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Development of numerical methods based on the linearized field equations for efficient optimization of combustion processes

Combustion Instabilities (CIs), that is a temporal fluctuation of heat release, are the source of various problems in operating gas turbines. For a start, they can lead to an increase in pollutant emissions. Furthermore, an unstable flame produces acoustic energy, which can lead to significant difficulties especially in aeronautical engines, which have to satisfy increasingly stringent noise constrains. A third, and possibly the most prominent problem with unstable flames results from the fact that flames with fluctuating heat release do not only produce acoustics, but they also respond to acoustics with fluctuations in heat release. Therefore, a feedback cycle between an acoustic mode of the combustion chamber and the fluctuation of heat release can occur.  This phenomenon is called thermoacoustic instability. The in the process occurring pressure fluctuations are of such a high amplitude that significant damage of the combustion chamber through to a complete destruction of the engine can occur. 

igure 1: Temporally averaged and non-dimensional fields of absolute velocity and density of a turbulent swirl flame; The stream lines show the central and outer recirculation zones.

Large efforts are payed in both industry and academia to cope with these problems. Because of the complexity of the phenomena leading to thermoacoustic instabilities, an a prioriprediction viae.g. CFD is very challenging. And even if an unstable flame is correctly predicted, often only a trial-and-error parameter study can be applied in order to find solutions to the problem. A method that yields insight in the resonance mechanism of instabilities, and therefore would allow for more aimed approach is the Linear Stability Analysis (LSA) (see also: Kohärente Strukturen in turbulenten Strömungen und ihre Modellierung durch lineare Stabilitätsanalyse). With this method the stability or instability of a temporally averaged flow can be determined.  Additionally, the method provides additional information, for example the cause of the instability or regions which are especially receptive for external control. 

Figure 2: Response of the flow (Figure 1) to harmonic acoustic excitation at a frequency of 93 Hz: Fluctuations in non-dimensional velocity in radial and axial direction, as well as fluctuations in density; The upper half plane shows the results of the resolvent analysis, while the lower half plane shows the actual response of the flow in the experiment

A method, that like the LSA is based on the linearized field equations is the resolvent analysis. It answers the question how a given flow responds to a given external excitation. This way, for example the response of an a priori known temporally averaged flow to acoustic excitation can be estimated. This comes at numerical costs which are only a fraction of the costs of conventional numerical simulations. Figure 1 shows the temporally averaged flow of a turbulent swirl flame, as well as the temporally averaged density field, both based on experimental measurements. Based on the resolvent analysis the hydrodynamic response of the flow to a harmonic acoustic actuation at a frequency of 97 Hz was measured. Figure 2 shows the results, namely the fluctuation of the radial and axial velocity component as well as the density component in the upper half plane. The lower half plane shows the actual response of the flow measured in the experiment. However, with this method not only the response of the flow can be predicted. It also helps to investigate the cause of the oscillation and possibilities to affect it. 


In LSA as well as in resolvent analysis so far, the impact of the flame chemistry is neglected. For practical applications in combustion chambers the currently available methods therefore are insufficient. In order to close this gap, we further develop together with our industrial partners MAN Energy Solutions SEthese numerical tools and pursue our goal of applying them in the development process of state-of-the-art gas turbine combustors.

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