Displacement thickness evaluation for semi-empirical airfoil trailing-edge noise prediction model

Abstract

This study proposes a criterion for evaluating the turbulent boundary layer displacement thickness when predicting airfoil trailing-edge noise with semi-empirical methods. The boundary layer integral parameter is usually employed as the typical turbulence length-scale in the classic NASA-BPM semi-empirical airfoil self-noise prediction model and its variations. Although the semi-empirical noise prediction methods have been, in theory, superseded by more complex and demanding simplified-theoretical methods, they arguably remain the most suitable methods for noise investigation during the preliminary design phase of airfoils and wind turbine blades. The purpose of the criterion discussed is to limit the adverse impact of the uncertainty associated with the scaling parameter into the overall intrinsic quality of the semi-empirical noise prediction method. The criterion may be then employed, along with computational efficiency, to sort out methods for the task of feeding the popular BPM noise prediction model and its variations. As an illustration of the application of the proposed criterion, the performance of CFD-RANS and XFoil codes are examined and compared with experimental data from turbulent, incompressible flow available from the literature in the range $$5.0 \times 10^{5} < \text{Re}_{\text{C}} < 1.5\, \times 10^{6}$$ .