Numerical simulations of a dilute polymer solution in isotropic turbulence

A dilute polymer solution in isotropic turbulence is investigated using several simulation techniques in order to understand the interactions between the flow and the polymer. While the Newtonian isotropic turbulent flows can be accurately investigated using direct numerical simulations (DNS), the polymer additives result in an extra polymer induced stress tensor in the Navier-Stokes equation. In order to study the polymeric turbulent flow, an efficient and accurate polymer model needs to be used in a polymeric DNS. In this dissertation, the finitely extensible nonlinear elastic model with Peterlin approximation (FENE-P) is used in the polymeric DNS. In the first part of this dissertation, FENE-P is compared with FENE chains that are closer representations of a real polymer molecule in isotropic turbulence. The comparison is conducted along Lagrangian trajectories generated from a Newtonian DNS. We demonstrate that FENE-P with carefully chosen parameters is a good representation of real polymers when the polymers are highly stretched by the flow. Furthermore, through the same Lagrangian simulation techniques of the FENE-P model, we qualitatively show that the polymer field has finer spatial structures than the underlying flow and a much finer grid is required to fully resolve the polymer field.; In the second part of the dissertation, we conduct polymeric isotropic DNS using the FENE-P model. In this dissertation, we study the effects of the polymer concentration and the Weissenberg number. We show that polymers can alter the turbulent energy cascade and attenuate the small scale motions. This effect increases with both the concentration and the Weissenberg number.; Finally, a Reynolds-averaged Navier-Stokes (RANS) model of the FENE-P model in isotropic turbulence is proposed so that it is possible to avoid the expensive simulation cost of a DNS. In this RANS model, we first propose a statistical closure for the mean stretching term through stochastic modeling and then close the mean restoring term by assuming a simplified probability density function (PDF) of the polymer stretch. This RANS model is tested against DNS results in isotropic turbulence.