Resolvent-based modelling of coherent structures in a turbulent jet flame using a passive flame approach

Abstract

Motivated by the recent success in finding coherent structures in turbulent flows and describing their noise emission using the Resolvent Analysis (RA), the method is applied to a turbulent jet flame at Re=15,000 and a corresponding non-reacting flow to investigate their axisymmetric dynamics. The RA, which in this study assumes a passive flame and neglects compressibility effects, is based on the governing equations linearized around the temporal mean state. It is validated against Spectral Proper Orthogonal Decomposition (SPOD) obtained from time-resolved snapshots. Both the temporal mean state and the snapshots are obtained by Large Eddy Simulation (LES). The SPOD reveals that an axisymmetric, convective Kelvin–Helmholtz (KH) instability is the dominant hydrodynamic mechanism in the jet flame within a narrow frequency band and incorporates up to 40% of the turbulent kinetic energy. Results show that the RA is capable of reproducing the mode shapes seen in the SPOD. The RA furthermore allows to address the origin of these hydrodynamic structures: While the corresponding KH mode in a non-reacting turbulent jet flow is most sensitive to perturbations in the nozzle boundary layer, the same dominant mode in the turbulent Bunsen flame is most receptive to perturbations in the region between the nozzle edge and the annular pilot burner. The results suggest that the strong density gradients in this region initiate perturbations in the baroclinic torque, which are feeding the KH mode. Finally, a linear stability analysis proves that the high sensitivity of the KH structure is due to resonance with stable linear eigenmodes, which explains its high energy content. By applying the RA to a turbulent reacting flow, this study opens up a new pathway in analyzing the role of hydrodynamic structures in reacting flows.