Dominant Interscale Dynamics in Premixed Turbulent Combustion for Application to Large-Eddy Simulation

Download or read book Dominant Interscale Dynamics in Premixed Turbulent Combustion for Application to Large-Eddy Simulation written by Yash Girish Shah and published by . This book was released on 2021 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The large-eddy simulation (LES) approach has become an important tool for engineering design and optimization of combustion devices. In a properly designed LES, the larger-scale flow variations are resolved by the effective numerical grid, which incorporates the implicit/explicit filtering introduced by the spatial filtering from the grid, artificial diffusion from numerical schemes, and modeled terms. The dynamical consequences of the remaining subfilter-scale (SFS) fluctuations below the effective grid to the evolution of grid-resolved scales (RS) motions in dynamically relevant physical variables are modeled. The nonlinearities in the dynamical evolution of resolved-scale variables that result from the inherent nonlinear coupling between the resolved and subfilter scales are often not sufficiently well captured in turbulent combustion, as the intermediate species that participate in the heat release process are dominantly only at chemical length and time scales well within the subfilter scales. In this research work, we explore new LES modeling strategies that represent the RS-SFS interactions in the evolution of RS primary variables (momentum, energy and species concentrations) more directly by approximating the SFS content that contributes dominantly to the dynamical evolution of RS quantities using simple mathematical forms. To achieve this, we first obtain a highly resolved three-dimensional Direct Numerical Simulation (DNS) dataset of flame-turbulence interactions that capture the essential RS-SFS interactions in primary variables over a wide range of scales. To systematically analyze the RS-SFS interscale couplings for LES, we then obtain the scale content as the Fourier space representation of the inherently inhomogeneous DNS dataset by applying a discontinuity removal procedure that removes the unphysical gradients naturally introduced at the boundaries of the computational domain by the periodic extension that occurs with the Fourier transform over a bounded domain. The Fourier space representation of primary variables in turbulence-flame dynamical interactions are systematically analyzed. Variables that display high gradients across the flame front over length scales comparable to or larger than flame scales are found to have higher Fourier variance contributions at wavenumbers below flame scale wavenumber, while Fourier variance contributions from variables that are localized only within the flame are found to be distributed to higher wavenumbers in Fourier space. Using this Fourier space representation, we systematically determine the scales of the energy-dominant flow variations in momentum and enthalpy that are resolved by LES and objectively identify the RS and SFS fluctuations for other primary variables. Variables that display frontal variations surrounding the flame are found to be dominantly resolved while those variables that are localized only within the flame are found to be dominantly subfilter scale. These differences in Fourier variance distributions are shown to have implications to the extent of RS-SFS interactions between these variables. We take advantage of the mathematical property of the Fourier spectral description that allows the nonlinearities from the advective transport and chemical reaction rates in the dynamical system to be expressed as elemental sums over triadic interactions involving three wavevectors and quadrad interactions involving four wavevectors between the RS and SFS fluctuations. Using this elemental representation, the SFS content that contributes dominantly to the dynamical evolution of resolved-scales advective nonlinearity is identified by applying the triads downselection procedure [75]. We find that RS-SFS interactions involving SFS content from significantly larger scales compared to the smallest resolvable scales in the DNS are required to adequately estimate the resolved-scale advective nonlinearity in LES. These dynamically dominant SFS for RS advective nonlinearity span over a broader range of wavenumbers for dominantly SFS variables compared to variables that are dominantly resolved-scale. To study the dominant RS-SFS interactions in the chemical nonlinearity, a new two-stage downselection procedure is developed in this work, which expresses the quadrad interactions between the reaction rate constant and the species concentrations to the resolved chemical reaction rates first into triadic interactions between the chemical reaction rate constant and the product of species concentrations. The product of species concentrations is then expressed as a triadic sum over interactions between individual species concentrations and the corresponding dynamically dominant SFS is extracted from both stages using triad downselect procedure for second-order nonlinearities. The dynamically dominant SFS resulting from this procedure is found to be considerably reduced from the full SFS and is shown to be effective in adequately approximating the chemical reaction rates at resolved scales through RS-SFS interactions. The structure underlying the distribution of these dynamically dominant SFS fluctuations in species concentrations are identified for key species in representative reactions in regions where the incorporation of the SFS content is impactful to the estimation of chemical reaction rates in LES. The dynamically dominant SFS species structure is found in two groupings: ``single-banded'' structure characterized by one distinct peak, and ``double-banded'' structure characterized by two peaks of opposite signs. Species that are produced and consumed within the flame are observed to have single-banded structure and species displaying a frontal behavior are observed to have double-banded structure in their dynamically dominant SFS concentrations on average. The local structure of the dynamically dominant SFS species concentrations surrounding the flame is impacted by neighboring flame-flame interactions as well as by variations in flame curvature. The impacts of the flame-flame interactions are strong when the dynamically dominant SFS species structure has ``large'' length scales with concentration peaks significantly displaced from the flame front. Finally, mathematical forms to approximate the mean single and double banded structure in the dynamically dominant SFS concentrations are proposed for application within a structure-based SFS modeling strategy which directly embeds the interaction between the modeled dominant SFS content and the RS evolution within existing LES frameworks. This research lays the groundwork for future LES model developments that utilize this strategy for improving LES predictions of resolved-scale dynamics.