C1 Rational interpolating surface under local coordinate systems

A method of constructing rational interpolating surface under local coordinate systems is presented, which can be used to solve the large torsion problem of surfaces. This kind of surface has better approximating effect and its properties can be easily discussed, so it has practical applications not only in CAD but also infinite element analysis and other fields. An example is given in the paper.Projects Supported by the Science Fund of Education Committee.     

MICROCOSMIC BOUND THEOREM OF DAYCY＇S LAW AND ITS APPLICATION

By combining Chapman-Enskog expansion with the BGK approximation to Baltzmann equation and Navier-Stokes equation was obtained. And an expression of Darcy‘ s law was obtained through taking variable average over Navier-Stokes equation on some representative space in porous media, and finally an example was taken to prove its reliability.     

On the Domain of Validity of Brinkman’s Equation

An increasing number of articles are adopting Brinkman’s equation in place of Darcy’s law for describing flow in porous media. That poses the question of the respective domains of validity of both laws, as well as the question of the value of the effective viscosity μ ^e which is present in Brinkman’s equation. These two topics are addressed in this article, mainly by a priori estimates and by recalling existing analyses. Three main classes of porous media can be distinguished: “classical” porous media with a connected solid structure where the pore surface S _p is a function of the characteristic pore size l _p (such as for cylindrical pores), swarms of low concentration fixed particles where the pore surface is a function of the characteristic particle size l _s , and fiber-made porous media at low solid concentration where the pore surface is a function of the fiber diameter. If Brinkman’s 3D flow equation is valid to describe the flow of a Newtonian fluid through a swarm of fixed particles or fibrous media at low concentration under very precise conditions (Lévy 1983), then we show that it cannot apply to the flow of such a fluid through classical porous media.     

Low-Frequency Asymptotic Analysis of Seismic Reflection from a Fluid-Saturated Medium

Reflection of a seismic wave from a plane interface between two elastic media does not depend on the frequency. If one of the media is poroelastic and fluid-saturated, then the reflection becomes frequency-dependent. This paper presents a low-frequency asymptotic formula for the reflection of seismic plane p-wave from a fluid-saturated porous medium. The obtained asymptotic scaling of the frequency-dependent component of the reflection coefficient shows that it is asymptotically proportional to the square root of the product of the reservoir fluid mobility and the frequency of the signal. The dependence of this scaling on the dynamic Darcy’s law relaxation time is investigated as well. Derivation of the main equations of the theory of poroelasticity from the dynamic filtration theory reveals that this relaxation time is proportional to Biot’s tortuosity parameter.     

Derivation of a Darcy’s Law for a Porous Medium Composed of Two Solid Phases Saturated by a Single- Phase Fluid: A Homogenization Approach

The objective of this article is to derive a macroscopic Darcy’s law for a fluid-saturated moving porous medium whose matrix is composed of two solid phases which are not in direct contact with each other (weakly coupled solid phases). An example of this composite medium is the case of a solid matrix, unfrozen water, and an ice matrix within the pore space. The macroscopic equations for this type of saturated porous material are obtained using two-space homogenization techniques from microscopic periodic structures. The pore size is assumed to be small compared to the macroscopic scale under consideration. At the microscopic scale the two weakly coupled solids are described by the linear elastic equations, and the fluid by the linearized Navier–Stokes equations with appropriate boundary conditions at the solid–fluid interfaces. The derived Darcy’s law contains three permeability tensors whose properties are analyzed. Also, a formal relation with a previous macroscopic fluid flow equation obtained using a phenomenological approach is given. Moreover, a constructive proof of the existence of the three permeability tensors allows for their explicit computation employing finite elements or analogous numerical procedures.     

A Finite Element-based Heuristic Estimation of Local Preform Permeability for Resin Transfer Molding

Uniformity of fabrics significantly affects the resin flow behavior in the resin transfer molding (RTM) process. Due to fabric defects or improper fiber preform preparation/loading, non-uniformity in fabric structure frequently occurs in RTM processing and creates local permeability variations. Such variations often lead to unbalanced resin flow patterns and thus result in defects of finished composite parts. In RTM process modeling, an accurate estimation of the whole field permeability profile of the fiber preform is critical for predicting resin flow pattern correctly. In this article, a finite element-based heuristic computing method is introduced for estimating the in situ whole-field isotropic permeability profile of the preform using a steady flow of gas. Compared with conventional approaches, this method is effective in measuring local permeability variations and applicable to molds with complex 2-D geometries, as well as diverse injection strategies. Several case studies were presented with experimental designs and numerical computations to illustrate the effectiveness and efficiency of the method.     

A Model of Buoyancy-Driven Two-Phase Countercurrent Fluid Flow

We seek simple analytical solutions in a model of gas flow driven by a combination of buoyancy, viscous, and capillary forces. Traveling-wave solutions describe propagation of the top and bottom of the gas plume. The top of the plume has low gas saturation, but propagates much faster than the bottom. The theoretical maximum of the velocity of propagation of the top of the plume provides a simple conservative estimate of the time until plume evolution will dramatically slow down. A sequence of rarefaction and traveling-wave solutions characterizes the transition zones between the top and bottom stable regions. The analytical results are applied to studying carbon dioxide flow caused by leaks from deep geological formations used for CO₂ storage. The results are also applicable for modeling flow of natural gas leaking from seasonal gas storage, or for modeling of secondary hydrocarbon migration.     

Frictional passage of fluid through inhomogeneous porous system: a variational principle

A Fermat-like principle of minimum time is formulated for nonlinear steady paths of fluid flow in inhomogeneous isotropic porous media where fluid streamlines are curved by a location dependent hydraulic conductivity. The principle describes an optimal nature of nonlinear paths in steady Darcy’s flows of fluids. An expression for the total path resistance leads to a basic analytical formula for an optimal shape of a steady trajectory. In the physical space an optimal curved path ensures the maximum flux or shortest transition time of the fluid through the porous medium. A sort of “law of bending” holds for the frictional fluid flux in Lagrange coordinates. This law shows that—by minimizing the total resistance—a ray spanned between two given points takes the shape assuring that a relatively large part of it resides in the region of lower flow resistance (a ‘rarer’ region of the medium).     

Stokes＇ first problem for the fourth order fluid in a porous half space

In this study, the flow of a fourth order fluid in a porous half space is modeled. By using the modified Darcy’s law, the flow over a suddenly moving flat plate is studied numerically. The influence of various parameters of interest on the velocity profile is revealed. The English text was polished by Keren Wang.     

Thermal Analysis of Natural Convection Porous Fins

This work introduces a simple method of analysis to study the performance of porous fins in a natural convection environment. The method is based on using energy balance and Darcy’s model to formulate the heat transfer equation. The thermal performance of porous fins is then studied for three types of fins: long fin, finite-length fin with insulated tip and a finite-length fin with tip exposed to a known convection coefficient. It is found from the analysis that the effect of different design and operating parameters such as: Ra number, Da number, thermal conductivity ratio, Kr and length thickness ratio on the temperature distribution along the fin is grouped into one newly defined parameter called S_H. The effect of the variation of S_H on the porous fin thermal performance is established. The effect of varying the fin length and thermal conductivity ratio on the heat transfer rate from the fin is investigated and compared with that for a solid fin at certain conditions. It is found that the heat transfer rate from porous fin could exceed that of a solid fin. It is also found that increasing the fin length and effective thermal conductivity enhances the heat transfer from the fin up certain limit, where a further increase in these parameters adds no improvement to the fin performance. On Leave from Jordan University of Science and Technology, Irbid-Jordan