Vapor condensation in Rayleigh–Bénard convection

Abstract

In this work, the condensation process in the Rayleigh–Bénard convection is studied by a combination of theoretical analysis and numerical simulations. Depending on the domain size, three different patterns, namely, no condensation, critical condensation, and periodic condensation, are identified. By applying the order analysis to the energy equation, we show that the heat fluctuation is responsible to overcome the energy barrier of condensation and thus propose a new dimensionless number to describe the critical condition of condensation, which corresponds to zero value of the heat fluctuation. In addition, through the order analysis, a scaling law is established to quantify the condensation period when periodic condensation occurs. The scaling relations derived from the order analysis are well validated by the hybrid lattice Boltzmann finite difference simulations, where the Rayleigh number and the Prandtl number vary over the ranges of 104 ≤ Ra ≤ 106 and 1 ≤ Pr ≤ 10, respectively.

Analysis of the heat transfer fluctuations in the Rayleigh–Bénard convection of concentrated emulsions with finite-size droplets

“…[23][24][25] In the presence of multi-phase fluids, some studies also revealed enhanced heat transfer in comparison to the single-phase case, especially in proximity of the critical point, due to an increased occurrence of droplet condensation, or in the presence of the melting of a solid above a liquid melt. 26,27 RBC laden with bubbles/droplets has also been numerically studied in recent works, 4,[28][29][30][31][32][33] showing how the heat transport properties can be affected by the presence of the dispersed phase, 4,[28][29][30] the surface wettability, 32 the condensation conditions, 31 and the presence of non-trivial correlations between distant droplets. 33 Furthermore, experiments show that the introduction of a small percentage of a second component in a pure water solution is sufficient to affect the overall heat transfer.…”