Creeping flow over a composite sphere: Solid core with porous shell

Creeping flow past a solid sphere with a porous shell has been solved using the Stokes and Brinkman equations. The dimensionless solid core and shell radii, normalized by the square root of the shell permeability, are the two parameters that govern the flow. In the limiting cases, the analytical solution describing the flow past the composite sphere reduces to that for flow past a solid sphere and a homogeneous porous sphere. The settling rates of a solid sphere with attached threads are measured experimentally. This system can be considered a model for rigid linear molecules anchored or adsorbed onto a colloidal particle. The analytical solution for the composite sphere is in excellent agreement with the experimental results.     

Viscous flow in a channel partially filled with a porous medium and with wall suction

In this paper, we consider a coupled two-dimensional flow of a Newtonian fluid, both above and through a porous medium. In the fluid-only region, the two-dimensional flow field is governed by the Navier-Stokes equation. We consider the Brinkman-extended Darcy law relationship in the porous medium. Inertial terms are retained in the formulation and the interface conditions between the two domains are those as outlined by Ochoa-Tapia and Whitaker (Int. J. Heat Mass Transfer 38 (1995) 2635). It should be noted that these interface conditions are formulated with an empirical constant β that is unknown a priori. The model equations were solved using two independent methods. In the first method, we pose a similarity variable and reduce the governing equations to two, coupled, non-linear ordinary differential equations. In the second approach, the governing equations were re-posed as a one-domain problem, using the procedure outlined by Basu and Khalili (Phys. Fluids 11 (1999) 1031), so that the conditions at the interface need not be considered. The resulting equation was solved directly, in primitive variable form, using a finite volume formulation. This enabled us to determine β by comparing the resulting solutions.     

Viscous flow of a Newtonian fluid in a curved channel with flexible moving porous walls

We consider flow of a viscous Newtonian fluid in a curved channel with moving porous walls; the upper wall is flexible and its position in unknown a priori. This work is motivated from a papermaking application namely roll forming. We solve the leading order terms in equations of motion using perturbation methods and present analytical expressions for the variation in channel size, pressure, and viscous shear. The stability of the solution is also examined and we report the conditions for marginal stability.     

Numerical solution of viscous flow past a solid sphere with the control volume formulation

The control volume formulation with the QUICK finite difference scheme is used to solveincompressible liquid flow past a solid sphere in terms of stream function and vorticity.Several tech-nical points are addressed on improving the accuracy and efficiency of numerical simulation of similarproblems of fluid flow.In particular,the importance of suitable specification of the distortion func-tion to enforcing the far field boundarv conditions is emphasized.     

Boundary layer flow past a stretching/shrinking surface beneath an external uniform shear flow with a convective surface boundary condition in a nanofluid

The problem of a steady boundary layer shear flow over a stretching/shrinking sheet in a nanofluid is studied numerically. The governing partial differential equations are transformed into ordinary differential equations using a similarity transformation, before being solved numerically by a Runge-Kutta-Fehlberg method with shooting technique. Two types of nanofluids, namely, Cu-water and Ag-water are used. The effects of nanoparticle volume fraction, the type of nanoparticles, the convective parameter, and the thermal conductivity on the heat transfer characteristics are discussed. It is found that the heat transfer rate at the surface increases with increasing nanoparticle volume fraction while it decreases with the convective parameter. Moreover, the heat transfer rate at the surface of Cu-water nanofluid is higher than that at the surface of Ag-water nanofluid even though the thermal conductivity of Ag is higher than that of Cu.     

数值模拟中低Reynolds数下简单剪切流流过单液滴的稳态流场(英文)

This work presents a numerical investigation on steady internal, external and surface flows of a liquid sphere im-mersed in a simple shear flow at low and intermediate Reynolds numbers. The control volume formulation is adopted to solve the governing equations of two-phase flow in a 3-D spherical coordinate system. Numerical re-sults show that the streamlines for Re=0 are closed Jeffery orbits on the surface of the liquid sphere, and also closed curves outside and inside the liquid sphere. However, the streamlines have intricate and non-closed struc-tures for Re≠0. The flow structure is dependent on the values of Reynolds number and interior-to-exterior vis-cosity ratio.     

Numerical simulation of steady flow past a liquid sphere immersed in simple shear flow at low and moderate Re

This work presents a numerical investigation on steady internal, external and surface flows of a liquid sphere im-mersed in a simple shear flow at low and intermediate Reynolds numbers. The control vol...     

