Torque and pressure fluctuations in turbulent von Karman swirling flow between two counter-rotating disks. I

Abstract

We report the experimental studies of the statistical and scaling properties of the fully developed turbulent regime in von Karman swirling flow between counter-rotating disks with and without blades using the only global measurements of the spatially averaged torque Γ and pressure p fluctuations in water and water-sugar solutions of different viscosities in the same cell geometry. We show that for all fluids under investigation probability distribution functions (PDFs) of the torque fluctuations δΓ/Γrms are Gaussian in both the laminar and turbulent regimes and for the both types of the stirrers. On the contrary, PDFs of the pressure fluctuations change from Gaussian in the laminar regime into the skewed shape with the exponential tails toward low-pressure events for both the entrainment methods. Both the friction coefficient Cf and normalized rms of the pressure fluctuations Cp are independent of Re in the fully developed turbulent regime for all fluids under study and found in a good quantitative agreement with the previous results. We also observe that the internal flow variables such as the normalized torque \documentclass[12pt]{minimal}\begin{document}$\bar{\Gamma }/Vp_{rms}$\end{document}Γ¯/Vprms versus the “internal” Reynolds number Rerms = (prms/ρ)1/2Rρ/η instead of the global variables Cf, Cp versus Re show sharp transition into the well developed turbulent regime. We find that the scaling exponents of the fundamental characteristics based only on Γ and p measurements in the range of fully developed turbulent flow, namely, the integral, Taylor, and Kolmogorov dissipation lengths, as well as the Taylor-based Reynolds number Rλ, are in rather fair agreement with the predictions. We would like to emphasize that scaling of the main turbulent parameters Rλ, λ, ηd obtained via the global variables is a very non-trivial result. It is not obvious that measurements based on the global quantities will provide the predicted scaling relations. The result on such scaling obtained previously strongly disagrees with the scaling predictions. Indeed, both \documentclass[12pt]{minimal}\begin{document}$\bar{\Gamma }$\end{document}Γ¯ and prms are averaged over the cell volume as well as all spatial scales, whereas the swirling flow is neither isotropic nor homogeneous. So the global variables being averaged over all spatial scales get contributions from the scales larger and smaller than those from the inertial range of scales. And finally, the normalized characteristic frequencies fp/frot found in both the torque and pressure frequency power spectra in the fully developed turbulent regime have close values, are independent of Re, and associated with either the rotation or oscillation frequency of the main vortex.