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Pulsatile flow in a constricted channel: flow behaviour and equilibrium states

Published online by Cambridge University Press:  18 March 2019

João A. Isler Open the ORCID record for João A. Isler [Opens in a new window] ,
Rafael S. Gioria Open the ORCID record for Rafael S. Gioria [Opens in a new window]  and
Bruno S. Carmo Open the ORCID record for Bruno S. Carmo [Opens in a new window]
João A. Isler*
Affiliation:
Department of Mechanical Engineering, Escola Politécnica, University of São Paulo, Av. Prof. Mello Moraes, 2231, 05508-030, São Paulo, Brazil
Rafael S. Gioria
Affiliation:
Department of Mining and Petroleum Engineering, Escola Politécnica, University of São Paulo, Av. Prof. Mello Moraes, 2373, 05508-030, São Paulo, Brazil
Bruno S. Carmo
Affiliation:
Department of Mechanical Engineering, Escola Politécnica, University of São Paulo, Av. Prof. Mello Moraes, 2231, 05508-030, São Paulo, Brazil
*
†Email address for correspondence: [email protected]
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Abstract

Results are reported from linear and nonlinear stability analyses of pulsatile flow in a straight channel with a smooth constriction with 50 % occlusion. Physical mechanisms based on the energy variation of the two-dimensional modes are proposed to elucidate the equilibrium states and changes in the flow-field behaviour. When investigating how the energy of the two-dimensional modes varied with Reynolds number, an energy minimum was observed before the primary instability, so that it marked the Reynolds number value at which the flow field started to exhibit one pulse front per cycle downstream of the constriction. In addition, this flow is characterized by a bistable system in two dimensions, whose equilibrium states are related to the energy level of the two-dimensional mode. The energy difference between the equilibrium states surprisingly decreases from the lower to the higher Reynolds number, which indicates that the system should converge to a unique solution at high Reynolds number. Regarding the flow’s nature, the equilibrium state with higher energy presented a vortex pair soon after the constriction, with vorticity opposite to that of the base flow separating shear layers.

JFM classification

Waves/Free-surface Flows: Channel flow Instability: Nonlinear instability
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 866 , 10 May 2019 , R4
Copyright
© 2019 Cambridge University Press 

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