The flow and displacement in porous media of fluids with yield stress

We study the mobilization and subsequent flow in a porous medium of a fluid with a yield stress, modeled as a Bingham plastic. We use single-capillary expressions for the mobilization and flow in a pore-throat, and a pore-network model that accounts for distributed yield-stress thresholds. First, we extend the statistical physics method of invasion percolation with memory, which models lattice problems with thresholds, to incorporate dynamic effects due to the viscous friction following the onset of mobilization. Macroscopic relations between the applied pressure gradient and the flow rate for single-phase flow are proposed as a function of the pore-network microstructure and the configuration of the flowing phase. Then, the algorithm is applied to model the displacement of a Bingham plastic by a Newtonian fluid in a porous medium. The results find application to a number of industrial processes including the recovery of oil from oil reservoirs and the flow of foam in porous media.     

Revisit the adhesive contact between a nanoscale rigid sphere and an elastic half-space: considering the effect of sphere size

The current paper revisits the adhesive contact between a rigid nanoscale sphere and an elastic half-space. Using analytical solution for traction and a modified numerical scheme, a new simulation is proposed. The adhesive contact is simulated faster and more easily than previous researches. The effect of sphere size is investigated. A modified spherical JKR model and spherical DMT model are proposed. The results are compared with spherical JKR, spherical DMT, and rigid sphere model. The load–approach and contact radius–load relations can be predicted by the modified spherical JKR model for sphere radius larger than 50?. Finally, approximation equations for pull-off force vs. Tabor parameter and jump-in distance vs. Tabor parameter are proposed.     

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。     

Suction, viscous dissipation and thermal radiation effects on the flow and heat transfer of a power-law fluid past an infinite porous plate

This paper presents a study of the flow and heat transfer of an incompressible Ostwald de-Waele power-law fluid past an infinite porous plate, subject to suction at the plate. The power-law index n satisfies 0 < n < 1 (shear-thinning fluid only) provided that there is suction at the plate. Three cases are studied, namely, (i) the plate with constant surface temperature (CST case), (ii) the plate with prescribed surface temperature (PST case), and (iii) the plate with prescribed heat flux (PHF case). The effects of viscous dissipation and thermal radiation are also considered in the energy equation and the variations of dimensionless surface temperature and dimensionless surface temperature gradient with various parameters are graphed and tabulated.     

Hydrodynamics of a spouted bed with an impermeable draft tube for binary particle systems

A spouted bed with an impermeable draft tube was employed to obtain fundamental data of binary mixtures of glass beads for both the operating conditions and the design factors. These data were compared with those for the coarser particle system only. From this view point, minimum spouting velocity, pressure drop, hold-up of solid particles within a draft tube, upward gas flow rate within the annulus and solids circulation rate were determined by changing the total gas flow rate and mass fraction of finer particles as operating parameters and by changing distance of entrainment zone and draft tube diameter as geometric parameters.     

Stokes flow past an ellipsoid in a special ambient flow field: A marvelous cubic equation for a quadratic ambient field

A three-dimensional eigenspace appears in the analysis of an ellipsoid immersed in quadratic ambient viscous flow fields. To celebrate the mathematical achievements of Babatunde Ogunnaike, we focus on mathematical details of the eigenvalues and eigenfunctions of the double-layer operator that appears in the integral representation of velocity fields as a function of the shape parameters of the ellipsoid. Three special quadratic ambient fields that lack an ambient pressure gradient (toroidal fields) form a decoupled subsystem with eigenvalues associated with three real roots of a cubic equation. The discriminant of this cubic vanishes at discrete points in the parameter space of the ellipsoidal shape revealing repeated roots (and thus repeated eigenvalues) of the cubic. The discrete nature of these points is illustrated with explicit derivation of the discriminant's level set contours in the region near the repeated eigenvalues for the sphere.     

