2 research outputs found
Drag Reduction by Polymers in Turbulent Channel Flows: Energy Redistribution Between Invariant Empirical Modes
We address the phenomenon of drag reduction by dilute polymeric additive to
turbulent flows, using Direct Numerical Simulations (DNS) of the FENE-P model
of viscoelastic flows. It had been amply demonstrated that these model
equations reproduce the phenomenon, but the results of DNS were not analyzed so
far with the goal of interpreting the phenomenon. In order to construct a
useful framework for the understanding of drag reduction we initiate in this
paper an investigation of the most important modes that are sustained in the
viscoelastic and Newtonian turbulent flows respectively. The modes are obtained
empirically using the Karhunen-Loeve decomposition, allowing us to compare the
most energetic modes in the viscoelastic and Newtonian flows. The main finding
of the present study is that the spatial profile of the most energetic modes is
hardly changed between the two flows. What changes is the energy associated
with these modes, and their relative ordering in the decreasing order from the
most energetic to the least. Modes that are highly excited in one flow can be
strongly suppressed in the other, and vice versa. This dramatic energy
redistribution is an important clue to the mechanism of drag reduction as is
proposed in this paper. In particular there is an enhancement of the energy
containing modes in the viscoelastic flow compared to the Newtonian one; drag
reduction is seen in the energy containing modes rather than the dissipative
modes as proposed in some previous theories.Comment: 11 pages, 13 figures, included, PRE, submitted, REVTeX