Lecturer: Prof. Victor Steinberg
Affiliation: Department of Physics of Complex
Systems, Weizmann Institute of Science
Abstract:
A short review of our recent results on
turbulent drag reduction (TDR) in von
Karman swirling flow of water and water-
sucrose polymer solutions, where Re and
Wi as well as polymer concentration ϕ are
varied, is presented. First, we show
experimental quantitative results on the
transition to early turbulence in water- and
water-sugar-based polymer solutions than
the transition to turbulence in their
Newtonian solvents. The transition values
of Recturb to fully developed turbulence as
well as RecTDR to TDR regime are obtained
by measurements of only global quantities
as torque Γ(t) and pressure p(t) as functions
of Re and elasticity El =Wi/Re as well as
polymer concentration ϕ. Two scaling
regions for fundamental turbulent
characteristics are identified and they
correspond to the turbulent and TDR
regimes. The both Recturb and RecTDR are
found via the dependence of the friction
coefficients Cf and Cp defined through
average torque <Γ> and rms pressure
fluctuations prms for different El and ϕ and
via the limits of the two scaling regions.
The friction coefficients Cf and Cp for
different elasticity El =Wi/Re and ϕ vs.
Re/Rec collapse onto universal curves in
accord with theory, where Rec is Re at the
TDR onset. Power spectra for Γ and p at
Re/Rec >1 show a drastic reduction of low-
frequency noise and the emergence of a
peak corresponding to the main vortex
frequency in accord with TDR. Finally, we
report rather unexpected results on drastic
difference in the transition to the turbulent
regimes and their properties in von Karman
swirling flow of water-based polymer
solutions for viscous (by smooth disks) and
inertial (by disks with blades) forcing and
by tracking torque Γ(t) and pressure p(t).
For the viscous forcing, only single
turbulent regime is found with the transition
value Recturb = RecTDR ≃ 4.8 × 105
independent of ϕ, while for the inertial
forcing, two turbulent regimes are revealed:
first transition is to fully developed
turbulence and the second one is to the
TDR regime with the both onset values
Recturb and RecTDR depending on ϕ. The both
regimes differ by the scaling exponents of
the fundamental turbulent characteristics,
the dependence of skewness and flatness of
probability density functions of p on Re,
and the different frequency power spectra
of p with the different dependencies of the
peaks in the power spectra on ϕ.