From vortices to forces - a data-driven framework for unsteady lift generation in three-dimensional vortex-dominated flows

Abstract: Time-varying flow-induced forces on bodies immersed in fluid flows play a key role across a range of natural and engineered systems, from biological locomotion to propulsion and energy-harvesting devices. These transient forces often arise from complex, dynamic vortex interactions and can either enhance or degrade system performance. However, establishing a clear causal link between vortex structures and force transients remains challenging, especially in high-Reynolds number nominally three-dimensional flows. In this study, we investigate the unsteady lift generation on a rotor blade that is impulsively started with a span-based Reynolds number of 25,500. The lift history from this direct-numerical simulation reveals distinct early-time extrema associated with rapidly evolving flow structures, including the formation, evolution, and breakdown of leading-edge and tip vortices. To quantify the influence of these vortical structures on the lift transients, we apply the force partitioning method (FPM) that quantifies the surface pressure forces induced by vortex-associated effects. Two metrics - $Q$-strength and vortex proximity - are derived from FPM to provide a quantitative assessment of the influence of vortices on the lift force. This analysis confirms and extends qualitative insights from prior studies, and offers a simple-to-apply data-enabled framework for attributing unsteady forces to specific flow features, with potential applications in the design and control of systems where unsteady aerodynamic forces play a central role.