Effects of Permeable Cylinder on the Flow Structure in Deep Water

Flow behaviors around permeable cylinders were investigated using Particle Image Velocimetry technique in deep water. The height of deep water and free stream velocity were kept constant as h_w = 340 mm and U = 156 mm/s. To find out the effect of the permeable cylinders on the flow structure, eight different porosities (β = 0.4, 0.5, 0.6, 0.65, 0.7, 0.75, 0.8, and 0.85) were used. The results have indicated that the permeable cylinders are effective on the control of large-scale vortical structures downstream of the permeable cylinder. As the porosity increases, turbulent kinetic energy and Reynolds shear stress decrease. This means that the fluctuations in the wake region are significantly weakened by permeable cylinders. The permeable cylinders having the porosity higher than 0.6 do not pose an obstacle in the flow. Furthermore, for all diameter values of permeable cylinders, it can be concluded that the flow structures downstream of the permeable cylinder show similar trend with each other.     

Application of CFD-DEM to the study of solid exchange in a dual-leg fluidized bed

The CFD-DEM model was developed to simulate solid exchange behavior between two half beds in a bench-scale two-dimensional dual-leg fluidized bed （DL-FB）. Power spectrum density （PSD） analysis was applied to obtain the dominant frequency （F） of the simulated differential particle number （APLR） between the two half beds. Effects of fluidization velocity （u） and bed material inventory （H） on the solid exchange behavior were studied using the CFD-DEM model. Not only snapshots of the simulated particle flow patterns using the OpenGL code but also the dominant frequency of APLR was similar to the experimental results. The simulation results show that higher fluidization velocity assists the exchange of more particles between the two half beds, but the dispersion of clusters on the bed surface into single particles decreases the cluster exchange frequency. A greater bed material inventory results in more intense cluster exchange. The cluster exchange frequency decreases with an increase of the bed material inventory.     

Dispersion of particles in wall-bounded particle-laden turbulent flows with high wall permeability

A series of numerical simulations were performed to investigate the distribution and deposition properties of particles in turbulent flows bounded by permeable walls using the Large Eddy Simulation (LES) with a Lagrangian trajectory approach. The wall permeation speeds were taken from 10⁻⁴ to 10⁻² of the bulk velocity. The directions of the permeation speed were the same at both walls, and they were inward on one wall but outward on the other wall to reserve the fluid mass. Particles with Stokes number (respecting viscous time scale) around 0.1, 1 and 10 were released in the fully developed turbulent channel flow. The particle–particle interaction and the retroaction from particles to the fluid were neglected. The fluid-phase turbulence statistical properties and particle's transport characteristics by vortexes were then analyzed in details. If the wall permeation exists, the turbulence intensities will be depressed close to the outward permeable wall but increased near the inward permeable wall. Not influenced by the wall permeation, the suspended particles with St⁺ ∼O(1) tend to accumulate in the less vortical zones away from the wall, while those particles in the flow regions near the outward permeable wall will distribute disregarding of the vorticity. The turbulence structures near the outward permeable wall are found to exert promotional effects on the particle deposition rate, but such effects are different for particles with various Stokes number. A distribution tendency of streamwise streaks for the deposited particles is also found on the wall imposed by the high outward permeation speed and the clustering deposition pattern is more obvious with increasing particle Stokes number.     

Aerodynamic characteristics of permeable disks at subsonic free-stream flow velocities

A large number of investigations have been carried out to study the aerodynamic characteristics of grids and permeable plates completely covering a pipe section [1]. The theoretical bases of the external aerodynamics of permeable bodies are established in [2], where the concept of a uniformly permeable surface is introduced and the problem of flow past a permeable plate at a small angle of attack is solved. Papers [3, 4] are devoted to the solution of problems of a jet flow of ideal incompressible fluid past a permeable wedge and a plate. The flow past a wedge with a high degree of permeability at low subsonic velocities was investigated theoretically and experimentally in [5]. Papers [6, 7] are devoted to the experimental investigation of the aerodynamic characteristics of plates and disks at low subsonic velocities. The results of the experimental investigations of permeable bodies are given in [8]. In the present paper the aerodynamic characteristics of permeable disks positioned perpendicular to the direction of the oncoming flow are investigated experimentally in a wide range of variation of the perforation parameters and the subsonic free-stream flow velocities.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 123–128, July–August, 1986.     

