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Experimental and numerical investigation of flow instability in a transient pipe flow

Published online by Cambridge University Press:  14 June 2021

Avinash Nayak Open the ORCID record for Avinash Nayak [Opens in a new window]  and
Debopam Das Open the ORCID record for Debopam Das [Opens in a new window]
Avinash Nayak*
Affiliation:
Experimental Aerodynamics Division, CSIR - NAL, Bengaluru560017, India
Debopam Das
Affiliation:
Department of Aerospace Engineering, IIT Kanpur, Kanpur208016, India
*
†Email address for correspondence: [email protected]
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Abstract

This paper describes the study of instability in a transient pipe flow of decaying nature, considering variation of the base flow with time. Linear stability analysis on the decaying base flow is carried out and the effect of wavenumber on the perturbation energy growth is studied. Non-modal optimal-mode analysis, with time integration, utilising adjoint equations, is found to be suitable for the study of instability in such transient flows. The range of wavenumbers, sensitive to perturbation in providing maximum perturbation energy growth, and the magnitude of the order of growth supports the conjecture that the transient growth of the optimal perturbation is responsible for the observed instability. The findings regarding stability mechanism are substantiated by an experimental investigation accompanied by a numerical study. In an unsteady experiment, where a piston with trapezoidal velocity variation drives the flow, an impulsively blocked duct flow is emulated. Particle image velocimetry (PIV) measurement provides the velocity data; the analytical velocity profiles are obtained using a series solution available in the literature, with a trapezoidal flow-rate-variation approximation. The analytical profiles capture the centreline velocities, various time scales and the reverse-flow regions, which the experiment fails to resolve. Observation of the vorticity fields confirms the appearance of instability waves close to the reverse-flow boundary layer near the wall, and the growth and transformation of the instability waves into fully grown vortices. The coherent wave structures and their associated wavenumbers are extracted quantitatively through spatial dynamic mode decomposition (DMD) analysis. This comprehensive analysis recognises the dynamics of the flow-field development, which suggests that the loss of mean-flow energy and the perturbation energy growth compensate each other, with the remaining energy losses accounted for by viscous dissipation.

JFM classification

Mathematical Foundations: Variational methods
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 920 , 10 August 2021 , A39
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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