Mixing by Time-Dependent Orbits in Spatiotemporal Chaotic Advection

Author:

Karami Mohammad1,Shirani Ebrahim2,Jarrahi Mojtaba3,Peerhossaini Hassan4

Affiliation:

1. Department of Mechanical Engineering, Isfahan University of Technology, Isfahan 84156-83111, Iran

2. Foolad Institute of Technology, Fooladshahr, Isfahan 84916-63763, Iran

3. University Paris-Sud, LIMSI-CNRS UPR 3251, BP 133, Orsay Cedex 91403, France

4. University Paris Diderot, Sorbonne Paris Cité, Laboratoire Interdisciplinaire des Energies de Demain (LIED)–CNRS FRE 3597–BP 7040, Paris Cedex 13 75205, France e-mail:

Abstract

The simultaneous effects of flow pulsation and geometrical perturbation on laminar mixing in curved ducts have been numerically studied by three different metrics: analysis of the secondary flow patterns, Lyapunov exponents and vorticity vector analysis. The mixer that creates the flow pulsation and geometrical perturbations in these simulations is a twisted duct consisting of three bends; the angle between the curvature planes of successive bends is 90 deg. Both steady and pulsating flows are considered. In the steady case, analysis of secondary flow patterns showed that homoclinic connections appear and become prominent at large Reynolds numbers. In the pulsatile flow, homoclinic and heteroclinic connections appear by increasing β, the ratio of the peak oscillatory velocity component of the mean flow velocity. Moreover, sharp variations in the secondary flow structure are observed over an oscillation cycle for high values of β. These variations are reduced and the homoclinic connections disappear at high Womersley numbers. We show that small and moderate values of the Womersley number (6 ≤ α ≤ 10) and high values of velocity amplitude ratio (β ≥ 2) provide a better mixing than that in the steady flow. These results correlate closely with those obtained using two other metrics, analysis of the Lyapunov exponents and vorticity vector. It is shown that the increase in the Lyapunov exponents, and thus mixing enhancement, is due to the formation of homoclinic and heteroclinic connections.

Publisher

ASME International

Subject

Mechanical Engineering

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