Wind-induced period-doubling bifurcation and stability loss of a ducted fan in urban boundary layer

Ducted fans are widely used in electric vertical takeoff and landing vehicles because of their high efficiency, safety, and low noise. Under urban boundary-layer (UBL) winds, however, crosswind shear and unsteadiness introduce strong aerodynamic interference and degrade thrust stability. In this paper, realistic UBL inflow profiles generated by meteorological models are connected with fluid dynamics simulation to quantify the instability mode transition across increasing crosswind. As wind speed increases, the thrust response evolves sequentially from steady to periodic and then to chaotic. Rotor thrust rises while duct thrust decreases, yielding a net total thrust reduction of up to 14%. Power-spectral and return-map diagnostics reveal a clear period-doubling route to chaos, with an observed scaling ratio of 4.742, close to the Feigenbaum constant (∼4.669). The onset of period-2 oscillations occurs at ∼4.2 m/s (crosswind ratio ∼0.09), triggered by tip-leakage-vortex wake impingement on the adjacent blade. Higher-order periods and chaotic behavior are driven by intensified blade/duct separation and vortex shedding, with chaos emerging beyond ∼8 m/s (crosswind ratio ∼0.18). A period-3 window is observed near ∼10 m/s (crosswind ratio ∼0.22). These quantitative thresholds and flow-structure mechanisms provide stability-relevant guidance for ducted-fan operation and control under realistic UBL crosswinds.