Breakdown to turbulence in non-Newtonian flow

Abstract

Transition to turbulence in polymeric channel flow is investigated, with the FENE-P model used to characterize the viscoelastic behaviour of the flow. Simulations are performed to study transition through both the natural and bypass routes.

In the linear growth regime of natural transition, differences in the growth rate of a TS wave are explained by appealing to the production of the perturbation energy budget. At high Weissenberg number, the growth rate is substantially lower in comparison to Newtonian flow. As a result, the transition process is prolonged. Upon the introduction of three dimensional disturbances, Newtonian and non-Newtonian cases undergo transition through the H-type instability. The spanwise extent of the lambda structures during transition is larger in non-Newtonian flow.

Bypass transition is initiated by an initially-localized disturbance. In the linear growth regime, the flow response is stabilized by viscoelasticity, and the maximum attainable disturbance-energy amplification is reduced with increasing polymer concentration. The reduction in the energy growth rate is attributed to the polymer work, which plays a dual role: First, a spanwise polymer-work term develops, and is explained by the tilting action of the wall-normal vorticity on the mean streamwise conformation tensor. This resistive term weakens the spanwise velocity perturbation thus reducing the energy of the localized disturbance. The second action of the polymer is analogous, with a wall-normal polymer work term that weakens the vertical velocity perturbation. Its indirect effect on energy growth is substantial since it reduces the production of Reynolds shear stress and in turn of the streamwise velocity perturbation, or streaks. During the early stages of non-linear growth, the dominant effect of the polymer is to suppress the large scale streaky structures which are strongly amplified in Newtonian flows. As a result, the process of transition to turbulence is prolonged and, after transition, a drag reduced turbulent state is attained.