Porous Obstacle Research Articles

Porous Barriers Efficiency Research under the Compact Elements High-Speed Loading (Part Two)

The paper discusses the results of the numerical simulation of high-speed impact effect of compact projectiles made of steel and tungsten alloy with steel obstacles of equal mass. The obstacles have different initial porosity of the material. Conducted the final evaluation of the penetration speed of the projectile depending on the porosity of the obstacle and the initial speed of the shock interaction. The initial impact velocity range from 1 to 16 [km/s]. The destruction, melting and evaporation of the interacting bodies are taken into account. The analysis of porosity influence evaluation of obstacles material revealed that the protective advantage of porous obstacles disclose at the higher impact velocities, greater than 1.5 [km/s] for steel strikers and 2 [km/s] for projectiles of tungsten alloy. The more impact velocity the more protective effect of porous obstacles.

Multiple-relaxation-time Lattice Boltzmann model for flow and convective heat transfer in lid driven cavity with porous obstacle

In this work, we study numerically a problem of mixed convection in lid driven square cavity, filled with air (Pr = 0.71), whose upper wall is movable and kept at constant cold temperature TC. The cavity contains a porous obstacle of height h and width b, placed on the bottom wall maintained at a constant hot temperature TH. The side walls are adiabatic. Darcy-Brinkmann-forchheimer model is used for modelling the momentum equations in porous medium. This numerical study is based on the multiple relaxation time lattice Boltzmann method (MRT -LBM). The D2Q9 two-dimensional model is adopted to the dynamic part, while the D2Q5 model is applied for the thermal part. The objective of the study is to analyze the effect of Darcy number (10-1 ≼ Da ≼ 10-5), Richardson number (0.01 ≼ Ri ≼ 100) and the aspect ratio w = b/H (0.2 ≼ w ≼ 1) on the hydrodynamic and thermal characteristics in the cavity through the velocity and temperature as well as the average Nusselt number. The results obtained show a considerable effect of these parameters on the structure of the flow and on the heat exchange in the cavity.

LBM simulation of MHD nanofluid heat transfer in a square cavity with a cooled porous obstacle: effects of various temperature boundary conditions

Nanofluid natural convection inside a cavity with a porous square obstacle in the presence of magnetic field is simulated by lattice Boltzmann method. The porous obstacle is adopted by Sierpinski carpets fractal pattern, and three kinds of temperature boundary conditions are set up on the hot walls. The combination of five topics including LBM, Sierpinski carpets, nanofluid, magnetic field and various temperature boundary conditions is the main novelty of the present paper. The effects of temperature boundary condition, configuration of Sierpinski carpets porous obstacle, Rayleigh number, nanoparticle volume fraction and Hartmann number on the flow pattern, temperature distribution and heat transfer characteristics are studied. The results show that the local and average Nusselt numbers are increasing functions of ϕ and Ra, but a decreasing function of Ha, regardless of the boundary conditions. The heat transfer enhancement by adding nanoparticles is more effective at low ϕ. The rate of heat transfer with different temperature boundary conditions is Case 3 ˃ Case 2 ˃ Case 1. At high Hartmann number, the obstacle configuration affects the rate of heat transfer very slightly. However, at low Hartmann number, the effect of obstacle configuration on the average Nusselt number should be considered. The effect of obstacle configuration on the rate heat transfer is also influenced by the temperature boundary conditions.

