Localization of Mean Flow and Apparent Transmissivity Tensor for Bounded Randomly Heterogeneous Aquifers

We explore the concept of apparent transmissivity for bounded randomly heterogeneous media under steady-state flow regime. The novelty of our study consists of investigating a tensorial nature of apparent transmissivity. We demonstrate that apparent transmissivity of bounded domains is anisotropic even though an underlying local transmissivity field is statistically isotropic. For rectangular flow domains, we derive an analytical expression for the apparent transmissivity tensor via localization and perturbation expansion of the nonlocal mean flow equations in the variance of log-transmissivity. In this expression, almost everywhere the off-diagonal terms are several orders of magnitude smaller than the diagonal terms. When the domain size relative to the log-transmissivity correlation scale is large, the longitudinal and transverse components of the apparent transmissivity tensor approach the geometric mean of local transmissivity. While rigorously valid for mean uniform flows only, our expression for the apparent transmissivity tensor leads to mean hydraulic head distributions that compare favorably with those obtained through Monte-Carlo simulations and the nonlocal mean flow equations even in the presence of pumping wells. This agreement deteriorates in the vicinity of wells and as pumping rates increase.     

Optically sliced measurement of velocity and pH distribution in microchannel

A simultaneous measurement technique for the velocity and pH distribution was developed by using a confocal microscope and a 3CCD color camera for investigations of a chemical reacting flow field in a microchannel. Micron-resolution particle image velocimetry and laser induced fluorescence were utilized for the velocity and pH measurement, respectively. The present study employed fluorescent particles with 1 μm diameter and Fluorescein sodium salt whose fluorescent intensity increases with an increase in pH value over the range of pH 5.0–9.0. The advantages of the present system are to separate the fluorescence of particles from that of dye by using the 3CCD color camera and to provide the depth resolution of 5.0 μm by the confocal microscope. The measurement uncertainties of the velocity and pH measurements were estimated to be 5.5 μm/s and pH 0.23, respectively. Two aqueous solutions at different pH values were introduced into a T-shaped microchannel. The mixing process in the junction area was investigated by the present technique, and the effect of the chemical reaction on the pH gradient was discussed by a comparison between the proton concentration profiles obtained from the experimental pH distribution and those calculated from the measured velocity data. For the chemical reacting flow with the buffering action, the profiles from the numerical simulation showed smaller gradients compared with those from the experiments, because the production or extinction of protons was yielded by the chemical reaction. Furthermore, the convection of protons was evaluated from the velocity and pH distribution and compared with the diffusion. It is found that the ratio between the diffusion and convection is an important factor to investigate the mixing process in the microfluidic device with chemical reactions.     

Creeping flow of Newtonian fluids in curved rectangular channels

The object of this paper is to present accurate numerical data concerning the creeping flow in curved annular channels with rectangular cross sections of which the outer wall is rotating with constant angular velocity. Dimensionless expressions for velocity profiles, flow rates and friction factors are obtained analytically for both the “drag” and “pressure” flow contributions. Numerical data were obtained on a digital computer and are presented in tabular and graphical form. The results of the theoretical analysis are also expressed in terms of the flow rate correction factors widely used in calculating the pumping efficiency of screw-pumps, agitators and extruders. This enables to estimate the effect of flight curvature on the pumping capacity.     

Numerical simulation and design optimization of an electrohydrodynamic pump for dielectric liquids

With an ever increasing demand for more effective heat sinks, liquid based electronic cooling has become a new prospect in the field. The present study introduces an electrohydrodynamic (EHD) pump with a simple design for dielectric liquids which have potential applications for electronic cooling. The pump consists of an eccentrically sandwiched wire electrode placed at the horizontal centerline between two parallel flat-plate electrodes. The EHD flow of dielectric liquid induced by the space charge generated due to the Onsager effect was obtained by the numerical solution of the Poisson–Nernst–Planck equations for ion transport and the Navier–Stokes equations for fluid flow. Good agreement obtained in the comparison of the numerical and the experimental results of velocity for the centrally sandwiched wire electrode case confirmed the validity of the numerical results. For a fixed voltage, the pump flow rate depends on the eccentricity of the wire electrode with respect to the plate electrodes and also with the electrode dimensions. By using the Taguchi method an optimum design for the EHD pump is obtained considering the wire electrode diameter, the flat plate electrode length and the eccentricity (the horizontal distance between the centers of wire and flat-plate electrodes) as the design parameters for fixed channel dimensions.     

