Dynamics of a submerged plate of different optical properties in a heated by radiation convective cell

Abstract

Thermal convection in a fluid layer heated by radiation from above, in which a horizontal plate with different optical properties floats at a fixed depth, has been studied experimentally and numerically. The plate floats near the bottom and is realized in the experimental setup as a disk with a diameter slightly smaller than the cavity width, which determines the one-dimensional character of its displacements. The numerical modeling is performed in a two-dimensional formulation, which implies a square shape of the plate. Four versions of the optical properties of the disk are considered: absorbing, transparent, reflecting, and mixed, i.e., partly reflecting - partly transmitting. Both experiments and simulations have shown that a plate that absorbs or transmits all radiation does not drift in the convective flow, while a mirror-reflecting plate can lead to a stable periodic oscillations (‘convective pendulum’ mode). The dynamics of a plate that partially transmits the incident radiation and reflects the rest of the radiation flux is studied for the whole range of transmittance $K$ (the ratio of the transmitted radiation to the incident radiation) from zero to one. It is shown that $K$ is a governing parameter of the system. Changes of transmittance provide variety of regimes from the quasi-periodic plate motions to the very complex dynamics with chaotic wandering and long idle times at the sidewall.The numerical simulations were carried out for a wide range of radiation fluxes. Over the whole range considered, the mirror reflecting plate exhibits the convective pendulum mode. It is shown that the transition from the first to the second type of boundary conditions has no particular influence on the character of the motion, in contrast to the vertical location of the plate. The intensity of the convective flow is characterized by the Reynolds number, which follows a power law $\mathrm{Re}\sim {\mathrm{Ra}}^{\alpha }$, with a slightly larger value of the scaling exponent compared to classical Rayleigh–Bénard convection (0.59 versus 0.5). The plate motions accelerate with the convective flows and the plate oscillation frequency increases with the Reynolds number. The Nusselt number, which determines the dimensionless convective heat flux, follows the usual law for convective systems $\mathrm{Nu}\sim {\mathrm{Ra}}^{0.28}$.