Fundamental physics underlying polymer drag reduction from DNS of homogeneous shear and isotropic turbulence with the FENE-P model

Open Access
Author:
Robert, Ashish
Graduate Program:
Mechanical Engineering
Degree:
Doctor of Philosophy
Document Type:
Dissertation
Date of Defense:
March 28, 2008
Committee Members:
  • James Gordon Brasseur, Committee Chair
  • Philip John Morris, Committee Member
  • Vigor Yang, Committee Member
  • Daniel Connell Haworth, Committee Member
Keywords:
  • Homogeneous isotropic turbulence
  • Homogeneous shear turbulence
  • Polymer drag reduction
  • DNS
Abstract:
Reduction in surface shear stress in turbulent boundary layers implies suppression of turbulent momentum flux, a large-eddy phenomenon. The mechanisms by which dilute concentrations of long-chain molecules alter large-eddy structure and momentum flux are not fully understood. Experiment, however, indicates that the phenomenon requires a mix of turbulent velocity fluctuations, polymer molecules, and mean shear. The consequences of this essential mix were studied through direct numerical simulation (DNS) of homogeneous shear-driven turbulence, with polymer-turbulence interactions modeled using the finitely extensible nonlinear elastic model with the Peterlin closure (FENE-P) for polymer stress and the conformation equation solved using a newly-designed hyperbolic algorithm. Progressive increases in nondimensional polymer relaxation time (Weissenberg number) and concentration produced progressive reductions in Reynolds stress and turbulence kinetic energy concurrent with increasing polymer stress and elastic energy. Concentration, polymer relaxation time and percent drag reduction dependent variations in statistical variables underlying polymer drag reduction with polymer were consistent with experiment. The predicted influence of polymer on 1-D spectra change was also found to be consistent with experiment. Comparison of polymer stretch and elastic energy budgets with the channel flow simulation showed good qualitative agreement. Also good qualitative trends of various flow and polymeric quantities within the polymer-active elastic layer were predicted by the homogeneous shear flow simulations. Progressive increase in Weissenberg number showed ``low', ``high' and maximum drag reduction (MDR) regimes, consistent with the experiments, with each regime showing different physics of polymer-turbulence interactions. We show that suppression in momentum flux arises from suppression in vertical velocity fluctuations. Polymer is found to be the most sensitive to slow pressure-strain-rate fluctuations, primary mechanism of energy transfer to vertical velocity fluctuations. In the high Wessienberg limit polymer shuts down slow pressure-strain-rate energy transfer to vertical velocity fluctuations, but sustains vertical velocity fluctuations by transferring energy from spanwise velocity fluctuations via polymer pressure-strain-rate. We show slow pressure-strain-rate energy transfer being related to the vortical structure. Polymer reduces vorticity by strongly suppressing vortex stretching by suppressing strain rate fluctuations. Weaker vortical structure was found to be inefficient in transferring energy into vertical velocity fluctuations. Certain aspects of polymer drag reduction theories proposed by Lumley and DeGennes were found to be consistent with our homogeneous isotropic and shear flow simulations. Polymer-turbulence energy exchange rate in spectral space was found to be active in the Taylor microscales in homogeneous isotropic flow and in shear flow in the ``low' drag reduction regime. Integral scales for polymer-turbulence energy exchange rate were found to be linearly correlated with the Taylor microscales with the variation in Weissenberg number and time, in isotropic and in the ``low' drag reduction regime of the shear flow. At ``high' and maximum drag reduction regimes polymer operated at the energy containing eddies at the large scale. During the ``onset' of drag reduction polymer-turbulence energy exchange rate was found to be operating at the same scales as the slow pressure-strain-rate and therefore directly influenced the turbulence at the scales where vertical velocity fluctuations get their energy.