Grid turbulence in dilute polymer solutions: PEO in water

Abstract

AbstractGrid turbulence of polyethylene oxide (PEO) solutions (Polyox WSR-301 in${\mathrm{H} }_{2} \mathrm{O} $) has been investigated experimentally for three concentrations of 25, 50 and 100 weight ppm, at a turbulence Reynolds number based on a Taylor microscale of${\mathit{Re}}_{\lambda } \approx 100$. For the first time, time sequences of turbulence spectra have been acquired at a rate of 0.005 Hz to reveal the spectral evolution due to mechanical degradation of the polymers. In contrast to spectra averaged over the entire degradation process, the sequence of spectra reveals a clear but time-dependent Lumley scale at which the energy spectrum changes abruptly from the Kolmogorov${\kappa }^{- 5/ 3} $inertial range to a${\kappa }^{- 3} $elastic range, in which the rate of strain is maintained constant by the polymers. The scaling of the initial Lumley length with Kolmogorov dissipation rate${\epsilon }_{0} $and molecular weight is determined, and a cascade model for the temporal decrease of molecular weight, i.e. for the breaking of polymer chains is presented. Finally, a heuristic model spectrum is developed which covers the cases of both maximum and partial turbulence reduction by polymers.