Conditional Source-term Estimation (CSE) methods are used to obtain chemical closure in turbulent combustion simulation. A Laminar Flamelet Decomposition (LFD) and then a Trajectory Generated Low-Dimensional Manifold (TGLDM) method are combined with CSE in Reynolds-Averaged Navier Stokes (RANS) simulation of non-premixed autoigniting jets. Despite the scatter observed in the experimental data, the predictions of ignition delay from both methods agree reasonably well with the measurements. The discrepancy between predictions of these two methods can be attributed to different ways of generating libraries that contain information of detailed chemical mechanism. The CSE-TGLDM method is recommended for its seemingly better performance and its ability to transition from autoignition to combustion. The effects of fuel composition and injection parameters on ignition delay are studied using the CSE-TGLDM method. The CSE-TGLDM method is then applied in Large Eddy Simulation of a non-premixed, piloted jet flame, Sandia Flame D. The adiabatic CSE-TGLDM method is extended to include radiation by introducing a variable enthalpy defect to parameterize TGLDM manifolds. The results are compared to the adiabatic computation and the experimental data. The prediction of NO formation is improved, though the predictions of temperature and major products show no significant difference from the adiabatic computation due to the weak radiation of the flame. The scalar fields are then extracted and used to predict the mean spectral radiation intensities of the flame. Finally, the application of CSE in turbulent premixed combustion is explored. A product-based progress variable is chosen for conditioning. Presumed Probability Density Function (PDF) models for the progress variable are studied. A modified version of a laminar flame-based PDF model is proposed, which best captures the distribution of the conditional variable among all PDFs under study. A priori tests are performed with the CSE and presumed PDF models. Reaction rates of turbulent premixed flames are closed and compared to the DNS data. The results are promising, suggesting that chemical closure can be achieved in premixed combustion using the CSE method. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate

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Les écoulements cisaillés en rotation sont fréquents en ingénierie — par exemple en turbo- machines et dans la production d’énergie hydraulique — et en géophysique et astrophysique. L’étude de leurs propriétés de stabilité en lien avec la production de turbulence est donc essentielle. Dans la présente étude, nous ne considérons pas d’éventuels effets inhomogènes, et nous nous concentrons sur la complexité de la dynamique anisotrope, qui ne peut se représenter facilement par les seuls modèles statistiques en un point. La thèse porte donc sur l’étude des propriétés de la turbulence homogène anisotrope (HAT) avec champ moyen uniforme et effet Coriolis, à l’aide de modèles statistiques en deux points. Un modèle orig- inal est proposé qui permet de prédire la dynamique de la turbulence cisaillée en rotation, et sépare les effets de déformation linéaire de la dynamique turbulente non linéaire, afin de proposer un traitement adapté pour chaque contribution. Le modèle proposé porte sur les équations qui régissent l’évolution du tenseur spectral du second ordre des corrélations de vitesse en deux points. Il permet d’aborder les gradients de vitesse moyenne arbitraires, avec ou sans rotation d’ensemble du système. L’effet direct linéaire des gradients moyens est exact dans le modèle, alors que les effets non linéaires con- stitués des corrélations d’ordre trois en deux points sont fermés par un modèle anisotrope de type EDQNM. Dans ce modèle de fermeture, l’anisotropie est restreinte à un développe- ment tronqué en termes d’harmoniques angulaires d’ordre bas Mons et al. (2016). Notre nouveau modèle est validé pour le régime linéaire par comparaison à une solution trés pré- cise de distorsion rapide visqueuse (vRDT) dans plusieurs cas de cisaillement: stabilisant, déstabilisant ou neutre. Le modèle diffère des approches de simulation numérique directe (DNS) pseudo-spectrale pour les écoulements cisaillés proposées par Rogallo (1981) en ingénierie et par Lesur & Longaretti (2005) en astrophysique, en ce que l’opérateur de convection n’est pas résolu en suivant les courbes