Engineering and Physical Sciences Research Council

Manylion y Prosiect

The linear stability analysis of Rivlin-Ericksen fluids of second order is investigated for boundary layer flows, where a semi-infinite wedge is placed symmetrically with respect to the flow direction. Second order fluids belong to a larger family of fluids called Order fluids, which is one of the first classes proposed to model departures from Newtonian behaviour. Second order fluids can represent non-zero normal stress differences, which is an essential feature of viscoelastic fluids. The linear stability properties are studied for both signs of the elasticity number K, which characterises the non-Newtonian response of the fluid. 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 flow 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 fluids, 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 flows of UCM, Oldroyd B, Phan-Thien Tanner and Giesekus fluids 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 flow obtained can be used as a starting point for a modal and nonmodal linear stability analysis, following the analysis performed for second order models.

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