Drag enhancement and drag reduction in viscoelastic flow

Creeping flow of polymeric fluid without inertia exhibits elastic instabilities and elastic turbulence accompanied by drag enhancement due to elastic stress produced by flow-stretched polymers. However, in inertia-dominated flow at high Re and low fluid elasticity El, a reduction in turbulent frictional drag is caused by an intricate competition between inertial and elastic stresses. Here we explore the effect of inertia on the stability of viscoelastic flow in a broad range of control parameters El and (Re,Wi). We present the stability diagram of observed flow regimes in Wi-Re coordinates and find that the instabilities' onsets show an unexpectedly nonmonotonic dependence on El. Further, three distinct regions in the diagram are identified based on El. Strikingly, for high-elasticity fluids we discover a complete relaminarization of flow at Reynolds number in the range of 1 to 10, different from a well-known turbulent drag reduction. These counterintuitive effects may be explained by a finite polymer extensibility and a suppression of vorticity at high Wi. Our results call for further theoretical and numerical development to uncover the role of inertial effect on elastic turbulence in a viscoelastic flow.