Competing instabilities in wide-gap viscoelastic Taylor-Couette flow: Taylor vs. helical vortices

Abstract

This paper presents a numerical study of the stability of a polymer solution flow between concentric cylinders with a rotating inner cylinder. The case of a small-radius inner cylinder is considered. The fluid motion is described using a specific case of the Kelvin-Voigt model, often referred to as the Oskolkov model. This model is applicable to very dilute polymer solutions, where the retardation time is much smaller than the characteristic time of the problem and elastic forces are much smaller than viscous forces. The stability of the steady-state motion is investigated using a fully nonlinear approach by means of direct numerical simulation of a perturbation introduced as finite-duration white noise. Depending on the Reynolds number, the perturbation either decays or grows. The critical Reynolds numbers obtained for both Newtonian and non-Newtonian fluids are found to be in agreement with the predictions of the linear theory. It is also shown that an increase in the elastic forces makes helical perturbations more dangerous than their axisymmetric counterparts.