Early turbulence in viscoelastic flow past a periodic cylinder array

Early turbulence in periodic cylinder arrays is of particular interest in many practical applications to enhance mixing and material/heat exchange. In this study, we reveal a new early transition pathway to a chaotic wavy state and drag enhancement with the addition of polymers. Using 2D direct numerical simulations with sufficiently small polymer diffusion ($\epsilon=10^{-5}$), we show that viscoelastic flow past periodic cylinder arrays become unstable at a Reynolds number $Re\approx 10$, significantly lower than the Newtonian counterpart of $Re\approx 150-200$. The chaotic wavy state which ensues exhibits sheets and `arrowhead' polymer conformation structures, consistent with the saturated centre-mode instability observed in wall-bounded parallel flows (Page et al., Phys. Rev. Lett., 125, 154501, 2020). Analysis of the kinetic energy budget reveals the purely elastic origin of the chaos. However, inertial forces, in conjunction with elastic forces, can reshape the base state, affecting the formation of an invariant polymer sheet. This sheet facilitates the stretching and recoiling of polymers, which in turn induces flow fluctuations and maintains the chaos. Exploring various maximum polymer extensions $b$, and polymer concentrations $\beta$ highlights the role of elastic forces in stretching the upstream separation zone while suppressing the downstream separation zone, resulting in drag enhancement at finite $Re$. Surprisingly, these modifications to the base state can suppress the invariant polymer sheet under large elastic forces (large $b$ or small $\beta$), thereby achieving a stable polymer-modified laminar state.