Gravity Affected Lateral Dispersion and Diffusion in a Stationary Horizontal Porous Medium Shear Flow

Transport of dissolved species by a carrier fluid in a porous medium comprises advection and diffusion/dispersion processes. Hydrodynamic dispersion is commonly characterized by an empirical relationship, in which the dispersion mechanism is described by contributions of molecular diffusion and mechanical dispersion expressed as a function of the molecular Peclét number. Mathematically these two phenomena are modeled by a constant diffusion coefficient and by velocity dependent dispersion coefficients, respectively. Here, the commonly utilized Bear--Scheidegger dispersion model of linear proportionality between mechanical dispersion and velocity, and the more complicated Bear--Bachmat model derived on a streamtube array model porous medium and better describing observed dispersion coefficients in the moderate molecular Peclét number range, will be considered. Analyzing the mixing flow of two parallelly flowing confluent fluids with different concentrations of a dissolved species within the frames of boundary layer theory one has to deal with transverse mixing only. With the Boussinesq approximation being adopted approximate analytical solutions of the corresponding boundary layer system of equations show that there is no effect of density coupling on concentration distributions across the mixing layer in the pure molecular diffusion regime case. With the Peclét number of the oncoming flow growing beyond unity, density coupling has an increasing influence on the mixing zone. When the Peclét number grows further this influence is successively reduced until its disappearance in the pure mechanical dispersion regime.     

A micro-aerodynamic decelerator based on permeable surfaces of nanofiber mats

This work deals with nonwoven permeable light mats made of submicron-diameter nanofibers. The nanofibers were obtained through electrospinning of polymer solutions. The mats were positioned on light pyramid-shaped frames. These platforms fell freely through the air, apex down, at a constant velocity. The drag of such passive airborne platforms is of significant interest in a number of modern aerodynamics applications including, for example, dispersion of "smart dust" carrying various chemical and thermal sensors, dispersion of seeds, as well as movement of small organisms with bristle appendages. In the present work, drag is measured using the free fall method supplemented by extensive flow visualization. The effects of platform weight, average nanofiber diameter, and porosity of the nonwoven mats on the drag force are studied. The results are compared to data for the corresponding impermeable structures that are covered with plastic wrap. The data are presented in the form of standard dependencies of drag coefficient on the Reynolds number of the structure. It was found that permeable platforms with holes on the order of several microns (which is about ten times the diameter of the nanofibers) are essentially impermeable for airflow.     

Heat dispersion in stationary mixed convection flow about horizontal surfaces in porous media

An analysis has been performed to study the influence of velocity dependent dispersion on transverse heat transfer in mixed convection flow above a horizontal wall of prescribed temperature in a saturated porous medium. The Boussinesq approximation and boundary layer analysis were used to numerically obtain gravity affected temperature and velocity distributions within the frames of Darcy's law and a total thermal diffusivity tensor comprising both of constant coefficient heat conduction and velocity proportional mechanical heat dispersion. Dependending on Pe_∞, the molecular Peclét number basing on the effective thermal diffusivity and the velocity of the oncoming flow, density coupling has distinct influences on heat transfer rates between the wall surface and the porous medium flow region. For small Peclét numbers, when heat conduction is the prevailing mechanism, wall heat fluxes are the higher the larger the density difference between the oncoming and the near wall fluid is. The opposite is true for larger Peclét numbers, when mechanical heat dispersion is the main cause of heat spreading. For Pe_∞ tending to infinity these wall heat fluxes approach finite maximum values in the total heat diffusivity model, they grow beyond any limit if only constant coefficient heat conduction is considered. Thus, the inclusion of mechanical heat dispersion effects yields physically more realistic predictions. Received on 18 September 1996     

混合层中粒子扩散的实验研究

本文应用流动显示和LDA测量,对混合层中粒子的扩散问题进行了实验研究。结果表明：粒子的扩散强烈地依赖于St数,具有较小St的粒子的扩散近似地与流体示踪粒子相同,随着St的增大,扩散角度增大,也就是说粒子扩散加快,并且随着粒子惯性的增大,它对湍流脉动的响应将会减弱。     

