Analysis of Turbulent, Non-Reacting and Reacting Jet Flows Using Resolvent Analysis and Spectral Proper Orthogonal Decomposition

Describing turbulence is one of the most challenging, if not the most challenging, problem in fluid mechanics. Recent advancements in this field are due to the so called resolvent analysis. This method is based on the flow equations linearized around the temporal mean of a turbulent flow, which must be provided as input to the analysis. It has recently been shown for non-reacting flow applications that this method is capable of identifying the dominant mechanisms, which are driving turbulence. In our current work we attempt to generalize this approach to reacting flows.

The flow we are investigating is a turbulent jet under non-reacting as well as a reacting conditions at a Reynolds number of 15000. For both configurations, we compare the results based on the resolvent analysis to Spectral Proper Orthogonal Decomposition(SPOD) modes based on time resolved snapshots of the flow. These are obtained together with the temporal mean flows, which serve as input to the analysis by high fidelity Large Eddy Simulations (LES).

First, we analyze the non-reacting jet flow, where we obtain energy spectra from the SPOD analysis where the first and the second azimuthal mode exceed the energy of the zeroth mode in the low frequency regime up to Strouhal numbers of 0.52. Comparing these spectra to the resolvent's gains we observe a very good agreement. However, where the SPOD does not show a strong separation of the leading eigenvalues, being typical for a turbulent jet, the resolvent gains show this so called low-rank behavior. Additionally, the mode shapes of resolvent analyisis and SPOD align very well.
As a source for the mode strucutures being amplified within the shear layer, we identify the boundary layer close to the nozzle exit, shown by the SPOD modes, as well as by the resolvent's harmonic forcing.

Second, we continue our analysis with the reacting jet flow, where we first adapt our methods to cover the additional influence of density fluctuations correlating with the velocity variations. In both SPOD as well as resolvent analysis we observe the flame's influence on the spectra and mode shapes. First, the spectra show a high amplitude at around St=0.1 for azimuthal modes 0,1 and 2, being significantly different from the spectra observed in the non-reacting flow. Additionally, this frequency regime shows a clearer separation of eigenvalues pursuing a low-rank behavior, indicating a dominant flow structure. Also the mode shapes obtained by the SPOD-analysis show a spatial shift and show a stronger amplification further downstream compared to the non-reacting configuration.

Finally, we compare our mean field based approach to the SPOD analysis for the reacting jet flow and observe not only a very good alignment of mode shapes again, but also obtain similar behaviour within the resolvent gains, compared to the SPOD spectra, concerning the different azimuthal mode numbers, indicating that the resolvent analysis is capable of obtaining dominant flow structures also for reacting flows.