Inertial Deposition of Aerosol Particles in a Periodic Row of Porous Cylinders

The aerosol flow through a periodic row of parallel porous cylinders is investigated. The air flow field outside the cylinders is described by the Navier–Stokes equations of viscous incompressible fluid. The extended Darcy–Brinkman equations are used to calculate the flow velocity inside a porous cylinder. The dependence of the efficiency of the deposition of aerosol particles by inertial impaction and interception on the Stokes number for various values of the Darcy number is studied. Comparison of the results obtained from the numerical model and an approximate analytical model is given. The combined approximate formula for the deposition efficiency of a cylindrical fiber in a parallel array proposed by Müller et al. (2014) is extended for the porous cylindrical fiber. The aerosol flow through the porous body composed by a random array of cylinders is calculated to estimate the interior deposition.

Copyright 2015 American Association for Aerosol Research     

考虑局部非热平衡的流体层流横掠多孔介质中恒热流平板的传热分析

对流体层流横掠多孔介质中恒热流加热的平板,应用Brinkman-Forchheime-extended Darcy流动模型和流体与多孔介质之间局部非热平衡理论建立守恒方程组,应用数量级分析和积分法,得出了速度边界层厚度、热边界层厚度、壁面黏性摩擦系数和对流传热系数、流体与多孔介质之间局部温差的计算公式。结果表明,速度边界层与光板时明显不同,其在平板前端迅速增长,之后越来越平坦,趋于一个恒定值;而热边界层则沿着流动方向不断增长,类似于光板时的情况;局部的表面对流传热系数在平板前端达最大值,之后逐渐减小,也类似于光板时的情况;多孔介质与流体间的局部温差在平板前端达最大值,之后呈现沿着流动方向逐渐减小的变化趋势。     

Drag on a large spherical aggregate with self-similar structure: An asymptotic analysis

A porous particle with radially varying permeability is used to model a large self-similar (fractal-like) aggregate in the continuum fluid flow regime. The Stokes flow in the viscous fluid around the aggregate is coupled with the solution of the flow inside the aggregate. This internal flow is shown to be composed of a central core governed by Darcy equation and a thin shell at the aggregate edge where the flow is described by Brinkman's equation. Solutions to the governing equations in each of these regions are sought as asymptotic expansions in terms of a suitably small permeability parameter k. The hydrodynamic jumps across the Brinkman layer are systematically established and used to compute the viscous drag experienced by the aggregate. These conditions, which generalize the widely used Saffman (tangential flow) boundary conditions, are more broadly applicable to flows past/through fine-grained deposits of arbitrary shape, and many other configurations of technological interest.     

多孔介质中受限层流冲击射流的流动与换热特性

基于两区(two-domain)模型采用基于预处理的时间推进法对铺设有多孔介质层的恒温平板在受限层流冲击射流作用下的流动与换热特性进行了研究,其中多孔区域动量方程采用Brinkman-Forchheimer拓展Darcy模型,能量方程则采用局部热平衡(LTE)模型,并对porous/fluid交界面切应力跳跃条件对多孔介质冲击射流的影响进行了分析。流体的控制方程采用基于密度的有限体积法来求解,并针对于多孔区域低速流动特点采用相对应的预处理矩阵来消除控制方程的刚性。还对Reynolds数、孔隙率、Darcy数、热导率比、多孔介质层厚度等参数的变化对流动结构及换热特性的影响进行了分析。研究结果表明,在目前的计算条件下,在其他参数一定时,Reynolds数、孔隙率对通道内流动结构的影响有限;Darcy数、多孔介质层厚度则对流动结构的影响很大;上述参数对受冲击平板的总体换热性能均有明显的影响。在受冲击平板上铺设适当厚度的高渗透率、高热导率的多孔材料能有效地增强换热性能。     

An experimental study on fluid flow characteristics of superposed porous and fluid layers

In the present study, fluid flow characteristics of a porous layer overlaid by a fluid layer were investigated through experiments. The experimental results were analyzed in comparison with theoretical results of a porous medium bounded by impermeable walls. With spheres, the slip coefficient was found to be 0.0107 for Poiseuille flow over a porous layer. As the permeability decreased, the experimental results approached the values calculated by Darcy’s law and Forchheimer’s equation. In addition, the effects of the presence of a fluid layer over a porous medium were examined in terms of the friction factor. The present experimental data placed in the range of the Darcy to the non-Darcy region are shown to be in reasonable agreement with the proposed correlation.     

