Lamination and folding in electromagnetically driven flows of specified geometries

Abstract

In this paper, a new characterization and a quantification of lamination are presented. The lamination is identified by tracking material lines and by the estimation of the ratio between the length of the material lines within circles and the diameter of the circles. The quantification of the lamination rate relies on the interlaced structure of velocity and Lagrangian acceleration, which allows the determination of the spatial variation of the Lagrangian angular velocity. Those definitions are illustrated using quasi-steady flows driven by electromagnetic forces using mono-and multi-scale configurations with turbulent-like properties. Both experimental and numerical data are used to compute folding rate intensities and lamination for a large range of length scales. Good agreement is found between grid deformation and the prediction of lamination rate, an agreement further confirmed by the measure of lamination. The quantification of lamination is simple and well defined at chosen length-scales. Also, the present form applies to any lines and can be extended to 3D flows. The lamination rate process rely on physical quantities which scale according to the structures' length-scales. It is shown that the lamination rate increases with the reduction of the length-scales and in particular it is found thatṘ f ol ∼ ℓ −3/4 . In turbulent flows, the lamination should then be faster within small coherent structures. This quantification of lamination rate, complemented by a measure of lamination opens new routes for the description and the quantification of mixing in complex and turbulent flows.

A new method to calculate unsteady particle kinematics and drag coefficient in a subsonic post-shock flow

“…To understand the post-shock particle dynamics, one needs to determine time-resolved velocity ( ẋp ) and acceleration (ẍ p ) from particle position (x p ) data. Recent advances in highspeed imaging and time-resolved velocimetry techniques have provided promising avenues in the field of unsteady flow measurements, especially in tracking Lagrangian trajectories over a significantly long period of time (La Porta et al 2001, Mordant et al 2004, Ferrari and Rossi 2008, Rossi and Lardeau 2011. In an unsteady high-speed environment, such as the motion of a particle immediately behind a shock, the particle may undergo abrupt changes in acceleration.…”

Chaotic advection at large Péclet number: Electromagnetically driven experiments, numerical simulations, and theoretical predictions

“…In fact, electromagnetic forcing has been widely used experimentally to produce mixing in shallow layers of liquid metals 3 or electrolytes. [4][5][6] The basic idea is to generate a rotational Lorentz force in a thin layer of a conducting fluid by the interaction of electric currents with a steady external magnetic field. As a matter of fact, under certain conditions these flows may present a quasi-two-dimensional (Q2D) behavior.…”

Lamination and mixing in laminar flows driven by Lorentz body forces

“…To date, despite being of importance for mixing processes and chemical reactions, e.g. [30,35], the lamination of complex flows is still partially explored [32,[36][37][38][39] and is often considered as a sub product of stretching. Rossi and Lardeau [36] propose a new measure to explore lamination within flows.…”

“…[30,35], the lamination of complex flows is still partially explored [32,[36][37][38][39] and is often considered as a sub product of stretching. Rossi and Lardeau [36] propose a new measure to explore lamination within flows. This local measure of lamination, M lam , is defined as the ratio of the total length of a material line within a circle centred on the material line to the circle's diameter φ:…”