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Register a new userLarge-Scale Thermal Convection in a Horizontal Porous Layer
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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.
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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.
We simulate three-dimensional, horizontally periodic Rayleigh-Benard convection between free-slip horizontal plates, rotating about a distant horizontal axis. When both the temperature difference between the plates and the rotation rate are sufficiently large, a strong horizontal wind is generated that is perpendicular to both the rotation vector and the gravity vector. The wind is turbulent, large-scale, and vertically sheared. Horizontal anisotropy, engendered here by rotation, appears necessary for such wind generation. Most of the kinetic energy of the flow resides in the wind, and the vertical turbulent heat flux is much lower on average than when there is no wind.
We consider the problem of horizontal convection in which non-uniform buoyancy, $b_{rm s}(x,y)$, is imposed on the top surface of a container and all other surfaces are insulating. Horizontal convection produces a net horizontal flux of buoyancy, $mathbf{J}$, defined by vertically and temporally averaging the interior horizontal flux of buoyancy. We show that $overline{mathbf{J}cdotmathbf{ abla}b_{rm s}}=-kappalangle|boldsymbol{ abla}b|^2rangle$; overbar denotes a space-time average over the top surface, angle brackets denote a volume-time average and $kappa$ is the molecular diffusivity of buoyancy $b$. This connection between $mathbf{J}$ and $kappalangle|boldsymbol{ abla}b|^2rangle$ justifies the definition of the horizontal-convective Nusselt number, $Nu$, as the ratio of $kappa langle|boldsymbol{ abla}b|^2rangle$ to the corresponding quantity produced by molecular diffusion alone. We discuss the advantages of this definition of $Nu$ over other definitions of horizontal-convective Nusselt number currently in use. We investigate transient effects and show that $kappa langle|boldsymbol{ abla}b|^2rangle$ equilibrates more rapidly than other global averages, such as the domain averaged kinetic energy and bottom buoyancy. We show that $kappalangle|boldsymbol{ abla} b|^2rangle$ is essentially the volume-averaged rate of Boussinesq entropy production within the enclosure. In statistical steady state, the interior entropy production is balanced by a flux of entropy through the top surface. This leads to an equivalent surface Nusselt number, defined as the surface average of vertical buoyancy flux through the top surface times the imposed surface buoyancy $b_{rm s}(x,y)$. In experiments it is likely easier to evaluate the surface entropy flux, rather than the volume integral of $|mathbf{ abla}b|^2$ demanded by $kappalangle|mathbf{ abla}b|^2rangle$.
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.
The transient processes of a turbulent large-scale convective circulation (LSC) in a cubic cell are investigated using large-eddy simulations for Rayleigh number $Ray=10^8$ and Prandtl number $Pran=0.7$. For the first time, we have explicitly shown that LSC is accompanied by large-scale azimuthal flows with non-zero total angular momentum. It is also shown that solid-body rotation of the entire fluid is not realized. It is found that correlation between rotation of LSC plane and the mean azimuthal motion is high during quasiperiodic oscillations of LSC near the diagonal plane and relatively weak during LSC reorientations. We propose a new plausible scenario for the reorientations of the LSC in a cube that does not involve a mean azimuthal flow. Instead of a single-roll, we introduce the superposition of a pair of large-scale orthogonal quasi-two-dimensional (Q2D) rolls and the reorientation of the LSC occurs as a result of the cessation of one of the Q2D rolls. This scenario is consistent with all known experimental and numerical data.
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