Predicting dynamo self-generation in liquid metal experiments has been an ongoing question for many years. In contrast to simple dynamical systems for which reliable techniques have been developed, the ability to predict the dynamo capacity of a flow and the estimate of the corresponding critical value of the magnetic Reynolds number (the control parameter of the instability) has been elusive, partly due to the high level of turbulent fluctuations of flows in such experiments (with kinetic Reynolds numbers in excess of 10(6)). We address these issues here, using the von Kármán sodium experiment and studying its response to an externally applied magnetic field. We first show that a dynamo threshold can be estimated from analysis related to critical slowing down and susceptibility divergence, in configurations for which dynamo action is indeed observed. These approaches are then applied to flow configurations that have failed to self-generate magnetic fields within operational limits, and we quantify the dynamo capacity of these configurations.
Shear layers in confined liquid metal magnetohydrodynamic (MHD) flow play an important role in geo- and astrophysical bodies as well as in engineering applications. We present an experimental and numerical study of liquid metal MHD flow in a modified cylindrical annulus that is driven by an azimuthal Lorentz force resulting from a forced electric current under an imposed axial magnetic field. Hartmann and Reynolds numbers reach Mmax ≈ 2000 and Remax ≈ 1.3 × 104, respectively, in the steady regime. The peculiarity of our model geometry is the protruding inner disk electrode which gives rise to a free Shercliff layer at its edge. The flow of liquid GaInSn in the experimental device ZUCCHINI (ZUrich Cylindrical CHannel INstability Investigation) is probed with ultrasound Doppler velocimetry. We establish the base flow in ZUCCHINI and study the scaling of velocities and the free Shercliff layer in both experiment and finite element simulations. Experiment and numerics agree well on the mean azimuthal velocity uϕ(r) following the prediction of a large-M theoretical model. The large-M limit, which is equivalent to neglecting inertial effects, appears to be reached for M ≳ 30 in our study. In the numerics, we recover the theoretical scaling of the free Shercliff layer δS ∼ M−1/2 whereas δS appears to be largely independent of M in the experiment.
A new type of velocimeter, capable of local velocity measurements in conducting fluids, is introduced. The principle of the "magnetic-distortion probe" is based on the measurement of the induced magnetic field by the flow of a conducting fluid in the vicinity of a localized magnetic field. The new velocimeter has no moving parts, and can be enclosed in a sealed cap, easing the implementation in harsh environments, such as liquid metals. The proposed method allows one to probe both the continuous part and fluctuations of the velocity, the temporal and spatial resolution being linked to the actual geometric configuration of the probe. A prototype probe has been tested in a gallinstan pipe flow and in a fully turbulent flow of liquid gallium generated by the counter rotation of two coaxial impellers in a cylinder. The signals have been compared to a reference potential probe and show very good agreement both for time-averaged velocities and turbulent fluctuations. The prototype is shown to detect motion from a few cm s(-1) to a few m s(-1). Moreover, the use of the magnetic-distortion probe with large-scale applied magnetic field is discussed.
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