### Abstract

Modelling of aerodynamically generated noise for airborne vehicles has been extensively studied in the past decades. Hybrid computational aeroacoustics (CAA), which cou- ples computational fluid dynamics (CFD) for noise sources identification with integral methods, i.e., Ffowcs Williams and Hawkings (FW-H) equation or Kirchhoff formula, for acoustic propagation, has become the de facto standard for aircraft noise computation. However, noise prediction for rotating configurations is still a challenging issue due to its complexity.The blades of rotors or propellers generally tend to operate at high tip speeds in forward flight. In this condition, supersonic rotating sources in the flow, such as loading noise on the advancing blades with supersonic tip speeds or convected quadrupole noise outside the sonic cylinder, are encountered. Many of the hybrid CAA methods are restricted to subsonic moving sources in a flow, due to the Doppler singularity. Despite the availability of some acoustic formulas in the hybrid CAA category for supersonic moving sources, either the effect of asymmetric flow was not accounted for or the implementations were indirect and computationally expensive. Consequently, the objective of the present work is to develop new hybrid CAA formulae, to handle supersonic rotating sources in a flow with arbitrary direction, and to improve noise prediction for rotating configurations.

The main contributions of this dissertation can be divided into two primary parts:

Firstly, a frequency-domain acoustic pressure formulation is suggested and numerically implemented. As the solution of the convected FW-Hpds equation in the frequency domain, the suggested formula is free of the Doppler singularity, and thus applicable to subsonic and supersonic moving sources. Besides, since the formula is derived in a moving medium frame, the effects of mean flow and angle of attack are explicitly considered. The Isom thickness noise case, as a simplified representative of a propeller with supersonic rotation tip speed in a subsonic constant flow at incidence, is first conducted for validation purpose. Then, the high-speed impulsive (HSI) noise generated by helicopter rotors is computed and compared with experimental data. The good agreement proves the capability of the applied formula to simulate supersonic rotating quadrupole sources in a flow for practical problems.

Secondly, the convected FW-Hpds equation is solved in the time domain, where the emission surface method is adopted to integrate the Dirac delta functions, instead of the conventional retarded time method. By using the emission surface scheme, the derived time-domain formula avoids the Doppler singularity, thus allowing it for arbitrarily mov- ing sources. In addition, the moving medium frame technique, applied to the time-domain formula as well, dramatically decreases computation cost in comparison to the moving ob- server method because of a simplified emission surface construction. The merit of explicitly including the effect of uniform mean-flow with arbitrary orientation on noise radiation is also exhibited just as in the frequency domain. To implement the proposed time-domain formula, the key procedure of emission surface construction at each time instant is realized using the K-algorithm, originally conceived for supersonic rotating bodies in a flow at rest, by adding the impact of a flow for the first time through the Isom case. Moreover, the HSI noise for helicopter rotors is evaluated again using the derived time-domain formula. By comparing with experimental data, its ability to deal with supersonic rotating quadrupole sources in a flow is demonstrated.

The developed hybrid CAA methods in the frequency domain and in the time domain can be interpreted as extended solutions of the convected FW-Hpds equation. They can handle the supersonic rotating sources in a subsonic constant uniform mean-flow of ar- bitrary direction. The methodologies can be broadly applied to any kinds of rotating machines operating at high tip speeds such as helicopter rotors, aircraft propellers, and contra-rotating open rotors.

Date of Award | 25 Jan 2019 |
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Original language | English |

Supervisor | Tim De Troyer (Promotor) & Ghader Ghorbaniasl (Promotor) |

### Keywords

- aeroacoustics