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Direct Numerical Simulation Analysis of the Partially Stirred Reactor Model for Turbulent Reacting Flows

par Pequin, Arthur
Président du jury Coussement, Axel
Promoteur Parente, Alessandro
Publication Non publié, 2023-07-06

Thèse de doctorat

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Résumé :

To support industrial sectors in facing the challenges from the energy transition, it is essential to develop accurate Computational Fluid Dynamics (CFD) models for combustion applications.In particular, turbulence-chemistry interactions (TCI) models that can predict pollutant emissions and energy efficiency from simulated systems are sought. Among many combustion closures, reactor-based models have recently drawn interest for their ability to treat chemistry with detailed descriptions at an affordable cost. Originally derived from the intermittency theory of highly turbulent reacting flows, such models have evolved to provide a valuable solution to any type of flame, up to non conventional combustion technologies.In numerical simulations employing the Partially Stirred Reactor (PaSR) approach as combustion closure, chemical processes are assumed to take place in sub-grid flow regions of typical length scale smaller than numerical control volumes. Each computational cell is then partitioned into two locally uniform regions, namely the inert surroundings, solely driven by turbulent mixing, and the reacting fine structures. The mean reaction rates, contributing to the transport equations of the chemical species, are estimated as the reaction rates from the fine structures multiplied by the cell reacting fraction, i.e., the volume fraction of the cell occupied by the fine structures. Characteristic time scales for mixing and chemistry are used to estimate the cell reacting fraction.Many time scales formulations exist and modelling efforts are to be put in selecting the most suitable candidates. Among the available computational approaches, Large Eddy Simulation (LES) has recently gained interest for its ability to provide accurate numerical solutions up to industrial scale problems. Conversely to costly Direct Numerical Simulation (DNS) where all scales are resolved, LES solves only the scales down to the computational grid resolution level, the shorter scales and their interactions being modelled. Nevertheless, DNS of turbulent combustion can supply key information on turbulence-chemistry interactions occurring at the smallest scales.A priori testing is an example of modelling routes making use of DNS data for the development and validation of LES combustion models.The present Thesis reports modelling advances of the Partially Stirred Reactor combustion approach by means of a priori investigations on DNS data of turbulent reacting flows.First, a layer decomposition of the Partially Stirred Reactor combustion model was conducted.Predictions of the chemical source terms and heat release rates from several combustion models have been compared. Various formulations of the chemical time scale for the PaSR model were considered.A class of mathematical functions was constructed to provide modelling guidance. Several potential modelling improvements were identified throughout the discussion and were grouped in three categories, namely parameter selection, cell reacting fraction reformulation and deep model revision. Parameter selection aims at finding an optimal set of parameters or submodels to improve model accuracy. Such a study was conducted on the PaSR model in the context of Moderate or Intense Low-oxygen Dilution (MILD) combustion, an appealing non conventional combustion technology in terms of fuel flexibility, pollutant emissions, and thermal efficiency. An optimal set of sub models was found for the specific modelling of MILD combustion where turbulence-chemistry interactions are naturally strengthened. Also, the layer decomposition demonstrated that finding an optimal submodel can be a local concept, i.e., depending on the local flow region.In this context, a data-driven methodology employing supervised clustering algorithms has been proposed for the local estimation of the optimal chemical time scale formulation in the PaSR model.A binning operation was used to partition the data into clusters of similar thermo-chemical states. Within each cluster, the best formulation was found by means of distance minimisation.Coupling the PaSR model with clustered solutions yielded a systematic modelling error cut-off.The method was found applicable to any type of flames.Besides parameter selection, the functional form of the cell reacting fraction in the PaSR model has been investigated more carefully. A methodology was proposed to extract sub-grid quantities from DNS data matching the physical representation of the cell reacting volume fraction.Each cell from the DNS was supposed extinct or reacting depending on the local intensity of heat release.Down-sampling on coarser LES grids, the extracted cell reacting fractions were given by the proportion of active DNS cells within the larger LES control volumes.Questioning the true representation of the modelled cell reacting fractions, the extracted quantities may cope with modelling needs by means of algebraic fraction forms.This illustrated the complexity of remodelling the cell reacting fraction form by hand.Within this context, machine learning and sparse-promoting techniques have been used to explore broad libraries of potential functional forms.Such approaches returned the solution best balancing accuracy and modelling complexity.An original functional form of the cell reacting fraction was found and provided higher accuracy results with respect to standard approaches. The results were validated on combustion datasets operating at different regimes.Lastly, the PaSR combustion model has been revised more in-depth to cope with the fundamental limitation of relying on a unique cell reacting fraction for all chemical species. In particular, tools from the machine learning community and arguments from the Computational Singular Perturbation theory have been employed to respectively derive two modelling frameworks.In the first approach, the closure of a progress variable transported equation with a PaSR approach was developed. Such equation left an unclosed term, namely the fine structures progress variable, that required modelling.To this purpose, neural networks (NN) have been trained and tested on DNS data of different turbulent flames. Great generalisation capabilities were obtained while regressing the subgrid scale variable from information at grid level. This methodology has showed its ability to be a valuable alternative to the classic closures for the source term of a progress variable transported equation.The second framework consisted in the integration of multiple chemical time scales in a PaSR approach.Abandoning the concept of the fine structures, a modal decomposition of the Jacobian matrix of the chemical source terms was performed. Each mode contributing to the final estimation of the mean reaction rates was multiplied by its modal coefficient resembling a cell reacting fraction.This innovative framework provided promising results on a rather simple test case, requiring further modelling attention.