Local manifold learning and its link to domain-based physics knowledge

In many reacting flow systems, the thermo-chemical state-space is known or assumed to evolve close to a low-dimensional manifold (LDM). Various approaches are available to obtain those manifolds and subsequently express the original high-dimensional space with fewer parameterizing variables. Principal component analysis (PCA) is one of the dimensionality reduction methods that can be used to obtain LDMs. PCA does not make prior assumptions about the parameterizing variables and retrieves them empirically from the training data. In this paper, we show that PCA applied in local clusters of data (local PCA) is capable of detecting the intrinsic parameterization of the thermo-chemical state-space. We first demonstrate that utilizing three common combustion models of varying complexity: the Burke-Schumann model, the chemical equilibrium model and the homogeneous reactor. Parameterization of these models is known a priori which allows for benchmarking with the local PCA approach. We further extend the application of local PCA to a more challenging case of a turbulent non-premixed $n$-heptane/air jet flame for which the parameterization is no longer obvious. Our results suggest that meaningful parameterization can be obtained also for more complex datasets. We show that local PCA finds variables that can be linked to local stoichiometry, reaction progress and soot formation processes

Non-Premixed Filtered Tabulated Chemistry for LES: Evaluation on Sandia Flames D and E

The non-premixed filtered tabulated chemistry for large eddy simulations employs numerical filtering to resolve a thin flame front on practical LES numerical grids. The flame structure is modified to be coherent with the domain discretization. The first turbulent combustion application of the non-premixed filtered tabulated chemistry approach is presented. A keen comparison of the flamelet filtering transformation in the premixed and non-premixed regimes is carried out. Three distinctive features are outlined: the flame thickness variation, the filtered manifold transformation, and the model activation dependence on the chosen diffusion flamelet configuration for a non-premixed filtered approach. The model performance is assessed on two real turbulent flame configurations, Sandia flames D and E, employing a three-dimensional tabulation strategy, where the numerical grid is coupled with the model by the third parameter, i.e., the computational cell size. The repercussions of the above cited aspects are carefully assessed. The results demonstrate that the formalism coupling with an SGS modeling function can adequately describe wrinkled flame front effects. The predictions for both the major stable species and the minor ones accurately correspond with the underlying physics. It turns out that there is a substantial variation of the filter effect as a function of the strain rate of the flame and the considered species. The varying filter sensitivity along the manifold influences the response of the model correction terms and the retrieved variables. The non-premixed FTACLES formalism possibilities and conditions for the model’s utilization and optimal performance are clearly stated, to confirm the idea that SGS closure in diffusive combustion can be derived based on filtering arguments, and not only based on statistical approaches

Direct numerical simulation and reduced chemical schemes for combustion of perfect and real gases

La première partie de cette thèse traite du développement du code de simulation numérique directe YWC, principalement du développement des conditions aux limites. En effet, une forte contribution scientifique a été apportée aux conditions aux limites appelées "Three dimensional Navier-Stokes characteristic boundary condtions" (3D-NSCBC). Premièrement, la formulation de ces conditions aux arêtes et coins a été complétée, ensuite une extension de la formulation a été proposée pour supprimer les déformations observées en sortie dans le cas d'écoulements non-perpendiculaires à la frontière. De plus, ces conditions ont été étendues au cas des gaz réels et une nouvelle définition du facteur de relaxation pour la pression a été proposée. Ce nouveau facteur de relaxation permet de supprimer les déformations observées en sortie pour des écoulements transcritiques. Les résultats obtenus avec le code YWC ont ensuite été utilisés dans la seconde partie de la thèse pour développer une nouvelle méthode de tabulation basée sur l'analyse en composantes principales. Par rapport aux méthodes existante telles que FPI ou SLFM, la technique proposée, permet une identification automatique des variables à transporter et n'est, de plus, pas lié à un régime de combustion spécifique. Cette technique a permis d'effectuer des calculs d'interaction flamme-vortex en ne transportant que 5 espèces à la place des 9 requises pour le calcul en chimie détaillée complète, sans pour autant perdre en précision. Finalement, dans le but de réduire encore le nombre d'espèces transportées, les techniques T-BAKED et HT-BAKED PCA ont été introduites. En utilisant une pondération des points sous-représentés, ces deux techniques permettent d'augmenter la précision de l'analyse par composantes principales dans le cadre des phénomènes de combustion.Doctorat en Sciences de l'ingénieurinfo:eu-repo/semantics/nonPublishe

Direct numerical simulation and reduced chemical schemes for combustion of perfect and real gases

