If a permanent magnet is located near a liquid metal flow, the magnet experiences a Lorentz force, which depends on the velocity of the flow. This effect is embodied in a noncontact flow measurement technique called Lorentz force velocimetry (LFV). Although LFV is already under way for global flow measurement in metallurgy, the possibility of using LFV for local velocity measurement has not yet been explored. The present work is devoted to a comprehensive investigation of the Lorentz force acting upon a permanent magnet near a liquid metal flow in a square duct when the size of the magnet is sufficiently small to be influenced by only parts of the fluid flow. We employ a combination of laboratory experiments in the turbulent regime, direct numerical simulations of laminar and turbulent flows using a custom-made code, and Reynolds-averaged Navier-Stokes (RANS) simulations using a commercial code. We address three particular flow regimes, namely the kinematic regime where the back-reaction of the Lorentz force on the flow is negligible, the low-Reynolds number dynamic regime and the high-Reynolds number dynamic regime both being characterized by a significant modification of the flow by the Lorentz force. In all three regimes, the Lorentz force is characterized by a nondimensional electromagnetic drag coefficient CD, which depends on the dimensionless distance between the magnet and the duct h, the dimensionless size of the magnet d, the Reynolds number Re, and the Hartmann number Ha. We demonstrate that in the kinematic regime, CD displays a universal dependence on the distance parameter, expressed by the scaling laws CD ∼ h−2 for h ≪ 1 and CD ∼ h−7 for h ≫ 1. In the dynamic regime at low Re, the magnet acts as a magnetic obstacle and expels streamlines from its immediate vicinity. In the dynamic regime at high Re, we present experimental data on CD(Re) for 500 ≤ Re ≤ 104 and on CD(h) for 0.4 ≤ h ≤ 1 and demonstrate that they are in good agreement with numerical results obtained from RANS simulations for the same range of parameters.

Particles in the shape of chiral dipoles show a preferential rotation in three dimensional homogeneous isotropic turbulence. A chiral dipole consists of a rod with two helices of opposite handedness, one at each end. We can use 3d printing to fabricate these particles with length in the inertial range and track their rotations in a turbulent flow between oscillating grids. High aspect ratio chiral dipoles will align with the extensional eigenvectors of the strain rate tensor and the helical ends will respond to the strain field by spinning around its long axis. The mean of the measured spinning rate is non-zero and reflects the average stretching the particles experience. We use Stokesian dynamics simulations of chiral dipoles in pure strain flow to quantify the dependence of spinning on particle shape. Based on the known response to pure strain, we build a model that gives the spinning rate of small chiral dipoles using Lagrangian velocity gradients from high resolution direct numerical simulations. The statistics of chiral dipole spinning determined with this model show surprisingly good agreement with the measured spinning of much larger chiral dipoles in the experiments.

The electromagnetic drag force and torque acting on a magnetic dipole due to the translatory motion of an electrically conducting bar with square cross section and infinite length is computed by numerical analysis for different orientations and locations of the dipole. The study is motivated by the novel techniques termed Lorentz force velocimetry and Lorentz force eddy current testing for noncontact measurements of the velocity of a conducting liquid and for detection of defects in the interior of solid bodies, respectively. The present, simplified configuration provides and explains important scaling laws and reference results that can be used for verification of future complete numerical simulations of more realistic problems and complex geometries. The results of computations are also compared with existing analytical solutions for an infinite plate and with a newly developed asymptotic theory for large distances between the bar and the magnetic dipole. We finally discuss the optimization problem of finding the orientation of the dipole relative to the bar that produces the maximum force in the direction of motion.

We consider liquid metal flow in a square duct with electrically insulating walls under the influence of a magnetic point dipole using three‐dimensional direct numerical simulations with a finite‐difference method. The dipole acts as a magnetic obstacle. The Lorentz force on the magnet is sensitive to the velocity distribution that is influenced by the magnetic field. The flow transformation by an inhomogeneous local magnetic field is essential for obtaining velocity information from the measured forces. In this paper we present a numerical simulation of a spatially developing flow in a duct with laminar inflow and periodic boundary conditions. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

The flow transformation and the generation of vortex structures by a strong magnetic dipole field in a liquid metal duct flow is studied by means of three-dimensional direct numerical simulations. The dipole is considered as the paradigm for a magnetic obstacle which will deviate the streamlines due to Lorentz forces acting on the fluid elements. The duct is of square cross-section. The dipole is located above the top wall and is centred in spanwise direction. Our model uses the quasistatic approximation which is applicable in the limit of small magnetic Reynolds numbers. The analysis covers the stationary flow regime at small hydrodynamic Reynolds numbers Re as well as the transitional time-dependent regime at higher values which may generate a turbulent flow in the wake of the magnetic obstacle. We present a systematic study of these two basic flow regimes and their dependence on Re and on the Hartmann number Ha, a measure of the strength of the magnetic dipole field. Furthermore, three orientations of the dipole are compared: streamwise-, spanwise-and wall-normaloriented dipole axes. The most efficient generation of turbulence at a fixed distance above the duct follows for the spanwise orientation, which is caused by a certain configuration of Hartmann layers and reversed flow at the top plate. The enstrophy in the turbulent wake grows linearly with Ha which is connected with a dominance of the wall-normal derivative of the streamwise velocity.