A wave is better for the prediction of elevated left ventricular end-diastolic pressure (sensitivity 55%, specificity 75%) than pulmonary A-wave duration exceeding mitral A-wave duration (sensitivity 9%, specificity 96%). However, overall, both methods are limited for clinical use.     

Transient Head Development due to Flood Induced Seepage under Levees

The purpose of this study was to predict the uplift force during floods on confining layers that overlay extensive horizontal confined aquifers that intersect a large river in response to the water level changes that occur with time in a flooding river. Transient flow of water through the confined aquifer was described by a diffusion type of equation with a boundary condition at the river in which the river head varied with time. The transient head distribution developed from the unsteady flow model applied to the aquifer was compared with the hydraulic head distributions obtained from U.S. Army Corps of Engineers steady-state flow model and a finite-element seepage model. This study concluded that the transient flow model has the potential to analyze time lag in head development, and to predict the seepage condition and heaving potential at various times and distances landside of a levee during a flood cycle, but additional case histories are needed to justify widespread use of the model.     

Scattering of Harmonic Waves by a Circular Cavity in a Porous Medium: Complex Functions Theory Approach

An analytical solution for the evaluation of scattering of waves by a circular cavity in infinite isotropic elastic porous media is presented. Two groups of complex functions for solid skeleton and pore fluid in a two-dimensional complex plane are introduced in order to solve the Biot equations. Stress, displacement, and pore pressure fields induced by incident and scattered waves in the medium and especially in the vicinity of the cavity are evaluated in this complex plane. The validation of the proposed solution is shown by various numerical examples. A parametric study including the effects of fluid compressibility changes, shear modulus, and permeability variations, several wave numbers, and wave types (fast, slow, and shear waves) is performed.     

Leaky One-Dimensional Flow with Storage and Skin Effect in Finite-Width Sink

One-dimensional horizontal flow in a semiinfinite confined aquifer can be described in terms of mathematical solutions that relate drawdown in the aquifer to aquifer parameters and flow into or out of a line sink. A new solution that considers the effects of a low-permeability skin along with storage in a finite-width sink is developed for the leaky-aquifer case. A coefficient Sk is defined to represent the skin effect for one-dimensional flow. The transient solution, which is obtained by inverting the Laplace-space solution using the Stehfest numerical algorithm, calculates drawdowns in the sink as well as in the aquifer. A nondimensional drain function D(u,x/B,A/x,Sk/x)q is defined based on the solution. Selected type curves for the drain function are plotted, and a match-point procedure is described that is based on matching observed drawdowns at observation wells to an appropriate type curve. The match-point procedure is illustrated by fitting simulated drawdown data to a type curve and determining the aquifer parameters. The drawdown solution is also represented by dimensional time–drawdown plots, which can be used to determine aquifer parameters by adjusting the parameters until model-calculated drawdowns match observed values. This new solution can be used to analyze drawdowns that result from a canal pumping test in which the discharge from the canal is derived from water stored in the canal and from a leaky aquifer and in which the drawdowns are affected by storage and a low-permeability skin in the canal.     

Flow separation and liquid rundown in a gas-atomization process

“Rundown≓ filming mode was studied in a confined design gas-atomization nozzle of converging/ diverging construction. In this mode, liquid metal runs down to a certain distance up to ≈3 mm on the outer surface of the metal delivery tube in the form of a thin film. Atomization then takes place through the disintegration of this film by the oncoming gas. The rundown effect was simulated by water, and the supersonic gas flow outside the nozzle was visualized by Schlieren photography. It was found that rundown is caused by the liquid being drawn into a separated flow region on the wall of the delivery tube. This separation comes about as a result of the action on the boundary layer of adverse pressure gradients associated with the shock waves in the gas flow. Geometric conditions required for observing rundown are discussed, and a method is outlined for assessing whether a given nozzle design is likely to produce the effect. Evidence is also presented for the filming of the liquid on the tip of the nozzle by radial spreading.     

Laboratory Studies on the Coupled Oscillations between an Internal Density Interface and a Shear Layer

The results from experiments conducted in a 2?m high flow compartment at large Reynolds numbers are reported in this paper. Flow entered the compartment through an opening at the base on one side of the compartment and exited from an opening at the bottom of the opposite wall of the compartment. A shear layer is formed at the boundary between the incoming flow and the ambient fluid in the compartment. The impingement of the shear layer on the opposite wall of the compartment gives rise to periodic vortex formation and highly organized oscillations in the shear layer. When a density interface is present inside the compartment, resonance conditions were set up when the oscillations of the internal standing waves were “locked in” with the shear layer oscillations. Under resonance conditions, internal standing waves with amplitudes of up to 0.1?m were observed. The formation of the internal standing waves is linked to the shear layer oscillations. Resonance conditions result when the shear layer is oscillating close to the natural frequency of the stratified fluid system in the compartment. The results of this investigation are applicable for fresh water storage in floating bottom-opened tanks in the sea, where under resonance conditions, entrainment rates could be significantly increased.     

Solution for Flow Rates across the Wellbore in a Two-Zone Confined Aquifer

A closed-form solution for transient flow rates across the wellbore in a confined aquifer is derived from a two-zone radial ground-water flow equation subject to the boundary condition of keeping a constant head at the well radius. An aquifer may be considered as a two-zone system if the formation properties near the wellbore are significantly changed due to the well construction and/or well development. An efficient numerical approach is used to evaluate this newly derived solution. Values of the transient flow rate are provided in a tabular form and compared with those obtained by numerical inversion for the Laplace-domain solution. The results show that the two solutions are in good agreement. This newly derived solution can be used not only for predicting the transient flow rate across the wellbore but also for identifying the effects of a skin with a finite thickness on the estimation of transient flow rates in a ground-water system with two different formation properties.     

