Abstract
The aim of the current study is to characterize key multidimensional relationships between coherent structures in physical vs Fourier/scale space representations of flame–turbulence interactions, as a basis for future analysis of the nonlinear couplings between key resolved scale (RS) and subfilter scale (SFS) motions in large-eddy simulation (LES) of premixed turbulent combustion. However, applying the bounded Fourier transform (FTF) in the nonperiodic flame-normal direction requires the removal of nonphysical Fourier content from the boundary discontinuities. To this end, we have developed a broadly applicable “discontinuity pollution removal” procedure for application to the FTF of multidimensional signals with a single nonperiodic direction. The procedure balances periodization of the signal near the boundaries with minimization of signal modification away from the boundaries. We applied the procedure in a physical–Fourier space analysis of the interactions between a flame and single-scale eddies modeled as the impact of a train of two-dimensional (2D) vortices on an initially planar premixed flame. We find that a specific spectrally broad localized coherent structure in Fourier space connects RS to SFS fluctuations in thermal energy and species concentration that, in physical space, are localized to the corrugations in the flame front in response to eddy–flame interactions. Within the RS fluctuations of energy and species concentration, the flame corrugation structure in physical space is found to be localized to sub-volumes within the RS region of 2D Fourier space. This new understanding of physical–Fourier space relationships categorizes classes of RS–SFS interactions relevant to SFS modeling in LES of premixed turbulent combustion.
Highlights
AND AIMSThe large-eddy simulation (LES) framework centers on decomposition in scale; LES modeling centers on the interactions between larger “resolved scale” (RS) and smaller “subfilter scale” (SFS) fluctuations in all dependent variables
The current study has two interrelated motivations: (1) the development of a “discontinuity pollution removal” procedure that removes nonphysical Fourier content arising from boundary discontinuities when the Fourier transform (FTF) of a bounded analytic signal is taken in a nonperiodic direction, without significantly modifying the signal away from the boundaries
II and Appendix B) and (2) analysis of the relationship between the same coherent structure in physical space and in Fourier space with data from a reduced physics simulation designed to have key characteristics of flame–turbulence interactions that are characteristic of flame–turbulence interactions in premixed turbulent combustion
Summary
The large-eddy simulation (LES) framework centers on decomposition in scale; LES modeling centers on the interactions between larger “resolved scale” (RS) and smaller “subfilter scale” (SFS) fluctuations in all dependent variables. The specific objectives of the current paper are (1) to identify the spurious Fourier content created from nonphysical boundary discontinuities when the FTF is taken of nonperiodic variables on a bounded domain and develop a procedure to systematically remove the spurious content (pollution) from the boundary discontinuities without significantly altering the signal away from the boundaries, (2) to develop a reduced physics simulation of the interaction between an initially unstretched flame and a train of vortices and apply the simulation to validate the discontinuity-pollution-removal method, and (3) to analyze the 2D flame–vortex interaction model concurrently in Fourier and physical space to characterize the kinematic relationships between the localized coherent structure in physical space and the localized coherent structure in Fourier space within the LES framework. This analysis provides the foundation for the proposed “discontinuity pollution removal” procedure
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