caractéristiques moyennes spectrales ou physiques, mais grâce à un schéma original de type différences finies d’ordre élevé qui permet de calculer les dérivées ∂ i iv par rapport au vecteur d’onde k. On évite ainsi la déformation du maillage et l’obligation de remailler, ce qui autorise l’obtention aisée des harmoniques angulaires à chaque instant, grâce au fait que l’espace physique ou spectral n’est pas déformé. La capacité de prédiction de cette nouvelle approche est significativement améliorée par rapport au modèle de Mons et al. (2016), pour lequel la solution linéaire peut être remise en cause à grand temps d’évolution, particulièrement pour le cas non tournant. Le nouveau modèle est suffisamment universel puisqu’il est implémenté pour plusieurs cas de gradients de vitesse moyenne compatibles avec l’approximation homogène. Les validations ont notamment été réalisées dans des cas de déformation plane. Pour la turbulence cisaillée, dont la modélisation est demeurée jusqu’à présent un point dur des approches en un point et aussi de l’approche en deux points de Mons, nous proposons une version adaptée de notre modèle en deux points, en l’hybridant avec un modèle de retour à l’isotropie proposé par Weinstock (2013). Ce nouveau modèle hybride pour la turbulence cisaillée fournit des résultats extrêmement satisfaisants. / Stability and turbulence in rotating shear flows is essential in many contexts ranging from engineering—as in e.g. turbomachinery or hydraulic energy production—to geophysics and astrophysics. Apart from inhomogeneous effects which we discard in the present study, these flows are complex because they involve an anisotropic dynamics which is difficult to represent at the level of one-point statistics. In this context, the properties of these flows, such as scale-by-scale anisotropy or turbulent cascade can be studied via two-point statistical models of Homogeneous Anisotropic Turbulence (HAT), in which the distorting mean flow is represented by uniform mean velocity and density gradients, and by body forces as the Coriolis one. The context of HAT can be relevant for flows in a plane channel with spanwise rotation, or for a Taylor-Couette flow. We propose a new model for predicting the dynamics of homogeneous sheared rotating turbulence. The model separates linear distortion effects from nonlinear turbulent dynamics, so that each contribution can be treated with an adapted model. Our model deals with equations governing the spectral tensor of two-point second-order velocity correlations, and is developed for arbitrary mean velocity gradients with or with- out system rotation. The direct linear effect of mean gradients is exact in our model, whereas nonlinear effects come from two-point third-order correlations which are closed by an anisotropic EDQNM model. In the closure, the anisotropy is restricted to an expansion in terms of low-degree angular harmonics (Mons et al., 2016). The present model has been validated in the linear regime, by comparison to the accurate solution of viscous Rapid Distortion Theory (vRDT), in several cases, stabilizing, destabilizing or neutral. In contrast with pseudo-spectral DNS adapted to shear flow by Rogallo (1981) in en- gineering and by Lesur & Longaretti (2005) in astrophysics, the advection operator is not solved by following characteristic lines in spectral or physical space, but by an original high- order finite-difference scheme for calculating derivatives ∂ i with respect to the wave vector k. One thus avoids mesh deformation and remeshing, thus one can easily extract angular ii harmonics at any time since physical or spectral space are not distorted. With this new approach, we are able to improve the prediction of the previous model by Mons et al. (2016), in which the linear resolution is questioned at large time, especially in the case without rotation. The proposed new model is versatile since it is implemented for several cases of mean velocity gradients consistent with the homogeneity approximation. Validations have been done for several cases of plane deformations. In the case of sheared turbulence, whose modelling resists most one-point approaches and even the two-point model by Mons, we propose an adaptation of our two-point model in a new hybrid model, in which return-to- isotropy is explicitly introduced in the guise of Weinstock (2013)’s model. Predictions of the new hybrid model are extremely good.

