Studies of Turbulence in a von Kármán Swirling Flow

Abstract

The aim of the present thesis was to improve our fundamental understanding of the dynamics of turbulence at the small and large-scales produced in a von Kármán swirling flow. The body of the work was based on the particle image velocimetry (PIV) measurements performed within a large-size facility which enabled large Reynolds numbers but with large length-scales accessible to PIV. This thesis has focused primarily on three topics that are connected to each other through a wellknown concept in turbulence theory, the energy cascade. The first study investigated the small-scale dynamics and kinematics of turbulence. The second study investigated the free decay of turbulence, a phenomenon that facilitates evaluating the large-scales to the small-scales energy transfer through the cascade process. Finally, the third study investigated the large-scale, energetic harmonic motions in the flow with and without modulations in the turbulent forcing. In the small-scale study, the interactions between the vortices at the dissipation scale with the surrounding fluid were investigated. An experimental data set of homogenous turbulence from scanning PIV [Lawson and Dawson, 2014, 2015] at the center of the von Kármán swirling flow along with a direct numerical simulation (DNS) data set of homogeneous isotropic turbulence were studied. A recent definition of objective vortex structure [Haller et al., 2016] was implemented for the first time on a fully resolved 3D experimental dataset of small-scale turbulence to detect the vortex structures in the flow fields. Various statistics conditioned on the structures and volume of the flow were presented and compared. To investigate the interaction of the vortices with the background fluid, enstrophy transport equation was evaluated in the radial and axial direction of the vortices. In addition, the entrainment velocity was calculated on the boundary of the vortices. Overall, it was shown that the vortices interacted with the surrounding fluid by exchanging mass, enstrophy, and momentum in a manner that is very similar to turbulent entrainment in free shear flows. In the decay study, the stationary homogeneous turbulence generated by the counterrotating impellers went though a free decay process by stopping the impellers. This decay process was characterized by measuring the flow field using stereoscopic PIV. This procedure was repeated many times to ensure a reasonable convergence of turbulence statistics. It was shown that when considering the velocity magnitude from all three velocity components to monitor the decay of the turbulent kinetic energy, an exponential decay in time was obtained with an exponent of n = -1.62,k(t) ~ tn, steeper than the theoretical predictions of Saffman (n = -1.2) and Loitsiansky (n = -1.43). However, analyzing the individual velocity components, revealed that the decay in the axial direction closely followed Loitsiansky prediction with an exponent of n = -1.38 whereas, the radial and circumferential velocity components were in the saturation/confinement regime with an exponent of n = -1.99. The growth rates of the integral length-scales in time also confirmed the Loitsiansky prediction in the axial direction, and the saturation/confinement regime in the other directions. The third study was motivated by the findings of Baj et al. [2019] who identified the presence of an energetic slowly rotating structure in a von Kármán swirling flow. To investigate this, various cases were designed and measured using stereoscopic PIV. It was shown that when the Reynolds number was lower than a critical value as hypothesized by Cortet et al. [2010], an energetic large-scale structure emerged in the stationary flow oscillating in all directions at approximately twice the frequency of the impellers. However, at a Reynolds number beyond the critical range, the structure was not observed. Various scenarios of harmonic and random modulations were imposed on the impellers to investigate the dependence on turbulent boundary conditions on the appearance or suppression of the instability. The structure clearly emerges when a harmonic phase shift is imposed in between the impellers during the modulation. The structure accounted for approximately 40% of the kinetic energy of the flow and oscillated in the axial and circumferential directions. The oscillation in the axial direction was more pronounced. Moreover, the structure had an oval shape and the frequency of its oscillation was locked to the modulation frequency. The cross-correlation between the velocity field and forcing revealed that the axial oscillation phase was approximately 0.2p ahead of the oscillation phase in the circumferential direction.