井筒变质量流与油藏渗流耦合参数研究

为进一步研究水平井筒变质量流与油藏渗流的耦合流动,本文将复杂的油藏—井筒区域流体动力学问题转化为油藏渗流、井筒附近Brinkman渗流和井筒管流3种流动形式的耦合问题,建立了油藏—井筒耦合流体动力学有限元数值模型,采用多物理场耦合软件COMSOL对所建模型进行求解。定量描述了油藏—井筒区域流动形态,并分析了储层渗透率、原油动力粘度、井径、井长等因素对井筒内压力损失和井筒入流剖面的影响规律。     

Stokes–Brinkman flow and diffusional deposition of nanoparticles onto a layer of porous and composite granules

A numerical simulation of a three-dimensional Stokes–Brinkman flow in the model filtering membranes, the role of which is played by a monolayer of the contiguous porous permeable homogeneous spherical granules and a monolayer of the granules coated with porous permeable shells, has been performed. Approximation formulas for calculating the resistance forces of the permeable granules to the flow in a layer with square and hexagonal packing have been obtained. The applicability limits of the solutions obtained within the cell model for the evaluating the resistance and permeability of a layer of porous granules have been shown. The diffusional deposition of point particles from the flow in the monolayer of porous granules with a square structure has been studied. The nanoparticle collection efficiencies by granules in a broad range of Péclet diffusion numbers depending on the permeability of granules are calculated.     

Shear-thinning film on a porous substrate: Stability analysis of a one-sided model

The temporal stability of a Carreau fluid flowing down an inclined porous substrate is considered. A reduced model is derived under the assumption of small permeability which decouples the flow in the liquid layer from the filtration flow in the porous medium and incorporates the effect of the porous medium by means of an effective slip condition at the liquid–solid interface. The slip coefficient in the effective slip condition is a function of the structure, permeability of the porous medium and the rheology of the fluid saturating the porous medium. The effects of shear-thinning rheology and permeability of the substrate on the stability of the film flow system are investigated. This problem gives rise to a generalized eigenvalue formulation which is solved through two approaches. The problem is solved analytically for long waves in the limiting cases of weakly and strongly non-Newtonian behaviors (power-law limit). A numerical investigation is carried out in the general case. The results are shown to agree well for the weakly non-Newtonian limit. Further, the power-law model and the Carreau model agree on a wide range of shear-thinning parameter values for a thin film over a rigid substrate. However, when considering a porous medium, this trend is not observed. The Carreau model gives valid results for the entire range of shear-thinning parameter values for a film over a rigid/porous substrate. The novelty of the present investigation lies in the inclusion of both the effects of bottom permeability and shear-thinning rheology. Both permeability and shear-thinning rheology have a destabilizing effect on the film flow system. The numerical results indicate the correlation between the effects due to shear-thinning properties and permeability. An energy balance analysis performed on the perturbation fields shows that destabilization induced by both shear-thinning and permeability is linked to the viscous shear work rate on the free surface.     

布液板对重力式油水分离器流动与分离特性的影响

为提高重力式油水分离器的分离效率,从改善设备内流场的角度出发,对布液板进行了数值模拟,并研究分析了其孔径和开孔率对轴向速率相对标准偏差的影响,对无布液板、单布液板和双布液板3种结构情况进行了试验研究。结果表明：布液板的加入能有效地消除返混,提高流场分布均匀性。当开孔率20%~25%,孔径8 mm时稳流效果最好。单布液板相对于无布液板结构能显著提高分离效率,但当处理量增大时,其处理能力不稳定,而双布液板结构在处理量较大时仍保持较稳定的处理能力。     

Effect of vertically varying permeability on the onset of convection in a porous medium

Considering the vertically varying permeability of a porous medium, we conducted theoretical and numerical analyses on the onset of buoyancy-driven instability in an initially quiescent, fluid-saturated, horizontal porous layer. Darcy’s law was employed to explain the fluid flow through a porous medium and linear and nonlinear analyses are conducted. In the semi-infinite domain, the growth of disturbance and the onset of convection were analyzed with and without the quasi-steady state approximation. The present analysis of initial growth rate shows that the system is initially unconditionally stable regardless of a vertical heterogeneity parameter. The onset conditions of buoyancy-driven instabilities were investigated as a function of the Darcy-Rayleigh number and the heterogeneity parameter. To find the effect of a vertical heterogeneity on the flow after the onset of convection, nonlinear numerical simulations also were conducted using the result of the linear analysis as a starting point. Nonlinear numerical simulations show that the finger-like instability motion is not readily observable at a critical time and it becomes visible approximately when a mass transfer rate substantially increases.     

