Fan Broadband Self Noise Prediction Model (2002)

Recent studies and assessments of the modeling of aircraft engine fan broadband source noise have focused on turbulencecascade (or blade-row) interaction as the key mechanism of fan broadband noise generation. Blade row self-noise is also a potential mechanism for fan broadband noise, but its importance relative to turbulencecascade interaction has not been assessed to any significant degree. This paper reports a study carried out to quantify the relative importance of self-noise to the total broadband noise spectrum. An extension of previous semi-empirical modeling was employed to develop a prediction method for fan broadband self-noise and compared with a turbulencecascade interaction model with comparable modeling assumptions. Predictions were compared with a set of scale-model fan acoustic data, and the new self-noise model was shown to provide predictions more consistent with the experimental data. Introduction Recent studies and assessments of the modeling of aircraft engine fan broadband source noise have identified several key mechanisms thought to be important contributors to the total fan broadband noise spectrum. The currently favored physical mechanisms include the following: 1. Inlet end-wall boundary layer turbulence interaction with the rotor tip (ITRI) 2. Rotor wake turbulence interaction with the downstream stators (RWSI) 3. Rotor tip endwall turbulence interaction with the downstream stators (RTSI) ___________________________________ *Consulting Engineer, Acoustics Technology Programs, Advanced Engineering Programs Department 4. Rotor hub endwall turbulence interaction with the downstream stators (RHSI) 5. Rotor blade surface boundary layer and trailing edge noise (RSN) 6. Stator vane surface boundary layer and trailing edge noise (SSN) Mechanisms 1 through 4 are thought to be the major contributors, but the self-noise mechanisms 5 and 6 could be setting a “floor” the total fan broadband noise spectrum, and therefore may limit the noise reduction achievable by developing technologies for reducing mechanisms 1 4. It is important to therefore quantify the self-noise mechanisms for fan broadband noise generation, to the same level of approximation as the turbulence interaction mechanisms (1-4), if possible. This would allow a more accurate assessment of the benefits of reducing the various interaction mechanisms, and provide insight into the proximity of the “self-noise floor.” A physics-based understanding of self-noise generation may also provide insight on how to reduce it and therefore increase the fan broadband noise reduction potential. The physical modeling of rotor and stator self noise is the subject of this study. Objectives and Approach The objective of the work reported herein was to develop a quantitative prediction method for fan rotor and stator self noise that is theoretically consistent with the turbulence-cascade interaction models currently being developed. By “theoretically consistent” we mean that the modeling assumptions and formulation approach are the about the same and/or to the same level of approximation. The approach taken was to build upon the fan rotor self noise formulations suggested by Sharland and expanded upon by Mugridge and 8th AIAA/CEAS Aeroacoustics Conference & Exhibit Fire 17-19 June 2002, Breckenridge, Colorado AIAA 2002-2490 Copyright © 2002 by the author(s). Published by the American Institute of Aeronautics and Astronautics, Inc., with permission. Page 2 American Institute of Aeronautics and Astronautics Morfey. The model proposed by Mugridge and Morfey is based on the physical mechanism of airfoil surface boundary layer pressure fluctuations producing noise, especially at the airfoil trailing edge, where the upper and lower surface boundary layers meet and form an airfoil wake. It was suggested that strong correlation occurs at the trailing edge between the upper and lower surface pressure fluctuations resulting in a trailing edge unsteady loading or force fluctuation related to the boundary layer turbulent pressure spectra near the trailing edge. A similar approach was proposed by Brooks and Marcolini for airfoils, to quantify the noise produced by aircraft wings. The Mugridge and Morfey formulation, however, contains many simplifying assumptions and approximations, done for the purpose of arriving at a scaling law or parameter dependence relationship. Although the resulting formulation gives guidance on the sensitivity of fan rotor self-noise to various operating and geometric parameters (e.g., tip speed, flow coefficient, blade chord, etc.), it is still a relatively crude formulation compared to the formulations available and being developed for turbulence-cascade interaction (TCI). For example, the Mugridge-Morfey model uses an empirical spectrum shape function which is only dependent on fan parameters in the sense of scaling of the peak frequency the shape itself is invariant. There is no connection between the airfoil or rotor blade surface pressure turbulent spectrum characteristics and the result acoustic spectrum. Secondly, the model does not contain the effects of duct acoustics, i.e., no accounting for propagating and nonpropagating wave-number energy is included. The approach taken herein was to review and critique the Mugridge-Morfey formulation in detail, to identify each simplifying assumption in the formulation, and to extend or improve the model formulation as required to achieve consistency with TCI formulations where possible. The Mugridge-Morfey Model For Rotor Self Noise Using the compact dipole unsteady force acoustic modeling approach developed by Sharland, Mugridge begins with the following expression for the radiated acoustic power from an airfoil with an unsteady, random-span-wise loading: W c dL dt h s = ⋅ ⋅ ⋅ 1 12 3 2