High-Fidelity Simulations and Data-Driven Analysis
Open Access DepositedFree-Surface Turbulence and Bubble Dynamics
Turbulent air entrainment in free-surface turbulence (FST) and bubble dynamics underpin critical processes in natural and industrial systems, from ocean-atmosphere interactions, to chemical reactors and naval hydrodynamics. This thesis presents a cohesive exploration of FST and bubble behavior in two-phase flows, blending high-fidelity direct numerical simulations (DNS) with innovative data-driven methodologies to unravel the complex interplay of turbulence, interfacial dynamics, and energy exchange.The investigation begins with the challenge of simulating turbulent free-surface flows, where computational costs have historically constrained scale-resolving studies. To overcome this, an efficient computational framework was used, integrating Fast Poisson Solvers (FPS) and the Ghost Fluid Method (GFM) for sharp interface treatment. Coupled with a conservative level set approach, this framework enables efficient simulations of air-water interfaces subjected to homogeneous isotropic turbulence (HIT). Different turbulence forcing strategies are explored, including linear forcing in physical space and a synthetic Fourier boundary condition, achieving reduced domain sizes. Stationary statistics are captured such as entrained bubble sizes and Reynolds stresses, setting the stage for detailed analysis of interfacial phenomena. Central to the thesis is the examination of energy exchange in SFST under varying physical regimes, characterized by Reynolds (Re), Froude (Fr), and Weber (We) numbers. The analysis shows a dual energy cascade near the free-surface, and employs discrete wavelet transforms to identify distinct scaling laws in the inertial subrange, as well as scale filtering to compute inter-scale energy fluxes. These findings illuminate the proximity- and scale-dependent mechanisms governing gas-liquid flows, with implications for sub-grid modeling. Bubble breakup and deformation emerge as pivotal phenomena, explored through numerical experiments in decaying HIT at moderate We. Bubbles near the turbulence integral scale exhibit maximal deformation and energy extraction, aligning with the Kolmogorov-Hinze hypothesis, while smaller bubbles show limited interaction with larger eddies. To address large deformations beyond the linear regime, a data-driven approach combining large deformation diffeomorphic metric mapping (LDDMM) and proper orthogonal decomposition (POD) was developed, offering robust analysis of resonant breakup behaviors compared to traditional spherical harmonic methods. In conclusion, the integration of efficient DNS frameworks with novel analytical tools highlights the potential to probe complex interfacial flows, paving the way for future research into sub-grid modeling and multiphase dynamics.
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