Numerical prediction of flow in a model of a (potential) soft acting peristaltic blood pump

This paper presents a numerical study of the flow field in a novel ‘soft’ acting peristaltic pump. The pump has potential applications wherever pumping of biological or sensitive fluids with reduced damage is required. The application of the device presented is as a blood pump. The model of the pump comprises a cylindrical tube that forms three chambers. The walls of these chambers move radially as a function of time. The pumping action is initiated by applying phased movement between the chambers. The flow is treated as laminar, unsteady, incompressible, Newtonian, and with a moving boundary. The governing equations are solved using a finite element method (FEM). An operating speed of 60 cycle min⁻¹ has been chosen. The results show that a periodic solution can be achieved after four cycles. The velocity field, streamline and shear stress are presented and discussed. The flow has generally a two‐way pulsatile nature, moving forwards and backwards. However, at the outlet, there is a net outflow over one cycle against a zero pressure head. Net flow linearly decreases to zero with increasing pressure head. Copyright © 2000 John Wiley & Sons, Ltd.     

Plane flow of a fluid of second grade through a contraction

We have studied the flow of a fluid of second grade through three types of plane channels with a contraction. The numerical method makes use of non-symmetric first- and third-order derivatives for maximizing the diagonal terms of the iterative systems. We have examined, in particular, the growth and decay of the corner eddies as a function of the Reynolds and Weissenberg numbers.     

Two-fluid mixing in a microchannel

A numerical study of the mixing of two fluids (pure water and a solution of glycerol in water) in a microchannel was carried out. By varying the glycerol content of the glycerol/water solution, the variation in mixing behavior with changes in the difference in the properties of the two fluids (e.g., viscosity, density and diffusivity) was investigated. The mixing phenomena were tested for three micromixers: a squarewave mixer, a three-dimensional serpentine mixer and a staggered herringbone mixer. The governing equations of continuity, momentum and solute mass fraction were solved numerically. To evaluate mixing performance, a criterion index of mixing uniformity was proposed. In the systems considered, the Reynolds number based on averaged properties was Re=1 and 10. For low Reynolds number (Re=1), the mixing performance varied inversely with mass fraction of glycerol due to the dominance of molecular diffusion. The mixing performance deteriorated due to a significant reduction in the residence time of the fluid inside the mixers.     

Automatic grid generation of complex geometries in Cartesian co-ordinates

A method of automatic grid generation for complex boundaries in Cartesian co-ordinates is proposed in this paper. In addition to the Cartesian grid lines the diagonal segments are used for the approximations of complex geometries in Cartesian co-ordinates. A structured Cartesian grid is employed for the sake of the numerical simplicity and the potential of automatic grid generation. The automatic grid generation is achieved by this diagonal Cartesian method and the accuracy estimations of geometry approximations are given. The approximations of a few complex geometries, such as the multibody system in porous media, lake banks, grooved channels and spheres are shown and analyzed. The proposed method is verified by the numerical solutions of a rotated cavity flow. It is shown that the diagonal Cartesian method improves both the accuracy of geometry approximations and the numerical solution of a rotated cavity flow, comparing with the traditional saw-tooth method in which only Cartesian grid lines are utilized for geometry approximations. The stability and convergence of the proposed method is demonstrated. Finally, the application of the diagonal Cartesian method for the prediction of a grooved channel flow is presented. © 1998 John Wiley & Sons, Ltd.     

Experimental and numerical investigation of thermal chaotic mixing in a T-shaped microchannel

In this paper, thermal chaotic mixing characteristics of two miscible fluids in a T-shaped microchannel are investigated experimentally and numerically. In the experiments, fluorescent dye Acid Yellow and Rhodamine B was employed to show the mass mixing behavior and temperature field, respectively. Power input and flow rate were studied to investigate the thermal mixing characteristics in the microchannel. The mixing efficiency increases with increasing power input, while decreases with increasing flow rate. A numerical simulation of conjugate forced convection-conduction heat and mass transfer was employed to investigate the thermal chaotic mixing processes in the T-shaped microchannel. The measured mixing efficiency versus applied voltage and flow rate were compared with numerical simulation results, which showed reasonably agreement.     

