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.

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.

Experimental Investigation on Convective Heat Transfer Enhancement of Laminar Slot Jet Impingement in the Presence of Porous Medium

An experimental study using Liquid crystal thermography technique is conducted to study the convective heat transfer enhancement in jet impingement cooling in the presence of porous media. Aluminium porous sample of 10 PPI with permeability 2.48e−7 and porosity 0.95 is used in the present study. Results are presented for two different Reynolds number 400 and 700 with four different configurations of jet impingement (1) without porous foams (2) over porous heat sink (3) with porous obstacle case (4) through porous passage. Jet impingement with porous heat sink showed a deterioration in average Nusselt number by 10.5% and 18.1% for Reynolds number of 400 and 700 respectively when compared with jet impingement without porous heat sink configuration. The results show that for Reynolds number 400, jet impingement through porous passage augments average Nusselt number by 30.73% whereas obstacle configuration enhances the heat transfer by 25.6% over jet impingement without porous medium. Similarly for Reynolds number 700, the porous passage configuration shows average Nusselt number enhancement by 71.09% and porous obstacle by 33.4 % over jet impingement in the absence of porous media respectively.

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.

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.