Dynamics of a convective system with a floating extended thermal insulator

Abstract

The paper presents an experimental study of a convective flow in a rectangular cell of length L, width W and depth H, filled with water, heated from the bottom and cooled from the top, with a heat-insulating disk floating at a fixed height h (the disk diameter is slightly smaller than the cavity width). Such a system exhibits a range of modes, including periodic movements of the float along the cavity, chaotic motions of various types, and drift of the disk to the edge of the cavity without further movements. In addition to the Rayleigh, Prandtl numbers and the cavity dimension ratio (L/H), usual for convective systems, the structure of convective flows in the cavity depends on geometric parameters associated with the floating disk: the relative height of the body position (h/H) and the body size to the cavity length ratio (D/L). Experiments were performed for fixed W=100mm, H=40mm, D=98mm, and h=4mm, but different lengths 170mm < L < 500mm. It is shown that periodic motions occur only in a limited range of the body size to the cavity size ratio. As the length of the cavity increases, a chaotic mode of intermittent motion of the disc occurs; at the maximum cavity length considered, the disk is shifted to the extreme position and remains there. The structure of the convective flow at different phases of periodic motions has been reconstructed by PIV (particle image velocimetry) technique.

A random 2D walk of a submerged free-floating disc in a convective layer

“…Even in the 1D case, a number of parameters control the behaviour of the convective flow and motion of the free-floating disc. The governing parameters, besides the Rayleigh and Prandtl numbers, are geometrical characteristics, two aspect ratios Γ 1 = L/H and Γ 2 = L/D, and the relative vertical disc location d = h/H (Popova and Frik, 2003;Popova et al, 2022).…”

“…Recent experiments by Popova et al (2022) performed for various cells have shown that the structure and dynamics of convective flows with a free-floating insulating disc strongly depend not only on the basic control parameters for convective systems, such as Rayleigh number, Prandtl number, and aspect ratio, but also on geometric parameters associated with the floating disc: its submergence depth and its aspect ratio to the cavity length. It has been shown that periodic motions occur only within a limited range of the body-to-cavity aspect ratio.…”