Turbulent superstructures in Rayleigh-Bénard convection for varying Prandtl numbers. - In: Proceedings in applied mathematics and mechanics, ISSN 1617-7061, Bd. 17 (2017), 1, S. 15-18
https://doi.org/10.1002/pamm.201710005
Electromagnetic interaction between a permanent magnet and laminar flow of a moving sphere in a conducting liquid. - In: Magnetohydrodynamics, ISSN 0024-998X, Bd. 53 (2017), 4, S. 653-665
Lorentz force velocimetry (LFV) is a non-contact electromagnetic flow measurement technique for electrically conducting liquids. It is based on measuring the flow-induced force acting on an externally arranged permanent magnet. Motivated by extending LFV to liquid metal two-phase flow measurement, in a previous test we considered the free rising of non-conductive bubbles/particles in a thin tube of liquid metal (GaInSn) initially at rest. We observed that the Lorentz force signals strongly depend on the size of the bubble/particle and on the position, where it is released. Moreover, the force signals cannot be reproduced in detail, which necessitates a statistical analysis. This is caused by chaotic trajectories due to the rising velocities of about 200 mm/s. Therefore, in this paper, we use an improved setup for controlled particle motions in liquid metal. In this experiment, the particle is attached to a straight fishing line, which suppresses any lateral motion, and is pulled by a linear driver at a controllable velocity (0-200 mm/s). For comparison, we solve the induction problem numerically using Oseen's analytical solution of the flow around a translating sphere that is valid for small but finite Reynolds numbers. This simplification is made since the precise hydrodynamic flow is difficult to measure or to compute. The aim of the present work is to check if our simple numerical model can provide Lorentz forces comparable to the experiments. Although Oseen's solution becomes inaccurate near the sphere for finite Reynolds numbers, it provides a fore-aft asymmetry of the flow and is globally well-behaved. It provides an upper limit to the measurement results. We recover the peak-delay of the Lorentz force signals as well.
Numerical study of the interaction between a bubble rising in a column of conducting liquid and a permanent magnet. - In: Magnetohydrodynamics, ISSN 0024-998X, Bd. 53 (2017), 4, S. 619-631
Electromagnetic induction in a conducting liquid that moves in an external magnetic field can be used for contactless flow measurement. In Lorentz Force Velocimetry (LFV), the induced force on the magnet is determined to obtain velocity information. This measurement principle may also be applied to conducting flows with gas bubbles encountered in metallurgical processes. This provides the motivation for our work, in which we study a single bubble rising in a liquid metal column as a model problem for LFV in two-phase flows. By using a small permanent magnet, one can not only detect the presence of a bubble but also obtain information on its position and velocity. Our numerical investigation aims at reproducing experiments with Argon bubbles in GaInSn alloy and at studying the electromagnetic induction in the flow in more detail. For three-dimensional and phase-resolving simulations we use the Volume of Fluid method provided by ANSYS FLUENT. The induction equation in the quasistatic limit is an elliptic problem for the electric potential. It is implemented in FLUENT with a user-defined scalar. The electric conductivity varies between the phases, and the magnetic field is given by an analytical expression for a uniformly magnetized cube. The comparison with the experiments also helps to validate the numerical simulations.
Predicting transition ranges to fully turbulent viscous boundary layers in low Prandtl number convection flows. - In: Physical review fluids, ISSN 2469-990X, Bd. 2 (2017), 12, 123501, insges. 23 S.
