Assessment of LES-ADM Accuracy for Modelling of Auto-Ignition and Flame Propagation in a Temporally-Evolving Nitrogen-Diluted Hydrogen Jet

Abstract

The aim of the research is to analyze the accuracy of the approximate deconvolution method (ADM) for large eddy simulation (LES) modelling of auto-ignition and flame propagation in a turbulent, temporally-evolving nitrogen-diluted hydrogen jet. In ADM, filtered chemical reaction terms are not modelled; instead, they are directly computed based on deconvolved scalar variables, approximately inverting the spatial LES filter. The deconvolution process employs an iterative van Cittert method based on an assumed filter function. The study assesses the dependence of ADM accuracy on various filter types, such as Gaussian and finite/compact difference filters, used both as the LES filter (\({\mathcal {G}}_\Delta\)) and the filter for deconvolution (\({\mathcal {G}}_E\)). The results obtained with ADM are compared with those obtained from the Eulerian stochastic field (ESF) combustion model, the laminar chemistry model (LCM) - a ’no-model’ approach, and direct numerical simulation (DNS). Particular attention is given to situations in which the filter \({\mathcal {G}}_E\) differs from \({\mathcal {G}}_\Delta\), whose explicit form is generally unknown in LES. It is shown that LES-ADM performs similarly to the LES-ESF model and, in general yields better results than obtained with LES-LCM. However, in certain combinations of the \({\mathcal {G}}_E\) and \({\mathcal {G}}_\Delta\) filters, the results of simulations are worse than those using LES-LCM and sometimes even unstable. The reasons for such behaviour of the ADM method are identified, explained in 1D a priori tests, and then confirmed in 3D LES. It is shown that when the filter \({\mathcal {G}}_E\) is of a higher order than \({\mathcal {G}}_\Delta\) (\({\mathcal {O}}{({\mathcal {G}}_E)}>{\mathcal {O}}({\mathcal {G}}_\Delta )\)) or it has a transfer function close to one over a wide range of wave numbers, the energy at small scales of the deconvolved variables is attenuated. Conversely, if the opposite situation takes place (\({\mathcal {O}}{({\mathcal {G}}_E)}<{\mathcal {O}}({\mathcal {G}}_\Delta )\)), the small scale’s energy is amplified. Moreover, in this case, the apparent improvement in deconvolution accuracy by increasing the number of van Cittert iterations actually worsens the results and can lead to instability.