Influence of polymer additives on turbulence in von Karman swirling flow between two disks. II
Authors: Burnishev Yuri , Steinberg Victor 
Published: March 2016

We present the experimental studies of the influence of polymer additives on the statistical and scaling properties of the fully developed turbulent regime in a von Karman swirling flow driven either by the smooth or bladed disks using only the global measurements of torque Γ and pressure p fluctuations in water- and water-sugar-based solutions of different viscosities, or elasticity El, and different polymer concentrations ϕ as a function of Re in the same apparatus. There are three highlights achieved and reported in the paper: (i) An observation of turbulent drag reduction (TDR) at both the inertial and viscous flow forcing, in a contradiction to a currently accepted opinion that only the viscous forcing leads to TDR, and the unexpected drastic difference in the transition to the fully developed turbulent and TDR regimes in von Karman swirling flow of water-based polymer solutions depending on the way of the forcing; (ii) a continuous transition to TDR in both the normalized torque drop and the rms pressure fluctuations drop and universality in scaling behavior of Cf in an agreement with theoretical predictions; and (iii) the dramatic differences in the appearance of the frequency power spectra of Γ and in particular p due to the different ways of the forcing are also observed. We discuss and summarize further the results in accordance with these three main achievements. The main message of these studies is that both the inertial forcing and viscous forcing of von Karman swirling flow between two counter-rotating disks lead to TDR in the sharp contrast to the currently accepted opinion [O. Cadot et al., “Turbulent drag reduction in a closed flow system: Boundary layer versus bulk effects,” Phys. Fluids 10, 426 (1998); D. Bonn et al., “From scale scales to large scales in three-dimensional turbulence: The effect of diluted polymers,” Phys. Rev. E 47, R28 (1993); and D. Bonn et al., “Turbulent drag reduction by polymers,” J. Phys.: Condens. Matter 17, S1195 (2005)] that TDR can be observed only at the viscous driving. In this observation, Cadot et al. and Bonn et al., relate to exclusively boundary effect, whereas the existence of TDR in both ways of the flow forcing suggests that both boundary and bulk effects are responsible for TDR. The unexpected result of the striking difference in the transition to the fully developed turbulent and TDR regimes and in their properties in von Karman swirling flow of water-based polymer solutions for the viscous and inertial forcing is reported. For the viscous forcing, just the single turbulent regime is found with the transition values Recturb=RecTDR≃(4.8±0.2)×105 independent of polymer concentration ϕ, while for the inertial forcing two turbulent regimes are revealed: fully developed turbulence and the TDR regime with the transition values Recturb&lt;RecTDR and both depending on ϕ. Thus in the case of the viscous forcing, the onset to turbulence is not altered by the addition of polymers in the contrast to the inertial forcing, where early turbulence is found. Both regimes differ by the scaling exponents of the fundamental turbulent characteristics, by the dependence of skewness and flatness of probability density functions of p on Re, and by the drastically different frequency power spectra of Γ and p with the different dependencies of their frequency peaks on ϕ. It is also demonstrated that the transition to the TDR state is a continuous one for both Γ̄ and prms in accord with theoretical arguments and simulations presented in the work of Boffetta et al. [“Drag reduction in the turbulent Kolmogorov flow,” Phys. Rev. E 71, 036307 (2005)]. Indeed, Cf presented as a function of Re/RecTDR for different El show impressive collapse of the data and universal behavior above RcTDR with the functional dependencies in a full agreement with the prediction from the numerical simulations (Boffetta et al.). Moreover, the crucial issue for the existence of TDR followed from the analysis of stresses in the TDR model is also satisfied in the experiment (Boffetta et al.). As pointed out in the work of Boffetta et al., understanding the reasons of this inequality meaning that the larger effectiveness of the momentum transfer to velocity fluctuations than to elastic stress would reveal the TDR physical mechanism. The power spectra of both Γ and p in the case of the inertial forcing are characterized by the emerging pronounced peaks and their higher harmonics in parallel with up to two orders of magnitude reduction of low frequency fluctuation amplitudes in both the water- and water-sugar-based polymer solutions compared with the power spectra for the Newtonian solvents. The peaks appear at Re≥RecTDR and their normalized peak frequency fp/frot = 0.43 ± 0.02 is independent of El, ϕ, and Re. These observations agree with the numerical results, where the enhancement of the main flow compared to the Newtonian case and the strong reduction of turbulent fluctuations were also observed and quantified. On the other hand, in the case of the viscous forcing, polymers do not alter the appearance of the power spectra of p compared with water, though the scaled peak frequencies fp/frot vary with Re for all ϕ from unity at smaller Re to fp/frot = 0.6 ± 0.02 independent of ϕ and Re in the turbulent regime. Thus the inertial forcing turns out to be much more effective in the pumping energy from turbulent fluctuations into the main vortex due to stronger polymer stretching in the TDR regime that also reveals in more pronounced TDR. We suggest an explanation of the observed effects.