Combustion science must necessarily go through a deep process of innovation, as only improving the energy efficiency and the fuel flexibility it will be possible to mitigate the impact of the anthropogenic activities on the climate and the environment. Because of the strong relation that is observed in chemically reacting flows between the fluid-dynamic conditions and the chemical kinetics, the use of Computational Fluid Dynamics (CFD) simulations with detailed kinetic mechanisms represents the best tool to optimize and develop novel combustion systems. In fact, while the CFD provides for the possibility to retrieve information that cannot be extracted by using experimental means (such as the turbulence-chemistry interaction and the local straining rates) and it avoids the costs associated to the scale-up process from laboratory scale experiments, the use of detailed kinetic mechanisms offers the possibility to correctly describe process conditions which are relevant from an industrial point of view (i.e. in which the chemical and mixing time scales are comparable), as well as to predict the formation of complex chemical species, such as the pollutants. Nevertheless, the use of detailed kinetic mechanisms in numerical simulations adds a considerable number of differential equations to be solved (because of the large number of species which are taken into account), and therefore increases the computational complexity of the CFD model. Thus, Machine Learning (ML) algorithms and Reduced-Order Models (ROMs) can be effectively included in the numerical description of chemically reacting flows. In fact, they can be used either to reduce the computational cost associated to the large number of equations in CFD simulations carried out with detailed chemistry, or to leverage the detailed information which can be found in massive, high-fidelity, data obtained from Direct Numerical Simulations (DNS), for model development and validation. In this Thesis, unsupervised and supervised learning algorithms were employed to design a novel adaptive-chemistry approach: the Sample-Partitioning Adaptive Reduced Chemistry (SPARC). This framework can be used to reduce the computational effort required by detailed CFD simulations thanks to a kinetic reduction accomplished in light of the local conditions of the thermochemical field. Several machine-learning algorithms, such as the Principal Component Analysis (PCA), the Local Principal Component Analysis (LPCA), and Artificial Neural Networks (ANNs) were coupled with the Direct Relation Graph with Error Propagation (DRGEP), a graph-based tool for the automatic reduction of kinetic mechanisms. The aforementioned algorithms were compared to achieve the optimal formulation of the adaptive approach, such that the best performances, in terms of accuracy and computational speed-up with respect to the CFD simulation carried out with detailed kinetics, could be obtained. Finally, PCA-based algorithms were proposed and tested to perform feature extraction and local feature selection from high-fidelity data, which were obtained by means of a DNS of a n-heptane jet reacting in air. The PCA, as well as two formulations of LPCA, and the Procrustes analysis were employed and compared with the aim to extract the main features of the turbulent reacting jet in an unsupervised fashion (i.e. to perform data mining tasks), as well as to aid the formulation of local optimized ROMs. All the codes employed to perform the unsupervised and supervised machine learning tasks in the current work were also included in an open-source Python framework, called OpenMORe, designed to perform reduction, clustering and data analysis, and specifically conceived for reacting flows. In fact, although many open-source Python software are already available, they often cannot be adapted to the user’s specific needs, unlike OpenMORe. In addition, many features such as the PCA-based clustering algorithm, or the local feature selection via PCA, are not yet available on any commercial or open-source software, to the best of the author’s knowledge. / Doctorat en Sciences de l'ingénieur et technologie / This thesis is submitted to the Université Libre de Bruxelles (ULB) and to the Politecnico di Milano for the degree of philosophy doctor. This doctoral work has been performed at the Université Libre de Bruxelles, École polytechnique de Bruxelles, Aero-Thermo-Mechanics Laboratory, Bruxelles, Belgium with Professor Alessandro Parente and at the Politecnico di Milano, CRECK Modelling Lab, Department of Chemistry, Materials and Chemical Engineering, Milan, Italy with Professor Alberto Cuoci. / info:eu-repo/semantics/nonPublished

We study the existence of flows in infinite networks and extend basic theorems due to Gale and Hoffman and to Ford and Fulkerson. The classical approach to finite networks uses a constructive combinatorical algorithm that has become known as the labelling algorithm. Our approach to infinite networks involves Hahn--Banach type theorems on the existence of certain linear functionals. Thus the main tools are from the theory of functional and convex analysis. In Chapter II, we discuss sublinear and linear functionals on real vector spaces in the spirit of the work of K"{o}nig. In particular, a generalization of K"{o}nig's minimum theorem is established. Our theory leads to some useful interpolation results. We also establish a variant of the main interpolation theorem in the context of convex cones. We reformulate the results of Ford--Fulkerson and Gale--Hoffman in terms of certain additive and biadditive set functions. In Chapter III, we show that the space of all additive set functions may be canonically identified with the dual space of a space of certain step functions and that the space of all biadditive set functions may be identified with the dual space of a space of certain step functions in two variables. Our work an additive set functions is in the spirit of classical measure theory, while the case of biadditive set functions resembles the theory of product measures. In Chapter IV, we develop an extended version of the Gale--Hoffman theorem on the existence of flows in infinite networks in a setting of measure-theoretic flavor. This general flow theorem is one of our central results. We discuss, as an application of our flow theorem, a Ford--Fulkerson type result on maximal flows and minimal cuts in infinite networks containing sources and sinks. In addition, we present applications to flows in locally finite networks and to the existence of antisymmetric flows under certain natural conditions. We conclude with a discussion of the case of triadditive set functions. In the appendix, we review briefly the classical theory of maximal flows and minimal cuts in networks with finitely many nodes.

