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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: joao.isler@usp.br
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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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References

Ahmed, S. A. & Giddens, D. P. 1984 Pulsatile poststenotic flow studies with laser Doppler anemometry. J. Biomech. 17, 695–705.Google Scholar
Blackburn, H. M. & Sherwin, S. J. 2007 Instability modes and transition of pulsatile stenotic flow: pulse-period dependence. J. Fluid Mech. 573, 57–88.Google Scholar
Blackburn, H. M., Sherwin, S. J. & Barkley, D. 2008 Convective instability and transient growth in steady and pulsatile stenotic flows. J. Fluid Mech. 607, 267–277.Google Scholar
Cherdron, W., Durst, F. & Whitelaw, J. H. 1978 Asymmetric flows and instabilities in symmetric ducts with sudden expansions. J. Fluid Mech. 84, 13–31.Google Scholar
Durst, F., Melling, A. & Whitelaw, J. H. 1974 Low Reynolds number flow over a plane symmetric sudden expansion. J. Fluid Mech. 64 (1), 111–128.Google Scholar
Fani, A., Camarri, S. & Salvetti, M. V. 2012 Stability analysis and control of the flow in a symmetric channel with a sudden expansion. Phys. Fluids 24, 084102.Google Scholar
Fearn, R. M., Mullin, T. & Cliffe, K. A. 1990 Nonlinear flow phenomena in a symmetric sudden expansion. J. Fluid Mech. 211, 595–608.Google Scholar
Griffith, M. D., Leweke, T., Thompson, M. C. & Hourigan, K. 2009 Pulsatile flow in stenotic geometries: flow behaviour and stability. J. Fluid Mech. 622, 291–320.Google Scholar
Isler, J. A., Gioria, R. S. & Carmo, B. S. 2018 Bifurcations and convective instabilities for steady flows in a constricted channel. J. Fluid Mech. 849, 777–804.Google Scholar
Karniadakis, G. E. 1990 Spectral element–Fourier methods for incompressible turbulent flows. Comput. Methods Appl. Mech. Engng 80, 367–380.Google Scholar
Karniadakis, G. E., Israeli, M. & Orszag, S. A. 1991 High-order splitting methods for the incompressible Navier–Stokes equations. J. Comput. Phys. 97, 414–443.Google Scholar
Karniadakis, G. E. & Sherwin, S. J. 2005 Spectral/hp Element Methods for Computational Fluid Dynamics, 2nd edn. Oxford University Press.Google Scholar
Khair, A., Wang, B.-C. & Kuhn, D. C. S. 2016 Study of laminar–turbulent flow transition under pulsatile conditions in a constricted channel. Intl J. Comput. Fluid Dyn. 29, 447–463.Google Scholar
Lashgari, I., Tammisola, O., Citro, V., Juniper, M. P. & Brandt, L. 2014 The planar x-junction flow: stability analysis and control. J. Fluid Mech. 753, 1–28.Google Scholar
Mittal, R., Simmons, S. P. & Najjar, F. 2003 Numerical study of pulsatile flow in a constricted channel. J. Fluid Mech. 485, 337–378.Google Scholar
Ojha, M., Cobbold, R. S. C., Johnston, K. W. & Hummel, R. L. 1989 Pulsatile flow through constricted tubes: an experimental investigation using photochromic tracer methods. J. Fluid Mech. 203, 173–197.Google Scholar
Pitt, R.2005 Numerical simulation of fluid mechanical phenomena in idealised physiological geometries: stenosis and double bend. PhD thesis, Imperial College London.Google Scholar
Pralits, J. O., Brandt, L. & Giannetti, F. 2010 Instability and sensitivity of the flow around a rotating circular cylinder. J. Fluid Mech. 650, 513–536.Google Scholar
Sherwin, S. J. & Blackburn, H. M. 2005 Three–dimensional instabilities and transition of steady and pulsatile axisymmetric stenotic flows. J. Fluid Mech. 533, 297–327.Google Scholar