Spatially localized multi-scale energy transfer in turbulent premixed combustion

Abstract

A three-dimensional wavelet multi-resolution analysis of direct numerical simulations of a turbulent premixed flame is performed in order to investigate the spatially localized spectral transfer of kinetic energy across scales in the vicinity of the flame front. A formulation is developed that addresses the compressible spectral dynamics of the kinetic energy in wavelet space. The wavelet basis enables the examination of local energy spectra, along with inter-scale and subfilter-scale (SFS) cumulative energy fluxes across a scale cutoff, all quantities being available either unconditioned or conditioned on the local instantaneous value of the progress variable across the flame brush. The results include the quantification of mean spectral values and associated spatial variabilities. The energy spectra undergo, in most locations in the flame brush, a precipitous drop that starts at scales of the same order as the characteristic flame scale and continues to smaller scales, even though the corresponding decrease of the mean spectra is much more gradual. The mean convective inter-scale flux indicates that convection increases the energy of small scales, although it does so in a non-conservative manner due to the high aspect ratio of the grid, which limits the maximum scale level that can be used in the wavelet transform, and to the non-periodic boundary conditions, which exchange energy through surface forces, as explicitly elucidated by the formulation. The mean pressure-gradient inter-scale flux extracts energy from intermediate scales of the same order as the characteristic flame scale, and injects energy in the smaller and larger scales. The local SFS-cumulative contribution of the convective and pressure-gradient mechanisms of energy transfer across a given cutoff scale imposed by a wavelet filter is analysed. The local SFS-cumulative energy flux is such that the subfilter scales upstream from the flame always receive energy on average. Conversely, within the flame brush, energy is drained on average from the subfilter scales by convective and pressure-gradient effects most intensely when the filter cutoff is larger than the characteristic flame scale.

A semi-Lagrangian direct-interaction closure of the spectra of isotropic variable-density turbulence

“…This is consistent with recent observations using wavelet analysis of reacting flame spectra by Kim et al. (2018).…”

Time–frequency localisation of intermittent dynamics in a bistable turbulent swirl flame

“…2017; Kim et al. 2018). A large library of wavelet filters (as well as methods) are easily accessible via either the Wavelet toolbox in Matlab or in Python.…”

“…2017; Kim et al. 2018). A large library of wavelet filters (as well as methods) are easily accessible via either the Wavelet toolbox in Matlab or in Python. Despite its relative ease of use, as mentioned in § A.3, wavelet basis only allows a rigid frequency splitting and the constructed subbands may deviate significantly from an ideal bandpass.…”

“…Non-periodic and unsteady dynamics often rejected by Fourier analysis is preserved in MRA. Besides direct implementation of MRA on data series acquired in turbulent flows (Ruppert-Felsot, Farge & Petitjeans 2009;Indrusiak & Möller 2011;Rinoshika & Omori 2011;Mancinelli et al 2017;Kim et al 2018), the concept of MRA has also given rise to multiresolution DMD (MRDMD) (Kutz, Fu & Brunton 2016) and multi-scale POD (Mendez, Scelzo & Buchlin 2018;Mendez, Balabane & Buchlin 2019) that can potentially overcome the shortcomings of conventional modal analyses when treating complex dynamic systems. To further the understanding of the bistable phenomenon, this work proposes a novel approach to combine POD with wavelet-based MRA for deriving unambiguous modal descriptions of intermittent dynamics from the high-speed experimental data series obtained in the bistable flame.…”

Wavelet-spectral analysis of droplet-laden isotropic turbulence

“…For example, wavelets have been used to analyse particle-laden flows (Bassenne, Moin & Urzay 2018) and turbulent combustion (Kim et al. 2018). A similar approach was used to compute spectra on non-periodic domains by using spatial filtering with a customized non-wavelet basis (Sadek & Aluie 2018).…”