Analysis of subgrid scale mixing using a hybrid LES-Monte-Carlo PDF method

This contribution introduces a hybrid LES-Monte-Carlo method for a coupled solution of the flow and the multi-dimensional scalar joint pdf in two complex mixing devices. For this purpose an Eulerian Monte-Carlo method is used. First, a complex mixing device (jet-in-crossflow, JIC) is presented in which the stochastic convergence and the coherency between the scalar field solution obtained via finite-volume methods and that from the stochastic solution of the pdf for the hybrid method are evaluated. Results are compared to experimental data. Secondly, an extensive investigation of the micromixing on the basis of assumed shape and transported SGS-pdfs in a configuration with practical relevance is carried out. This consists of a mixing chamber with two opposite rows of jets penetrating a crossflow (multi-jet-in-crossflow, MJIC). Some numerical results are compared to available experimental data and to RANS based results. It turns out that the hybrid LES-Monte-Carlo method could achieve a detailed analysis of the mixing at the subgrid level.     

Taylor补丁对新型动脉旁路移植流场影响的数值分析

为了研究Taylor补丁对新型(S型)动脉旁路移植术中吻合口处流场的影响,使用数值方法研究了采用Taylor补丁和未采用该补丁的两个S型旁路移植模型内流场的血流动力学差异. 对流速、壁面切应力和切应力梯度等参数进行了比较分析. 结果表明,Taylor补丁对吻合口的流场有显著影响. 采用Taylor补丁的模型其下游吻合口处的流场分布较未采用补丁的模型更均匀,二次流平均流速减小约34.48%,壁面切应力梯度减小约52.22%,从壁面切应力梯度方面分析,这将有助于改善血流动力学分布,抑制动脉粥样硬化. 但从壁面切应力值分析,其动脉底部的壁面低切应力区明显增大,平均壁面切应力值减小30.33%,这又将促使动脉粥样硬化. 因此,Taylor补丁是否对S型搭桥术具有治疗优越性,仅从血流动力学分析尚不能定论,配合数值计算结果进行动物和临床实验研究是十分必要的.      

Flow pattern visualization of liquid film conduction pumping using flush mounted electrodes

Conduction pumping is one convenient method for pumping of dielectric liquid films. Flow visualization can be useful for understanding the hydrodynamic behavior of this kind of flow. In this study, the flow pattern of the liquid film conduction pumping using flush mounted electrodes has been visualized for various electrode arrangements. Symmetric and asymmetric configurations of electrodes have been examined for pumping of silicon oil. Two major factors affect the conduction pumps; ion mobility difference and electrodes configuration. For known ion mobility difference two cases have been considered: Case 1 in which electrode configuration strengthens the ion mobility difference pumping effect and Case2 in which electrode configuration has the opposite effect. The results show that, for one pair of electrodes acting as unit pump, a primary vortex is generated on the electrodes which arises from rotational part of the Coulomb force. For more than one pair of electrodes, secondary vortices appeared which are generated by the primary vortices. For Case 1, the vorticity of primary and secondary vortices increases with electrode width ratio because of the strengthening effect of the two factors but it decreases for Case 2 because of weakening effect of them.     

Analysis of liquid circulation and mixing in a partitioned electrolytic tank

The performance of an electrochemical process depends critically on the mobility of the reacting species or ions towards the electrode surface. In this work, a partitioned electrolytic cell is studied. Here the fluid flow is induced by gases which evolve at the electrode surface. The liquid circulation induced by the rising bubbles is primarily responsible for mixing. In this study, the liquid circulation in a cell where an alkaline solution of water is electrolyzed using different Nickel designs of electrodes is investigated using PIV. For each electrode, the optimum operating conditions such as voltage and concentration of electrolyte which resulted in good mixing are found. The flow-field is quantified by calculating time averaged velocity profiles along the horizontal line and by analyzing the temporal variation of liquid velocity at a point. It is found that there are differences in the circulation and hence vorticity in the two compartments, anode and cathode. The effect of gas evolution on mixing between the two chambers is studied by taking uric acid in the cathode half and NaOH in the anode half. The flow induced by the evolved gas bubbles leads to convective mixing in the two chambers. The mixing time is calculated by measuring the variation of current with time under potentiostatic conditions. This is verified by measuring the pH in anode and cathode compartments during the electrolysis.     

