We study the topology and the temporal dynamics of turbulent Rayleigh–Bénard convection in a liquid metal with a Prandtl number of 0.03 located inside a box with a square base area and an aspect ratio of $\varGamma = 5$ . Experiments and numerical simulations are focused on the Rayleigh number range $6.7 \times 10^{4} \leqslant Ra \leqslant 3.5 \times 10^{5}$ , where a new cellular flow regime has been reported previously (Akashi et al., Phys. Rev. Fluids, vol. 4, 2019, 033501). This flow structure shows symmetries with respect to the vertical planes crossing at the centre of the container. The dynamic behaviour is dominated by strong three-dimensional oscillations with a period length that corresponds to the turnover time. Our analysis reveals that the flow structure in the $\varGamma = 5$ box corresponds in key features to the jump rope vortex structure, which has recently been discovered in a $\varGamma = 2$ cylinder (Vogt et al., Proc. Natl Acad. Sci. USA, vol. 115, 2018, pp. 12674–12679). While in the $\varGamma = 2$ cylinder a single jump rope vortex occurs, the coexistence of four recirculating swirls is detected in this study. Their approach to the lid or the bottom of the convection box causes a temporal deceleration of both the horizontal velocity at the respective boundary and the vertical velocity in the bulk, which in turn is reflected in Nusselt number oscillations. The cellular flow regime shows remarkable similarities to properties commonly attributed to turbulent superstructures.

Turbulent Rayleigh-Bénard convection was investigated within a liquid metal layer, Prandtl number Pr = 0.03, in a square vessel having a moderate aspect ratio, = 5. Laboratory experiments were performed at moderate Rayleigh numbers, 7.9 × 10 3 < Ra < 3.5 × 10 5 . Ultrasonic velocity profiling was used to visualize the spatiotemporal flow structure in two horizontal planes, while temperature fluctuations were monitored simultaneously in the fluid layer. By using multiple ultrasonic sensors, a grid of orthogonal measurement lines was created. This configuration enabled the identification of coherent flow structures showing periodic oscillations. In particular, oscillatory roll-like structures were observed for Ra 6 × 10 4 , while the transition to a new-found, fully three-dimensional cellular structure occurs around Ra = 7 × 10 4 . The Fourier analysis of the temperature fluctuations indicates that the convection reaches the developed state of thermal turbulence at this Ra number. This cellular structure of the flow field is recognized as a representation of the large-scale circulation in thermal turbulence for the specific situation of confined convection in the rectangular vessel. The transition from laminar convection to thermal turbulence manifests itself in the occurrence of unstable intermediate regimes accompanied by a stepwise increment in the horizontal scale. We suggest scaling laws for the characteristic velocity and the dominating oscillation frequency and based on that for the horizontal length scale as a function of the Ra number. The comparison to corresponding values of characteristic length scales published for thermal convection in air in larger aspect ratios [

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In the present work, the dynamics of a downward gas injection into a liquid metal bath is studied using a numerical modeling approach, and validated with experimental data. As in a top-submerged-lance (TSL) smelter, gas is injected through the lance into the melt. By this means, the properties of the liquid are closer to the actual industrial process than the typically used water/glycerol–air/helium systems. The experimental activity was carried out in a quasi-2D vessel $$(144\times 144\times 12\,{\hbox {mm}}^{3})$$ ( 144 × 144 × 12 mm 3 ) filled with GaInSn, a metal alloy with eutectic at room temperature. Ar was used as the inert gas. The structure and behavior of the gas phase were visualized and quantitatively analyzed by X-ray radiography and high-speed imaging. Computational Fluid Dynamics (CFD) was applied to simulate the multiphase flow in the vessel and the Volume Of Fluid (VOF) model chosen to track the interface using a geometric reconstruction of the interface. Three different vertical lance positions were investigated, applying a gas flow rate of $$Q_{\text {gas}}=6850\,{\hbox {cm}}^{3}/{\hbox {min}}.$$ Q gas = 6850 cm 3 / min . The CFD model is able to predict the bubble detachment frequency, the average void fraction distributions, and the bubble size and hydrodynamic behavior, demonstrating its applicability to simulate such complex multiphase systems. The use of numerical models also provides a deep insight into fluid dynamics to study particular phenomena such as bubble break-up and free surface oscillations.