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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.
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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Status: Unpublished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: 20 Mar 2020 10:17
URI: http://orca.cf.ac.uk/id/eprint/130521

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