Theoretical and Computational Analysis of Aerodynamic Haystacks in the Turbulence–Cascade Interactions

The haystack phenomenon is a hallmark of turbulence–propeller interaction and a major source of unsteady thrust and aerodynamic noise in aircraft and underwater applications. This phenomenon is characterized by distinct broadband spectral humps in the unsteady thrust and noise at blade passing frequency harmonics. These humps tend to shift to higher frequencies under certain conditions, known as blue-shifting. Understanding the mechanics behind the haystack is crucial for developing effective flow and noise control strategies. This work introduces a theoretical model to predict unsteady thrust caused by these interactions. This model is validated through comparisons with numerical simulations under various inflow conditions, including single-frequency gusts and broadband turbulence. In addition, we examine the mechanisms of the haystack, with a focus on the influence of key parameters. Beyond its predictive capabilities, the model reveals certain flow structures ingested by the rotor that are related to the unsteady thrust and finally addresses the mechanisms of the blue-shifting phenomenon. This research not only deepens our understanding of the fluid mechanics underlying the haystacks but also provides valuable insights for designing the next generation of low-noise propellers, thereby contributing directly to quieter and more sustainable green aviation.