Rough surfaces have been widely used as an efficient way to enhance the heat-transfer efficiency in turbulent thermal convection. In this paper, however, we show that roughness does not always mean a heat-transfer enhancement, but in some cases it can also reduce the overall heat transport through the system. To reveal this, we carry out numerical investigations of turbulent Rayleigh–Bénard convection over rough conducting plates. Our study includes two-dimensional (2D) simulations over the Rayleigh number range $10^{7}\leqslant Ra\leqslant 10^{11}$ and three-dimensional (3D) simulations at $Ra=10^{8}$. The Prandtl number is fixed to $Pr=0.7$ for both the 2D and the 3D cases. At a fixed Rayleigh number $Ra$, reduction of the Nusselt number $Nu$ is observed for small roughness height $h$, whereas heat-transport enhancement occurs for large $h$. The crossover between the two regimes yields a critical roughness height $h_{c}$, which is found to decrease with increasing $Ra$ as $h_{c}\sim Ra^{-0.6}$. Through dimensional analysis, we provide a physical explanation for this dependence. The physical reason for the $Nu$ reduction is that the hot/cold fluid is trapped and accumulated inside the cavity regions between the rough elements, leading to a much thicker thermal boundary layer and thus impeding the overall heat flux through the system.

We investigate the dynamic couplings between particles and fluid in turbulent Rayleigh–Bénard (RB) convection laden with isothermal inertial particles. Direct numerical simulations combined with the Lagrangian point-particle mode were carried out in the range of Rayleigh number $1\times 10^6 \le {Ra}\le 1 \times 10^8$ at Prandtl number ${Pr}=0.678$ for three Stokes numbers ${St_f}=1 \times 10^{-3}$ , $8 \times 10^{-3}$ and $2.5 \times 10^{-2}$ . It is found that the global heat transfer and the strength of turbulent momentum transfer are altered a small amount for the small Stokes number and large Stokes number as the coupling between the two phases is weak, whereas they are enhanced a large amount for the medium Stokes number due to strong coupling of the two phases. We then derived the exact relation of kinetic energy dissipation in the particle-laden RB convection to study the budget balance of induced and dissipated kinetic energy. The strength of the dynamic coupling can be clearly revealed from the percentage of particle-induced kinetic energy over the total induced kinetic energy. We further derived the power law relation of the averaged particles settling rate versus the Rayleigh number, i.e. $S_p/(d_p/H)^2{\sim} Ra^{1/2}$ , which is in remarkable agreement with our simulation. We found that the settling and preferential concentration of particles are strongly correlated with the coupling mechanisms.

Abstract

External modulation on thermal convection has been studied extensively to achieve the control of flow structures and heat-transfer efficiency. In this paper, we carry out direct numerical simulations on Rayleigh–Bénard convection accounting for both the modulation of wall shear and roughness over the Rayleigh number range $1.0 \times 10^6 \le Ra \le 1.0 \times 10^8$ , the wall shear Reynolds number range $0 \le Re_w \le 5000$ , the aspect-ratio range $2 \le \varGamma \le 4{\rm \pi}$ , and the dimensionless roughness height range $0 \le h \le 0.2$ at fixed Prandtl number $Pr = 1$ . Under the combined actions of wall shear and roughness, with increasing $Re_w$ , the heat flux is initially enhanced in the buoyancy-dominant regime, then has an abrupt transition near the critical shear Reynolds number $Re_{w,cr}$ , and finally enters the purely diffusion regime dominated by shear. Based on the crossover of the kinetic energy production between the buoyancy-dominant and shear-dominant regimes, a physical model is proposed to predict the transitional scaling behaviour between $Re_{w,cr}$ and $Ra$ , i.e. $Re_{w,cr} \sim Ra^{9/14}$ , which agrees well with our numerical results. The reason for the observed heat-transport enhancement in the buoyancy-dominant regime is further explained by the fact that the moving rough plates introduce an external shear to strengthen the large-scale circulation (LSC) in the vertical direction and serve as a conveyor belt to increase the chances of the interaction between the LSC and secondary flows within cavities, which triggers more thermal plumes, efficiently transports the trapped hot (cold) fluids outside cavities.

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