The effect of a concentration‐dependent viscosity on particle transport in a channel flow with porous walls

The transport of a dilute suspension of particles through a channel with porous walls, accounting for the concentration dependence of the viscosity, is analyzed. In particular, we study two cases of fluid permeation through the porous channel walls: (1) at a constant flux and (2) dependent on the pressure drop across the wall. We also consider the effect of mixing the suspension first compared with point injection by considering inlet concentration distributions of different widths. We find that a pessimal inlet distribution width exists that maximizes the required hydrodynamic pressure for a constant fluid influx. The effect of an external hydrodynamic pressure, to compensate for the reduced transmembrane pressure difference due to osmotic pressure, is investigated. © 2014 American Institute of Chemical Engineers AIChE J, 60: 1891–1904, 2014     

Drag coefficient of flow around a sphere: Matching asymptotically the wide trend

An empirical relationship of drag coefficient of flow around a sphere is developed for the entire range of Particle Reynolds numbers reported in the literature from Stokes regime to the condition when turbulent boundary layer prevails. The relationship is obtained using an approach to match asymptotically the wide trend of drag coefficient. The matching approach, which relies on dividing the wide trend into smaller segments that can be combined into an overall relationship, employs regression techniques and thus warrants the best-fit accuracy results. The relationship is calibrated with experimental data available in the literature covering the entire range for Reynolds numbers up to ~ 10⁶. For Reynolds values greater than 10⁶, the relationship renders a drag coefficient of 0.2. The performance of the relationship is tested and compared with other suitable models found in the literature. This relationship is also transformed into an explicit expression for settling velocity calculations.     

Viscous flow on the outside of a horizontal rotating cylinder: The roll coating regime with a single fluid

The flow of a viscous fluid on the outside of a horizontal rotating drum partially submerged on the fluid, has many instances of interesting practical applications. The purpose of this paper is to present a well rounded set of theoretical, numerical and experimental results for a set of parameters within the range of interest of coating processes.     

Flow through porous media of a shear-thinning liquid with yield stress

Darcy's law for the laminar flow of Newtonian fluids through porous media has been modified to a more general form which will describe the flow through porous media of fluids whose flow behavior can be characterized by the Herschel-Bulkley model. The model covers the flow of homogeneous fluids with a yield value and a power law flow behavior. Experiments in packed beds of sand were carried out with solutions of paraffin wax in two oils and with a crude oil from the Peace River area of Canada. The model fitted the data well. A sensitivity analysis of the fitting parameters showed that the model fit was very sensitive to errors in the flow behavior index, n , of the Herschel-Bulkley model. A comparison of the “n” values calculated from viscometer measurements and from flow measurements agreed well. A more general Reynolds number for flow through porous media, which includes a fluid yield value, was developed. The data were fitted to a Kozeny-Carman type equation using this Reynolds number. The constant in the Kozeny-Carman equation was determined for the two packed beds studied using Newtonian oils. The data could all be represented, within the experimental error, by the relationship f^* = 150/Re^*. Since the mean volume to surface diameter of the packing was determined by the measurement of its permeability to a Newtonian oil, assuming C' = 150, the new definition of the Reynolds number allows the direct use of the Kozeny-Carman equation with Herschel-Bulkley type fluids.     

Viscous flow through a bed of settled aggregates: Evolution of tubes void of particles

Observations show that, when a viscous fluid flows vertically through a bed of settled flocculated aggregates, particles are emerged from locations on the upper surface of the bed, as a volcano process, and hollow tubes are created in the bed though the latter remains basically stable. A theoretical model is presented to explain this odd phenomenon from the onset of particle motion to the development of the tubular cavities and the particles' deposits around them. Analytical and numerical calculations are performed to show fluid streamlines and particle trajectories.     

Thermal radiation effect on unsteady MHD free convection flow past a vertical plate with temperature‐dependent viscosity

This article investigates the influence of radiation and temperature‐dependent viscosity on the problem of unsteady MHD flow and heat transfer of an electrically conducting fluid past an infinite vertical porous plate taking into account the effect of viscous dissipation. The governing equations are converted into a system of nonlinear ordinary differential equations via a local similarity parameter which is taken as a function of time. The resulting system of coupled nonlinear ordinary differential equations is solved numerically using the fourth order Runge–Kutta integration scheme with the shooting method. The numerical results for the velocity and the temperature are displayed graphically showing the effects of various parameters. The results show that increasing the Eckert number and decreasing the viscosity of air leads to a rise in the velocity, while increasing in the magnetic or the radiation parameters is associated with a decrease in the velocity. Also, an increase in the Eckert number leads to an increase in the temperature, whereas an increase in radiation parameter leads to a decrease in the temperature.