![[image]](graphic1.gif)
![[image]](graphic2.gif)
![[image]](graphic3.gif)
|
The signature imprint that differentiates turbulence from the smooth streamlines of nonturbulent flow is whirling eddies, big and little whirlpools, known in fluid dynamics as vortices. An important technique for observing and analyzing the effect of these eddies is a laser snapshot through a 2D slice of the flow. The "streaky structures" observed with this technique, which depict fluctuations in the flow velocity, change noticeably depending on whether the flow is viscous or viscoelastic, and they give a visual indication of the drag-reduction phenomenon.
Visualizations from Beris's simulations correspond to the observed streaky structures, and they show the same features seen experimentally. "We're able to see all the complicated structure exemplified by the streaks," says Beris. "By following how the colors merge and fade, you follow the correlation among velocity values, which represents the underlying large-scale structure that feeds the turbulence. Each structure represents the core of an eddy."
Streaky structures from the simulations and other quantitative results show--for the first time numerically--a decrease in vorticity that corresponds to lowered drag. Introducing the polymer not only reduces intensity of the velocity fluctuations, says Beris, but also shifts the most intense fluctuations away from the wall and toward the bulk of the flow.
This result tends to confirm a prominent explanation for the lowered drag. Eddy formation along the wall is what sustains turbulence throughout the flow, according to theory, and several researchers--including Beris's University of Delaware colleague Arthur Metzner--proposed as far back as the 1960s that the elastic memory of the polymers, which pulls back against the flow, reduces turbulence by making it harder for these near-wall eddies to get started. "There were other ways to explain the drag-reduction phenomenon," says Beris. "By providing these data independently, we've given credence to the eddy assumption."
The simulations also provide quantitative findings that relate the onset of drag reduction to characteristics of the polymer. The potential for the polymer to resist flow extension is represented by a parameter, L, that corresponds to how much the long-chain molecules can stretch. Simulations show no drag reduction at L = 2 and increasing drag reduction as L increases from 10 to 30. "It's strong evidence," says Beris, "that extensional behavior is critical."
Another important parameter, known as the Weissenberg or Deborah number, relates the relaxation time of the polymer to how fast the flow can stretch it. As this parameter increases, the solution has a stronger tendency to resist extension. "It's critical," says Beris, "that the characteristic relaxation time of the material is higher than the characteristic flow time." The simulations show that a high Weissenberg number, 10 or above, is required for drag reduction.
|