La première partie de cette thèse traite du développement du code de simulation numérique directe YWC, principalement du développement des conditions aux limites. En effet, une forte contribution scientifique a été apportée aux conditions aux limites appelées "Three dimensional Navier-Stokes characteristic boundary condtions" (3D-NSCBC). Premièrement, la formulation de ces conditions aux arêtes et coins a été complétée, ensuite une extension de la formulation a été proposée pour supprimer les déformations observées en sortie dans le cas d'écoulements non-perpendiculaires à la frontière. De plus, ces conditions ont été étendues au cas des gaz réels et une nouvelle définition du facteur de relaxation pour la pression a été proposée. Ce nouveau facteur de relaxation permet de supprimer les déformations observées en sortie pour des écoulements transcritiques. Les résultats obtenus avec le code YWC ont ensuite été utilisés dans la seconde partie de la thèse pour développer une nouvelle méthode de tabulation basée sur l'analyse en composantes principales. Par rapport aux méthodes existante telles que FPI ou SLFM, la technique proposée, permet une identification automatique des variables à transporter et n'est, de plus, pas lié à un régime de combustion spécifique. Cette technique a permis d'effectuer des calculs d'interaction flamme-vortex en ne transportant que 5 espèces à la place des 9 requises pour le calcul en chimie détaillée complète, sans pour autant perdre en précision. Finalement, dans le but de réduire encore le nombre d'espèces transportées, les techniques T-BAKED et HT-BAKED PCA ont été introduites. En utilisant une pondération des points sous-représentés, ces deux techniques permettent d'augmenter la précision de l'analyse par composantes principales dans le cadre des phénomènes de combustion.Doctorat en Sciences de l'ingénieurinfo:eu-repo/semantics/nonPublishe

Filtered Tabulated Chemistry for non-premixed flames

International audienceThe objective of the present study is to design a modeling strategy for LES of laminar diffusion flame regimes, i.e. without SGS wrinkling. A non-premixed model dedicated to capture unresolved laminar flame structure is then proposed. For that purpose, the Filtered Tabulated Chemistry for Large Eddy Simulation is adapted to diffusion flames. A filtered look-up table computed from a collection of strained 1-D coun-terflow flames is generated. The filtered flame structure and thickness is captured with three controlling variables which are the filtered mixture fraction, the filtered progress variable and the filter size. This approach is successfully applied to 1-D and 2-D unresolved counter-flow flame simulations. The filter size governs the minimal thickness of the filtered thermal layer

MG-local-PCA method for reduced order combustion modeling

Chemistry tabulation techniques such as flamelet models are a popular way to account for detailed chemistry effects in numerical simulation. These techniques are based on the identification of a low dimensional manifold in chemical space that accurately represents chemical evolutions associated to a specific combustion regime. During the last years, several authors used the Principal Component Analysis (PCA) to identify low dimensional manifold for combustion problems. However, full coupling between this manifold and flow solver has not yet been performed to the authors knowledge. The present paper introduces a new approach called Manifold Generated by a Local PCA or MG-L-PCA, which fully couple the manifold identified by a PCA and a DNS flow solver. The first part of the paper presents the PCA approach. Then, the coupling between this manifold and a DNS solver is presented. The MG-L-PCA approach is finally validated against a DNS simulation of flame vortex interaction using both detailed mechanism and a FPI manifold. Unlike FPI, the MG-L-PCA reproduces the dispersion in the chemical space induced by the flame-vortex interaction both for the species and the source terms.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

Numerical investigations of a Pulsed Jet in Crossflow

It has been recognized that jets in crossflow are more efficient mixer than free-jets or mixing layers. This enhanced mixing is attributed to the counter-rotating vortex pair. The work of Cortelezzi and al. makes evidence of this by explaining the process involved in the formation of the two counter-rotating vortices. Pulsed jet in crossflow can further improve the mixing of the two streams by changing the nature of the flow. Some au- thors have already studied experimentally the structure of pulsed jet in crossflow. Here, we propose to study the phenomena involved in the formation and development of a pulsed jets in crossflow via large eddy simulation (LES).info:eu-repo/semantics/nonPublishe

Application of the PCA framework to premixed combustion

info:eu-repo/semantics/nonPublishe

Kernel Density Weighted Principal Component Analysis of Combustion Process

Principal component analysis (PCA) has been successfully applied to the analysis of combustion data-sets. However using PCA on a raw direct numerical simulation or an experimental data-set is not straightforward. Indeed, those data-sets usually show non homogenous data density, hot and cold zones being generally over represented. This can introduce bias in the PCA reconstruction, especially when strong non-linear relationships characterize the data sample. To tackle this problem, a combination of the kernel density method and PCA is introduced here. This new PCA algorithm, called Temperature BAsed KErnel Density weighted PCA ( T-BAKED PCA) allows to enhance the PCA accuracy especially in the flame front zone, which is the principal zone of interest. The performance of this new approach is benchmarked against classical PCA. Moreover, a new method called Hybrid T-BAKED PCA or HT-BAKED PCA, combining both classical and T-BAKED PCA, is proposed to provide an optimal representation of all flame regions.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

Large eddy simulation of a pulsed jet in cross-flow

This study quantifies the mixing that results from a pulsed jet in cross-flow in the near jet region. By large eddy simulation computations, it also helps to understand the physical phenomena involved in the formation of the pulsed jet in cross-flow. The boundary conditions of the jet inlet are implemented via a Navier-Stokes characteristic boundary condition coupled with a Fourier series development. The signals used to pulse the jet inlet are a square or a sine wave. A new way of characterizing the mixing is introduced with the goal of easily interpreting and quantifying the complicated mixing process involved in a pulsed jet in cross-flow flow fields. Different flow configurations, pulsed and non-pulsed, are computed and compared, keeping the root mean square value of the signal constant. This comparison not only allows the characterization of the mixing but also illustrates some of the properties of the mixing characterization. © Cambridge University Press 2012.SCOPUS: ar.jinfo:eu-repo/semantics/publishe