Structure of large-scale flows and their oscillation in the thermal convection of liquid gallium

Magnetoconvection transient dynamics by numerical simulation

We investigate the transient and stationary buoyant motion of the Rayleigh-Bénard instability when the fluid layer is subjected to a vertical, steady magnetic field. For Rayleigh number, Ra, in the range 10³-10⁶, and Hartmann number, Ha, between 0 and 100, we performed three-dimensional direct numerical simulations. To predict the growth rate and the wavelength of the initial regime observed with the numerical simulations, we developed the linear stability analysis beyond marginal stability for this problem. We analyzed the pattern of the flow from linear to nonlinear regime. We observe the evolution of steady state patterns depending on [Formula: see text] and Ha. In addition, in the nonlinear regime, the averaged kinetic energy is found to depend on Ra and to be independent of Ha in the studied range.

Ultrasound Velocity Measurement in a Liquid Metal Electrode

A growing number of electrochemical technologies depend on fluid flow, and often that fluid is opaque. Measuring the flow of an opaque fluid is inherently more difficult than measuring the flow of a transparent fluid, since optical methods are not applicable. Ultrasound can be used to measure the velocity of an opaque fluid, not only at isolated points, but at hundreds or thousands of points arrayed along lines, with good temporal resolution. When applied to a liquid metal electrode, ultrasound velocimetry involves additional challenges: high temperature, chemical activity, and electrical conductivity. Here we describe the experimental apparatus and methods that overcome these challenges and allow the measurement of flow in a liquid metal electrode, as it conducts current, at operating temperature. Temperature is regulated within ±2 °C using a Proportional-Integral-Derivative (PID) controller that powers a custom-built furnace. Chemical activity is managed by choosing vessel materials carefully and enclosing the experimental setup in an argon-filled glovebox. Finally, unintended electrical paths are carefully prevented. An automated system logs control settings and experimental measurements, using hardware trigger signals to synchronize devices. This apparatus and these methods can produce measurements that are impossible with other techniques, and allow optimization and control of electrochemical technologies like liquid metal batteries.

Convection patterns in a liquid metal under an imposed horizontal magnetic field

We performed laboratory experiments of Rayleigh-Bénard convection with liquid gallium under various intensities of a uniform imposed horizontal magnetic field. An ultrasonic velocity profiling method was used to visualize the spatiotemporal structure of the flows with simultaneous monitoring of the temperature fluctuations in the liquid gallium layer. The explored Rayleigh numbers Ra range from the critical value for onset of convection to 10(5); the Chandrasekhar number Q covers values up to 1100. A regime diagram of the convection patterns was established in relation to the Ra and Q values for a square vessel with aspect ratio 5. We identified five flow regimes: (I) a fluctuating large-scale pattern without rolls, (II) weakly constrained rolls with fluctuations, (III) a continuous oscillation of rolls, (IV) repeated roll number transitions with random reversals of the flow direction, and (V) steady two-dimensional (2D) rolls. These flow regimes are classified by the Ra/Q values, the ratio of the buoyancy to the Lorentz force. Power spectra from the temperature time series indicate that regimes I and II have the features of developed turbulence, while the other regimes do not. The region of steady 2D rolls (Busse balloon) extends to high Ra values in the present setting by a horizontal magnetic field and regime V is located inside the Busse balloon. Concerning the instabilities of the steady 2D rolls, regime III is the traveling wave convection developed from the oscillatory instability. Regime IV can be regarded as a state of phase turbulence, which is induced by intermittent occurrences of the skewed-varicose instability.

Turbulent convection in liquid metal with and without rotation

The magnetic fields of Earth and other planets are generated by turbulent, rotating convection in liquid metal. Liquid metals are peculiar in that they diffuse heat more readily than momentum, quantified by their small Prandtl numbers, Pr << 1. Most analog models of planetary dynamos, however, use moderate Pr fluids, and the systematic influence of reducing Pr is not well understood. We perform rotating Rayleigh-Bénard convection experiments in the liquid metal gallium (Pr = 0.025) over a range of nondimensional buoyancy forcing (Ra) and rotation periods (E). Our primary diagnostic is the efficiency of convective heat transfer (Nu). In general, we find that the convective behavior of liquid metal differs substantially from that of moderate Pr fluids, such as water. In particular, a transition between rotationally constrained and weakly rotating turbulent states is identified, and this transition differs substantially from that observed in moderate Pr fluids. This difference, we hypothesize, may explain the different classes of magnetic fields observed on the Gas and Ice Giant planets, whose dynamo regions consist of Pr < 1 and Pr > 1 fluids, respectively.

