Identification of Combustion Noise and Flame Dynamics of Confined Turbulent Flows

**Principal Investigator:**

Wolfgang Polifke

**Affiliation:**

Department of Mechanical Engineering, Technische Universität München

**Local Project ID:**

pr94yu

**HPC Platform used:**

SuperMUC, Phase I and II

**Date published:**

Combustion noise is an undesirable but unavoidable by-product of every applied turbulent combustion device, such as stationary gas turbines or aeronautical engines. This project deals with the thermoacoustic modeling of confined combustion systems. Large Eddy Simulation (LES) is combined with advanced System Identification (SI) techniques - a form of supervised Machine Learning to infer reduced order models for the subsequent prediction of combustion noise. In a first step, a reactive compressible LES is applied to reproduce directly the experimentally measured sound pressure spectra of a confined lab-scale combustor. Thereby, qualitative and quantitative agreement is found. In a second step, the validated LES setup is used to generate broadband time series data that is consequently post-processed via advanced SI techniques. Models for the combustion noise source and the flame dynamic response are estimated, allowing a computationally efficient prediction of combustion noise across a wide parameter space of combustor configurations.

**1 Scientific work accomplished and results obtained**

During the project a coherent framework was developed for the investigation of combustor dynamics and combustor noise. First, both aspects were addressed directly via a reactive compressible LES and validated against experimental data. After assuring that the compressible LES describes correctly the generation of combustion noise as well as the flame dynamics, the validated LES setup was used to generate acoustic broadband data time series. The resulting time series data were post-processed via advanced SI techniques to infer simultaneously reduced order models for the flame dynamic response and the generation of combustion noise. The scientific work accomplished during the project may be divided into two sub-projects. Section 1.1 focuses on the direct assessment of the sound pressure distribution by means of compressible LES. Section 1.2 describes subsequently the outcome and the value of the results obtained from the combined use of broadband LES data and SI techniques.

**1.1 Sub-Project 1: direct assessment of sound pressure distribution via LES**

From a thermoacoustic perspective, a compressible LES was particularly suited in the current project for the study of a confined turbulent flame: a compressible LES describes not only the turbulent reactive flow but also takes into account all relevant acoustic mechanisms involved: the flame dynamics, the generation of combustion noise by resolved turbulent structures and the acoustic wave propagation in a complex geometry.

For a first validation, the flame motion during a thermoacoustic instability, i.e. during a limit cycle oscillation, was compared between LES and experiment. Figure 1 reproduced from depicts phase averaged flame images over one limit cycle at 185 Hz across radius normalized by injector radius. The left hand side of each picture shows a LES generated heat release rate iso-contour averaged over 20 frames. The right hand side depicts the experimental OH* phase averaged and Abel transformed flame pictures over 100 frames. It can be observed that the general flame motion during the oscillation cycle was satisfyingly described by the compressible LES in Fig. 1. The position of the largest structures of the flame and the respective flame length were fairly well reproduced by the LES at each phase of the oscillation cycle. This overall satisfying agreement between LES and experiment allowed the conclusion that flame dynamics are correctly describe by the LES.

The next step was the comparison of computed and measured sound pressure distributions. Figure 2 reproduced from demonstrates the capability of the compressible LES setup to reproduce not only qualitatively, but also quantitatively measured sound pressure distributions for stable and unstable working conditions. Compared to existing literature on confined combustor configurations, such quantitative agreement between experiments and LES was not yet achieved and may therefore be considered as a novelty. In the framework of this project, LES/SI procedure yields a data driven models for flame dynamic response and combustion noise source which is not yet done in literature for confined systems. This is possible only when responsible mechanisms are correctly reproduced in LES.

Since the LES/SI procedure subsequently used yields data-driven models for the flame dynamic response and the combustion noise source, physically correct models can only be estimated if the responsible mechanisms are correctly reproduced within the LES [1, 2].

**1.2 Sub-Project 2: generation of broadband input-output time series data**

As shown in sub-project 1, assessing combustion noise and the sound pressure distribution directly via LES is generally possible, but a study across a wide parameter space would be prohibitively expensive in terms of computational resources needed. So after having validated the LES setup in sub-project 1, sub-project 2 focused on the generation of broadband LES time series data. By means of the obtained time series data reduced order models were estimated for the combustion noise source and the flame dynamics, which, in turn, allowed a computationally efficient prediction of the sound pressure distribution within a confined combustor system.

