ESCAPE - Erroneous Sources of Combustion noise in Acoustic Perturbation Equations
Motivation
Combustion instabilities pose a significant challenge in the development and improvement of combustion systems, such as gas turbines and aeroengines. In an effort to predict these instabilities, numerical simulations are on of the most powerful tools available today. However, the computational effort required for fully resolved CFD of all relevant scales remains prohibitively expensive, especially if it is to be employed early in the combustor design process. To address this issue, several modelling approaches exist which aim to reduce the complexity of the system, among them are so called hybrid CFD/CAA approaches.
At their core, hybrid CFD/CAA (Computational Fluid Dynamics/Computational Aero-Acoustics) approaches exploit the disparity in scales between the sound-generating flow/flame structures and the resulting acoustic perturbations. The relevant length scales in the flame are very small and thus the computational grid must be very fine in this region. In contrast the length scales of acoustics in combustion chambers are typically larger by multiple orders of magnitude. This allows to define hybrid models which separate the flame dynamics from the acoustics and solve each on a dedicated numerical grid. The interaction between both is included by formulating coupling relations for sound sources in the acoustic equations resulting from the flame and conversely acoustic-flame interaction terms in the reactive flow equations. The second coupling mechanism is essential in thermoacoustic investigations but is often neglected in combustion noise investigations.
The acoustics are typically described by CAA formulations such as Linearized Euler Equations (LEEs), Linearized Navier-Stokes Equations (LNSEs), and acoustic analogies such as the Acoustic Perturbation Equations (APEs). Depending on the particular acoustic formulation chosen different source terms arise. These source terms can provide insight into the mechanisms by which the flame generates sound. However, source terms might also arise from non-steady mean flow effects or other modelling choices. This makes their physical interpretation difficult and may thus lead to erroneous conclusions on the driving mechanisms of combustion noise and thermoacoustic instabilities.
Objectives and Strategy
In this project, we aim to clarify the sound generation mechanism of a flame and find a physically consistent formulation for the acoustic source terms arising from them. We focus this investigation on the APEs because several sound source investigations using this mechanism found that a source term related to the acceleration of entropy waves at the flame front was of significant importance, and even dominant, in some cases [1, 2, 3]. The findings of these studies challenge a long standing consensus that held unsteady heat release by the flame as the primary acoustic driver.
The following explanations for this apparent contradiction between the new findings and literature seem possible:
- The implications of the APE analysis are valid, i.e. acceleration of entropy gradients across the flame front constitutes indeed a significant, sometimes dominant source, of sound. In this case, one would like to fully understand the exact mechanism behind this source, and why it has escaped discovery until recently. Importantly, established formulations for thermo-acoustic interactions in combustion would have to be revised. In particular, hybrid models of thermoacoustic instability – which so far rely exclusively on unsteady rate of heat release as a direct source of sound – would have to be extended.
- Although APE results are overall valid and quantitatively correct, the interpretation of source term is fallacious, because APE misrepresents the effects of flame movement – in particular displacement of the flame by velocity perturbations – in a misleading way.
- The APE formulation is fundamentally flawed. For example, it seems conceivable that the source term filtering of APE eliminates important contributions to the flow / flame / acoustic interactions, which when included would interact or superpose with other terms. A system of equations that is “imbalanced” in this sense might give rise to spurious sources of sound or perturbation energy. It is also conceivable that misrepresentation of flame movement in the framework of a perturbation equation with non-uniform base flow leads to errors.
In the course of this project different source term formulations will be tested on flames of varying complexity to understand the occurrence of these source terms in the APE formulation. The results will be cross-compared with results of compressible CFD and of the Linearized Reactive Flow (LRF) equations to identify spurious sources, or confirm their validity. Figure 1. shows a schematic representation of the cross comparison.
Current & Future Work
Current work deals primarily with identifying a case of minimal complexity which exhibits sound contributions resulting from the entropy source terms in the APE formalism. Pausch et al. [3] reported a significant contribution of this source term in the sound pressure spectrum of a laminar premixed flame. Thus our research focuses in a first stage on understanding this mechanism in laminar premixed flames, before any findings can be tested on more complex and eventually turbulent configurations.
If you are a student or researcher interested in collaborating, please contact Andreas Strittmatter.
Acknowledgement
The funding for this project is provided by the Deutsche Forschungsgemeinschaft (DFG). We gratefully acknowledge their support.
References
[1] Geiser, G., Hosseinzadeh, A., Nawroth, H., Zhang, F., Bockhorn, H., Habisreuther, P., Janicka, J., Paschereit, C.O., Schroeder, W., 2014. Thermoacoustics of a turbulent premixed flame, in: 20th AIAA/CEAS Aeroacoustics Conference. American Institute of Aeronautics and Astronautics. https://doi.org/10.2514/6.2014-2476
[2] Pausch, K., Herff, S., Schröder, W., 2020. Noise sources of an unconfined and a confined swirl burner. Journal of Sound and Vibration 115293. https://doi.org/10.1016/j.jsv.2020.115293
[3] Pausch, K., Herff, S., Zhang, F., Bockhorn, H., Schröder, W., 2019. Noise sources of lean premixed flames. Flow Turb. and Comb. 103, 773–796. https://doi.org/10.1007/s10494-019-00032-0