Interaction Effects In Premixed Turbulent Combustion

Author : Paulo Lucena Kreppel Paes
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (11 download)

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Download or read book Analysis of Inter-scale Turbulence-Chemistry Dynamics with Reduced Physics Simulations for Application to Large-Eddy Simulation of Premixed Turbulent Combustion written by Paulo Lucena Kreppel Paes and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Large Eddy Simulation (LES) is a powerful formulation to model turbulent reacting flows with tradeoffs between complexity and resolution. The classical LES framework assumes that the evolution of the more energetic grid-filtered motions are dominated by the dynamical interactions that are explicitly resolved on an "effective grid" that incorporates implicit and/or explicit filtering at the smallest grid-resolvable scales by non-physical friction introduced by the numerical algorithm and modeled terms. The dynamical effects of the unresolved Sub-Filter-Scale (SFS) motions on the evolution of the Resolved-Scale (RS) motions are higher order modulations. However, the application of the classical LES framework to turbulent reacting flows is not clear since dynamically first-order chemical kinetics associated with heat release reside within mostly unresolved SFS thin flame regions. Consequently, key dynamics underlying the function of combustion devices often reside dominantly within unresolved SFS motions in contradiction to the fundamental requirement underlying accurate prediction of resolved-scale dynamics with LES. Furthermore, the topological structure of the flame is necessarily frontal in nature (i.e., sheet-like structure), which poses difficulties for an LES strategy that must model coherent structures that live partially in resolved and partially in subfilter scale fluctuations with a method that treats turbulence eddies as either resolved or subfilter scale. In my research program, we explore the introduction of new modeling elements embedded within current state-of-the-art LES frameworks to capture the impacts of the dynamically dominant inter-scale couplings between RS and SFS motions to improve the predictive accuracy of premixed turbulent combustion evolution at the resolved scales. We aim to systematically refine understanding of the inter-scale interactions between coherent structural features in physical space and in scale space in LES of premixed turbulent combustion. Given the complexity of the interaction between a flame and a complete range of turbulence eddy scales, we analyze reduced physics two-dimensional simulations of the interactions between single-scale vortex arrays and laminar premixed flames, with systematically increasing relative vortex strength creating higher complexity in flame corrugation. To characterize physical-scale space relationships, we apply the Fourier description using a newly developed procedure that removes the broadband Fourier spectral content associated with boundary discontinuities in the non-periodic directions of variables simulated within a finite domain without significant modification of the scales of interest in the original signals. This procedure allows for the analysis of any signal with the Fourier spectral decomposition regardless of the boundary conditions. Using Fourier-space filters, we identify characteristic coherent structural features concurrently in physical and Fourier space in response to flame-eddy interaction and their relative contributions to the SFS and RS variance content of the primary variables of interest. Momentum, energy and species concentrations display different distinct structural features that undergo systematic transition from weak to strong flame-vortex interactions. The primary variables within the dynamical system were classified based on the RS vs. SFS variance content, and distinct structural features in physical and Fourier space were identified for each class. We show that the SFS variance for all variables analyzed is associated with the SFS corrugated flame front, which in 2D Fourier space is associated with a coherent broadband "star-like" pattern that extends from the resolved to the flame subfilter scales. The directional dependences, magnitudes and phase relationships among the Fourier coefficients within the "legs" of the star reflect the power-law spectral representation of fronts and are shown to be closely connected with the direction and magnitude of flame-normal gradients of key variables within the corrugated flame front. We take advantage of the mathematical simplicity of the Fourier spectral description of the nonlinearities in the equations of motion to identify the dominant nonlinear couplings between SFS and RS fluctuations, and from these the SFS content involved in the dominant SFS-RS interactions. In Fourier space the nonlinear terms appear as sums of elemental scale interactions each of which have a well-defined geometrical relationship among wave vectors that form polygons in multidimensional Fourier space. Whereas the shape of the polygon is triangular within advective nonlinearities (triads), it is quadrangular for the chemical nonlinearities (quadrads). This elemental representation of key nonlinearities is used to develop a novel strategy to arrange and down-select the dominant nonlinear inter-scale couplings between SFS and RS motions, from which the corresponding SFS content associated with dynamically dominant RS-SFS dynamics are extracted. The procedure is applied to advective, triadic, and chemical, quadratic, nonlinearities within the LES-filtered governing equations. For primary variables that have most of its energy content at large scales and rapid drops in energy towards small scale, the large-scale features of the dynamically dominant SFS content are shown to be coupled with the smallest resolved scales leading to the corrugations and thickness of the RS flame front. In contrast, the dynamically dominant SFS content of intermediate species involved in heat release rate is shown to follow the smallest corrugations of the flame front reaction zone, which deviate from the RS flame centerline in regions with higher corrugations, such as the flame cusps. The distinct structural features of dynamically dominant SFS content are used for the development of simplified mathematical representations that could be applied within a modeling strategy that directly embeds the interaction between the modeled dominant SFS content and RS evolution within existing LES frameworks to improve the dynamical evolution of resolved-scale motions. From our analysis we develop a number of primary mathematical forms that encapsulate dominant SFS content of momentum, energy and key species variables within advective nonlinearities and show that these produce significant improvements in the time derivatives underlying evolution of the resolved scales. The analysis demonstrates the potential for incorporating directly key energetic and structural features of SFS that significantly impact the evolution of RS motions through key nonlinear dynamic couplings in LES frameworks employing highly simplified mathematical representations. This research lays the groundwork for a Galerkin-like modeling strategy that incorporates highly reduced numbers of basis functions that encapsulate previously determined dominant nonlinear couplings between subfilter-scale structure and resolved-scale evolution.