Energy transfer in von Kármán swirling flow of dilute polymer solutions

We present an experimental study of the effects of polymer additives on the energy cascade in a turbulent von Kármán swirling (VKS) flow. The velocity near the center of VKS is measured by tomographic particle image velocimetry. The energy transfer across different scales and directions is investigated by means of the Kármán–Howarth–Monin–Hill (KHMH) equation. We find that the anisotropy of VKS manifests itself as significant differences in both the second order velocity structure function and inertial energy transfer rate in different directions within the scale space. And in polymeric turbulence the elastic scaling is not affected by the anisotropy, as the slope of the power law scaling remains almost the same in different orientations; while the magnitude is highly orientation dependent. In turn, polymer additives increase the existing anisotropy especially in the elastic range. Furthermore, in the axial direction of VKS, the intermittency is enhanced and very weak inverse energy transfer appears locally, which may be related to the polymer-enhanced anisotropy in VKS flow. The spherically averaged KHMH equation also reveals that most terms associated with the energy transfer are suppressed by polymer additives, and in addition, the viscous diffusion terms exhibit power-law relationships with scale, demonstrating the profound impact of polymers on the turbulent energy cascade.