PIV mapping of pressure and velocity fields in the plane magnetohydrodynamic Couette flow
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RESEARCH ARTICLE
PIV mapping of pressure and velocity fields in the plane magnetohydrodynamic Couette flow B. Moudjed1,2 · A. Pothérat1 · M. Holdsworth1 Received: 7 September 2020 / Revised: 15 October 2020 / Accepted: 24 October 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract We present the first simultaneous mapping of two-dimensional, time-dependent velocity and pressure fields in a plane Couette flow pervaded by a transverse magnetic field. While electromagnetic forces are strongest in fluids of high electric conductivity such as liquid metals, their opacity excludes optical measurement methods. We circumvent this difficulty using a transparent electrolyte (sulphuric acid), whose weaker conductivity is offset by higher magnetic fields. We describe an experimental rig based on this idea, where the Couette flow is entrained by a tape immersed in sulphuric acid and positioned flush onto the bore of large superconducting magnet, so that most of the flow is pervaded by a sufficiently homogeneous transverse magnetic field. Velocity and pressure fields are obtained by means of a bespoke PIV system, capable of recording the fluid’s acceleration as well as its velocity. Both fields are then fed into a finite difference solver that extracts the pressure field from the magnetohydrodynamic governing equations. This method constitutes the first implementation of the pressure PIV technique to an MHD flow. Thanks to it, we obtain the first experimental velocity and pressure profiles in an MHD Couette flows and show that the transitional regime between laminar and turbulent states is dominated by near-wall, isolated, anisotropic perturbations. Graphic abstract
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1 Introduction * A. Pothérat [email protected] B. Moudjed [email protected] 1
Fluid and Complex Systems Research Centre, Coventry University, Priory Street, Coventry CV1 5FB, UK
Laboratoire National des Champs Magnétiques Intenses, CNRS/UGA-UPS-INSA, Grenoble, France
2
We report the first mapping of velocity and pressure fields in a plane Couette flow pervaded by a transverse magnetic field, also called the plane MagnetoHydroDynamic (MHD) Couette flow. The Couette flow is one of the classical problems of fluid mechanics. It owes its popularity to its generic simplicity—a unidirectional flow driven by the shear due to the relative movement of its boundaries—and to its relevance to a very wide range of ideal and practical problems
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Experiments in Fluids
(lubrication, local shear in turbulent flows, atmospheric, geophysical phenomena etc.). Despite its apparent simplicity, the Couette flow, with or without magnetic field remains an ideal playground to understand transition to turbulence and sheared turbulence, two of the major challenges of fluid dynamics (Grossmann et al. 2016). Nevertheless, a good experimental approximation to the ideal Couette flow—i.e the flow between two infinitely extended planes, unspoilt by unwanted physical phenomena
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