The general concept of the broadband time series generation is to impose an acoustic excitation signal at the LES domain boundaries. If, for example, an ingoing acoustic wave is imposed at the LES inlet, it may be regarded as an input signal that causes a certain system response, i.e. heat release rate fluctuations across the flame. Figure 3 depicts a typical set of time series generated by LES with applied broadband forcing. The acoustic input signal *u’* causes in the LES a certain flame response in terms of heat release rate fluctuations *Q’*, which is considered as output. By post-processing this input-output time series data set via advanced SI techniques, a causal relation between *u’* and *Q’* may be formulated, i.e. a model for the flame dynamics as well as a model for the generation of combustion noise.

Compared to repeated mono-frequent acoustic excitation across a certain frequency range, as it is usually done in an experimental approach, the broadband forcing technique reduces the computationally effort significantly in LES. The input-output time series data contains not only information a one given frequency, but instead across a given range of frequencies. Figure 4 shows the identified model of the flame dynamics, i.e. the Flame Transfer Function (FTF), as well as the experimentally measured FTF, which was determined via subsequent mono-frequent excitation at different frequencies.

Figure 5 shows also the identified noise model which was identified with time series data obtained from the LES. As mentioned earlier, by means of identified FTF and noise model, reduced order models were estimated for computationally efficient prediction of sound pressure distribution in a confined combustion system [3–5].

Results obtained in this sub-project were mainly published in [3, 4] and [5].

**2 Realization of the project**

In this study the flame dynamic response to perturbations in acoustic velocity upstream of the flame holder is studied computationally. For this purpose, the Large Eddy Simulation (LES) solver AVBP developed at CERFACS (www.cerfacs.fr) based on Fortran 95 was used. Typically, AVBP is used in modelling unsteady turbulent combustion problems. AVBP has been successfully applied in various combustion related areas such as ignition, blow-off, flashback and combustion instabilities. The AVBP solver can be highly parallelized with optimal average load for each CPU. It may be used for different processor architectures and has a very high performance especially in HPC environment. The optimal load distribution between processors and the parallel scaling follow a linear behavior for a wide range of CPU cores used.

In any Computational Fluid Dynamics simulation, the domain of interest is discretized into finite volumes where conservation equations of mass, momentum and energy are solved iteratively. The exercise of constructing mesh (finite volumes) should be done in such a way that the results in terms of velocity profile and sound pressure distribution are independent of the refinement of the mesh. In this case a tetrahedral mesh of 20 million cells yielded grid independent results. Refined mesh (small size cells) are required to capture appropriate physics and are used in upstream and reaction zone of the domain. Coarse mesh is used in downstream region as not much physics happens in this zone and hence save computational cost.

As mentioned earlier, AVBP has good parallelization performance. With the current mesh of 20 million tetrahedral cells, an optimum number of 600 cores can be used with good load distribution among processors. The governing equations are stiff in nature and hence a time step size of *1e — 07s* is used to maintain the Courant-Friedrichs-Lewy (CFL) number less than *1*. Due to this time step, a typical simulation of 48 hours wall clock time resulted in 120 ms of simulated physical time. Depending on the purpose of the simulation, time series between 120 ms and 360 ms were needed. The identification of a robust and accurate transfer behavior of the system through one time series data of input (velocity fluctuations) and output (heat release fluctuation) needed 85000 core hours which corresponds to roughly 350ms of data.

**3 List of Publications**

The following publications made use of the computational resources granted for the SuperMUC project pr94yu and acknowledged these resources accordingly:

- M. Merk, R. Gaudron, M. Gatti, C. Mirat, T. Schuller, and W. Polifke. Measurement and Simulation of Combustion Noise and Dynamics of a Confined Swirl Flame. AIAA Journal, 56(5):1930–1942, 2018. doi: 10.2514/1.J056502
- M. Merk, R. Gaudron, C. Silva, M. Gatti, C. Mirat, W. Polifke, and T. Schuller. Direct assessment of the acoustic scattering matrix of a turbulent swirl combustor by combining system identification, large eddy simulation and analytical approaches. In ASME Turbo Expo 2018: Turbomachinery Technical Conference and Exposition, GT2018-75529, Lillestrom, Norway, 2018. ASME. doi: 10.1115/GT2018-75529
- M. Merk, R. Gaudron, C. Silva, M. Gatti, C. Mirat, T. Schuller, and W. Polifke. Direct Assessment of the Acoustic Scattering Matrix of a Turbulent Swirl Combustor by Combining System Identification, Large Eddy Simulation and Analytical Approaches. Journal of Eng. for Gas Turbines and Power, 2018. doi: 10.1115/1.4040731
- M. Merk, R. Gaudron, C. Silva, M. Gatti, C. Mirat, T. Schuller, and W. Polifke. Prediction of Combustion Noise of an Enclosed Flame by Simultaneous Identification of Noise Source and Flame Dynamics. Proceedings of the Combustion Institute, 37, 2018. doi: 10.1016/j.proci.2018.05.124
- M. Häringer, M. Merk, and W. Polifke. Inclusion of higher Harmonics in the Flame Describing Function for Predicting Limit Cycles of self-excited Combustion Instabilitites. Proceedings of the Combustion Institute, 37, 2018. doi: 10.1016/j.proci.2018.06.150
- M. Meindl, M. Merk, F. Fritz, and W. Polifke. Determination of acoustic scattering matrices from linearized compressible flow equations. Journal of Theoretical and Computational Acoustics, 26(0):1850027–1 – 1850027–27, 2018. doi: 10.1142/S2591728518500275

