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Attenuation of shear-layer instabilities in steady and pulsatile axisymmetric shear-thinning flows

Published online by Cambridge University Press:  24 January 2025

Moira Barnes Open the ORCID record for Moira Barnes [Opens in a new window] ,
Giuseppe A. Rosi Open the ORCID record for Giuseppe A. Rosi [Opens in a new window]  and
David E. Rival
Moira Barnes
Affiliation:
Department of Mechanical and Materials Engineering, Queen's University, Kingston, Ontario KL7 3N6, Canada
Giuseppe A. Rosi*
Affiliation:
Institute of Fluid Mechanics, Technische Universität Braunschweig, Braunschweig, Niedersachsen 38108, Germany
David E. Rival
Affiliation:
Department of Mechanical and Materials Engineering, Queen's University, Kingston, Ontario KL7 3N6, Canada Institute of Fluid Mechanics, Technische Universität Braunschweig, Braunschweig, Niedersachsen 38108, Germany
*
†Email address for correspondence: [email protected]
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Abstract

The current study characterizes the attenuation of instabilities in steady and unsteady shear layers by investigating shear-thinning flows downstream of a confined axisymmetric sudden expansion. Flow fields were captured using particle image velocimetry. Tested fluids exhibited approximate power-law indices of 1, 0.81, 0.61 and 0.47 and measurements were performed at mean throat-based Reynolds numbers of ${Re_m} = 4800$ and 14 400. Unsteady flows were tested at a Strouhal number and amplitude-to-mean velocity ratio of $St = 0.15$ and $\lambda = 0.95$, respectively. For unsteady shear layers, shear-layer roll-up regardless of shear-thinning strength was evidenced by collapse of average circulation over time. For steady shear layers, consistent shear-layer behaviour regardless of shear-thinning strength was evidenced by similar shear-layer trajectories and by growth rates in vorticity thickness. However, vorticity fields of the unsteady and steady shear layers, standard deviations of shear-layer trajectory, thickness of steady shear layers and Reynolds shear-stress spectra of the steady shear layers reveal an attenuation of shear-layer instabilities not captured by Reynolds number. Specifically, shear-layer instabilities exhibit increased diffusion with increasing shear-thinning strength and, in the case of steady shear layers, shear-thinning strength is shown to promote shear-layer stabilization. Also, evidenced by vorticity fields and through Reynolds shear-stress spectra, instabilities frequently coalesce into large rollers, a result that would suggest the presence of an inverse eddy cascade. The behaviour of shear-thinning fluids is shown to stabilize shear layers through attenuating shear-layer instabilities, complementing observations from previous studies showing how shear-thinning fluids promote turbulence in the dominant flow direction.

JFM classification

Instability: Shear-flow instability Vortex Flows: Vortex dynamics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1003 , 25 January 2025 , A30
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Copyright
© The Author(s), 2025. Published by Cambridge University Press

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Supplementary material: File

Barnes et al. supplementary movie 1

Shear-layer roll-up occurs downstream of the sudden expansion when unsteady pulsatile boundary conditions are imposed. Representative instantaneous normalized vorticity and velocity vectors are animated for t/T = 0 to 1. In figures(a, c, e, & g): cases at Rem = 4800 are shown, and in figures(b, d, f, & h): cases at Rem = 14400 are shown. Shear-layer roll-up for pure-water cases is shown in figures(a & b), 35PPM in figures(c & d), 450PPM in figures(e & f), and 900PPM in figures(g & h). All cases were prescribed a frequency of St = 0.15. Every third velocity vector is plotted for clarity. With increasing shear-thinning strength, the number of instabilities generally reduce but shear-layer roll-up persists.
Download Barnes et al. supplementary movie 1(File)
File 7.9 MB
Supplementary material: File

Barnes et al. supplementary movie 2

Shear-layer instabilities develop and convect downstream of the sudden expansion when steady boundary conditions are imposed. Representative instantaneous normalized vorticity and velocity vectors are animated to show shear-layer instability formation and evolution. In figures(a, c, e, &g): cases at Rem = 4800 are shown, and in figures(b, d, f, &h): cases at Rem = 14400 are shown. Shear-layer instability formation and evolution for pure-water cases is shown in figures(a & b), 35PPM in figures(c & d), 450PPM in figures(e & f), and 900PPM in figures(g & h). Every third velocity vector is plotted for clarity.
Download Barnes et al. supplementary movie 2(File)
File 9.6 MB