金属材料内部非金属夹杂超声检测的数值模拟

在金属材料内部夹杂物的超声检测中,如何通过检测获得的回波信号辨识夹杂物的属性和位置,一直是其重点和难点问题.通过建立包含夹杂物缺陷的二维金属板模型,采用有限元数值模拟的方法,对材料内部超声波场进行计算,获得了两种最典型的夹杂物Al₂O₃和TiN,以及二者在材料内部不同深度时的超声回波信号.研究了夹杂物类型和夹杂物深度对超声回波时域波形以及对界面波、夹杂物缺陷回波和底面回波频谱分布的影响规律.      

Dynamic Analysis of Multilayered Soils to Water Waves and Flow

In nature, a soil profile generally consists of several heterogeneous layers. This study is aimed at discussing the interactive problem of oscillatory water waves and flow passing over multilayered soils. The soil behavior is considered as viscoelastic in the present mathematical model modified from Biot’s poroelastic theory. Employing this model, the dynamic response including the profiles of pore water pressure and effective stress in the multilayered soils is discussed. The results reveal that the perturbed pore pressure is different from that inside a single-layered soil where the thickness of the first soil layer is less than the water wavelength. The discrepancy of the vertical effective stresses between multilayered and single-layered soils is even much more apparent under the same conditions. Moreover, seepage force is examined and is found to be larger near the bed surface and the bottom of the first soil layer where soils are easily disturbed by external disturbance. The locations where soil failure might happen are found near the troughs of surface water waves.     

承压开采技术在地下矿山废水减排中的应用

地下矿山的废水减排是针对地下矿山开采过程中造成的水环境严重破坏问题而提出的。承压开采是在尽量不影响矿井水文地质条件下所使用的带压开采技术,可以很好地解决资源开采对地下水原始赋存状态的破坏问题,从而取得良好的经济、社会和环境效益。论文以冀中能源股份有限公司葛泉矿东井1195回采工作面为例,系统总结了地下矿山承压开采的技术方法和途径,分析了承压开采在矿山废水减排中的意义和作用及取得的社会和经济效益。     

Flow Depletion Induced by Pumping Well from Stream Perpendicularly Intersecting Impermeable/Recharge Boundary

Analytical solutions for rate and volume of flow depletion induced by pumping a well from a stream that intersects an impermeable or a recharge boundary at right angles are derived using the basic flow depletion factor defined earlier by the author. A new concept of directly obtaining stream flow depletion using the method of images is proposed. The solutions are derived for five different management cases of a stream and boundary intersecting at right-angles, assuming the aquifer to be confined with semi-infinite areal extent. A computationally simple function is proposed for accurately approximating the error function. The existing analytical solution in the case of a right-angle bend of stream given by Hantush was obtained for unconfined aquifers using a linearization of the governing partial differential equation. The solution for this case obtained using the proposed method for confined aquifer is the same as obtained by Hantush for unconfined aquifers, which shows that the linearization adopted by Hantush does not actually solve this problem for unconfined aquifers.     

Investigations on Flow Pattern and Pressure inside SEN below Stopper Rod

In continuous casting of steel, the casting rate is often controlled by a stopper rod placed in the tundish outlet where the submerged entry nozzle (SEN) tube begins. The flow pattern inside the SEN plays an important role for the bubble formation at the argon injection nozzle at the stopper rod tip. High flow velocities are reached in the small gap between stopper rod and the surrounding SEN walls, and a flow separation has to be expected after the gap due to the fast expansion of the cross section. According to theoretical considerations and to the simulations, the absolute pressure in the gap becomes very low for liquid steel, which can cause cavitation‐like effects. PIV‐flow measurements in a 1:1 scaled water model of the caster show a highly oscillating and asymmetric flow pattern with rapidly changing separation regions. The low pressure effects expected in liquid steel cannot be investigated on the water‐model due to the lower density of water. In numerical simulations of the water‐model, the choice of the turbulence model and the usage or the non‐usage of geometrical symmetries for the bound of the computational domain have a great impact on the resulting flow pattern and the accuracy of the predicted pressure drop. The results of various turbulence models are compared with results from measurements on a water‐model. It turns out that only a 3D model using advanced turbulence models (SST k‐ω or Large Eddy) produce acceptable results, while 2D simulations completely fail and the standard turbulence models (e.g. k‐ε) significantly underestimate the pressure drop even in a 3D simulation.     

Pressure Waves in Porous Medium Saturated with Liquid Containing Gas Bubbles

Theoretical analyses on nonlinear pressure waves evolution in porous medium saturated with a liquid containing gas bubbles is carried out. The evolution equations for fast and slow longitudinal modes are derived for slightly nonlinear, disperse, and dissipation processes. The pressure wave distribution in gas bubble liquid-saturated porous media was investigated experimentally. It was revealed that both modes might have oscillating structure induced by bubble oscillation in the wave. It is shown that the wave damping is determined by a combined impact of heat losses due to gas cooling in the bubbles and dissipation due to longitudinal displacement of liquid and porous skeleton, both influenced by the wave. Experimental data on the velocity and structure of fast and slow modes are compared with results of theoretical modeling.