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

摘要

It is well established that the extra tensor Gamma in constant stretch history (csh) flow can be expressed either in terms of D, the rate of strain tensor. and omega, the (relative) rate of rotation, or as an isotropic function of D and its first two Jaumann derivatives. Explicit results are reported here for planar and non-swirling axisymmetric csh flows. Even the term directly proportional to D already allows for shear thinning and extension thickening. If this quasi-Newtonian fluid is used in numerical calculations a flow classification parameter X is needed which locally distinguishes weak from strong flows. It is shown that X depends upon the type of flow, i.e. X in planar flow differs fundamentally from the classification parameter for non-swirling axisymmetric flows. [References: 21]