Nonlinear evolutions of streaky structures in viscoelastic pipe flows

Abstract

The dynamics of streaky structures in a viscoelastic pipe flow of FENE-P fluids is studied numerically. The values of Weissenberg number ( W i , polymer relaxation time over flow turn-over time) and viscosity ratios are varied to evaluate the effects of viscoelasticity in the pipe. For Reynolds numbers 3000 ∼ 3500 (based on pipe radius and maximum laminar velocity) near the transition boundary, we select finite-amplitude two-dimensional rolls as initial conditions and add infinitesimal three-dimensional perturbations to trigger the transition. The 2D streamwise rolls are highly unstable to small 3D disturbances, which helps to better understand the evolution of large scale structures. The stronger temporal intermittency in viscoelastic flows makes it more difficult to identify a successful transition; we found that quantities directly related to viscoelasticity can serve as better indicators of transition to turbulence. The role of polymer stress is studied through the kinetic energy budget and it is found that polymer torque opposes the vorticity and become more dominant for higher W i , consistent with previous studies. The results show that the secondary instability of the streaky structures can be enhanced by viscoelasticity at low W i , while at high W i viscoelasticity delays the transition to turbulence, sometimes leading to relaminarization. • Direct numerical simulations of viscoelastic pipe flow of FENE-P fluids are conducted. • Viscoelasticity changes the evolution of streaks and causes strong intermittency. • Polymer stress is studied via turbulent kinetic energy budget in streak breakdown. • Non-monotonic influence of Weissenberg number on threshold boundary of transitions.