This two-part paper describes a new approach to determine the effect of surface waviness, arising from manufacture of composite fan blades, on transition onset location movement and hence fan profile losses. The approach includes analysis and computations of unsteady disturbances in boundary layers over a wavy surface, assessed and supported by wind tunnel measurements of these disturbances and the transition location. An integrated framework is developed for analysis of surface waviness effects on natural transition. The framework, referred to as the extended e~N method, traces the evolution of disturbance energy transfer in flow over a wavy surface, from external acoustic noise through exponential growth of Tollmien-Schlichting (TS) waves, to the start and end of the transition process. The computational results show that surface waviness affects the transition onset location due to the interaction between the surface waviness and the TS boundary layer instability, and that the interaction is strongest when the geometric and TS wavelengths match. The condition at which this occurs, and the initial amplitude of the boundary layer disturbances that grow to create the transition onset is maximized, is called receptivity amplification. The results provide first-of-a-kind descriptions of the mechanism for the changes in transition onset location as well as quantitative calculations for the effects of surface waviness on fan performance due to changes in surface wavelength, surface wave amplitude, and the location at which the waviness is initiated on the fan blade.
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