高层框架分析的状态变量传递法

取高层框架柱端位移和对应的柱端力作为状态变量,利用传递矩阵和逐层分析的方法来分析以框架。文中取框架的每一层作为基本单元,建立基本单元端部的状态变量与相邻基本单元端部状态变量之间的转换关系。分析过程中,框架烽的增加仅增加上乘的次数,而待求的基本未知量的数目始终保持不变,从而提高了计算机分析问题的能力。     

Dispersion in spatially periodic porous media

The method of volume averaging is applied to ordered and disordered spatially periodic porous media in two dimensions in order to compute the components of the dispersion tensor for low Peclet numbers ranging from 0.1 to 100. The effect of different parameters on the dispersion tensor is studied. The longitudinal dispersion coefficient decreases with an increase in disorder while the transverse dispersion coefficient increases. The location of discs in the unit cell influences the longitudinal dispersion coefficient significantly, compared to the transverse dispersion coefficient. Under a laminar flow regime, the dispersion coefficient is independent of Re_p. The predicted functional dependency of dispersion on the Peclet number agrees with experimental data. The predicted longitudinal dispersion coefficient in disordered porous media is smaller than that of the experimental data. However, the predicted transverse dispersion coefficient agrees with the experimental data.     

Method of moments for laminar dispersion in an oscillatory flow through curved channels with absorbing walls

The unsteady dispersion of a solute, when the fluid is driven through a curved channel with absorbing walls by an imposed pulsatile pressure gradient, is studied using the method of moments. The study examines the effect of oscillatory Reynolds number, amplitude/frequency of the pressure pulsation and boundary absorption on the longitudinal dispersion. The methodology involves a set of unsteady integral moment equations obtained by applying the Aris-Barton method of moments on the convective-diffusion equation for a curved channel. Central moments are obtained from the moment equations which are solved by a finite-difference implicit scheme. The effect of curvature and boundary absorption on the effective dispersion coefficient from the initial to the stationary stage of the oscillatory flow is studied. Amplitude of the effective dispersion coefficient is found to increase with curvature and decrease with frequency of the pressure pulsation. For large Peclet number and Schmidt number, the amplitude of the dispersion coefficient can be 1.6 times that in a straight channel at large times. Also, for large times, the amplitude of the dispersion coefficient is twice the amplitude of the dispersion coefficient as α, the frequency parameter changes from 0.5 to 1.0. The axial distributions of mean concentration are determined from the first four central moments by using the Hermite polynomial representation. The effect of curvature is to delay the stationary state and also the approach to normality of the concentration distribution. The study has importance in understanding the spreading of pollutants in tidal basins and natural current fields.     

Propagation of SH waves in an irregular monoclinic crustal layer

The present paper discusses the dispersion equation for SH waves in a monoclinic layer over a semi-infinite elastic medium with an irregularity. In the absence of the irregularity, the dispersion equation reduces to standard dispersion equation for SH waves in a monoclinic layer over an isotropic semi-infinite medium. The dispersion curves for different size of the irregularity are computed and compared for the half-space without any irregularity. It can be seen that the phase velocity is strongly influenced by the wave number and the depth of the irregularity.     

Flow effects resulting from relative motion between shocks and supersonic bodies

The effect relative motion between a shock and supersonic flow has on the Mach number of flow behind a planar shock is considered. It is shown that for multiple moving reference frames, such as that encountered in a shock-wave/moving-body interaction the choice of reference frame can result in a Mach number that can either increase or decrease across the shock. This depends on the relative velocities of the reference frames and under certain conditions can remain unchanged for a given shock of finite strength. Euler simulations run at the various computationally predicted transitions have numerically confirmed the idealised analysis presented here.Received: 14 October 2002, Revised: 21 February 2003, Accepted: 29 July 2003, Published online: 12 November 2003     

Linear gravity waves on Maxwell fluids of finite depth

Linear surface gravity waves on Maxwell viscoelastic fluids with finite depth are studied in this paper. A dispersion equation describing the spatial decay of the gravity wave in finite depth is derived. A dimensionless memory (time) number 0 is introduced. The dispersion equation for the pure viscous fluid will be a specific case of the dispersion equation for the viscoelastic fluid as θ=0. The complex dispersion equation is numerically solved to investigate the dispersion relation. The influences of θ and water depth on the dispersion characteristics and wave decay are discussed. It is found that the role of elasticity for the Maxwell fluid is to make the surface gravity wave on the Maxwell fluid behave more like the surface gravity wave on the inviscid fluid.     