Mixed convection boundary layer flow past a wedge with permeable walls

The effects of suction/injection on steady laminar mixed convection boundary layer flow over a permeable horizontal surface of a wedge in a viscous and incompressible fluid is considered in this paper. The similarity solutions of the governing boundary layer equations are obtained for some values of the suction/injection parameter f ₀, the constant exponent m of the wall temperature as well as the mixed convection parameter λ. The resulting system of nonlinear ordinary differential equations is solved numerically for both assisting and opposing flow regimes using an implicit finite-difference scheme known as the Keller-box method. Numerical results for the reduced skin friction coefficient, the local Nusselt number, and the velocity and temperature profiles are obtained for various values of parameters considered. Dual solutions are found to exist for the case of opposing flow.     

Velocity Measurements of a Free-Surface Turbulent Flow Penetrating a Porous Medium Composed of Uniform-Size Spheres

We present a laboratory experimental investigation of the interaction between the turbulent flow in an open channel and the turbulent flow within its very permeable bed. The bed was composed of uniform-size spheres packed in a cubic pattern. Fluid velocities were measured by Particle Image Velocimetry (PIV), which allowed us to investigate the spatial distribution of the time-averaged flow properties in the zone where they are strongly affected by the geometry of the rough bed. We investigate the effect of bed porosity on these flow properties by comparing the results of two experimental configurations: one with an impermeable bed composed of a single layer of spheres and another with a permeable bed composed of five layers. For the latter case, PIV measurements of velocities were also carried out inside two pores adjacent to the bed surface. This data provides an insight into the mechanisms of momentum transfer between the turbulent open channel flow and the turbulent flow within its very permeable bed.     

Flow fields and packing states in the discharge flow of noncircular particles—A SIPHPM simulation

Although the discharge flow of spherical materials has been extensively explored, the effect of particle shape on discharge is still poorly understood. The present work explores the two-dimensional discharge flow fields of noncircular particles using the soft-sphere-imbedded pseudo-hard particle model method. Rectangular particles having different aspect ratios (R_a = 1, 1.5, 2–5) and regular polygonal particles having different numbers of sides (N_s = 3–8, 10) are discharged through hopper beds having different orifice widths (D_i = 40, 70.77, 99.13, 125.74, 151.13 mm). The discharge rates of differently shaped particles in different beds are consistent with Beverloo’s relation. Moreover, the flow fields are computed and evaluated to study the effects of R_a, N_s, and D_i on particle discharge. The characteristics of particle–particle connections in the discharge process are evaluated according to the temporal evolution and spatial distribution of the contact points. Additionally, the effect of the initial packing on the discharge profile is investigated. The findings help clarify the discharge of noncircular particles.     

Dissipative Processes in a One-Dimensional Supersonic Gas Flow Across a Permeable Obstacle

One-dimensional supersonic gas flow across an infinite permeable surface (obstacle of zero thickness) is investigated by the direct statistical simulation (Monte-Carlo) method. Both the characteristic features of the formation of a shock perturbation in the interaction between the plane supersonic flow and the permeable obstacle and the effect of the perturbation on the flow parameters behind the obstacle are found. It is concluded that the accommodation coefficient can be determined from the data on the equilibrium flow macroparameters behind the obstacle.     

