Type of Document Dissertation Author LePoudre, Philip Paul URN etd-04212011-010704 Title Computational Aeroacoustics Cascade Model of Fan Noise Degree Doctor of Philosophy Department Mathematics, Department of Advisory Committee
Advisor Name Title Christopher Tam Committee Chair Kyle Gallivan Committee Member Xiaoming Wang Committee Member Yousuff Hussaini Committee Member Chiang Shih University Representative Keywords
- Computational Aeroacoustics
- Fan Noise
- Rotor-Stator Interaction Noise
- Dispersion Relation Preserving Scheme
- Parallel Computing
Date of Defense 2011-03-30 Availability unrestricted AbstractA Computational Aeroacoustics [CAA] cascade model has been built to study the generation and propagation mechanisms of noise resulting from the interaction of the fan and outlet guide vanes in a high-bypass ratio turbofan engine. Also called rotor-stator interaction noise, this noise source is a dominant contributor to the total tone and broadband noise levels produced by the engine, and therefore an improved understanding of the noise generation processes will assist in developing successful noise reduction strategies. The CAA cascade model directly solves the non-linear compressible Navier-Stokes equations on a two-dimensional linear cascade representation of the fan blade rows. The model incorporates real blade geometry and the rotor and stator blade rows are joined together with a sliding interface method. The fully-coupled aerodynamic flow and acoustic field are directly captured in one high resolution simulation, and therefore the noise production and propagation mechanisms can be visualized and measured in detail. The model includes the fully-coupled physics of the non-linear sound generation and propagation in swirling wake flow, as well as the transmission and reflection of sound through the blade rows. Previous models of rotor-stator interaction noise have typically involved some level of decoupling between the blade rows in order to simplify the noise problem.
State-of-the-art CAA methodology is used to produce a high quality numerical solution with minimal dissipation and dispersion of supported waves. The multi-size-mesh multi-time-step Dispersion Relation Preserving [DRP] scheme is used for efficient computation of the wide range of length and time scales in the problem. A conformal mapping technique is used to generate body-fitted grids around the blade shapes, which are overset on a background grid to create the blade rows. An optimized interpolation scheme is employed for data transfer between the overset grids and also to create the sliding interface between the moving rotor-fixed grid and stationary stator-fixed grid. A completely new computer program was built for efficient implementation of the cascade model on parallel computers using Message Passing Interface [MPI], and the code was shown to have good parallel performance. The program is a general purpose solver for CAA calculations involving complex flow and geometry, and is a valuable resource for future research.
A representative rotor-stator cascade with three rotor blades and five stator blades was constructed using real fan and outlet guide vane cross-sectional shapes from the NASA Glenn 22-in. model fan. A fully developed flow was obtained through the blade rows at the approach condition of the model fan. The performance of the sliding interface method was analyzed by comparing the solution on the rotor-fixed and stator-fixed grids at the coincident sliding interface mesh line, and the error in grid transfer interpolation was found to be comparable to the low error levels of the underlying DRP scheme. The simulation was used to produce animations of pressure and Mach contour, which provided a wealth of visual information about the flow field and noise generation and propagation behaviour in the cascade. The ability of the CAA cascade model to produce a high fidelity picture of the interaction noise has been demonstrated. In addition, the velocity and pressure fields were measured at various axial locations in the domain to quantify the mean and fluctuating components of the swirling wake flow between the blade rows and after the stator.
The tone noise results were compared with interaction tone linear theory. The theory predicted the existence of a small number of propagating spinning wave modes at harmonics of rotor blade passing frequency [BPF]. In particular, the dominant interaction tone at BPF, labelled , was predicted to have two wave fronts in the circumferential domain period and to spin counter to the direction of the rotor. This interaction tone was clearly visible in animations of the pressure contour as an intense shock wave moving at an oblique spiral angle between the blade rows and after the stator. The wave shape was measured using a moving average, and the high amplitude waveform showed characteristic non-linear steepening, which calls into question the common assumption that the interaction tones can be adequately represented by single linear wave modes. The spinning modes in the solution were measured at various axial locations using a joint temporal-spatial modal decomposition of the fluctuating pressure field, and very good agreement was observed with the modal content predicted by linear theory. The relationship of the mode spiral angle to blade stagger angle and the phase velocity of the spinning modes were shown to govern the transmission and reflection behaviour of the modes through the blade rows. The mode was reflected and frequency shifted by the rotor, and the reflected mode propagated through the stator blade row to the outlet. Only co-rotating modes were able to propagate through the rotor to the inlet, and hence the sound levels in the inlet were significantly lower than in the outlet. This behaviour is in good agreement with the trends observed in experimental studies of fan noise. The unsteady flow and surface pressure fluctuations around a stator blade were also measured. Spectral analysis of the surface pressure fluctuations revealed the highest sound pressure levels occurred near the blade leading edge and on the upper blade surface near the trailing edge. The sound source mechanisms on the stator blade are related to the fluctuating loading on the blade as it cuts through the rotor wake profile and experiences significant variation in the local angle of attack.
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