FENE-P bead–spring chains unravel in the presence of large
enough velocity gradients.
In a turbulent flow, this can result in intermittent added stresses and exchanges of
energy between the chains and the fluid, whose magnitudes depend on the degree of
unravelling and on the orientations of the bead–spring chains. These effects
are studied
by calculating the average behaviour at different times of an ensemble of chains,
contained in a fluid particle that is moving around in a random velocity field
obtained
from direct numerical simulation of turbulent flow of a Newtonian fluid in a channel.
The results are used to evaluate theoretical explanations of drag reduction
observed in very dilute solutions of polymers.In regions of the flow in which the energy exchange with the fluid is positive,
the possibility arises that turbulence can be produced by mechanisms other than the
interaction of Reynolds stresses and the mean velocity gradient field. Of particular
interest, from the viewpoint of understanding polymer drag reduction, is the finding
that the exchange is negative in velocity fields representative of the wall
vortices that
are large producers of turbulence. One can, therefore, postulate that polymers cause
drag reduction by selectively changing the structures of eddies that produce Reynolds
stresses. The intermittent appearance of large added shear stresses is
consistent with the
experimental finding of a stress deficit, whereby the total local shear stress
is greater
than the sum of the Reynolds stress and the time-averaged shear stress
calculated from
the time-averaged velocity gradient and the viscosity of the solvent.
Model-based design of transverse wall oscillations for turbulent drag reduction