Fracture analysis of circular-arc interface cracks in piezoelectric materials

The anti-plane problem of N arc-shaped interfacial cracks between a circular piezoelectric inhomogeneity and an infinite piezoelectric matrix is investigated by means of the complex variable method. Cracks are assumed to be permeable and then explicit expressions are presented, respectively, for the electric field on the crack faces, the complex potentials in media and the intensity factors near the crack-tips. As examples, the corresponding solutions are obtained for a piezoelectric bimaterial system with one or two permeable arc-shaped interfacial cracks, respectively. Additionally, the solutions for the cases of impermeable cracks also are given by treating an impermeable crack as a particular case of a permeable crack. It is shown that for the case of permeable interfacial cracks, the electric field is jumpy ahead of the crack tips, and its intensity factor is always dependent on that of stress. Moreover all the field singularities are dependent not only on the applied mechanical load, but also on the applied electric load. However, for the case of a homogeneous material with permeable cracks, all the singular factors are related only to the applied stresses and material constants.     

On the analogy in slip flows—II

In the present paper two examples of (i) generalized plane Couette flow over a smooth stationary plate and (ii) flow past a smooth solid sphere have been discussed to confirm the analogy in slip flows. It has been shown that the results can directly be carried over to the flow over corresponding naturally permeable surfaces up to the order of \(\sqrt K \) (K being the permeability of the medium, which is taken to be small).     

Mathematical modeling of the motion of a portion of helium under pulsed injection over a fixed bed of cenospheres

A mathematical model is constructed and an analytical solution is obtained for the problem of a one-dimensional steady flow of a mixture of different gases with hollow permeable particles. The case of a one-dimensional unsteady flow of such a mixture is analyzed numerically. The numerical solutions are compared with experimental data on the motion of the peak concentration of helium in a fixed bed filled with cenospheres (solid hollow permeable spherical particles). The permeability of cenosphere walls and the drag coeficient of cenospheres in the gas flow are determined. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 3, pp. 92–102, May–June, 2007.     

Computational Modeling of Fluid Flow through a Fracture in Permeable Rock

Laminar, single-phase, finite-volume solutions to the Navier–Stokes equations of fluid flow through a fracture within permeable media have been obtained. The fracture geometry was acquired from computed tomography scans of a fracture in Berea sandstone, capturing the small-scale roughness of these natural fluid conduits. First, the roughness of the two-dimensional fracture profiles was analyzed and shown to be similar to Brownian fractal structures. The permeability and tortuosity of each fracture profile was determined from simulations of fluid flow through these geometries with impermeable fracture walls. A surrounding permeable medium, assumed to obey Darcy’s Law with permeabilities from 0.2 to 2,000 millidarcies, was then included in the analysis. A series of simulations for flows in fractured permeable rocks was performed, and the results were used to develop a relationship between the flow rate and pressure loss for fractures in porous rocks. The resulting friction-factor, which accounts for the fracture geometric properties, is similar to the cubic law; it has the potential to be of use in discrete fracture reservoir-scale simulations of fluid flow through highly fractured geologic formations with appreciable matrix permeability. The observed fluid flow from the surrounding permeable medium to the fracture was significant when the resistance within the fracture and the medium were of the same order. An increase in the volumetric flow rate within the fracture profile increased by more than 5% was observed for flows within high permeability-fractured porous media.     

Viscous fluid flow around a semipermeable particle

The problem of hydrodynamic interaction between a laminar flow of a viscous fluid and a partially permeable spherical particle is formulated and solved analytically. The filtration flow inside the particle is assumed to obey the Darcy law. Expressions for the filtration flow velocity, drag, sedimentation velocity, and stream functions are obtained. The effect of the permeability of the particle on the flow characteristics is studied. Stream functions of the flow are constructed. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 4, pp. 48–53, July–August, 2009.     

