From Rayleigh-Bénard convection to porous-media convection: how porosity affects heat transfer and flow structure

Abstract

We perform a numerical study of the heat transfer and flow structure of Rayleigh-Bénard (RB) convection in (in most cases regular) porous media, which are comprised of circular, solid obstacles located on a square lattice. This study is focused on the role of porosity $\varphi$ in the flow properties during the transition process from the traditional RB convection with $\varphi =1$ (so no obstacles included) to Darcy-type porous-media convection with $\varphi$ approaching 0. Simulations are carried out in a cell with unity aspect ratio, for the Rayleigh number $Ra$ from $10^5$ to $10^{10}$ and varying porosities $\varphi$, at a fixed Prandtl number $Pr=4.3$, and we restrict ourselves to the two dimensional case. For fixed $Ra$, the Nusselt number $Nu$ is found to vary non-monotonously as a function of $\varphi$; namely, with decreasing $\varphi$, it first increases, before it decreases for $\varphi$ approaching 0. The non-monotonous behaviour of $Nu(\varphi )$ originates from two competing effects of the porous structure on the heat transfer. On the one hand, the flow coherence is enhanced in the porous media, which is beneficial for the heat transfer. On the other hand, the convection is slowed down by the enhanced resistance due to the porous structure, leading to heat transfer reduction. For fixed $\varphi$, depending on $Ra$, two different heat transfer regimes are identified, with different effective power-law behaviours of $Nu$ vs $Ra$, namely, a steep one for low $Ra$ when viscosity dominates, and the standard classical one for large $Ra$. The scaling crossover occurs when the thermal boundary layer thickness and the pore scale are comparable. The influences of the porous structure on the temperature and velocity fluctuations, convective heat flux, and energy dissipation rates are analysed, further demonstrating the competing effects of the porous structure to enhance or reduce the heat transfer.

References in corpus (23)

• An Immersed Boundary Method with Direct Forcing for the Simulation of Particulate Flows
• Large scale dynamics in turbulent Rayleigh-Benard convection
• Scaling in thermal convection: A unifying theory
• Thermal convection for large Prandtl numbers
• Radial boundary layer structure and Nusselt number in Rayleigh-Benard convection
• Flow reversals in thermally driven turbulence
• Comparison between two and three dimensional Rayleigh-Bénard convection
• Prandtl-, Rayleigh-, and Rossby-number dependence of heat transport in turbulent rotating Rayleigh-Benard convection
• Roughness-facilitated local 1/2 scaling does not imply the onset of the ultimate regime of thermal convection
• Transitions between turbulent states in rotating Rayleigh-Benard convection
• Confined Rayleigh-Bénard, Rotating Rayleigh-Bénard, and Double Diffusive Convection: A unifying view on turbulent transport enhancement through coherent structure manipulation
• Controlling heat transport and flow structures in thermal turbulence using ratchet surfaces
• Heat transport in boiling turbulent Rayleigh-Bénard convection
• A parallel interaction potential approach coupled with the immersed boundary method for fully resolved simulations of deformable interfaces and membranes
• Solutal convection in porous media: Comparison between boundary conditions of constant concentration and constant flux
• Counter-gradient heat transport in two-dimensional turbulent Rayleigh-Bénard convection
• The distribution of local fluxes in porous media
• Scaling laws and flow structures of double diffusive convection in the finger regime
• Salinity transfer in bounded double diffusive convection
• A fast moving least squares approximation with adaptive Lagrangian mesh refinement for large scale immersed boundary simulations
• Sidewall effects in Rayleigh-Bénard convection
• Robustness of heat-transfer in confined inclined convection at high-Prandtl-number
• Buoyancy-driven flow through a bed of solid particles produces a new form of Rayleigh-Taylor turbulence

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