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Impinging planar jets: hysteretic behaviour and origin of the self-sustained oscillations

Published online by Cambridge University Press:  03 March 2021

Alessandro Bongarzone Open the ORCID record for Alessandro Bongarzone [Opens in a new window] ,
Arnaud Bertsch Open the ORCID record for Arnaud Bertsch [Opens in a new window] ,
Philippe Renaud Open the ORCID record for Philippe Renaud [Opens in a new window]  and
François Gallaire Open the ORCID record for François Gallaire [Opens in a new window]
Alessandro Bongarzone
Affiliation:
Laboratory of Fluid Mechanics and Instabilities, École Polytechnique Fédérale de Lausanne, LausanneCH-1015, Switzerland
Arnaud Bertsch
Affiliation:
Microsystems Laboratory LMIS4, École Polytechnique Fédérale de Lausanne, LausanneCH-1015, Switzerland
Philippe Renaud
Affiliation:
Microsystems Laboratory LMIS4, École Polytechnique Fédérale de Lausanne, LausanneCH-1015, Switzerland
François Gallaire*
Affiliation:
Laboratory of Fluid Mechanics and Instabilities, École Polytechnique Fédérale de Lausanne, LausanneCH-1015, Switzerland
*
†Email address for correspondence: [email protected]
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Abstract

The experimental and numerical investigation presented by Bertsch et al. (Phys. Rev. Fluids, vol. 5, 2020a, p. 054202) describes the self-sustained oscillations induced by the interaction of two impinging jets in microfluidic devices. While the oscillatory regime induced by interacting jets has been studied in detail, the physical mechanism behind these oscillations remains still undetermined. The present paper focuses on two-dimensional oscillators subjected to a fully developed inlet flow, as in Bertsch et al. (Phys. Rev. Fluids, vol. 5, 2020a, p. 054202) and in contradistinction with Pawlowski et al. (J. Fluid Mech., vol. 551, 2006, pp. 117–139), who focused on plug inlet flow. The linear global stability analysis performed confirms the existence of an oscillating global mode, whose spatial structure qualitatively coincides with that computed numerically by Bertsch et al. (Phys. Rev. Fluids, vol. 5, 2020a, p. 054202), suggesting that the physical mechanism from which the oscillations would originate is predominantly two-dimensional. The interaction of the oscillating mode with a steady symmetry-breaking mode is examined making use of the weakly nonlinear theory, which shows how the system exhibits hysteresis in a certain range of aspect ratios. Lastly, sensitivity analysis is exploited to identify the wavemaker associated with the global modes, whose examination allows us to spot the core of the symmetry-breaking instability at the stagnation point and to identify the Kelvin–Helmholtz instability, located in the jets interaction region, as the main candidate for the origin of the oscillations observed in fluidic devices.

JFM classification

Micro-/Nano-fluid dynamics: Microfluidics Nonlinear Dynamical Systems: Bifurcation Wakes/Jets: Jets
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 913 , 25 April 2021 , A51
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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