Steady planar and non-swirling axisymmetric flows: flow classification and its use in numerical calculations of a quasi-Newtonian fluid

Abstract

It is well established that the extra tensor τ in constant stretch history (csh) flow can be expressed either in terms ofD, the rate of strain tensor, and ω, the (relative) rate of rotation, or as an isotropic function ofD and its first two Jaumann derivatives. Explicit results are reported here for planar and non-swirling axisymmetric csh flows. Even the term directly proportional toD already allows for shear thinning and extension thickening. If this quasi-Newtonian fluid is used in numerical calculations a flow classification parameterX is needed which locally distinguishes weak from strong flows. It is shown thatX depends upon the type of flow, i.e.X in planar flow differs fundamentally from the classification parameter for non-swirling axisymmetric flows.