Dynamic Insights into Non-Local Energy Transfer in Non-Stationary Turbulence: Theory, Energy Transfer Mechanisms, Methodology and Experiments

The scale-locality in the Richardson-Kolmogorov energy cascade is under heightened scrutiny. The current work focuses on the non-local energy transfer in non-stationary flows. Phase average is demonstrated as the equivalence to the ensemble average in periodical flows. The classic scale-by-scale energy budget equation (van Kármán- Howarth–Monin–Hill equation) is only employed for stationary incompressible flows. In the realm of non-stationary flows, two points at different space and time are substituted into the Navier-Stoke equations and reproduce the KHMH equation by phase average. Subsequently, a novel form of the scale-by-scale energy budget equation for non-stationary flows is introduced, elucidating the significance of each term. The equivalence among the new energy budget equation, KHMH equation, and K41 results is demonstrated under specific assumptions.

The dissertation introduces the Phase Proper Orthogonal Decomposition (Phase POD) method, utilizing phase averaging for the optimized decomposition of spatiotemporal behavior in statistically non-stationary turbulent flows. Applied to a periodically forced statistically non-stationary lid-driven cavity flow, the Phase POD method employs the snapshot algorithm to extract space-phase modes, revealing four central flow patterns that describe the evolution of energetic structures as a function of phase. The modal components of the energy transport equation are showcased with a focus on the triadic interaction term (nonlinear energy transfer term), interpreted as the convective transport of bi-modal interactions. Non-local energy transfer is observed, stemming from the non-stationarity of dynamical processes and inducing triadic interactions across a broad range of mode numbers.

In pursuit of empirical evidence, the dissertation introduces a novel volumetric velocity measurement method of micron-scale seeding tracer air-filled soap bubbles (AFSB) with diameter 5 μm ∼100 μm for volume ≥ 500 cm³. The proposed methodology, situated tracer size between helium-filled soap bobbles (HFSB) and di-ethylhexyl- sebacic acid ester (DEHS) droplets, is designed to enhance turbulence measurement resolution in large volume of interest. The targeted measurement volume dimension equal to the volume of HFSB seeding, which will give a higher resolution of turbulence study. Formulations for the relationships between particle size, imaging, and light intensity are presented, with computed estimations for the setup design. The methodology is demonstrated through turbulence velocity measurements in jet flow, showcasing the experimental facility’s cutting-edge implementation. Details of the experimental design are thoroughly expounded, and considerations for alternative options not adopted by this facility are provided. Despite functional challenges with the micro-scale AFSB bubble generator, experiment results with larger AFSB sizes are presented in this dissertation.