Subgrid-scale statistics and energy transfer in polymer-laden turbulence determined from tomographic particle image velocimetry measurements

To investigate how polymers influence energy transfer in three-dimensional turbulence, we conduct experiments in homogeneous bulk turbulence generated by a von Kármán swirling flow, using tomographic particle image velocimetry. A filtering approach is applied to the measured three-dimensional velocity fields to extract subgrid-scale (SGS) statistics, focusing on the filtered strain-rate tensor and SGS stress tensor. We find that polymer additives induce significant changes in the tensorial geometry: the strain-rate tensor shows a tendency towards an eigenvalue ratio of $1 : 0 : -1$ , while the SGS stress tensor favours a $2 : -1 : -1$ configuration. The local energy flux – quantified by the inner product of the strain-rate and SGS stress tensors – is systematically suppressed by polymers and becomes increasingly intermittent. This suppression is linked to a reduced energy transfer efficiency, associated with the misalignment between the principal eigendirections of the two tensors. Anisotropic effects are also observed in the energy flux components, indicating that polymers affect vertical and horizontal energy transfer differently. Finally, the obtained SGS statistics allow for an a priori assessment of SGS models. Our results reveal that the nonlinear gradient model significantly outperforms the Smagorinsky model, particularly in polymer-laden turbulence. The diminished alignment between the strain-rate and SGS stress tensors may underlie the limitations of the Smagorinsky model, which assumes a scalar eddy-viscosity closure. These results provide new experimental insights into the SGS dynamics of polymeric turbulence and highlight the potential of nonlinear models for large-eddy simulations of viscoelastic flows.