Global Stability and Receptivity Analysis of Transitional Rotor Boundary Layers

The goal of the proposed research is to improve the fundamental understanding of boundary-layer stability and laminar-turbulent transition on helicopter rotor blade. It is motivated by the recognition that there are prominent theoretical deficiencies and gaps in understanding in the current state of the art, which is to apply localized, instantaneous spatial stability analysis along streamwise strips. Such an approach neglects any spanwise-global behavior or radial inhomogeneity. The role of ambient disturbances and free-stream turbulence on the rotor boundary-layer transition process is effectively unknown, as are the influence of surface imperfections. To address these technical barriers, the proposed research will employ a computational approach to analyze the global stability characteristics and boundary-layer receptivity on representative helicopter rotor for which experimental transition measurements areavailable in the literature. Four specific research objectives have been identified in pursuit of the goal, and are to assess the role of spanwise variations on the streamwise growth rate of instability for various transition mechanisms, to quantify the influenceof the rotating reference frame on the receptivity to ambient disturbances that are uniform in an inertial reference frame, to determine the influence of unsteadiness on the transition behavior for both cyclic pitch and edgewise translation of the rotor disk, andto investigate the influence of surface imperfections on the transition process in rotating reference frames. These objectives willbe met using a two-pronged computational strategy. The first is based on a novel method for predicting linear spatial instability growth in a rotating reference frame that rigorously accounts for spanwise variations in both the mean flow and the instability wave form. The second is based on embedded implicit large-eddy simulations (ILES) of blade subdomains to supplement the global stability analyses and capturenon-linear behaviors and acoustic interactions not captured in spatial stability analyses. The stability calculations and large-eddy simulations will be performed using an in-house high-fidelity flow solver. The proposed research will provide the first-ever global stability analyses for the laminar boundary on a helicopter rotor, and the outcomes of this project are expected to improve the understanding of transitional boundary-layers of helicopter rotors and to provide guidance for the future development of engineering tools for transition modeling. Approved for Public Release