The development of a reduced-order unsteady airfoil theory is described for application to non-steady, subsonic compressible flows with variable free-stream Mach number. The airfoil theory, which is suitable for application to most types of comprehensive helicopter rotor analyses, is developed for arbitrary, time-dependent combined variations in angle of attack and Mach number. The approach is validated using CFD solutions based on the Euler equations. The new model is developed using the indicial theory as a basis, and shows excellent agreement with direct CFD solutions for a wide range of practical flows. For supercritical flows, nonlinearities associated with the formation and movement of shock waves are observed in the CFD solutions, which the unsteady airfoil theory proves inadequate. Overall, this study shows that the reduced-order unsteady aerodynamic theory provides significant improvements in sectional airloads predictions over existing methods that might be used in various types of comprehensive helicopter rotor analyses.
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