Stereophotographic study of impact on beams and frames

The method of double photogrammetry is commonly used for dynamic measurements. This paper describes the use of stereophotogrammetry for the study of impact on frames and beams. For this investigation, a special stereocamera must be equipped with another device. The time of exposure is controlled electronically. When measuring the impact effects on frames and beams, it is possible to obtain an instantaneous form of vibration. As the measurement is carried out to a large number of points, it is impossible to express these modes analytically and to obtain a more general solution for various types of beams. Practical solutions are presented for a simple beam, a fixed-end beam and a spatial frame.     

Thermal Dispersion Effects on Combined Convection in Non-Newtonian Fluids Along a Nonisothermal Vertical Plate in a Porous Medium

The method of non-similarity solution is used to study the influence of thermal dispersion on combined convection from vertical surfaces in a porous medium saturated with a power-law type non-Newtonian fluid. The coefficient of thermal diffusivity has been assumed to be the sum of molecular diffusivity and the dispersion thermal diffusivity due to mechanical dispersion. The transformed conservation laws are solved numerically for the case of variable surface heat flux conditions. Results for the details of the velocity and temperature fields as well as the Nusselt number have been presented.     

Forced convective heat transfer in porous medium of wire screen meshes

The hydrodynamic and heat transfer characteristics of a porous medium consisting of 20 wire screen meshes are examined theoretically and experimentally. The hydrodynamic experiments are conducted for the range of Reynolds number based on mean velocity and wire diameter from 1.5 to 12. The Ergun's constants and thermal dispersion coefficients are calculated in this range. Nusselt number variation is determined in both thermally developing and fully developed flows by the help of forced convection heat transfer experiments conducted for the uniform heat flux boundary condition. Correlation functions of Nusselt number in the range of fully developed and thermally developing, and of thermal entrance length are obtained from experimental data. Solutions of momentum and energy equations simulating the experimental model are obtained numerically with variable porosity and the anticipated thermal dispersion coefficients. The thermal dispersion coefficients well-adjusted to the experimental data are determined by numerical solution of the energy equation. Received on 22 November 1996     

Orientation behaviour of fibers in suspension flow through a branching channel

Fiber orientation and dispersion in the fiber suspension that flows through a T-shaped branching channel have been experimentally studied. The fiber dispersion is not uniform in a channel flow. In particular, in the suspension containing long fibers, there are no fibers near a wall at a low Reynolds number. However, the content ratio of fibers near the wall increases with an increasing Reynolds number. Fiber orientation angles of short fibers are widely distributed. Furthermore, a variance of orientation angle in the middle region of the channel has a minimum value at a Reynolds number from 10 to 20, and a size of secondary vortex in the branching corner also has a minimum value at a similar Reynolds number.     

Some applications of the concept of minimized integrated exponential error for low dispersion and low dissipation

Several techniques to optimize parameters that regulate dispersion and dissipation effects in finite difference schemes have been devised in our previous works. They all use the notion that dissipation neutralizes dispersion. These techniques are the minimized integrated square difference error (MISDE) and the minimized integrated exponential error for low dispersion and low dissipation (MIEELDLD). It is shown in this work based on several numerical schemes tested that the technique of MIEELDLD is more accurate than MISDE to optimize the parameters that regulate dispersion and dissipation effects with the aim of improving the shock‐capturing properties of numerical methods. First, we consider the family of third‐order schemes proposed by Takacs. We use the techniques MISDE and MIEELDLD to optimize two parameters, namely, the cfl number and another variable which also controls dispersion and dissipation. Second, these two techniques are used to optimize a numerical scheme proposed by Gadd. Moreover, we compute the optimal cfl for some multi‐level schemes in 1D. Numerical tests for some of these numerical schemes mentioned above are performed at different cfl numbers and it is shown that the results obtained are dependent on the cfl number chosen. The errors from the numerical results have been quantified into dispersion and dissipation using a technique devised by Takacs. Finally, we make use of a composite scheme made of corrected Lax–Friedrichs and the two‐step Lax–Friedrichs schemes like the CFLF4 scheme at its optimal cfl number, to solve some problems in 2D, namely: solid body rotation test, acoustics and the circular Riemann problem. Copyright © 2011 John Wiley & Sons, Ltd.     