储层流体流态判定方法研究

以低渗透油田的开发实践为背景,应用雷诺数法和压力数法综合判断地层流体渗流特征,指出了判定达西流非达西流的临界雷诺数和临界压力数,从而判断出地层流体渗流特征。     

Modelling the Effect of Particle Size in Microfiltration

Abstract

Particle deposition at the filter surface in microfiltration is studied to better understand the effect of particle size on cake morphology and permeability reduction. Numerical simulations are carried out on a Hele Shaw cell which consists of a representative unit element of a two dimensional spatially periodic flat plate with pores. The particle concentration in the fluid is assumed to be low so that particles enter one by one into the computation domain. Particles follow the flow streamlines under creeping flow conditions from a random initial location until they are subjected to physico‐chemical interactions near the filter surface or a particle already deposited. The computational domain consists of two regions: a fluid region and a porous medium region, i.e. the particle cake. The flow over the two regions of the Hele Shaw cell is computed using the Darcy model, including the variations of the permeability field due to the cake formation. Results show that both the permeability and the filtration efficiency are affected significantly by particle size.     

多孔介质中流体流动的格子气自动机模拟

介绍了 13-Bit正六边形多速格子气自动机模型的特点 ,讨论了多孔介质流体流动的格子气自动机模型的渗透率等参量算方法 ,应用该模型对计算机产生的多孔介质几何构型和焦炭多孔介质中的流体流动进行了模拟 ,其结果既可以给出多孔介质中的流动细节 ,也可统计得到表征多孔介质宏观流动特征的物理参量 .初步研究表明 :格子气自动机模型可用于模拟复杂边界条件下多孔介质的流体流动     

Darcy's law for two‐dimensional flows: Singularities at corners and a new class of models

As is known, Darcy's model for fluid flows in isotropic homogeneous porous media gives rise to singularities in the velocity field for essentially two‐dimensional flow configuration, like flows over corners. Considering this problem from the modeling viewpoint, this study aims at removing this singularity, which cannot be regularized via conventional generalizations of the Darcy model, like Brinkman's equation, without sacrificing Darcy's law itself for unidirectional flows where its validity is well established experimentally. The key idea is that as confirmed by a simple analogy, the permeability of a porous matrix with respect to flow is not a constant independent of the flow but a function of the flow field (its scalar invariants), decreasing as the curvature of the streamlines increases. This introduces a completely new class of models where the flow field and the permeability field are linked and, in particular problems, have to be found simultaneously. © 2017 American Institute of Chemical Engineers AIChE J, 2017     

DIFFUSION OF CHEMICALLY REACTIVE SPECIES IN BOUNDARY LAYER FLOW OVER A POROUS PLATE IN POROUS MEDIUM

Analysis was made to study the effect of diffusion of chemically reactive species in boundary layer flow of an incompressible fluid over a porous flat plate in porous medium. The first-order chemical reaction was considered and the reaction rate of the reactive species was taken in such a manner that it varied inversely along the plate. Self-similar equations were obtained using similarity transformations and were then solved by the shooting technique using the fourth-order Runge-Kutta method. This analysis revealed that at a fixed point, with increase of the permeability of the porous medium the velocity increases, but the concentration decreases. The suction reduces the thicknesses of momentum and concentration boundary layers but due to blowing the thicknesses become larger. With increase of both the Schmidt number and the reaction rate parameter, the reactive concentration profiles decrease. For a destructive chemical reaction, the concentration profiles exhibit negative value when the Schmidt number is large. It is very significant to note that in some constructive chemical reaction cases the mass absorption at the plate occurs for small Schmidt number.     

BLASIUS AND SAKIADIS FLOW WITH UNIFORM BLOWING OR SUCTION IN NON-NEWTONIAN POWER-LAW FLUIDS

The Blasius and Sakiadis flows of a non-Newtonian power-law fluid are considered. The plate is porous and fluid can be either injected or sucked through it. The boundary layer equations are transformed into a nondimensional form and are solved with a finite difference method. For the case of uniform suction, new results have been found, although this problem has been investigated in the past. Among them are analytical solutions for dilatant fluids of the Blasius flow and analytical solutions of the Sakiadis flow for all values of the power-law index. For the case of uniform injection, the characteristics of the flow until a separation state are investigated and discussed.     

