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An instability mechanism for particulate pipe flow

Published online by Cambridge University Press:  08 May 2019

Anthony Rouquier*
Affiliation:
Fluid and Complex Systems Research Centre, Coventry University, Priory Street, Coventry, CV1 5FB, UK
Alban Pothérat
Affiliation:
Fluid and Complex Systems Research Centre, Coventry University, Priory Street, Coventry, CV1 5FB, UK
Chris C. T. Pringle
Affiliation:
Fluid and Complex Systems Research Centre, Coventry University, Priory Street, Coventry, CV1 5FB, UK
*
Email address for correspondence: anthonyrouquier@gmail.com

Abstract

We present a linear stability analysis for a simple model of particle-laden pipe flow. The model consists of a continuum approximation for the particles, two-way coupled to the fluid velocity field via Stokes drag (Saffman, J. Fluid Mech., vol. 13 (01), 1962, pp. 120–128). We extend previous analysis in a channel (Klinkenberg et al., Phys. Fluids, vol. 23 (6), 2011, 064110) to allow for the initial distribution of particles to be inhomogeneous in a similar manner to Boronin (Fluid Dyn., vol. 47 (3), 2012, pp. 351–363) and in particular consider the effect of allowing the particles to be preferentially located around one radius in accordance with experimental observations. This simple modification of the problem is enough to alter the stability properties of the flow, and in particular can lead to a linear instability offering an alternative route to turbulence within this problem.