**4 Theses completed within the project**

- Fabian Fritz, Bachelor’s Thesis, 2016

Numerical Investigation on the Thermoacoustic Behavior of a Turbulent Combustion Test-Rig Based on Linearized Fields - Mathias Haeringer, Master’s Thesis, 2017

Numerical Determination of Thermoacoustic Modes for a Laminar Premixed Combustor - Malte Merk, Ph.D. Thesis, 2018

Identification of Combustion Dynamics and Noise of Confined Turbulent Flames

**5 Awards**

The project contributor, Malte Merk, won the Aerospace Travel Award for his conference contribution at the AIAA conference: Energy and Propulsion [2]. This conference publication laid the basis for the following journal publication [1] and contains mainly results that were computed on SuperMUC phase 1 and 2. Further details: www.mdpi.com/journal/aerospace/awards.pdf/0/145_2017_1_Winners%20Announcement.pdf

**6 Co-operations with external partners**

The Indian researcher, Nitin Babu, from the Indian Institute of Technology, Chennai, India, spend three months at the Professur f ¨ ur Thermofluiddynamik for a research visit. During his stay he investigated numerically the effect of conjugate heat transfer at the combustor boundaries on the thermoacoustic stability of a given configuration. The corresponding LES computations were carried out within the current project pr94yu.

**7 References**

[1] M. Merk, R. Gaudron, M. Gatti, C. Mirat, T. Schuller, and W. Polifke. Measurement and Simulation of Combustion Noise and Dynamics of a Confined Swirl Flame. AIAA Journal, 56(5):1930–1942, 2018. doi:10.2514/1.J056502.

[2] M. Merk, R. Gaudron, M. Gatti, C. Mirat, W. Polifke, and T. Schuller. Quantitative Comparisons Between LES Predictions and Experimental Measurements of Sound Pressure Spectra in a Confined Swirl Combustor. In 53rd AIAA/SAE/ASEE Joint Propulsion Conference, AIAA Propulsion and Energy Forum, Atlanta, GA, USA, 2017. American Institute of Aeronautics and Astronautics. doi:10.2514/6.2017-4687.

[3] M. Merk, R. Gaudron, C. Silva, M. Gatti, C. Mirat, T. Schuller, and W. Polifke. Prediction of Combustion Noise of an Enclosed Flame by Simultaneous Identification of Noise Source and Flame Dynamics. Proceedings of the Combustion Institute, 37, 2018. doi: 10.1016/j.proci.2018.05.124.

[4] M. Merk, R. Gaudron, C. Silva, M. Gatti, C. Mirat, W. Polifke, and T. Schuller. Direct assessment of the acoustic scattering matrix of a turbulent swirl combustor by combining system identification, large eddy simulation and analytical approaches. In ASME Turbo Expo 2018: Turbomachinery Technical Conference and Exposition, GT2018-75529, Lillestrom, Norway, 2018. ASME. doi:10.1115/GT2018-75529.

[5] M. Merk, R. Gaudron, C. Silva, M. Gatti, C. Mirat, T. Schuller, and W. Polifke. Direct Assessment of the Acoustic Scattering Matrix of a Turbulent Swirl Combustor by Combining System Identification, Large Eddy Simulation and Analytical Approaches. Journal of Eng. for Gas Turbines and Power, 2018. doi:10.1115/1.4040731.

[6] M. Häringer, M. Merk, and W. Polifke. Inclusion of higher Harmonics in the Flame Describing Function for Predicting Limit Cycles of self-excited Combustion Instabilitites. Proceedings of the Combustion Institute, 37, 2018. doi: 10.1016/j.proci.2018.06.150.

[7] M. Meindl, M. Merk, F. Fritz, andW. Polifke. Determination of acoustic scattering matrices from linearized compressible flow equations. Journal of Theoretical and Computational Acoustics, 26(0):1850027–1 – 1850027–27, 2018. doi: 10.1142/S2591728518500275.

**Scientific Contact**

Prof. Dr. Wolfgang Polifke

Department of Mechanical Engineering

Technical University of Munich

Boltzmannstr. 15, D-85747 Garching (Germany)

e-mail: polifke [@] tum.de

*LRZ Project ID: pr94yo*

*April 2020*