Numerical simulation of turbulent Taylor-Couette flow between conducting cylinders in an axial magnetic field at low magnetic Reynolds number. - In: Physics of fluids, ISSN 1089-7666, Bd. 30 (2018), 1, 015107, insges. 17 S.
Correction: Bd. 30 (2018), 2, 029901, insges. 1 S.
The effect of an axial homogeneous magnetic field on the turbulence in the Taylor-Couette flow confined between two infinitely long conducting cylinders is studied by the direct numerical simulation using a periodic boundary condition in the axial direction. The inner cylinder is rotating, and the outer one is fixed. We consider the case when the magnetic Reynolds number Rem 1, i.e., the influence of the induced magnetic field on the flow is negligible that is typical for industry and laboratory study of liquid metals. Relevance of the present study is based on the similarity of flow characteristics at moderate and high magnetic field for the cases with periodic and end-wall conditions at the large flow aspect ratio, as proven in the earlier studies. Two sets of Reynolds numbers 4000 and 8000 with several Hartmann numbers varying from 0 to 120 are employed. The results show that the mean radial induced electrical current, resulting from the interaction of axial magnetic field with the mean flow, leads to the transformation of the mean flow and the modification of the turbulent structure. The effect of turbulence suppression is dominating at a strong magnetic field, but before reaching the complete laminarization, we capture the appearance of the hairpin-like structures in the flow.
https://doi.org/10.1063/1.5003173
Boundary layer fluctuations in turbulent Rayleigh-Bénard convection. - In: Journal of fluid mechanics, ISSN 1469-7645, Bd. 840 (2018), S. 408-431
We report a combined experimental and numerical study of the effect of boundary layer (BL) fluctuations on the scaling properties of the mean temperature profile [theta](z) and temperature variance profile [eta](z) in turbulent Rayleigh-Bénard convection in a thin disk cell and an upright cylinder of aspect ratio unity. Two scaling regions are found with increasing distance z away from the bottom conducting plate. In the BL region, the measured [theta](z) and [eta](z) are found to have the scaling forms [theta](z/[delta]) and [eta](z/[delta]), respectively, with varying thermal BL thickness [delta]. The functional forms of the measured [theta](z/[delta]) and [eta](z/[delta]) in the two convection cells agree well with the recently derived BL equations by Shishkina et al. (Phys. Rev. Lett., vol. 114, 2015, 114302) and by Wang et al. (Phys. Rev. Fluids, vol. 1, 2016, 082301). In the mixing zone outside the BL region, the measured [theta](z) remains approximately constant, whereas the measured [eta](z) is found to scale with the cell height H in the two convection cells and follows a power law, [eta](z) (z/H)E , with the obtained values of E being close to 1. Based on the experimental and numerical findings, we derive a new equation for [eta](z) in the mixing zone, which has a power-law solution in good agreement with the experimental and numerical results. Our work demonstrates that the effect of BL fluctuations can be adequately described by the velocity-temperature correlation functions and the new BL equations capture the essential physics.
https://doi.org/10.1017/jfm.2018.68
Numerical and experimental study of the effect of the induced electric potential in Lorentz force velocimetry. - In: Measurement science and technology, ISSN 1361-6501, Bd. 29 (2018), 1, S. 015301, insges. 15 S.
Lorentz force velocimetry (LFV) is a contactless velocity measurement technique for electrically conducting fluids. When a liquid metal or a molten glass flows through an externally applied magnetic field, eddy currents and a flow-braking force are generated inside the liquid. This force is proportional to the velocity or flow rate of the fluid and, due to Newton's third law, a force of the same magnitude but in opposite direction acts on the source of the applied magnetic field which in our case are permanent magnets. According to Ohm's law for moving conductors at low magnetic Reynolds numbers, an electric potential is induced which ensures charge conservation. In this paper, we analyze the contribution of the induced electric potential to the total Lorentz force by considering two different scenarios: conducting walls of finite thickness and aspect ratio variation of the cross-section of the flow. In both the cases, the force component generated by the electric potential is always in the opposite direction to the total Lorentz force. This force component is sensitive to the electric boundary conditions of the flow of which insulating and perfectly conducting walls are the two limiting cases. In the latter case, the overall electric resistance of the system is minimized, resulting in a considerable increase in the measured Lorentz force. Additionally, this force originating from the electric potential also decays when the aspect ratio of the cross-section of the flow is changed. Hence, the sensitivity of the measurement technique is enhanced by either increasing wall conductivity or optimizing the aspect ratio of the cross-section of the flow.