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With the ever more stringent requirements of emissions and fuel economy imposed on the automotive industry, there is a need to understand more fully all aspects of the internal combustion engine to meet these requirements and at the same time the desire of the customer for acceptable performance. This research was aimed at investigating one part of the engine behaviour i.e. induction of the fresh charge to the engine cylinder. Conventionally, these measurements have been performed on a steady state flow rig, where bulk, integral measurements for mass flow rate and swirl or tumble ratio are performed. However, for some of the combustion strategies now being implemented on modern engines, the flow structure is becoming more important necessitating the use of techniques that can measure the flow field and its interaction with spray systems. This piece of work compares engine flow measurements on both a standard steady flow rig and in the cylinder of a motored engine. The flow bench measurements are both easier and cheaper to implement, but serve no real purpose unless there is a correspondence between the flow measured under steady state conditions and that measured in the transient environment of an engine cylinder. On the steady flow bench, both conventional measurements and also measurements of the detailed flow using laser Doppler anemometry have been made. This allowed a direct comparison to be performed between these two sets of measurements. Laser Doppler anemometry measurements were than performed in the cylinder of a motored engine, allowing a direct comparison between the results from the steady flow rig and the engine. Additionally, particle image velocimetry was used to investigate the data on the steady flow bench. It was found that the laser Doppler anemometry measurements were no substitute in terms of accuracy, when compared to the integral measurement of mass flow rate. They did however give some insight into the flow patterns being generated within the cylinder under these conditions. When compared to similar measurements in the engine, in most instances a high degree of correlation was found between the air velocity measurements, although the tumble ratio calculated from the engine was generally higher than that from the steady flow bench. A comparison of vector flows fields from the particle image velocimetry for the steady state and laser Doppler anemometry for the engine measurements, suggested that the influence of the piston on the flows, not present for steady state measurements, was only relevant in the neighbourhood of the piston itself. The transient nature of the flow in engine also seemed to show very little differences between the two sets of measurements. It was concluded that ideally both sets of measurements are required, but that a lot of the detail, with some additional work, could be extracted from the steady flow measurements, but only by using laser diagnostics to measure the flow fields. It was also observed that more than one plane of measurements is required using laser diagnostics to fully characterise the tumble flow field, which is not uniform across the cylinder. This also led to a simple form of weighting of the data in different planes which could be improved with a more detailed set of measurements to gain better insight into the weighting factors required.

<div>The dynamic performance of the momentum and thermal boundary layer linked to the acoustic response dictate the efficiency of heat exchangers and the operational limits of fluid machinery. The specific time required by the boundary layer to establish or adapt to the free stream variations is vital to optimize flow control strategies as well as the thermal management of fluid systems. The proper understanding of the wall fluxes, separated flow regions and free stream response to transient conditions becomes the fulcrum of the further improvement of fluid machinery performance and endurance. Throughout this dissertation the establishment sequence and the main parameters dictating the acoustic response and the boundary layer settlement are quantified together with their implication on the wall fluxes and boundary layer detachment. </div><div><br></div><div>Unsteady Reynolds Average Navier Stokes evaluations, Large Eddy Simulations, Direct Numerical Simulations and wind tunnel experiments are exploited to analyze the transient behavior of attached and detached flow aerodynamics. The core of the research is built upon URANS simulations allowing the realization of multiple detailed parametric analyses. Thanks to its reduced computational cost, hundreds of transient flow evaluations are carried out, enabling the determination of the establishment sequence, the main flow features and relevant non-dimensional numbers. The URANS methodology is verified against experimental and analytic results on the flow conditions of the study. The Large Eddy Simulations and Direct Numerical Simulations allow further characterization of the near wall flow region behavior with much higher resolution while providing an additional source of verification for the coarser numerical tools. An experimental campaign on a novel full visual access linear wind tunnel explores the impact of mean flow sudden accelerations on the boundary layer detachment and reattachment phenomena over an ad-hoc wall mounted hump. The wind tunnel is designed based on the premises of: full visual access, spatial and temporal stability of total and static pressure together with the total temperature and fast flow settlement, minimizing the start-up phase duration of the wind tunnel. A wall mounted hump that mimics the behavior of the aft portion of a low pressure turbine is inserted in the wind tunnel guaranteeing a 2D flow separation phenomena. After steady state test article characterization series of sudden flow discharge experiments reveal the impact of mean flow transients on the boundary layer detachment inception. Finally, taking advantage of the knowledge on transient flow performance, optimum flow control mechanisms to abate boundary layer detachment are proposed. The recommended control approach effectively prevents the boundary layer separation while minimizing the energy requirement.</div>

