Evaluation of Measured Anisotropic Turbulent Two-Point Correlation Data for the Accurate Prediction of the Turbulence Noise Sources

Abstract

Noise emitted from 2D subsonic airfoil sections depends strongly on the specific properties of the turbulent boundary-layer passing the trailing edge. The intention of the present paper is three folds: (1) wind tunnel measurement of the two-point turbulent velocity correlations to analyze the trailing-edge near wake flow structure in detail, (2) assessment of the measurement data and post-processing of the turbulence properties in a way so that it can be comparable to numerical results, and (3) development of a relationship between isotropic theory and anisotropic measurement data to approximate quantities like isotropic longitudinal length scale Λf . Measurements of two-point turbulent velocity correlations were conducted in 2D turbulent boundary layer flows over two airfoils (NACA 0012 & NACA 643-418 ) at high Reynolds numbers (Re=1.5e6 and Re=2.5e6) in the Laminar Wind Tunnel (LWT) of the University of Stuttgart. Correlation tensor components were measured by two X-wire probes shortly downstream of the airfoil trailing edge with separation in vertical direction for different cases of boundary layer development (angles-of-attack, natural and fixed transition). Two different approaches to evaluate turbulence integral correlation length scales from the measured two-point correlation data are presented. The first methods provides anisotropic turbulence integral length scales estimated by fitting an exponential function to the measured two-point velocity correlation coefficient. The second method established a local relationship between the results from isotropic theory and anisotropic experimental data. This relationship permits efficient approximation of the isotropic longitudinal integral length scale (Λf), and enables the consideration of anisotropy effects in RANS predicted data. The outcome of both methods are been compared with RANS results and lead to significant improvement of the prediction of the turbulence noise sources. The benefit of these efforts will be further applied to a Turbulent Boundary-Layer Trailing-Edge (TBLTE) interaction noise prediction method (Rnoise) to analyze anisotropy effects of the airfoil trailing-edge near-wake flow.