Theoretical Analyses of the Effects of Solute Dispersion on Chemical-Dissolution Front Instability in Fluid-Saturated Porous Media

This article deals with the theoretical aspects of chemical-dissolution front instability problems in two-dimensional fluid-saturated porous media including solute dispersion effects. Since the solute equilibrium concentration is much smaller than the molar density of the dissolvable mineral in a mineral dissolution system, a limit case, in which the ratio of the solute equilibrium concentration (in the pore fluid) to the molar density of the dissolvable mineral (in the solid matrix of the porous medium) approaches zero, is considered in the theoretical analysis. Under this assumption, the critical condition under which a planar chemical-dissolution front becomes unstable has been mathematically derived when solute dispersion effects are considered. The present theoretical results clearly demonstrated that: (1) the propagation speed of a planar chemical-dissolution front in the case of considering solute dispersion effects is the same as that when solute dispersion effects are neglected. This indicates that solute dispersion does not affect the propagation speed of the planar chemical-dissolution front in a fluid-saturated porous medium. (2) The consideration of solute dispersion can cause a significant increase in the critical Zhao number, which is used to judge whether or not a planar chemical-dissolution front may become unstable in the fluid-saturated porous medium. This means that the consideration of solute dispersion can stabilize a planar chemical-dissolution front, because an increase in the critical Zhao number reduces the likelihood of the planar chemical-dissolution front instability in a fluid-saturated porous medium. In addition, the present results can be used as benchmark solutions for verifying numerical methods employed to simulate detailed morphological evolution processes of chemical dissolution fronts in two-dimensional fluid-saturated porous media.     

Measurement of heat transfer coefficient and axial dispersion coefficient using temperature oscillations

A periodic transient test technique based on the axial dispersion model is proposed for the determination of both heat transfer coefficients and axial dispersion coefficients in heat exchangers. The model uses a parameter called the axial dispersive Peclet number to account for the deviation of the flow pattern from ideal plug flow. It takes both axial dispersion in the fluid and axial heat conduction in the wall into account and is solved analytically by means of a complex Fourier transform. Experiments conducted on dented copper tubes show that axial dispersion has a significant effect on the dynamic temperature response of a heat exchanger.     

Dispersion Waves of Two Fluids in a Porous Medium

The dispersion of two fluids in a porous medium is analyzed as a wave process. The wave equations are derived, and for plane wave solutions a wave number versus frequency dispersion relation is obtained. Suitable choices for the saturation dependence of terms in the equations of motion and the dynamic pressure difference equation lead to physical solutions.     

NUMERICAL STUDY OF PARTICLE DISTRIBUTION IN WAKE OF LIQUID-PARTICLE FLOWS PAST A CIRCULAR CYLINDER USING DISCRETE VORTEX METHOD

Particle-laden water flows past a circular cylinder were numerically investigated. The discrete vortex method (DVM) was employed to evaluate the unsteady water flow fields and a Lagrangian approach was applied for tracking individual solid particles. A dispersion function was defined to represent the dispersion scale of the particle. The wake vortex patterns, the distributions and the time series of dispersion functions of particles with different Stokes numbers were obtained. Numerical results show that the particle distribution in the wake of the circular cylinder is closely related to the particle's Stokes number and the structure of wake vortices: (1) the intermediate sized particles with Stokes numbers, St, of 0.25, 1.0 and 4.0 can not enter the vortex cores and concentrate near the peripheries of the vortex structures, (2) in the circular cylinder wake, the dispersion intensity of particles decreases as St is increased from 0.25 to 4.0.