Transition to asymmetry of generalised Newtonian fluid flows through a symmetric sudden expansion

The goal of the present study is to numerically investigate the effects, by the attributes of generalised Newtonian fluids, on the threshold of transition from symmetry to asymmetry with respect to the flow through a symmetric 1:2 sudden expansion. The study includes both shear-thickening and shear-thinning fluids covering a range of the index n of the Power–Law model from 0.3 to 3 whereas shear-thinning effects were investigated also with the use of the Casson model. The subsequent effects are investigated by means of different flow parameters namely the generalised Reynolds (Re) number, the Re number defined in accordance with the inlet wall viscosity and the Re number resulting from the non-dimensionalisation of the shear–stress versus shear–rate expression. Results reveal that for both the Power–Law and Casson model cases studied, the critical generalised Re number of transition from symmetry to asymmetry and subsequently the inverse dimensionless wall shear stress are linearly related to the dimensionless shear rate at the wall. Similar relation with the latter is exhibited by the factors defined by the product of the Re number defined in accordance with the inlet wall viscosity and either the dimensionless partial derivative of pressure or u-velocity with respect to x along the channel centreline.