Stokes flow past periodic rows of porous cylinders

The flow of a viscous incompressible fluid at low Reynolds numbers in model filters—systems of porous permeable cylinders—is studied. A single row and hexagonal and square arrays of parallel cylinders perpendicular to the flow direction are considered. The flow field outside and inside a porous cylinder is determined by solving the Brinkman and Stokes equations. The drag force on a porous cylinder versus the cylinder permeability and the distance between the axes of neighboring cylinders is calculated. It is shown that rows of porous cylinders arranged into a square array have almost no mutual hydrodynamic effect at any array spacing. The cell model is shown to be applicable to the hexagonal array of porous cylinders over a wide range of packing densities.     

Species-electrochemical transports in a free-breathing cathode of a PCB-based fuel cell

The species-electrochemical transport phenomena in a free-breathing cathode of a printed-circuit-board (PCB)-based fuel cell have been studied numerically. A perforated current collector is attached to the porous cathode that breathes the fresh air through an array of circular holes. Parametric studies include the breathing-hole diameter (d) and the cathode-layer thickness (δ). Gas flow in the porous cathode is governed by the Darcy equation with constant porosity and permeability. Electrochemical reaction on the surfaces of the porous matrices is depicted via the Butler-Volmer equation. The multi-species diffusive transports in the porous cathode are described using the Stefan-Maxwell equation. The charge transports in the porous matrices are dealt with the Ohm's law. The coupled equations are solved by a finite-element-based CFD technique. Results show that the mean flow of the gaseous mixture directs outward from the porous cathode to ambient. In addition, the species diffusion dominates the mass transports in the free-breathing cathode. Furthermore, the enhancement of species diffusion compromises the increase of Ohmic resistance shows the optimal breathing-hole diameter around d = 2.1 mm that provides the best electrochemical performance.     

Flow near the permeable boundary of an aligned fiber preform: An experimental investigation using laser doppler anemometry

The flow of fluid at the interface of an aligned fiber bed and an open flow is the governing phenomenon in a number of processes of industrial importance. Traditionally, this has been modeled by applying Brinkman's modification of Darcy's law to obtain the velocity profile in planar geometries in terms of an additional parameter called “apparent viscosity.” to test this ad hoc approach, a detailed experimental investigation of the flow was conducted using Laser Doppler Anemometry (LDA) in the close vicinity of the permeable boundary of aligned fiber preforms. The performs used in the experiments consisted of cylindrical fibers aligned in one direction. Two cases were investigated. In the first case, the axis of alignment was in the direction of flow and in the second case the axis of alignment was perpendicular to the flow direction. A Hele-Shaw cell is partially filled with a fibrous preform such that an open channel flow is coupled to the Darcy flow inside the fiber bed through the permeable interface of the bed. The unfilled portion of the Hele-Shaw cell acts as an ideal porous medium of known in-plane permeability, which is much higher than the permeability of the fibrous/porous bed. Modeling this flow situation using a Hele-Shaw cell is appropriate because most composite parts are long and wide in comparison with their thickness. When a viscous fluid is injected at a constant flow rate through the above arrangement, a steady state coupled flow is created. This coupling of the open flow and the Darcy flow through the fibrous bed occurs through the boundary layer zone inside the fibrous bed. Using LDA, steady state velocity profiles are accurately measured in the boundary layer zone by traversing the fibrous bed at a suitable location. For aligned fiber beds, the depth of the boundary layer zone inside the bed was found to be of the order of the mold depth, which is much larger as compared to the Brinkman's prediction. This finding indicates the presence of a length scale that is much larger than the known length scale $ \sqrt K $, where K is the permeability of the bed made up of aligned cylindrical fibers. Based on this finding, the depth of the boundary layer thickness is incorporated in the Brinkman's solution through a boundary condition. This results in a model that compares well with the experimental data for the planar geometry and the fibrous beds considered here.     

Stagnation‐point Flow towards a Stretching Surface

An exact similarity solution of the Navier‐Stokes equations is obtained. The solution represents steady axisymmetric stagnation‐point flow towards a stretching surface. It is shown that the flow displays a boundary‐layer structure when the stretching velocity of the surface is less than the free stream velocity. On the other hand, an inverted boundary layer is formed when the surface stretching velocity exceeds the free stream velocity. Temperature distribution in the flow is found when the surface is held at a constant temperature. It turns out that when the surface temperature exceeds the ambient temperature, heat flows from the surface to the fluid near the stagnation point but further away from the stagnation point, heat flows from the fluid to the stretching surface.