A generalised model for electro-osmotic flow in porous media

Purpose This study aims at developing a comprehensive model for the analysis of electro-osmotic flow (EOF) through a fluid-saturated porous medium. To fully understand and exploit a number of applications, such a model for EOF through porous media is essential. Design/methodology/approach The proposed model is based on a generalised set of governing equations used for modelling flow through fluid saturated porous media. These equations are modified to incorporate appropriate modifications to represent electro-osmosis (EO). The model is solved through the finite element method (FEM). The validity of the proposed numerical model is demonstrated by comparing the numerical results of internal potential and velocity distribution with corresponding analytical expressions. The model introduced is also used to carry out a sensitivity analysis of the main parameters that control EOF. Findings The analysis carried out confirms that EO in free channels without porous obstruction is effective only at small scales, as largely discussed in the available literature. Using porous media makes EO independent of the channel scale. Indeed, as the channel size increases, the presence of the charged porous medium is essential to induce fluid flow. Moreover, results demonstrate that flow is significantly affected by the characteristics of the porous medium, such as particle size, and by the zeta potential acting on the charged surfaces. Originality/value To the best of the authors’ knowledge, a comprehensive FEM model, based on the generalised equations to simulate EOF in porous media, is proposed here for the first time.

Effect of Obstacle Type on Methane–Air Flame Propagation in a Closed Duct: An Experimental Study

The combustion in a closed environment was the subject of many works in the past century due to its importance and complex nature compared with the combustion in an open environment. Most research works in this field have investigated different types of gas mixtures, the governing boundary conditions and their effect on the flame propagation structure. Additionally, several investigations have been performed on creating disturbance through obstacles in the flow path as well as the process of deflagration to detonation transition. This paper, for the first time, investigates the effect of porous and solid obstacles on the propagation and the structure of premixed methane–air flame in a closed duct with dimensions of 50 × 11 × 8 cm. The blockage created in the duct by obstacles is in such a way that the detonation process does not occur. The results for the unconstrained duct correctly represent the process of forming the classical tulip flame inside the closed duct. The location of the obstacles is changed in four different distance of 5, 10, 15, and 20 cm from the spark plug, and its effect on combustion characteristics has been evaluated. The results show that the obstacles create fundamental changes in the structure and flame propagation. A significant difference between solid and porous obstacles is that the porous obstacle, in proportion to the solid obstacle, creates less disturbance in the flow field and also does not cause excessive acceleration in the flame propagation. Porous obstacles also reduce the maximum pressure in the chamber during the process, more than the solid obstacles.

Numerical Simulation of Mixed Convection in a Lid Driven Cavity with Porous Obstacle Using (MRT-LBM)

In this work, we study numerically a problem of mixed convection in lid driven square cavity, filled with air (Pr = 0.71), whose upper wall is movable and kept at constant cold temperature TC. The cavity contains a porous obstacle of height h and width b, placed on the middle of bottom wall which maintained at a constant hot temperature TH. The side walls are adiabatic. Darcy-Brinkmann model is used for modeling the momentum equations in porous medium. The Boussinesq assumption is used and the viscous dissipation is assumed to be negligible. This numerical study is based on the multiple-relaxation-time Lattice Boltzmann method (MRT-LBM). The D2Q9 two-dimensional model is adopted to the dynamic part, while the D2Q5 model is applied for the thermal part. The objective of the study is to analyze the effect of Darcy number (10−6≼ Da ≼ 10−1), Richardson number (0.01 ≼Ri≼ 103) and the aspect ratio w = b/H (0.2 ≼ w ≼ 1) on the hydrodynamic and thermal characteristics in the cavity through the velocity and temperature as well as the average Nusselt number. The results obtained show a considerable effect of these parameters on the structure of the flow and the heat transfer in the cavity, which can not be neglected.

Lattice Boltzmann Method Simulations of High Reynolds Number Flows Past Porous Obstacles

Lattice Boltzmann Method (LBM) simulations for turbulent flows over fractal and non-fractal obstacles are presented. The wake hydrodynamics are compared and discussed in terms of flow relaxation, Strouhal numbers and wake length for different Reynolds numbers. Three obstacle topologies are studied, Solid (SS), Porous Regular (PR) and Porous Fractal (FR). In particular, we observe that the oscillation present in the case of the solid square can be annihilated or only pushed downstream depending on the topology of the porous obstacle. The LBM is implemented over a range of four Reynolds numbers from 12,352 to 49,410. The suitability of LBM for these high Reynolds number cases is studied. Its results are compared to available experimental data and published literature. Compelling agreements between all three tested obstacles show a significant validation of LBM as a tool to investigate high Reynolds number flows in complex geometries. This is particularly important as the LBM method is much less time consuming than a classical Navier–Stokes equation-based computing method and high Reynolds numbers need to be achieved with enough details (i.e., resolution) to predict for example canopy flows.

