Linear stability and transient behaviour of viscoelastic fluids in boundary layers

Cracco, Martina 2019. Linear stability and transient behaviour of viscoelastic fluids in boundary layers. PhD Thesis, Cardiff University. Item availability restricted.

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Abstract

The linear stability analysis of Rivlin-Ericksen uids of second order is investigated for boundary layer ows, where a semi-infinite wedge is placed symmetrically with respect to the ow direction. Second order uids belong to a larger family of uids called Order uids, which is one of the first classes proposed to model departures from Newtonian behaviour. Second order uids can represent non-zero normal stress differences, which is an essential feature of viscoelastic uids. The linear stability properties are studied for both signs of the elasticity number K, which characterises the non-Newtonian response of the uid. Stabilisation is observed for the temporal and spatial evolution of two-dimensional disturbances when K > 0, in terms of increase of critical Reynolds numbers and reduction of growth rates, whereas the ow is less stable when K < 0. By extending the analysis to three-dimensional disturbances, we show that a positive elasticity number K destabilises streamwise independent waves, while the opposite happens for K < 0. We show that, as for Newtonian uids, the nonmodal amplification of streamwise independent disturbances is the most dangerous mechanism for transient energy growth which is enhanced when K > 0 and reduced when K < 0. A preliminary study of boundary layer ows of UCM, Oldroyd B, Phan-Thien Tanner and Giesekus uids is performed. Asymptotic Suction Boundary Layer theory allows us to simplify the governing equations and obtain analytical solutions for the UCM and Oldroyd B models. The mean ow obtained can be used as a starting point for a modal and nonmodal linear stability analysis, following the analysis performed for second order models.

Item Type:	Thesis (PhD)
Date Type:	Completion
Status:	Unpublished
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Funders:	EPSRC
Date of First Compliant Deposit:	19 March 2020
Last Modified:	11 Dec 2020 02:30
URI:	https://orca.cardiff.ac.uk/id/eprint/130521

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