Announcements

Recent numerical investigations on pressure surges during pump trip in pumping installations showed that by including an air entrainment variable wave speed model, reasonable predictions of transient pressure surges with proper phasing and attenuation of pressure peaks can be obtained. These calculated results are consistent with similar field measurements made with the pumps operating at low pump cut-out levels, when air entrainment due to an attached surface vortex was observed. However, in the numerical calculation procedures it is assumed that the inertia of the moving elements of the check valve is small and that the check valve closes at zero reverse flow velocity. In practice, check valves seldom close precisely at zero reverse flow velocity. With the check valves not closing at zero reverse velocity, the present numerical computations show that the air content in a fluid system can adversely affect the check valve performance. With the fluid system operating within a critical range of air entrainment values, the present analysis showed that there is a possibility of ‘check valve slamming’ when the check valves are selected based only on the analysis of an air-free system. This phenomenon is confirmed through field observations.     

Compatible model for herringbone bond masonry: Linear elastic homogenization,failure surfaces and structural implementation

A simplified kinematic procedure at a cell level is proposed to obtain in-plane elastic moduli and macroscopic masonry strength domains in the case of herringbone masonry. The model is constituted by two central bricks interacting with their neighbors by means of either elastic or rigid-plastic interfaces with friction, representing mortar joints. The herringbone pattern is geometrically described and the internal law of composition of the periodic cell is defined.A sub-class of possible elementary deformations is a-priori chosen to describe joints cracking under in-plane loads. Suitable internal macroscopic actions are applied on the Representative Element of Volume (REV) and the power expended within the 3D bricks assemblage is equated to that expended in the macroscopic 2D Cauchy continuum. The elastic and limit analysis problem at a cell level are solved by means of a quadratic and linear programming approach, respectively.To assess elastic results, a standard FEM homogenization is also performed and a sensitivity analysis regarding two different orientations of the pattern, the thickness of the mortar joints and the ratio between block and mortar Young moduli is conducted. In this way, the reliability of the numerical model is critically evaluated under service loads.When dealing with the limit analysis approach, several computations are performed investigating the role played by (1) the direction of the load with respect to herringbone bond orientation, (2) masonry texture and (3) mechanical properties adopted for joints.At a structural level, a FE homogenized limit analysis is performed on a masonry dome built in herringbone bond. In order to assess limit analysis results, additional non-linear FE analyses are performed, including a full 3D numerical expensive heterogeneous approach and models where masonry is substituted with an equivalent macroscopic material with orthotropic behavior and possible softening. Reliable predictions of collapse loads and failure mechanisms are obtained, meaning that the approach proposed may be used by practitioners for a fast evaluation of the effectiveness of herringbone bond orientation.     

Simultaneous concentration and velocity field measurements in a shock-accelerated mixing layer

A novel technique to obtain simultaneous velocity and concentration measurements is applied to the Richtmyer–Meshkov instability. After acceleration by a Mach 2.2 shock wave, the interface between the two gases develops into a turbulent mixing layer. A time-separated pair of acetone planar laser-induced fluorescence images are processed to yield concentration and, through application of the Advection-Corrected Correlation Image Velocimetry technique, velocity fields. This is the first application of this technique to shock-accelerated flows. We show that when applied to numerical simulations, this technique reproduces the velocity field to a similar quality as particle image velocimetry. When applied to the turbulent mixing layer of the experiments, information about the Reynolds number and anisotropy of the flow is obtained.     