Implementation of heterogeneous detonation in a pulsed combustor – PDE model

ABSTRACTThis work is devoted to the use of detonative combustion of a liquid fuel in technical devices to obtain a jet thrust. The experimental and theoretical aspects of the organization of detonation in heptane/air/oxygen mixtures are considered. The pulsed regime of detonation at a frequency of 50 Hz has been implemented for the first time in a small-size tube (25 mm in diameter and 740 mm in length). The physical and technical methods that could accelerate the deflagration-to-detonation transition have been studied. The influence of thermal activation of a combustible mixture prior to its ignition and of the special form of a porous obstacle on the magnitude of the predetonation distance is established. The degree of this influence depends on the component composition, equivalence ratio, and the degree of filling the tube with a mixture.

Porous Barriers Efficiency Research under the Compact Elements High - Speed Loading

The paper discusses the results of the numerical simulation of high-speed impact effect of compact projectiles made of steel and tungsten alloy with steel obstacles of equal mass. The obstacles have different initial porosity of the material. Conducted the final evaluation of the penetration speed of the projectile depending on the porosity of the obstacle and the initial speed of the shock interaction. The initial impact velocity range from 1 to 16 [km/s]. The destruction, melting and evaporation of the interacting bodies are taken into account. The analysis of porosity influence evaluation of obstacles material revealed that the protective advantage of porous obstacles disclose at the higher impact velocities, greater than 1.5 [km/s] for steel strikers and 2 [km/s] for projectiles of tungsten alloy. The more impact velocity the more protective effect of porous obstacles.

Determination of the diffusivity, dispersion, skewness and kurtosis in heterogeneous porous flow. Part II: Lattice Boltzmann schemes with implicit interface

Abstract A simple local two-relaxation-time Lattice Boltzmann numerical formulation (TRT-EMM) of the extended method of moments (EMM) is proposed for analysis of the spatial and temporal Taylor dispersion in d-dimensional streamwise-periodic stationary mesoscopic velocity field resolved in a piecewise-continuous porous media. The method provides an effective diffusivity, dispersion, skewness and kurtosis of the mean concentration profile and residence time distribution. The TRT-EMM solves a chain of steady-state heterogeneous advection–diffusion equations with the pre-computed space-variable mass-source and automatically undergoes diffusion-flux jump on the abrupt-porosity streamwise-normal interface. The temporal and spatial systems of moments are computed within the same run; the symmetric dispersion tensor can be restored from independent computations performed for each periodic mean-velocity axis; the numerical algorithm recursively extends for any order moment. We derive an exact form of the bulk equation and implicit closure relations, construct symbolic TRT-EMM solutions and determine specific relation between the equilibrium and the collision degrees of freedom viewing an exact parameterization by the physical non-dimensional numbers in two alternate situations: “parallel” fracture/matrix flow and “perpendicular” Darcy flow through porous blocks in “series”. Two-dimensional simulations in linear Brinkman flow around solid and through porous obstacles validate the method in comparison with the two heterogeneous direct LBM-ADE schemes with different anti-numerical-diffusion treatment which are proposed and examined in parallel. On the coarse grid, accuracy of the three moments is essentially determined by the free-tunable collision rate in all schemes, and especially TRT-EMM. However, operated within a single periodic cell, the TRT-EMM is many orders of magnitude faster than the direct solvers, numerical-diffusion free, more robust and much more capable for accuracy improving, high Peclet range and free-parameter influence reduction with the mesh refinement. The method is an efficient predicting tool for the Taylor dispersion, asymmetry and peakedness; moreover, it allows for an optimal analysis between the mutual effect of the flow regime, Peclet number, porosity, permeability and obstruction geometry.