Flow reversals in turbulent convection via vortex reconnections

We employ detailed numerical simulations to probe the mechanism of flow reversals in two-dimensional turbulent convection. We show that the reversals occur via a vortex reconnection of two attracting corner rolls having the same sign of vorticity, thus leading to major restructuring of the flow. Large fluctuations in heat transport are observed during the reversal due to the flow reconfiguration. The flow configurations during the reversals have been analyzed quantitatively using large-scale modes. Using these tools, we also show why flow reversals occur for a restricted range of Rayleigh and Prandtl numbers.

Dynamics and symmetries of flow reversals in turbulent convection

Based on direct numerical simulations and symmetry arguments, we show that the large-scale Fourier modes are useful tools to describe the flow structures and dynamics of flow reversals in Rayleigh-Bénard convection (RBC). We observe that during the reversals, the amplitude of one of the large-scale modes vanishes, while another mode rises sharply, very similar to the "cessation-led" reversals observed earlier in experiments and numerical simulations. We find anomalous fluctuations in the Nusselt number during the reversals. Using the structures of the RBC equations in the Fourier space, we deduce two symmetry transformations that leave the equations invariant. These symmetry transformations help us in identifying the reversing and nonreversing Fourier modes.

Spontaneous flow reversals in Rayleigh-Bénard convection of a liquid metal

We report a finding of spontaneous flow reversals of roll-like patterns in liquid gallium Rayleigh-Bénard convection. The vessel has a square geometry with an aspect ratio of 5, and a horizontal magnetic field is applied to align the rolls. The flow patterns were visualized by ultrasonic velocity measurements, and the processes of the reversal were clearly observed. The basic flow pattern observed in the vessel is a four-roll structure with its axis parallel to the magnetic field. Emergence of a new circulation at a corner of the vessel causes flow reversal with reorganization of the whole pattern. The flow keeps relatively steady four-roll structure for most of the duration, while the reversal of it is over in a short time. The reversals of the flow occur randomly with the interval time between reversals being much longer than the circulation time.

Detailed investigation of thermal convection in a liquid metal under a horizontal magnetic field: suppression of oscillatory flow observed by velocity profiles

Thermal convection experiments in a liquid gallium layer were carried out with various intensities of uniform horizontal magnetic fields. The gallium layer was in a rectangular vessel with a 4:1:1 length ratio (1 is the height), where the magnetic field is applied in the direction normal to the longest vertical wall. An ultrasonic velocity profiling method was used to visualize the spatiotemporal variations in the flow pattern, and the temperature fluctuations in the gallium layer were also monitored. The observed flow pattern without a magnetic field shows oscillating rolls with axes normal to the longest vertical wall of the vessel. The oscillatory motion of the flow pattern was suppressed when increasing the applied magnetic field. The flow behavior was characterized by the fluctuation amplitude of the oscillation and the frequency in the range of Rayleigh numbers from 9.3 x 10³ to 3.5 x 10⁵ and Chandrasekhar numbers 0-1900. The effect of the horizontal magnetic field on the flow pattern may be summarized into three regimes with increases in the magnetic intensity: (1) no effect of the magnetic field, (2) a decrease in the oscillation of the roll structure, and (3) a steady two-dimensional roll structure with no oscillation. These regimes may be explained as a result of an increase in the dominance of Lorentz forces over inertial forces. The power spectrum from the temperature time series showed the presence of a convective-inertial subrange above Rayleigh numbers of 7 x 10⁴, which suggests that turbulence has developed, and such a subrange was commonly observed above this Rayleigh number even with applied magnetic fields when the rolls oscillate.