https://doi.org/10.1088/1361-6501/aa9095
Local Lorentz force and ultrasound Doppler velocimetry in a vertical convection liquid metal flow. - In: Experiments in fluids, ISSN 1432-1114, Bd. 59 (2018), 1, 3, S. 1-12
We report velocity measurements in a vertical turbulent convection flow cell that is filled with the eutectic liquid metal alloy gallium-indium-tin by the use of local Lorentz force velocimetry (LLFV) and ultrasound Doppler velocimetry. We demonstrate the applicability of LLFV for a thermal convection flow and reproduce a linear dependence of the measured force in the range of micronewtons on the local flow velocity magnitude. Furthermore, the presented experiment is used to explore scaling laws of the global turbulent transport of heat and momentum in this low-Prandtl-number convection flow. Our results are found to be consistent with theoretical predictions and recent direct numerical simulations.
https://doi.org/10.1007/s00348-017-2457-0
Maximum electromagnetic drag configurations for a translating conducting cylinder with distant magnetic dipoles. - In: Journal of engineering mathematics, ISSN 1573-2703, Bd. 108 (2018), 1, S. 123-141
We report a semianalytic and numerical investigation of the maximal induced Lorentz force on an electrically conducting cylinder in translation along its axis that is caused by the presence of multiple distant magnetic dipoles. The problem is motivated by Lorentz force velocimetry, where induction creates a drag force on a magnet system placed next to a conducting flow. The magnetic field should maximize this drag force, which is usually quite small. Our approach is based on a long-wave theory developed for a single distant magnetic dipole. We determine the optimal orientations of the dipole moments providing the strongest Lorentz force for different dipole configurations using numerical optimization methods. Different constraints are considered for dipoles arranged on a concentric circle in a plane perpendicular to the cylinder axis. In this case, the quadratic form for the force in terms of the dipole moments can be obtained analytically, and it resembles the expression of the energy in a classical spin model. When all dipoles are equal and their positions on the circle are not constrained, the maximal force results when all dipoles are gathered in one point with all dipole moments pointing in radial direction. When the dipoles are equal and have equidistant spacing on the circle, we find that the optimal orientations of the dipole moments approach a limiting distribution. It differs from the so-called Halbach distribution that provides a uniform magnetic field in the cross section of the cylinder. The corresponding force is about 10% larger than that for the Halbach distribution but 60% smaller than for the unconstrained dipole positions. With the so-called spherical constraint for a classical spin model, the maximal force can be found from the eigenvalues of the coefficient matrix. It is typically 10% larger than the maximal force for equal dipoles because the constraint is weaker. We also study equal and evenly spaced dipoles along one or two lines parallel to the cylinder axis. The patterns of optimal magnetic moment orientations are fairly similar for different dipole numbers when the inter-dipole distance is within a certain interval. This behavior can be explained by reference to the magnetic field distribution of a single distant dipole on the cylinder axis.
https://doi.org/10.1007/s10665-017-9916-8
Heat and mass transport in large aspect ratio Rayleigh-Bénard convection. - In: ExHFT-9 2017, (2017), insges. 8 S.
Turbulent and transitional sidewall jets in magnetohydrodynamic channels with a homogeneous magnetic field. - In: Proceedings in applied mathematics and mechanics, ISSN 1617-7061, Bd. 17 (2017), 1, S. 111-114
Liquid metal flows in the presence of a uniform magnetic field experience electromagnetic induction. The eddy currents and associated Lorentz force density modify the flow and give rise to thin electromagnetic boundary layers on the walls of the channel or duct. Hartmann layers develop on the walls perpendicular to the magnetic field whereas side layers develop on the parallel walls. The structure of the laminar flow depends on the conductivity of the walls. The side layers play a critical role in the transition to turbulence and are also strongly affected by the anisotropic character of the Lorentz force. We focus on duct flows with conducting Hartmann walls that give rise side-layers jets and report numerical studies of the transitional and turbulent regimes. We also examine one-point statistics and describe specific transitional patterns.
https://doi.org/10.1002/pamm.201710032
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.