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Register a new userPore-scale investigation on natural convection melting in a square cavity with gradient porous media
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In this paper, a numerical study on the melting behavior of phase change material (PCM) with gradient porous media has been carried out at the pore scales. In order to solve the governing equations, a pore-scale lattice Boltzmann method with the double distribution functions is used, in which a volumetric LB scheme is employed to handle the boundary. The Monte Carlo random sampling is adopted to generate a microstructure of two-dimensional gradient foam metal which are then used to simulate the solid-liquid phase transition in the cavity. The effect of several factors, such as gradient porosity structure, gradient direction, Rayleigh number and particle diameters on the liquid fraction of PCM are systematically investigated. It is observed that the presence of gradient media affect significantly the melting rate and shortens full melting time compared to that for constant porosity by enhancing natural convection. The melting time of positive and negative gradients will change with Rayleigh number, and there is a critical value for Rayleigh number. Specifically, when Rayleigh number is below the critical value, the positive gradient is more advantageous, and when Rayleigh number exceeds the critical value, the negative gradient is more advantageous. Moreover, smaller particle diameters would lead to lower permeability and larger internal surfaces for heat transfer.
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Natural convection in porous media is a fundamental process for the long-term storage of CO2 in deep saline aquifers. Typically, details of mass transfer in porous media are inferred from the numerical solution of the volume-averaged Darcy-Oberbeck-Boussinesq (DOB) equations, even though these equations do not account for the microscopic properties of a porous medium. According to the DOB equations, natural convection in a porous medium is uniquely determined by the Rayleigh number. However, in contrast with experiments, DOB simulations yield a linear scaling of the Sherwood number with the Rayleigh number (Ra) for high values of Ra (Ra>>1,300). Here, we perform Direct Numerical Simulations (DNS), fully resolving the flow field within the pores. We show that the boundary layer thickness is determined by the pore size instead of the Rayleigh number, as previously assumed. The mega- and proto- plume sizes increase with the pore size. Our DNS results exhibit a nonlinear scaling of the Sherwood number at high porosity, and for the same Rayleigh number, higher Sherwood numbers are predicted by DNS at lower porosities. It can be concluded that the scaling of the Sherwood number depends on the porosity and the pore-scale parameters, which is consistent with experimental studies.
We study the transport of inertial particles in water flow in porous media. Our interest lies in understanding the accumulation of particles including the possibility of clogging. We propose that accumulation can be a result of hydrodynamic effects: the tortuous paths of the porous medium generate regions of dominating strain/vorticity, which favour the accumulation/dispersion of the inertial particles. Numerical simulations show that essentially two accumulation regimes are identified: for low and for high flow velocities. When particles accumulate in high-velocity regions, at the entrance of a pore throat, a clog is formed. The formation of a clog significantly modifies the flow, as the partial blockage of the pore causes a local redistribution of pressure. This redistribution can divert the upstream water flow into neighbouring pores. Moreover, we show that accumulation in high velocity regions occurs in heterogeneous media, but not in homogeneous media, where we refer to homogeneity with respect to the distribution of the pore throat diameters.
In a range of physical systems, the first instability in Rayleigh-Bernard convection between nearly thermally insulating horizontal plates is large scale. This holds for thermal convection of fluids saturating porous media. Large-scale thermal convection in a horizontal layer is governed by remarkably similar equations both in the presence of a porous matrix and without it, with only one additional term for the latter case, which, however, vanishes under certain conditions (e.g., two-dimensional flows or infinite Prandtl number). We provide a rigorous derivation of long-wavelength equations for a porous layer with inhomogeneous heating and possible pumping.
We investigate the elastoviscoplastic flow through porous media by numerical simulations. We solve the Navier-Stokes equations combined with the elastoviscoplastic model proposed by Saramito for the stress tensor evolution. In this model, the material behaves as a viscoelastic solid when unyielded, and as a viscoelastic Oldroyd-B fluid for stresses higher than the yield stress. The porous media is made of a symmetric array of cylinders, and we solve the flow in one periodic cell. We find that the solution is time-dependent even at low Reynolds numbers as we observe oscillations in time of the unyielded region especially at high Bingham numbers. The volume of the unyielded region slightly decreases with the Reynolds number and strongly increases with the Bingham number; up to 70% of the total volume is unyielded for the highest Bingham numbers considered here. The flow is mainly shear dominated in the yielded region, while shear and elongational flow are equally distributed in the unyielded region. We compute the relation between the pressure drop and the flow rate in the porous medium and present an empirical closure as function of the Bingham and Reynolds numbers. The apparent permeability, normalized with the case of Newtonian fluids, is shown to be greater than 1 at low Bingham numbers, corresponding to lower pressure drops due to the flow elasticity, and smaller than 1 for high Bingham numbers, indicating larger dissipation in the flow owing to the presence of the yielded regions. Finally we investigate the effect of the Weissenberg number on the distribution of the unyielded regions and on the pressure gradient.
Immiscible fluid-fluid displacement in porous media is of great importance in many engineering applications, such as enhanced oil recovery, agricultural irrigation, and geologic CO2 storage. Fingering phenomena, induced by the interface instability, are commonly encountered during displacement processes and somehow detrimental since such hydrodynamic instabilities can significantly reduce displacement efficiency. In this study, we report a possible adjustment in pore geometry which aims to suppress the capillary fingering in porous media with hierarchical structures. Through pore-scale simulations and theoretical analysis, we demonstrate and quantify combined effects of wettability and hierarchical geometry on displacement patterns, showing a transition from fingering to compact mode. Our results suggest that with a higher porosity of the 2nd-order porous structure, the displacement can keep compact across a wider range of wettability conditions. Combined with our previous work on viscous fingering in such media, we can provide a complete insight into the fluid-fluid displacement control in hierarchical porous media, across a wide range of flow conditions from capillary- to viscous-dominated modes. The conclusions of this work can benefit the design of microfluidic devices, as well as tailoring porous media for better fluid displacement efficiency at the field scale.
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