Reduced-order model of a reacting, turbulent supersonic jet based on proper orthogonal decomposition
The present article deals with the spatiotemporal reduction of a reacting, supersonic, turbulent jet. A flowfield dataset is first obtained from a LES simulation including chemical reactions. The spatial reduction is accomplished by performing successively a Fourier transform in the azimuthal direction and a proper orthogonal decomposition (POD), while the temporal reduction is obtained through a selection of Fourier modes in the leading temporal POD modes (chronos). A prior low-pass temporal filter has been used to eliminate a significant portion of high-frequency content, the resulting reduced-order model (ROM) focusing only on the low-frequency, large-scale structures of the jet. The leading axisymmetric (\(m=0\)) POD mode describes a very low-frequency pulsation of the shock cells. The second and third axisymmetric POD modes are paired and describe a wave packet amplified along the potential core and with a rapid decay downstream. The two leading helical (\(m=1\)) POD modes, which are complex modes, appear to be mixed and together describe convecting wave packets of a longer wavelength and a lower frequency. They can be associated to the instability of the shear layer downstream of the potential core. Strong global cross-correlations are observed between the mass fractions and the axial velocity and temperature fields, which lead to similar energy decay rates and POD modes when they are included in the POD. The temporal reduction of the leading sets of chronos via an energy-based selection of Fourier modes has been shown to complement efficiently the spatial reduction, providing a complete spatiotemporal ROM of the flowfield.
KeywordsReduced-order model Proper orthogonal decomposition Turbulent jet Reacting flows
This work has been funded by the ONERA internal project PRF SIMBA. The authors would like to thank Aurélien Guy and Sidonie Lefebvre for a number of useful comments and suggestions.
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