Numerical Methods for Aeroacoustic Analysis of Turbomachines
Doctoral thesis, 2020

Numerical simulations are important tools for developing new aircraft that can meet future needs. When numerical simulations are used to compute aircraft noise, a two-step procedure is often employed. In the first step, the noise sources are determined using, e.g., computational fluid dynamics. In the second step, noise propagation between the sources and the observers is then computed, often by solving an acoustic analogy. In this thesis, a range of numerical methods that are useful when turbomachinery tonal noise is computed based on such a two-step procedure are considered. For the first step, the time-domain Harmonic Balance method proposed by Hall et al. is used. To improve the accuracy of this method, the impact of time sampling on aliasing is investigated for both the single frequency and the multiple frequency problem. A new oversampling strategy for the multiple frequency problem is also developed for this purpose. Another challenge associated with the Harmonic Balance method is numerical instabilities. This problem is investigated using a von Neumann stability analysis. Based on knowledge gained from this analysis, a novel preconditioner that stabilizes an explicit Harmonic Balance solver is then developed. To minimize reflections of waves against boundaries of the computational domain, a generic formulation of the exact, nonlocal, nonreflecting boundary condition introduced by Giles is also derived and implemented to work with the Harmonic Balance method. For the second step, the convective Ffowcs Williams - Hawkings equation for permeable surfaces proposed by Najafi-Yazidi et al. is used. A detailed derivation of this equation is first presented. The solution to this equation for the case when the surface is stationary relative to the observer is then derived. Finally, a tool for computing duct modes based on a normal mode analysis of the linearized Euler equations is presented. In summary, the work reported in this thesis provides a detailed analysis of the aforementioned methods, that should be valuable for people who are interested in adopting them. It also provides some improvements, which can help to further improve the results obtained with these methods.

Stability Analysis

Acoustic Analogy

Tonal Noise

Nonreflecting Boundary Conditions

Duct Modes


Harmonic Balance

Ffowcs Williams - Hawkings

Time Sampling


Opponent: Dr Edmane Envia, Acoustics Branch, NASA Glenn Research Center, Cleveland, OH, USA


Daniel Lindblad

Chalmers, Mechanics and Maritime Sciences (M2), Fluid Dynamics

Validating the Harmonic Balance Method for Turbomachinery Tonal Noise Predictions

AIAA SciTech Forum - 55th AIAA Aerospace Sciences Meeting,; (2017)

Paper in proceeding

Aeroacoustic Analysis of a Counter Rotating Open Rotor based on the Harmonic Balance Method

AIAA Aerospace Sciences Meeting, 2018,; Vol. 2018(2018)

Paper in proceeding

Noisyduck: An open-source python tool for computing eigenmode decompositions of duct flows

25th AIAA/CEAS Aeroacoustics Conference, 2019,; (2019)

Paper in proceeding

Minimizing Aliasing in Multiple Frequency Harmonic Balance Computations

Journal of Scientific Computing,; Vol. 91(2022)

Journal article

Most of us have heard the noise from an airplane that takes off, or is about to land. If you live far from an airport, you will only hear this noise if you, for example, decide to fly somewhere for vacation. For people who live close to an airport, however, aircraft noise is hard to escape. It is therefore important that new aircraft not only produce less greenhouse gas emissions, but also are quieter than those flying today. To achieve this goal, aircraft manufacturers rely on sophisticated computer simulations to test new designs, before moving on to real-world testing. Unlike real-world testing, however, computer simulations are based on mathematical models that sometimes give inaccurate results. To improve the accuracy of computer simulations, and thereby enable better aircraft to be manufactured, some widely used mathematical models for predicting aircraft noise have been evaluated in this thesis. The results show that some mathematical models can not be improved further. For other models, it is found that there is still some room for improvement. In these cases, new models that are shown to give better results are presented. The difference in results compared to existing models is not substantial. These small improvements may still give a significant impact on noise around airports if air travel continues to grow in the future.

Ultra Low emission Technology Innovations for Mid-century Aircraft Turbine Engines (ULTIMATE)

European Commission (EC) (EC/H2020/633436), 2015-09-01 -- 2018-09-01.

Värmelast i gasturbinens heta delar vid sameldning med vätgas

Swedish Energy Agency (2017-001166), 2017-06-01 -- 2020-06-01.

Areas of Advance


Subject Categories

Aerospace Engineering

Computational Mathematics

Fluid Mechanics and Acoustics


C3SE (Chalmers Centre for Computational Science and Engineering)



Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie: 4803




Opponent: Dr Edmane Envia, Acoustics Branch, NASA Glenn Research Center, Cleveland, OH, USA

More information

Latest update