Turbulent flow with added polymers The manner in which fluids enter a turbulent state is striking, and has significant biological, environmental and technological implications. It is important to be able to predict and control it. Industrial Technologies © Shutterstock Most advanced techniques for transition research have focused on the pathways to turbulence in Newtonian, or simple, fluids. These efforts have excluded complex and non-Newtonian fluids, which are at the core of the pharmaceutical industry, and oil and gas and plastic and papermaking processes. Long polymer molecules added to a fluid make it elastic and capable of storing stresses that depend on the history of deformation, giving the fluid a memory. The project NNJETS (Stability of non-Newtonian jets and implications for the onset of turbulence) used direct numerical simulations to study secondary instability of streaks and the transition to turbulence in viscoelastic Couette flow. Viscoelasticity was modelled using the FENE-P constitutive equations, and both the polymer concentration and Weissenberg number were varied to assess their effect on transitions at moderate Reynolds number, Re=400. Base streaks were obtained from non-linear simulations of the Couette flow in response to a streamwise vortex. The growth of streaks in both Newtonian and non-Newtonian flows is due mainly to the longitudinal vorticity. However, torque exerted by the polymers along the longitudinal direction opposes the vorticity, lowering the streak growth at large Weissenberg number. At every streak amplitude of interest, harmonic forcing was introduced to trigger the secondary instability and breakdown to turbulence. At low Weissenberg number the critical amplitude of this forcing decreased, while at large Weissenberg number the critical amplitude increased. For low-streak amplitudes the critical amplitude increases much more significantly than for large-streak amplitudes. This behaviour is explained by the two different mechanisms for triggering transition to turbulence, which are active at low and large amplitudes. For low amplitudes the transition is triggered by a two-stage mechanism. The streaks are initially distorted by the sinuous perturbation but, after a short period, they reach a maximum energy and return to a nearly stable state. They ultimately reach higher amplitude and break down to turbulence. Normal vorticity plays a fundamental role in this second growth and in the breakdown. At large Weissenberg, the polymer torque along the normal direction is opposing the vorticity, hindering the transition. Increasing the polymer concentration showed a clear decrease in the critical amplitude of the forcing for every analysed streak amplitude. Keywords Turbulent flow, non-Newtonian fluid, NNJETS, turbulence, Couette flow, streak amplitude
