Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-03T08:49:41.024Z Has data issue: false hasContentIssue false
  • English
  • Français

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]
Get access Rights & Permissions [Opens in a new window]

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
Check for updates
Copyright
© The Author(s), 2021. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Akhavan, R., Kamm, R.D. & Shapiro, A.H. 1991 An investigation of transition to turbulence in bounded oscillatory Stokes flows Part 2. Numerical simulations. J. Fluid Mech. 225, 423–444.CrossRefGoogle Scholar
Bergström, L. 1993 Optimal growth of small disturbances in pipe Poiseuille flow. Phys. Fluids A 5 (11), 2710–2720.CrossRefGoogle Scholar
Berkooz, G., Holmes, P. & Lumley, J.L. 1993 The proper orthogonal decomposition in the analysis of turbulent flows. Annu. Rev. Fluid Mech. 25 (1), 539–575.CrossRefGoogle Scholar
Budwig, R. 1994 Refractive index matching methods for liquid flow investigations. Exp. Fluids 17 (5), 350–355.CrossRefGoogle Scholar
Burridge, D.M. & Drazin, P.G. 1969 Comments on “Stability of pipe Poiseuille flow”. Phys. Fluids 12 (1), 264–265.CrossRefGoogle Scholar
Butler, K.M. & Farrell, B.F. 1992 Three-dimensional optimal perturbations in viscous shear flow. Phys. Fluids A 4 (8), 1637–1650.CrossRefGoogle Scholar
Das, D. & Arakeri, J.H. 1998 Transition of unsteady velocity profiles with reverse flow. J. Fluid Mech. 374, 251–283.CrossRefGoogle Scholar
Duke, D., Soria, J. & Honnery, D. 2012 An error analysis of the dynamic mode decomposition. Exp. Fluids 52 (2), 529–542.CrossRefGoogle Scholar
Farrell, B.F. 1988 Optimal excitation of perturbations in viscous shear flow. Phys. Fluids 31 (8), 2093–2102.CrossRefGoogle Scholar
Ghidaoui, M. & Kolyshkin, A.A. 2002 A quasi-steady approach to the instability of time-dependent flows in pipes. J. Fluid Mech. 465, 301–330.CrossRefGoogle Scholar
Hall, P. 1978 The linear stability of flat Stokes layers. Proc. R. Soc. Lond. A 359 (1697), 151–166.Google Scholar
Hall, P. & Parker, K.H. 1976 The stability of the decaying flow in a suddenly blocked channel. J. Fluid Mech. 75, 305–314.CrossRefGoogle Scholar
Jewell, N. & Denier, J.P. 2006 The instability of the flow in a suddenly blocked pipe. Q. J. Mech. Appl. Maths 59 (4), 651–673.CrossRefGoogle Scholar
Kosambi, D.D. 1943 Statistics in function space. J. Indian Math. Soc. 7, 76–88.Google Scholar
Lumley, J.L. 1967 The structure of inhomogeneous turbulent flows. In Atmospheric Turbulence and Radio Wave Propagation (ed. A.M. Yaglom & V.I. Tartarsky), pp. 221–227. Nauka.Google Scholar
Melling, A. 1997 Tracer particles and seeding for particle image velocimetry. Meas. Sci. Technol. 8 (12), 1406–1416.CrossRefGoogle Scholar
Nayak, A. & Das, D. 2017 Transient growth of optimal perturbation in a decaying channel flow. Phys. Fluids 29 (6), 064104.CrossRefGoogle Scholar
Nayak, A. & Das, D. 2019 A pseudospectral approach applicable for time integration of linearized N-S operator that removes pole singularity and physically spurious eigenmodes. Intl J. Numer. Meth. Fluids 91 (10), 473–486.CrossRefGoogle Scholar
Rowley, C.W., Mezić, I., Bagheri, S., Schlatter, P. & Henningson, D.S. 2009 Spectral analysis of nonlinear flows. J. Fluid Mech. 641, 115–127.CrossRefGoogle Scholar
Schmid, P.J. 2007 Nonmodal stability theory. Annu. Rev. Fluid Mech. 39 (1), 129–162.CrossRefGoogle Scholar
Schmid, P.J. 2010 Dynamic mode decomposition of numerical and experimental data. J. Fluid Mech. 656, 5–28.CrossRefGoogle Scholar
Schmid, P.J. & Henningson, D.S. 1994 Optimal energy density growth in Hagen–Poiseuille flow. J. Fluid Mech. 277, 197–225.CrossRefGoogle Scholar
Seminara, G., Hall, P. & Stuart, J.T. 1975 Linear stability of slowly varying unsteady flows in a curved channel. Proc. R. Soc. Lond. A 346 (1646), 279–303.Google Scholar
Toophanpour-Rami, M., Hassan, E.R., Kelso, R.M. & Denier, J.P. 2007 Preliminary investigation of impulsively blocked pipe flow. In 16th Australasian Fluid Mechanics Conference (AFMC), Crowne Plaza, Gold Coast, Australia, School of Engineering, The University of Queensland.Google Scholar
Weinbaum, S. & Parker, K.H. 1975 The laminar decay of suddenly blocked channel and pipe flows. J. Fluid Mech. 69, 729–752.CrossRefGoogle Scholar