Assessment of deconvolution-based flamelet methods for progress variable rate modeling

Abstract

A novel approach for modeling the progress variable reaction rate in Large Eddy Simulations of turbulent and reacting flows is proposed. This is done in the context of two popular flamelet models which require the progress variable variance as input. The approach is based on using a recently proposed deconvolution method for modeling the variance. The deconvolution-modeled variance, is used as an input in the flamelet models for modeling the filtered progress variable rate. The assessment of the proposed approach is conducted a priori using direct numerical simulation data of turbulent premixed flames. For the conditions tested in this study, deconvolution does not introduce a significant bias in the flamelet models' predictions, while a quantitatively good prediction of the progress variable rate is obtained for both flamelet models considered. method has both its merits and drawbacks, and an in-depth discussion on the subject can be found in the reviews [3]- [5].Flamelet methods in particular are popular since they are relatively straightforward to implement, and have been applied in a number of LES studies both for premixed and for non-premixed flames, with overall good results [6]- [16]. These studies include flows in complex geometries and for different flow configurations (freely-propagating, recirculating, etc.). The filtered progress variablec which is a main LES solution variable, and it's variance σ 2 = c 2 −cc as obtained from a suitable model, are used as parameters in prebuilt tables for obtaining important information and for providing closures for un-closed terms in the governing equations. This includes species mean (filtered) mass fractions, mean (filtered) reaction rates etc. Such methods offer a simple, yet effective way of providing detailed chemistry information (a posteriori), while keeping the computational requirements to a minimum.A key unclosed term in the transport equation for the progress variable,c, is the filtered progress variable reaction rate,w c , where the overbar denotes a spatial filtering operation as defined in the context of LES. This is a dominant term, particularly in the reaction zone of the flame [17], and an accurate model is required for this term. Two popular flamelet methods for modelingw c , and which involve the progress variable variance, are the presumed-pdf approach and the Filtered Laminar Flame (FLF) approach [7,13]. In the presumed-pdf approach, the progress variablec and it's variance σ 2 , are used to parameterise the progress variable pdfp(ζ;c, σ 2 ), where ζ is the sample-space variable forc. This pdf is usually taken to be a β-function. A usually steady, 1D, laminar flame solution is used for integrating with the pdf thus obtaining a closure for the rate. In the FLF approach, a 1D laminar flame solution is pre-filtered, and a table is constructed which contains values of the filtered reaction rate (or other variables of interest). This is done for discrete filter-width values, and the table contains the filtered values of the variables at all spatial p...

Modelling turbulent premixed flames using convolutional neural networks: application to sub-grid scale variance and filtered reaction rate

“…A stringent simulated LES mesh validation approach is employed [20,21], where the network training data size reduces with increasing filter width. These approximations are then used to model the variance, which is a key parameter in many combustion models [35,36]. At this point it is also important to note that a priori assessments do not guarantee functionality of the models in actual LES.…”