A timestepper approach for the systematic bifurcation and stability analysis of polymer extrusion dynamics

Kavousanakis, ME; Russo, L; Siettos, CI; Boudouvis, AG; Georgiou, GC

dc.contributor.author	Kavousanakis, ME	en
dc.contributor.author	Russo, L	en
dc.contributor.author	Siettos, CI	en
dc.contributor.author	Boudouvis, AG	en
dc.contributor.author	Georgiou, GC	en
dc.date.accessioned	2014-03-01T01:27:48Z
dc.date.available	2014-03-01T01:27:48Z
dc.date.issued	2008	en
dc.identifier.issn	0377-0257	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/18587
dc.subject	Bifurcation analysis	en
dc.subject	Extrusion instabilities	en
dc.subject	Floquet multipliers	en
dc.subject	Oldroyd-B fluid	en
dc.subject	Poiseuille flow	en
dc.subject	Timestepper approach	en
dc.subject.classification	Mechanics	en
dc.subject.other	Bifurcation (mathematics)	en
dc.subject.other	Fluid mechanics	en
dc.subject.other	Matrix algebra	en
dc.subject.other	Non Newtonian liquids	en
dc.subject.other	Steady flow	en
dc.subject.other	Viscoelasticity	en
dc.subject.other	Extrusion instabilities	en
dc.subject.other	Floquet multipliers	en
dc.subject.other	Timestepper approach	en
dc.subject.other	Extrusion	en
dc.subject.other	Bifurcation (mathematics)	en
dc.subject.other	Extrusion	en
dc.subject.other	Fluid mechanics	en
dc.subject.other	Matrix algebra	en
dc.subject.other	Non Newtonian liquids	en
dc.subject.other	Steady flow	en
dc.subject.other	Viscoelasticity	en
dc.title	A timestepper approach for the systematic bifurcation and stability analysis of polymer extrusion dynamics	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.jnnfm.2007.11.002	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.jnnfm.2007.11.002	en
heal.language	English	en
heal.publicationDate	2008	en
heal.abstract	We discuss how matrix-free/timestepper algorithms can efficiently be used with dynamic non-Newtonian fluid mechanics simulators in performing systematic stability/bifurcation analysis. The timestepper approach to bifurcation analysis of large-scale systems is applied to the plane Poiseuille flow of an Oldroyd-B fluid with non-monotonic slip at the wall, in order to further investigate a mechanism of extrusion instability based on the combination of viscoelasticity and non-monotonic slip. Due to the non-monotonicity of the slip equation the resulting steady-state flow curve is non-monotonic and unstable steady states appear in the negative-slope regime. It has been known that self-sustained oscillations of the pressure gradient are obtained when an unstable steady state is perturbed [M.M. Fyrillas, G.C. Georgiou, D. Vlassopoulos, S.G. Hatzikiriakos, A mechanism for extrusion instabilities in polymer melts, Polymer Eng. Sci. 39 (1999) 2498-2504]. Treating the simulator of a distributed parameter model describing the dynamics of the above flow as an input-output ""black-box"" timestepper of the state variables, stable and unstable branches of both equilibrium and periodic oscillating solutions are computed and their stability is examined. It is shown for the first time how equilibrium solutions lose stability to oscillating ones through a subcritical Hopf bifurcation point which generates a branch of unstable limit cycles and how the stable periodic solutions lose their stability through a critical point which marks the onset of the unstable limit cycles. This implicates the coexistence of stable equilibria with stable and unstable periodic solutions in a narrow range of volumetric flow rates. © 2007 Elsevier B.V. All rights reserved.	en
heal.publisher	ELSEVIER SCIENCE BV	en
heal.journalName	Journal of Non-Newtonian Fluid Mechanics	en
dc.identifier.doi	10.1016/j.jnnfm.2007.11.002	en
dc.identifier.isi	ISI:000256605100006	en
dc.identifier.volume	151	en
dc.identifier.issue	1-3	en
dc.identifier.spage	59	en
dc.identifier.epage	68	en