Understanding Fluid-Metamaterial Interactions through Dynamical Systems Analysis

This project aims to advance analysis methodologies and systematically investigate the interaction mechanisms in fluid-metamaterial systems. Fluid-metamaterial systems have recently emerged as a novel design concept, offering unique capabilities for controlling wave propagation in fluids. These capabilities arise from the coupled interactions between fluid flow instabilities and the wave-manipulating properties of metamaterials. In particular, fluid waves can be selectively suppressed or enhanced by tuning the metamaterial’s frequency response and aligning its stop and pass bands with the dominant frequencies of turbulent eddies that are aimed to be suppressed or amplified in turbulent flows. This project will develop and validate new theoretical and computational tools for efficient analysis of fluid–metamaterial interactions in turbulent flow systems. Harnessing fluid-metamaterial interactions in creative and novel ways provides extraordinary potential to transform the design and control of mechanical systems interacting with fluids. New technologies arising from this concept will increase resilience, durability, and energy efficiency of engineered systems and devices, fostering innovations with long-lasting impacts on aerospace, energy systems, and manufacturing technologies. The project will also contribute to Arizona’s STEM workforce and educational infrastructure by expanding research and outreach opportunities for K-12, undergraduate, and graduate students. A new theoretical framework for the efficient analysis of fluid–metamaterial interactions in turbulent flow systems will be developed, based on an input–output formulation that quantifies the linear amplification of harmonic disturbances using resolvent analysis. The developed framework will be further leveraged to systematically investigate fluid-metamaterial interactions under a broad range of flow conditions and metamaterial designs, in order to build a comprehensive knowledge of the coupled system dynamics. The project objectives include: (1) development and validation of new models and algorithms to elucidate the amplification properties in fully coupled fluid-metamaterial systems; (2) a comprehensive analysis of coupled interactions in both attached and separated flows interfacing various metamaterial architectures; and (3) interpretation and evaluation of the resulting input-output gains in the context of turbulent drag reduction and flow separation control. A scientific contribution will arise from an improved understanding of the fluid-metamaterial interactions, specifically elucidating: (i) the role of frequencies, bandgap sizes, truncation resonances and phases under different control objectives; (ii) mechanisms of local and nonlocal interventions in fluid-metamaterial systems with distinct features; and (iii) the role of tangential surface motions and shear-driven responses. Developed open-source computational and analysis tools will enrich scientific community and drive technological innovations across manufacturing, civil, mechanical, aerospace engineering, and related fields. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.