The effect of boundary layer fluctuations on the streamwise vortex structure in simulated plane turbulent mixing layers

This paper details the influence of the magnitude of imposed inflow fluctuations on Large Eddy Simulations of a spatially developing turbulent mixing layer originating from laminar boundary layers. The fluctuations are physically-correlated, and produced by an inflow generation technique. The imposed high-speed side boundary layer fluctuation magnitude is varied from a low-level, up to a magnitude sufficiently high that the boundary layer can be considered, in a mean sense, as nominally laminar. Cross-plane flow visualisation shows that each simulation contains streamwise vortices in the laminar and turbulent regions of the mixing layer. Statistical analysis of the secondary shear stress reveals that mixing layers originating from boundary layers with low-level fluctuations contain a spatially stationary streamwise structure. Increasing the high-speed side boundary layer fluctuation magnitude leads to a weakening of this stationary streamwise structure, or its removal from the flow entirely. The mixing layer growth rate reduces with increasing initial fluctuation level. These findings are discussed in terms of the available experimental data on mixing layers, and recommendations for both future experimental and numerical research into the mixing layer are made.     

Hydromagnetic Micropump and Flow Controller. Part A: Experiments with nickel particles added to the water

The novel idea of the Hydromagnetic Micropump and Flow Controller (HMFC) is used in this paper to construct a laboratory setup capable of bidirectional pumping and controlling the flow in microtubes. A laboratory setup, which contains no moving parts, is integrated with a pressure-driven flow setup to make the presented HMFC device. The device operation is based on controllable motion of magnetic particles, added to the carrier fluid, caused by the magnetic field, produced by solenoids located just next to the microtube. The magnitude of these forces is proportional to the strength and gradient of magnetic field which, in turn, is related to the electrical current and arrangement of the solenoids. When switching period is smaller than 0.19 s, the device operates as a pump; while, the flow controlling characteristic is obtained for long switching periods. The flow can be pumped up to 113% of the initial flow rate or can be controlled in a regular and predictable manner.A series of experiments was conducted when nickel particles are added to the water, as the carrier fluid, to examine the impact of different parameters such as switching period and switching mode of solenoids and particle concentration on the performance of the device. Moreover, an ethanol–nickel mixture is used to investigate the impact of carrier fluid on the performance of the device. The role of particle substance is examined comparing results obtained for water–nickel and water–iron mixtures.     

Identification of regions of fastest mixing in a system of point vortices

This paper describes a numerical method for efficiently identifying the regions of fastest mixing of a passive dye in a flow due to a system of point vortices. Results obtained from computations are presented for systems of three and four point vortices, both in the unbounded domain and inside a circular cylinder. The flow is two‐dimensional and the fluid is incompressible. The regions where mixing is possible are found by studying the largest Lagrangian Lyapunov exponent distribution with respect to various initial positions of tracer particles. The regions of fastest mixing are then identified from the Lyapunov exponent distribution at small times. The results of the method are verified by quantifying the mixing by using a traditional box counting technique. The technique is then applied to several different initial configurations of vortices and some interesting results are obtained. Some numerical findings about the nature of the exponents computed are also discussed. Copyright © 2002 John Wiley Sons, Ltd.     

Unsteady Flow to Wells Partially Penetrating in Two-Layered Aquifers

The unsteady flow of water to well in a layered aquifer with an interlayer flow is examined in this paper. The system studied comprises an aquifer consisting of two productive layers of finite thickness that are in a perfect hydraulic contact and a well which partially penetrates in one of the layers. Each layer is assumed to be homogeneous and isotropic and the water contained in the aquifer is of identical physical properties and small compressibility.The analytical solutions are derived for the case when the system is characterised by equality of hydraulic diffusivity of layers. These solutions give the results accurate enough for practical applications and allow to estimate the effects of partial penetration and contrast in parameters of formation on distribution of the flow potential both at large distances from wells and at the wells.The obtained solutions also provide a basis for predicting the interlayer flow arising from the performance of a pumping well as well as between a pair of wells which have an open interval located in different layers of the aquifer. Two cases have been analysed: (1) a pumping pair of wells which is used to prevent water inflow to the productive well, and (2) a pumping-injection pair of wells providing the demanded mixing of water from adjacent layers. Some examples of flow patterns and specially computed diagrams are given to illustrate the operation of such systems.