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. The results show quantitatively how surface waviness affects fan performance through movement of the natural transition onset location as a result of disturbance amplification via geometric resonance between the surface wavelength and the Tollmien-Schlichting instability waves in the boundary layer.In Part I, an integrated framework is developed for analysis of surface waviness effects on natural transition. The framework, referred to as the extended eN 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 initial step in the energy evolution process, from external disturbances to the initial amplitude of TS waves, is through boundary layer receptivity which we link to the surface geometry by using a distributed acoustic receptivity theory has been generalized that can address spatially inhomogeneous wavy surfaces. For the type of fan blade waviness of interest, the flow variations due to surface waviness are confined within the boundary layer, scale linearly with surface wave slope, and can be captured using Linearized Navier-Stokes Equations (LNS).The growth of the total disturbance level is found by integrating the disturbance energy from all temporal frequencies until a critical level is reached and transition starts. The onset and the end of transition are estimated based on the disturbance amplitude and the spatial extent of transition is estimated based on the most prominent (in terms of spectral energy density) TS wavelength.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.

Effects of Surface Waviness on Fan Blade Boundary Layer Transition and Profile Loss – Part I: Methodology and Computational Results

Paper Proceedings: https://asmedigitalcollection.asme.org/GT/GT2021/volume/84898

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