Stability of flows of non-newtonian Fluids

Imperial Users onl

Linear stability and transient behaviour of viscoelastic fluids in boundary layers

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

Modelling the nonlinear dynamics of polymer solutions in complex flows

The flow of polymer solutions in the high Elasticity number, El, regime in complex geometries may lead to strong viscoelastic behaviour and eventually become unstable as the Weissenberg number, Wi, is increased beyond a critical level. So far, the success of numerical simulations in predicting the highly non-linear behaviour of polymer solutions in complex flows has been limited. In this thesis, selected constitutive models are evaluated under the high El flow regime in the cross-slot and contraction benchmark flows using a numerical technique based on the finite volume method. The numerical technique is implemented within the OpenFOAM framework and thoroughly validated in the benchmark flow. A modification to the FENE dumbbell model based on the non-affine deformation of polymer solutions is proposed, which enabled the prediction of some non-linear material functions and also enhanced numerical stability, allowing a higher Wi to be attained. Asymmetric flow instability in the cross-slot flow has been studied. Time-dependent stability diagrams were constructed based on Wi and the strain, ε, both of which govern the stretching of a polymer chain. In the contraction flow, elastic instability is simulated for the first time in this geometry. Substantial time-dependent asymmetric flow patterns were predicted as seen in experiments. The effect of the contraction ratio is investigated through a stability diagram. Three-dimensional finite element simulations were also carried out to study the effect of the aspect ratio in the contraction flow of a Phan-Thien-Tanner fluid. The simulations suggest that a lip vortex mechanism is a signature for the onset of strong viscoelastic behaviour.EThOS - Electronic Theses Online ServiceOverseas Research Scholarship AwardUniversity of ManchesterGBUnited Kingdo