We discuss two aspects of turbulent Rayleigh-Bénard convection (RBC) on the basis of high-resolution direct numerical simulations in a unique setting: a closed cylindrical cell of aspect ratio of one. First, we present a comprehensive comparison of statistical quantities such as energy dissipation rates and boundary layer thickness scales. Data are used from three simulation run series at Prandtl numbers Pr that cover two orders of magnitude. In contrast to most previous studies in RBC the focus of the present work is on convective turbulence at very low Prandtl numbers including Pr 0.021 for liquid mercury or gallium and Pr 0.005 for liquid sodium. In this parameter range of RBC, inertial effects cause a dominating turbulent momentum transport that is in line with highly intermittent fluid turbulence both in the bulk and in the boundary layers and thus should be able to trigger a transition to the fully turbulent boundary layers of the ultimate regime of convection for higher Rayleigh number. Second, we predict the ranges of Rayleigh numbers for which the viscous boundary layer will transition to turbulence and the flow as a whole will cross over into the ultimate regime. These transition ranges are obtained by extrapolation from our simulation data. The extrapolation methods are based on the large-scale properties of the velocity profile. Two of the three methods predict similar ranges for the transition to ultimate convection when their uncertainties are taken into account. All three extrapolation methods indicate that the range of critical Rayleigh numbers Rac is shifted to smaller magnitudes as the Prandtl number becomes smaller.
https://doi.org/10.1103/PhysRevFluids.2.123501
Inductive detection of the free surface of liquid metals. - In: Measurement science and technology, ISSN 1361-6501, Bd. 28 (2017), 11, S. 115301, insges. 7 S.
A novel measurement system to determine the surface position and topology of liquid metals is presented. It is based on the induction of eddy currents by a time-harmonic magnetic field and the subsequent measurement of the resulting secondary magnetic field using gradiometric induction coils. The system is validated experimentally for static and dynamic surfaces of the low-melting liquid metal alloy gallium-indium-tin in a narrow vessel. It is shown that a precision below 1 mm and a time resolution of at least 20 Hz can be achieved.
https://doi.org/10.1088/1361-6501/aa7f58
Electromagnetic interaction between a rising spherical particle in a conducting liquid and a localized magnetic field. - In: Final LIMTECH Colloquium and International Symposium on Liquid Metal Technologies, (2017), S. 012025, insges. 10 S.
Lorentz force velocimetry (LFV) is a non-contact electromagnetic flow measurement technique for electrically conductive liquids. It is based on measuring the flow-induced force acting on an external permanent magnet. Motivated by extending LFV to liquid metal two-phase flow measurement, in a first test we consider the free rising of a non-conductive spherical particle in a thin tube of liquid metal (GaInSn) initially at rest. Here the measured force is due to the displacement flow induced by the rising particle. In this paper, numerical results are presented for three different analytical solutions of flows around a moving sphere under a localized magnetic field. This simplification is made since the hydrodynamic flow is difficult to measure or to compute. The Lorentz forces are compared to experiments. The aim of the present work is to check if our simple numerical model can provide Lorentz forces comparable to the experiments. The results show that the peak values of the Lorentz force from the analytical velocity fields provide us an upper limit to the measurement results. In the case of viscous flow around a moving sphere we recover the typical time-scale of Lorentz force signals.
https://doi.org/10.1088/1757-899X/228/1/012025
Magnetically induced instabilities in duct flows. - In: Final LIMTECH Colloquium and International Symposium on Liquid Metal Technologies, (2017), S. 012003, insges. 12 S.
The occurrence of magnetically induced instability in magnetohydrodynamic duct flows is studied for Hunt flow, where one pair of walls parallel to the magnetic field is electrically insulating and the Hartmann walls perpendicular to the field are electrically conducting. The onset of time-dependent flow patterns and their intensity depends on the strength of the magnetic field and on the flow rate in terms of the Hartmann and Reynolds numbers, respectively. The problem is studied by a complementary approach using laboratory experiments, linear stability analysis and high-resolution direct numerical simulations.