Clear water scour around a finite array of cylinders

This experimental study presents clear-water scour and deposition patterns around hexagonal arrays of circular cylinders in steady flow conditions. Understanding the scour processes around such configurations could facilitate the design of several hydraulic and marine engineering structures, such as bridge piers and piles. The flow alteration caused by the examined porous obstacles depends on the solid volume fraction of the obstacles and on the angle of attack of the incoming flow, due to the limited number of cylinders constituting the array. Flume experiments with erodible bed were carried out for four array densities (solid volume fractions: 0.14, 0.20, 0.32 and 0.56) under three different orientations (regular, angled and staggered configurations). The scour/deposition characteristics were obtained by means of laser scanner and the results were compared to solid cylinders of equal circumambient diameter. Different angles of attack of the incoming flow lead to different blockage ratios, which have direct impact on the scour characteristics and deposition patterns. The arrays with the higher solid volume fraction generated scour/deposition patterns similar to solid cylinder, while in the arrays with the lower solid volume fractions, local scour around the individual small cylinders became evident. Finally, considering that the load bearing capacity of a pier basically depends on the area of its cross-section, a comparison of the maximum induced scour depth and volume by the cylinder arrays and the solid cylinder with equal solid cross-sectional area is presented, in order to introduce an alternative pier configuration that induces less scour. The results showed that the array of cylinders could generate 27% less scour volume and 22% less scour depth compared to its single solid cylinder counterpart.

Assessment of Heat Transfer Enhancement Using Metallic Porous Foam Configurations in Laminar Slot Jet Impingement: An Experimental Study

An experimental study using the liquid crystal thermography technique is conducted to investigate the convective heat transfer performance in jet impingement cooling using various porous media configurations. Aluminum porous foams are used in the present study. Four impinging jet configurations are considered: jet impingement (1) without porous media, (2) over the porous heat sink, (3) with porous obstacle case, and (4) through porous passage. These configurations are evaluated on the basis of the convective heat transfer enhancement for two different Reynolds numbers of 400 and 700. Jet impingement with porous heat sink showed deterioration in the average Nusselt number by 9.95% and 18.04% compared to jet impingement without porous media configuration for Reynolds numbers of 400 and 700, respectively. Jet impingement with porous obstacles showed a very negligible enhancement in the average Nusselt number by 3.48% and 2.73% for Reynolds numbers of 400 and 700, respectively. However, jet impingement through porous passage configuration showed a maximum enhancement in the average Nusselt number by 52.71% and 74.68% and stagnation Nusselt numbers by 58.08% and 53.80% compared to the jet impingement without porous medium for Reynolds numbers of 400 and 700, respectively. Within the porous properties considered, it is observed that by decreasing the permeability and porosity the convective heat transfer performance tends to increase.

Active chimney effect using heated porous layers: optimum heat transfer

The purpose of the present work is to treat numerically the problem of the steady mixed convection that occurs in a vertical cylinder, opened at both ends and filled with a succession of three fluid saturated porous elements, namely a partially porous duct. The flow conditions fit with the classical Darcy-Brinkman model allowing analysing the flow structure on the overall domain. The induced heat transfer, in terms of local and average Nusselt numbers, is discussed for various controlling parameters as the porous medium permeability, Rayleigh and Reynolds numbers. The efficiency of the considered system is improved by the injection/suction on the porous matrices frontier. The undertaken numerical exploration particularly highlighted two possible types of flows, with and without fluid recirculation, which principally depend on the mixed convection regime. Thus, it is especially shown that recirculation zones appear in some domain areas under specific conditions, obvious by a negative central velocity and a prevalence of the natural convection effects, i.e., turnoff flow swirls. These latter are more accentuated in the areas close to the porous obstacles and for weak permeability. Furthermore, when fluid injection or suction is considered, the heat transfer increases under suction and reduces under injection.

Flow through a very porous obstacle in a shallow channel.