PIV investigation of flow behind surface mounted permeable ribs

The flow behind surface mounted permeable rib geometries, i.e. solid, slit, split-slit and inclined split-slit ribs have been studied using flow visualization and PIV (2-C and 3-C) technique in streamwise and cross-stream measurement planes. The objective behind this study is to understand the flow structures responsible for heat transfer/mixing enhancement with simultaneous pressure penalty reduction by permeable rib geometries. The Reynolds number based on the rib height has been set equal to 5,538 and the open area ratio of permeable ribs is equal to 20%. The permeable rib geometries have shorter reattachment length in comparison to the solid rib. The maximum 41% reduction in reattachment length is observed for the inclined split-slit rib. The splitter mounted inside the slit leads to two corner vortices behind it. The corner vortices drag the flow from the primary recirculation bubble region towards the rib resulting in drop of the reattachment length. Two horseshoe vortices are present in the flow through the slit at both sides of the splitter due to the upstream flow separation. The slit inclination moves these horseshoe vortices closer to the bottom wall. A film like flow through the slit is present near the downstream corner of the inclined split-slit rib. The spanwise velocity gradient due to the splitter leads to vorticity and turbulence enhancement by vortex stretching. The inclination of the slit and the use of a splitter inside the slit are two important design parameters responsible in generation of near-wall longitudinal vortices. The flow field behind permeable ribs is dominated by vortical structures with definable critical flow patterns, i.e. node, saddle and foci. These predominant swirling flow motions contribute to the mixing enhancement behind permeable rib geometries. On leave from Mechanical Engineering Department, IIT Kanpur, U.P. 208016, India     

A novel analytic solution of MHD flow for two classes of visco-elastic fluid over a sheet stretched with non-linearly (quadratic) velocity

The laminar boundary layer flow induced in a quiescent visco-elastic fluid by a permeable stretched flat surface with non-linearly (quadratic) velocity and appropriate wall transpiration under the influence of a magnetic field is investigated. It is shown that the problem permits a complete analytic exponentially decaying solution for the set of continuity and momentum equations with both magnetic field and visco-elasticity influences for two classes of visco-elastic fluid, namely, the second grade and Walters’ liquid B fluids. The effects on both the skin friction parameter α and velocity profiles of various physical parameters such as visco-elasticity, suction/blowing parameter and magnetic parameter are studied. The results for the velocity field are presented through graphs and discussed in detail.     

An inflow-outflow characterization of inhomogeneous permeable beds

It is proposed that the inflow to and outflow from a permeable bed be related by an integral. For vanishing fluid velocities, it is linear and its kernel is a material property characterizing the bed. Some of the properties of the kernel are considered here. The approach is particularly useful for tilted, fractured and other inhomogeneous beds, since no continuum characteristics need be assumed. The effects of nonlinearity are also discussed.     

PIV experiments in rough-wall, laminar-to-turbulent, oscillatory boundary-layer flows

Exploratory measurements of oscillatory boundary layers were conducted over a smooth and two different rough beds spanning the laminar, transitional and turbulent flow regimes using a multi-camera 2D-PIV system in a small oscillatory-flow tunnel (Admiraal et al. in J Hydraul Res 44(4):437–450, 2006). Results show how the phase lag between bed shear stress and free-stream velocity is better defined when the integral of the momentum equation is used to estimate the bed shear stress. Observed differences in bed shear stress and phase lag between bed shear stress and free-stream velocity are highly sensitive to the definition of the bed position (y = b). The underestimation of turbulent stresses close to the wall is found to explain such differences when using the addition of Reynolds and viscous stresses to define both the bed shear stress and the phase lag. Regardless of the flow regime, in all experiments, boundary-layer thickness reached its maximum value at a phase near the flow reversal at the wall. Friction factors in smooth walls are better estimated using a theoretical equation first proposed by Batchelor (An introduction to fluid dynamics. Cambridge University Press, Cambridge, 1967) while the more recent empirical predictor of Pedocchi and Garcia (J Hydraul Res 47(4):438–444, 2009a) was found to be appropriate for estimating friction coefficients in the laminar-to-turbulent transition regime.