https://doi.org/10.1088/1757-899X/228/1/012003
Complex patterns and elementary structures of solutal marangoni convection: experimental and numerical studies. - In: Transport Processes at Fluidic Interfaces, (2017), S. 445-488
The transfer of a solute between two liquid layers is susceptible to convective instabilities of the time-dependent diffusive concentration profile that may be caused by the Marangoni effect or buoyancy. Marangoni instabilities depend on the change of interfacial tension and Rayleigh instabilities on the change of liquid densities with solute concentration. Such flows develop increasingly complex cellular or wavy patterns with very fine structures in the concentration field due to the low solute diffusivity. They are important in several applications such as extraction or coating processes. A detailed understanding of the patterns is lacking although a general phenomenological classification has been developed based on previous experiments. We use both highly resolved numerical simulations and controlled experiments to examine two exemplary systems. In the first case, a stationary Marangoni instability is counteracted by a stable density stratification producing a hierarchical cellular pattern. In the second case, Rayleigh instability is opposed by the Marangoni effect causing solutal plumes and eruptive events with short-lived Marangoni cells on the interface. A good qualitative and acceptable quantitative agreement between the experimental visualizations and measurements and the corresponding numerical results is achieved in simulations with a planar interface, and a simple linear model for the interface properties, i.e. no highly specific properties of the interface are required for the complex patterns. Simulation results are also used to characterize the mechanisms involved in the pattern formation.
https://doi.org/10.1007/978-3-319-56602-3_16
Numerical calibration of a multicomponent local Lorentz force flowmeter. - In: Magnetohydrodynamics, ISSN 0024-998X, Bd. 53 (2017), 2, S. 233-243
Local Lorentz force velocimetry is a local velocity measurement technique for liquid metals. Due to the interaction between an electrically conducting liquid and an applied magnetic field, eddy currents and flow-braking Lorentz forces are induced in the fluid. Due to Newtons third law, a force of the same magnitude acts on the source of the applied magnetic field, which is a permanent magnet in our case. The magnet is attached to a gauge that has been especially developed to record all three force and three torque components acting on the magnet. This new-generation local Lorentz force flowmeter (L2F2) has already been tested in a test stand for continuous casting with a 15 mm cubic magnet providing an insight into the three-dimensional velocity distribution of the model melt GaInSn near the wide face of the mold. For better understanding of these results, especially regarding torque sensing, we propose dry experiments which consist in replacing a flowing liquid by a moving solid. Here, as the velocity field is fixed and steady, we are able to decrease considerably the variability and the noise of the measurements providing an accurate calibration of the system. In this paper, we present a numerical study of this dry calibration using a rotating disk made of aluminum and two different magnet systems that can be shifted along the rotation axis as well as in the radial direction.
Thermal Rayleigh-Marangoni convection in a three-layer liquid-metal-battery model. - In: Physical review, ISSN 2470-0053, Bd. 95 (2017), 5, 053114, insges. 23 S.
The combined effects of buoyancy-driven Rayleigh-Bénard convection (RC) and surface tension-driven Marangoni convection (MC) are studied in a triple-layer configuration which serves as a simplified model for a liquid metal battery (LMB). The three-layer model consists of a liquid metal alloy cathode, a molten salt separation layer, and a liquid metal anode at the top. Convection is triggered by the temperature gradient between the hot electrolyte and the colder electrodes, which is a consequence of the release of resistive heat during operation. We present a linear stability analysis of the state of pure thermal conduction in combination with three-dimensional direct numerical simulations of the nonlinear turbulent evolution on the basis of a pseudospectral method. Five different modes of convection are identified in the configuration, which are partly coupled to each other: RC in the upper electrode, RC with internal heating in the molten salt layer, and MC at both interfaces between molten salt and electrode as well as anticonvection in the middle layer and lower electrode. The linear stability analysis confirms that the additional Marangoni effect in the present setup increases the growth rates of the linearly unstable modes, i.e., Marangoni and Rayleigh-Bénard instability act together in the molten salt layer. The critical Grashof and Marangoni numbers decrease with increasing middle layer thickness. The calculated thresholds for the onset of convection are found for realistic current densities of laboratory-sized LMBs. The global turbulent heat transfer follows scaling predictions for internally heated RC. The global turbulent momentum transfer is comparable with turbulent convection in the classical Rayleigh-Bénard case. In summary, our studies show that incorporating Marangoni effects generates smaller flow structures, alters the velocity magnitudes, and enhances the turbulent heat transfer across the triple-layer configuration.
https://doi.org/10.1103/PhysRevE.95.053114