A theoretical model, informed by numerical simulations based on the shallow water equations, is developed to predict the flow passing through and around a uniform porous obstacle in a shallow channel, where background friction is important. This problem is relevant to a number of practical situations, including flow through aquatic vegetation, the performance of arrays of turbines in tidal channels and hydrodynamic forces on offshore structures. To demonstrate this relevance, the theoretical model is used to (i) reinterpret core flow velocities in existing laboratory-based data for an array of emergent cylinders in shallow water emulating aquatic vegetation and (ii) reassess the optimum arrangement of tidal turbines to generate power in a tidal channel. Comparison with laboratory-based data indicates a maximum obstacle resistance (or minimum porosity) for which the present theoretical model is valid. When the obstacle resistance is above this threshold the shallow water equations do not provide an adequate representation of the flow, and the theoretical model over-predicts the core flow passing through the obstacle. The second application of the model confirms that natural bed resistance increases the power extraction potential for a partial tidal fence in a shallow channel and alters the optimum arrangement of turbines within the fence.

Turbulent heat transfer past a sudden expansion with a porous insert using a nonlinear model

ABSTRACTThis work presents numerical investigations for turbulent flow and heat transfer in a backward-facing step with and without porous inserts. Two classes of the model were employed, namely linear and nonlinear turbulence closures. The entire set of transport equations was discretized by means of the control volume method and the system of algebraic equations obtained was relaxed using the SIMPLE (Semi Implicit Pressure-Linked Equations) method. Results were first validated against the experimental data and the simulations follow experimental values and trends. Computations further indicated that when using the porous insert, the size, shape, and length of the recirculating region were drastically reduced in addition to being pushed toward the channel exit, leading eventually to a complete bubble suppression for thicker inserts. A more permeable medium gave better results in quickly suppressing the circulatory motions. By including porous inserts in the channel, turbulence generated due to the shear inside the recirculating region was damped, whereas high levels of k were concentrated within the permeable structure. Large variations for the skin friction factor along the bottom wall were also smoothed out by placing inserts, spanning from a typical distribution for an unobstructed back-step flow to a standard parallel channel flow distribution as the inserts got ticker. On the other hand, at the upper wall, flow pushed toward the top surface gave rise to a sudden increase of the skin friction factor, which was later stabilized downstream the flow. Heat transfer analysis followed showing damping for Nu at the bottom wall as the thickness of the porous substrate was increased. Overall, the thickness of the insert played a dominant role in changing the final flow and heat transfer characteristics rather than the porosity or permeability of the porous material. Finally, this work indicated that the sudden increase of Nu around the reattachment point, known to be undesirable in many practical situations for causing additional thermomechanical loads on the surface, may by avoided by the use of a porous obstacle past the back-step.

On the boundary layer structure near a highly permeable porous interface

The method of matched asymptotic expansions is used to study the canonical problem of steady laminar flow through a narrow two-dimensional channel blocked by a tight-fitting finite-length highly permeable porous obstacle. We investigate the behaviour of the local flow close to the interface between the single-phase and porous regions (governed by the incompressible Navier–Stokes and Darcy flow equations, respectively). We solve for the flow in these inner regions in the limits of low and high Reynolds number, facilitating an understanding of the nature of the transition from Poiseuille to plug to Poiseuille flow in each of these limits. Significant analytical progress is made in the high Reynolds number limit, and we explore in detail the rich boundary layer structure that occurs. We derive general results for the interfacial stress and for the conditions that couple the flow in the outer regions away from the interface. We consider the three-dimensional generalization to unsteady laminar flow through and around a tight-fitting highly permeable cylindrical porous obstacle within a Hele-Shaw cell. For the high Reynolds number limit, we give the coupling conditions and interfacial stress in terms of the outer flow variables, allowing information from a nonlinear three-dimensional problem to be obtained by solving a linear two-dimensional problem. Finally, we illustrate the utility of our analysis by considering the specific example of time-dependent forced far-field flow in a Hele-Shaw cell containing a porous cylinder with a circular cross-section. We determine the internal stress within the porous obstacle, which is key for tissue engineering applications, and the interfacial stress on the boundary of the porous obstacle, which has applications to biofilm erosion. In the high Reynolds number limit, we demonstrate that the fluid inertia can result in the cylinder experiencing a time-independent net force, even when the far-field forcing is periodic with zero mean.