Type
JFM Papers
Copyright
© 2019 Cambridge University Press 

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References

Asmolov, E. S. 1999 The inertial lift on a spherical particle in a plane Poiseuille flow at large channel Reynolds number. J. Fluid Mech. 381, 6387.Google Scholar
Boffetta, G., Celani, A., De Lillo, F. & Musacchio, S. 2007 The Eulerian description of dilute collisionless suspension. Europhys. Lett. 78 (1), 14001.Google Scholar
Boronin, S. 2012 Optimal disturbances of a dusty-gas plane-channel flow with a nonuniform distribution of particles. Fluid Dyn. 47 (3), 351363.Google Scholar
Boronin, S. & Osiptsov, A. 2008 Stability of a disperse-mixture flow in a boundary layer. Fluid Dyn. 43 (1), 6676.Google Scholar
Boronin, S. & Osiptsov, A. 2014 Modal and non-modal stability of dusty-gas boundary layer flow. Fluid Dyn. 49 (6), 770782.Google Scholar
Boronin, S. & Osiptsov, A. 2018 Effect of settling particles on the stability of a particle-laden flow in a vertical plane channel. Phys. Fluids 30 (3), 034102.Google Scholar
Elghobashi, S. 1994 On predicting particle-laden turbulent flows. Appl. Sci. Res. 52 (4), 309329.Google Scholar
Ferrante, A. & Elghobashi, S. 2003 On the physical mechanisms of two-way coupling in particle-laden isotropic turbulence. Phys. Fluids 15 (2), 315329.Google Scholar
Han, M., Kim, C., Kim, M. & Lee, S. 1999 Particle migration in tube flow of suspensions. J. Rheol. 43, 11571174.Google Scholar
Hogg, A. J. 1994 The inertial migration of non-neutrally buoyant spherical particles in two-dimensional shear flows. J. Fluid Mech. 272, 285318.Google Scholar
Ismail, I., Gamio, J., Bukhari, S. & Yang, W. 2005 Tomography for multi-phase flow measurement in the oil industry. Flow Meas. Instrum. 16 (2), 145155.Google Scholar
Jackson, R. 2000 The Dynamics of Fluidized Particles. Cambridge University Press.Google Scholar
Klinkenberg, J., de Lange, H. & Brandt, L. 2011 Modal and non-modal stability of particle-laden channel flow. Phys. Fluids 23 (6), 064110.Google Scholar
Klinkenberg, J., Sardina, G., De Lange, H. & Brandt, L. 2013 Numerical study of laminar-turbulent transition in particle-laden channel flow. Phys. Rev. E 87 (4), 043011.Google Scholar
Kolesnikov, Y., Karcher, C. & Thess, A. 2011 Lorentz force flowmeter for liquid aluminum: laboratory experiments and plant tests. Metall. Mater. Trans. B 42 (3), 441450.Google Scholar
Loisel, V., Abbas, M., Masbernat, O. & Climent, E. 2013 The effect of neutrally buoyant finite-size particles on channel flows in the laminar-turbulent transition regime. Phys. Fluids 25 (12), 123304.Google Scholar
Mack, L. M. 1976 A numerical study of the temporal eigenvalue spectrum of the blasius boundary layer. J. Fluid Mech. 73 (3), 497520.Google Scholar
Matas, J.-P., Morris, J. F. & Guazzelli, E. 2003 Transition to turbulence in particulate pipe flow. Phys. Rev. Lett. 90, 014501.Google Scholar
Matas, J.-P., Glezer, V., Morris, J. F. & Guazzelli, E. 2004a Trains of particle at finite Reynolds number pipe flow. Phys. Fluids 16 (11), 41924195.Google Scholar
Matas, J.-P., Morris, J. F. & Guazzelli, E. 2004b Inertial migration of rigid spherical particles in Poiseuille flow. J. Fluid Mech. 515, 171.Google Scholar
Maxey, M. 2017 Simulation methods for particulate flows and concentrated suspensions. Annu. Rev. Fluid Mech. 49 (1), 171193.Google Scholar
Meseguer, A. & Trefethen, L. N. 2003 Linearized pipe flow to Reynolds number 107 . J. Comput. Phys. 186 (1), 178197.Google Scholar
Repetti, R. V. & Leonard, E. F. 1964 Segré–Silberberg’s annulus formation: a possible explanation. Nature 203, 13461348.Google Scholar
Rouquier, A., Pothérat, A. & Pringle, C. C. T.2019 Linear transient growth in particulate pipe flow. arXiv:1903.10389.Google Scholar
Saffman, P. G. 1962 On the stability of a laminar flow of a dusty gas. J. Fluid Mech. 13 (01), 120128.Google Scholar
Schonberg, J. A. & Hinch, E. J. 1989 Inertial migration of a sphere in Poiseuille flow. J. Fluid Mech. 203, 517524.Google Scholar
Segré, G. & Silberberg, A. 1962 Behaviour of macroscopic rigid spheres in Poiseuille flow. Part 2. Experimental results and interpretation. J. Fluid Mech. 14, 136157.Google Scholar
Squires, K. D. & Eaton, J. K. 1991 Preferential concentration of particles by turbulence. Phys. Fluids A 3 (5), 11691178.Google Scholar
Uhlmann, M. 2005 An immersed boundary method with direct forcing for the simulation of particulate flows. J. Comput. Phys. 209 (2), 448476.Google Scholar
Wang, G., Abbas, M. & Climent, E. 2018 Modulation of the regeneration cycle by neutrally buoyant finite-size particles. J. Fluid Mech. 852, 257282.Google Scholar
Wang, T. & Baker, R. 2014 Coriolis flowmeters: a review of developments over the past 20 years, and an assessment of the state of the art and likely future directions. Flow Meas. Instrum. 40, 99123.Google Scholar
Willis, A. P. 2017 The Openpipeflow Navier–Stokes solver. SoftwareX 6, 124127.Google Scholar
Yu, Z., Wu, T., Shao, X. & Lin, J. 2013 Numerical studies of the effects of large neutrally buoyant particles on the flow instability and transition to turbulence in pipe flow. Phys. Fluids 25, 043305.Google Scholar
Zhu, H. & Yu, A. 2002 Averaging method of granular materials. Phys. Rev. E 66 (2), 021302.Google Scholar