Experimental and numerical characterisation of mixing in a steady spatially chaotic flow by means of residence time distribution measurements

Abstract

This work describes an experimental study and a numerical simulation of residence time distributions (RTD) in a spatially chaotic three-dimensional flow. The experimental system is made up of a succession of bends in which centrifugal force generates a pair of streamwise Dean roll-cells. Fluid particle trajectories become chaotic through geometrical perturbation obtained by rotating the curvature plane of each bend ±90° with respect to the neighbouring ones. Different numbers of bends, ranging from 3 to 33, were tested. RTD is experimentally obtained by using a two-measurement-point conductimetric method, the concentration of the injected tracer being determined both at the inlet and at the outlet of the chaotic mixer. The experimental RTD is modelled by a plug flow with axial dispersion volume exchanging mass with a stagnant zone. RTD experiments were conducted for Reynolds numbers between 30 and 13,000. Péclet number based on the diameter of the pipe Pe D = W ̄ D D ax increases with Reynolds number, whatever the number of bends in the system. This reduction in axial dispersion is due to the secondary Dean flow and the chaotic trajectories. Globally, the flowing fraction increases with Reynolds number, whatever the number of bends, to reach a maximum value between 90 and 100%. For Reynolds numbers between 50 and 200, the flowing fraction increases with the number of bends. The stagnant zone models fluid particles located close to the tube wall. The pathlines become progressively chaotic in small zones in the cross section and then spread across the flow as the number of bends is increased, allowing more trapped particles to move towards the tube centre. In order to characterise more completely the efficiency of the device, a criterion is proposed that takes into account both the mixing characteristics and the pressure drop. The RTD for low Reynolds numbers has also been obtained numerically using a flow model based on Dean’s asymptotic perturbation solutions of the mean flow in a curved pipe. At the end of each bend, the velocity field is rotated by ±90° before entering the next bend. The RTD is calculated by following the trajectories of 250,000 ‘numerical’ particles along the device. Numerical results are in good agreement with experiments in the same Reynolds number range.