Dynamics of colloid accumulation under flow over porous obstacles.

The accumulation of colloidal particles to build dense structures from dilute suspensions may follow distinct routes. The mechanical, structural and geometrical properties of these structures depend on local hydrodynamics and colloidal interactions. Using model suspensions flowing into microfabricated porous obstacles, we investigate this interplay by tuning both the flow pattern and the ionic strength. We observe the formation of a large diversity of shapes, and demonstrate that growing structures in turn influence the local velocity pattern, favouring particle deposition either locally or over a wide front. We also show that these structures are labile, stabilised by the flow pushing on them, in low ionic strength conditions, or cohesive, in a gel-like state, at higher ionic strength. The interplay between aggregate cohesion and erosion thus selects preferential growth modes and therefore dictates the final shape of the structure.

Modelling the Effects of a Vegetation Barrier on Road Dust Dispersion

Atmospheric particulate matter (PM) is a well known risk to human health. Vehicular traffic is one of the major sources of particulates in an urban setting.We study a problem of road dust dispersion. Using CFD solver based on RANS equations, we investigate the effect of a vegetation barrier on the concentration of airborne PM induced by road traffic. Simplified 2D model of a porous obstacle adjacent to a road source of two classes of particles serves as an idealization of a real-world situation.Filtering efficiency of the barrier is investigated under varying atmospheric conditions. Our model indicate that the efficiency decreases for increasing wind speed. Effect of atmospheric stratification on~the~air quality behind the barrier is shown to be highly dependent on the wind speed.

Flow structure formed due to interaction of a supersonic jet with a porous obstacle

Results of studying impingement of a supersonic underexpanded air jet onto a finite-thickness porous metal obstacle whose frontal plane is normal to the jet axis and whose side surface is impermeable for the gas flow are reported. The case of a non-porous obstacle of the same diameter is considered for determining the effect of porosity on gas-dynamic characteristics of jet–obstacle interaction.

Pore-scale simulation of fluid flow passing over a porously covered square cylinder located at the middle of a channel, using a hybrid MRT-LBM–FVM approach

A comprehensive study was performed to analyze the unsteady laminar flow characteristics around a porously covered, a fully porous, and a solid squared section cylinder located in the middle of a plane channel. In order to simulate fluid flow inside porous media and porous–fluid interface accurately (minimizing modeling error), the porous region was analyzed in pore scale, using LBM. Additionally, to minimize the LBM-related compressibility error through the porous region, a multi-block multiple relaxation time lattice Boltzmann method (MRT-LBM) was used. Also, to decrease CPU time, a Navier–Stokes flow solver, based on finite volume method and SIMPLE algorithm, was coupled with MRT-LBM to simulate flow around the porous obstacle. It should be noted that the flow inside the porous layer is in continuum regime, and hence, the no-slip boundary condition was used to treat the solid walls inside the porous media. In our simulations, we considered variations of porosity and Reynolds number ranging from 0.75 to 0.94 and from 60 to 240, respectively. The effects of porosity and Reynolds number on vortex pattern, mean drag coefficient, amplitude of lift coefficient, and Strouhal number were investigated. Comparison of our results with the ones obtained using Open FOAM, as well as published by others, shows the suitable accuracy of our computations. It is seen that at low Reynolds numbers or at low porosities, where the mean flow does not have large enough momentum to penetrate porous media, the resulting flow field and aerodynamic coefficients are relatively close for three different configurations used. However, as the flow Reynolds number or permeability increases, the mean flow penetrates easier into the porous media and thus provides different shedding characteristics and aerodynamic coefficients for different obstacle shapes.