Session T17: Free Convection and Rayleigh-Benard III

A Free Boundary Takes a Surprising Spin in RBC

Inspired by a geophysical phenomenon, as the solid core of the earth undergoes the so-called super-rotation, we study the dynamics of a solid body immersed in a thermally convective fluid. In our experiment, the freely-moving solid body is a symmetric plate that closely interacts with the large-scale circulation (LSC) in a symmetric fluid cavity. Symmetry breaking bifurcations are observed as the plate corotates with the LSC. The seemingly steady rotational rate increases monotonically with the Rayleigh number (Ra) and its rotation direction also switches spontaneously, also happening at an ever increasing rate with Ra. Whether our experimental findings can be related to the geophysical process remains an open question.   

Experimental study of a turbulent natural convection flow in a cubic enclosure with a large inner block partially heated

In this study, a turbulent natural convection flow occurring inside a closed cavity is investigated. The top, bottom, front and back walls of the cavity are adiabatic whereas the two other vertical walls are at imposed temperature (equal to the ambiant temperature of the room). A large inner block is placed inside the cavity. A vertical face of this block is heated, inducing a natural convection flow. The dynamical behavior of the flow is investigated using Particle Image Velocimetry and its thermal behavior using micro-thermocouples. Boundary layers, recirculation zones and instabilities developing inside the cavity are highlighted and discussed. A focus is made on a boundary layer instability of Tollmien-Schlichting type and the subsequent formation of an oscillating buoyant jet.   

Morphology of melting ice surfaces

Melting surfaces, for example in glaciers and icebergs, develop complex underwater patterns, including scallops. In this study we look at formation of scallops for an ice block (L ≈ 30 cm) in quiescent salty water reaching Ra ≈ 10¹¹. Using profilometry techniques, in particular the spatiotemporal phase shifting method (ST-PSM), we obtain the 3-D surface morphology of the ice as a function of time. We characterize the typical timescale of the pattern-formation, the scallops wavelength and their drift velocity. We also show that the melting rate and the local slope of the ice are strongly correlated.   

Heat transfer enhancement in turbulent Rayleigh Bénard convection with liquid-liquid emulsions

In this study, we investigate the heat transfer in a liquid-liquid emulsion and flow properties in a three-dimensional Rayleigh-Bénard convection cell at fixed Ra = 1e8 and Pr = 4. By varying the droplet volume fraction (Φ) from 0 to 0.5, while keeping thermophysical property ratios constant at unity, we uncover intriguing insights. The introduction of droplets into the single-phase flow significantly enhances heat transfer between the plates, resulting in a remarkable 9% increase in the Nusselt number for Φ = 0.5. This enhancement is attributed to augmented diffusion near the walls and convection in the central region due to the presence of dispersed droplets, more at higher volume fractions. Despite the decrease in carrier-phase diffusion and convection heat transfer at higher Φ, droplets exhibit increased rates of diffusion and convection, leading to an overall enhancement in total diffusion and convection. Moreover, we examine turbulent kinetic energy budgets, providing deeper insights into the emulsion dynamics in the Rayleigh-Bénard convection cell. At higher concentrations of secondary phase, we observe a simultaneous increase in both production and energy dissipation. Finally, we investigate the influence of different viscosity ratios on heat transfer rates. Remarkably, utilizing more viscous droplets (μd / μc = 10) in a moderately concentrated flow (Φ = 0.2) shows a significant enhancement in heat transfer rate, which becomes less pronounced as the droplet volume fraction increases (Φ = 0.5).   

On the heat transfer fluctuations in concentrated emulsions with finite-size droplets under Rayleigh-Bénard thermal convection

In this study, we utilize numerical simulations at the mesoscale to investigate the heat transfer mechanism in Rayleigh-Bénard convection of emulsions with finite-size droplets, specifically focusing on the regime just above the transition from conduction to thermal convection. In this regime, we observe anomalous fluctuations in heat transfer, which are attributed to the collective motion of droplets [1]. Employing the lattice Boltzmann TLBfind code [2], we present a comprehensive understanding of the correlation between macroscopic heat transfer fluctuations and droplet statistics at the mesoscale. Notably, we systematically increase the droplet concentration and examine the emergence of these fluctuations, alongside the segregation of "extreme events" within the boundary layers. Additionally, we conduct a statistical analysis involving droplet displacements to characterize the spatial extension (S) and duration (T) of coherent droplet motion associated with these extreme events. Our findings reveal that a power-law behavior in the probability distribution function of S and T is observed only for very high droplet concentrations, indicative of an avalanche-like behavior [3].

References

[1] F. Pelusi et al, Soft Matter 17(13), 3709 - 3721 (2021).

[2] F. Pelusi et al, Comp. Phys. Comm. 273, 108259 (2022).

[3] F. Pelusi et al, submitted paper arXiv:2306.02404v1   

What shape melts the slowest?

We investigate the melting rate of a variety of shapes of ice melting in quiescent water using direct numerical simulations. We vary the size and shape of the ice, varying the Rayleigh number from 500 to 10^9. The shape for which the ice melt slowest ("optimal shape") strongly depends on the Rayleigh number. Due to the density anomaly of water, also the ambient temperature dramatically affects the optimal melting shape. We rationalize the obtained numerical results, based on the flow field.   

Melting of olive oil

We experimentally and theoretically study the melting process of frozen olive oil in water (Ra = O(10^8)). The melt is immiscible with the surrounding, creating a thin viscous film as it melts. We derive an analytical expression for the film thickness and the melt rate for three different geometries. We perform experiments for these geometries and compare these to our theoretical model.