Vapor condensation in Rayleigh-Bénard convection

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.