Trailing Edge Noise Prediction Using a RANS-based Statistical Method (RSNM)

Abstract

Airfoil self noise is produced when an airfoil is immersed in an undisturbed flow. Flow turbulence created in the boundary layer and wake of the airfoil generates pressure fluctuations, which are scattered by the trailing edge (TE), radiating noise to the far field. TE noise is one of the dominant mechanism of airfoil self noise in low Mach number, high Reynolds Number flows. These conditions occur in many applications such as wind turbines, aircraft, submarines, fans, air conditioning units and turbomachinery in general. The overall aim of this research is to investigate and develop a RANS-based Statistical Noise Model (RSNM) for trailing edge noise. The method combines Reynolds-averaged Navier-Stokes (RANS) turbulent ow solutions with statistical models of the turbulent ow field, namely the turbulent velocity cross-spectrum. Hot wire anemometry is used to investigate the flow in the boundary layer of sharp edged struts with zero pressure gradient (ZPG) and adverse pressure gradients (APG). Single-point and two-point statistics are presented, including mean and RMS velocity profiles, probability density functions, third and fourth order moments, power spectral density, two-point correlations and coherence function. An empirical model for the turbulent velocity cross-spectrum is developed, based on the measured statistics. The cross-spectrum model is constructed by combining an auto-spectrum model and a model for the spatial coherence function. RANS computational fluid dynamics (CFD) simulations are performed for three different two-dimensional airfoils (NACA 0012, DU-96-180 and the FP12 at sharp-edged strut) at a wide range of operating conditions. The simulation results are validated against new experimental data, as well as data from the literature. The CFD results are sampled in the region around the trailing edge and used as input data to the noise prediction model. Noise calculations are performed for all cases using different turbulent velocity cross-spectrum models. The baseline model is an adaptation of the Gaussian formulation used in jet noise predictions by Morris and Farassat (2002), which is modified to account for the presence of the sharp trailing edge. Modifications to the cross-spectrum model are assembled by changing the auto-spectrum model and/or the model for the spatial coherence function. Noise predictions for the NACA 0012 and DU-96-10 airfoils using the baseline model are in excellent agreement with experimental data. Noise predictions for the FP12 airfoil produced the correct slope, but underpredicted the noise levels by up to 15 dB. The baseline model outperformed all the modifications investigated in this thesis.