Hybrid Eulerian-Lagrangian simulations for polymer-turbulence interactions

The effects of polymer additives on decaying isotropic turbulence are numerically investigated using a hybrid approach consisting of Brownian dynamics simulations for an enormous number of dumbbells (of the order of 10 billion, O(10(10))) and direct numerical simulations of turbulence making full use of large-scale parallel computations. Reduction of the energy dissipation rate and modification of the kinetic energy spectrum in the dissipation range scale were observed when the reaction term due to the polymer additives was incorporated into the equation of motion for the solvent fluid. An increase in the polymer concentration or Weissenberg number W-i yielded significant modifications of the turbulence statistics at small scales, such as a suppression of the local energy dissipation fluctuations. A power-law decay of the kinetic energy spectrum E(k, t) similar to k(-4.7) was observed in the wavenumber range below the Kolmogorov length scale when W-i = 25. The generation of intense vortices was suppressed by the polymer additives, consistent with previous studies using the constitutive equations. The field structures of the trace of the polymer stress depended on the intensity of its fluctuation: sheet-like structures were observed for the intermediate intensity region and filamentary structures were observed for the intense region. The results obtained with few polymers and large replicas could approximate those with many polymers and smaller replicas as far as the large-scale statistics were concerned.