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Direct numerical simulations of isotropic turbulence with polymer additives are used to analyse the relevant terms for large- eddy simulations (LES) of turbulent flows with polymer solutions, the rheology of which is described by the finitely extensible nonlinear elastic-Peterlin (FENE-P) model for polymers. Equations for the evolution of the kinetic energy and subgrid-scale kinetic energy are derived including the effects of polymer additives, where the grid and subgrid-scales of motion are defined through the application of a box filter. With this decomposition it is possible to isolate the effects of the (i) ’classical’ energy cascade, (ii) grid/subgrid-scale inter- actions induced by the polymer, and (iii) the subgrid-scale/polymer interactions. The energy transfer between GS and SGS induced by the polymer is predominantly to the SGS, even if there are important contributions from inverse cascade, as in the classical (Newtonian) GS/SGS energy transfer. The results show that the energy transfer between GS/SGS and the energy transfer between the SGS/polymer are strongly correlated with the (Newtonian) viscous dissipation. The results suggest that SGS closures could be developed for vis- coelastic turbulence based on a transport equation for the SGS kinetic energy.
Author(s):
Antonio Mosca
IST/Technical University of Lisbon
Portugal
Carlos B. da Silva
IST/Technical University of Lisbon
Portugal
Fernando T. Pinho
FEUP/faculdade de Engenharia da Universidade do Porto
Portugal
Pedro Valente