An experimental program is designed to study the salient features of separated and reattached flows in pressure gradients generated in asymmetric diverging and converging channels. The channels comprised a straight flat floor and a curved roof that was preceded and followed by straight parallel walls. Reference measurements were also made in a parallel-wall channel to facilitate the interpretation of the pressure gradient flows. A transverse square rib located at the start of convergence/divergence was used to create separation inside the channels. In order to simplify the interpretation of the relatively complex separated and reattached flows in the asymmetric converging and diverging channels, measurements were made in the plain converging and diverging channel without the rib on the channel wall. All the measurements were obtained using a high resolution particle image velocimetry technique. The experiments without the ribs were conducted in the diverging channel at Reynolds number based on half channel depth (Reh) of 27050 and 12450 and in the converging channel at Reh = 19280. For each of these three test conditions, a high resolution particle image velocimetry technique (PIV) was used to conduct detailed velocity measurements in the upstream parallel section, within the converging and diverging section, and downstream of the converging and diverging sections. From these measurements, the boundary layer parameters and profiles of the mean velocities, turbulent quantities as well as terms in the transport equations for turbulent kinetic energy and Reynolds stresses were obtained to document the effects of pressure gradient on the flow. In the adverse pressure gradient case, the turbulent quantities were enhanced more significantly in the lower boundary layer than the upper boundary layer. On the other hand, favorable pressure gradient attenuated the turbulence levels and the effect was found to be similar on both the upper and the lower boundary layers. For the separated and reattached flows in the converging, diverging and parallel-wall channels at Reh = 19440, 12420 and 15350, respectively. The Reynolds number based on the approach velocity and rib height was Rek  2700. From these measurements, profiles of the mean velocities, turbulent quantities and the various terms in the transport equations for turbulent kinetic energy and Reynolds stresses were also obtained. The flow dynamics in the upper boundary layer in the separated region and the early stages of flow redevelopment were observed to be insensitive to the pressure gradients. In the lower boundary layer, however, the flow dynamics were entirely dominated by the separated shear layer in the separated region as well as the early region of flow redevelopment. The effects of the separated shear layer diminished in the redevelopment region so that the dynamics of the flow were dictated by the pressure gradients. The proper orthogonal decomposition (POD) was applied to educe the dominant large scale structures in the separated and reattached flows. These dominant scales were used to document structural differences between the canonical upstream flow and the flow field within the separated and redeveloping region. The contributions of these dominant structures to the dynamics of the Reynolds normal and shear stresses are also presented and discussed. It was observed that the POD recovers Reynolds shear stress more efficiently than the turbulent kinetic energy. The reconstruction reveals that large scales contribute more to the Reynolds shear stress than the turbulent kinetic energy. / February 2009

An experimental program is designed to study the salient features of separated and reattached flows in pressure gradients generated in asymmetric diverging and converging channels. The channels comprised a straight flat floor and a curved roof that was preceded and followed by straight parallel walls. Reference measurements were also made in a parallel-wall channel to facilitate the interpretation of the pressure gradient flows. A transverse square rib located at the start of convergence/divergence was used to create separation inside the channels. In order to simplify the interpretation of the relatively complex separated and reattached flows in the asymmetric converging and diverging channels, measurements were made in the plain converging and diverging channel without the rib on the channel wall. All the measurements were obtained using a high resolution particle image velocimetry technique. The experiments without the ribs were conducted in the diverging channel at Reynolds number based on half channel depth (Reh) of 27050 and 12450 and in the converging channel at Reh = 19280. For each of these three test conditions, a high resolution particle image velocimetry technique (PIV) was used to conduct detailed velocity measurements in the upstream parallel section, within the converging and diverging section, and downstream of the converging and diverging sections. From these measurements, the boundary layer parameters and profiles of the mean velocities, turbulent quantities as well as terms in the transport equations for turbulent kinetic energy and Reynolds stresses were obtained to document the effects of pressure gradient on the flow. In the adverse pressure gradient case, the turbulent quantities were enhanced more significantly in the lower boundary layer than the upper boundary layer. On the other hand, favorable pressure gradient attenuated the turbulence levels and the effect was found to be similar on both the upper and the lower boundary layers. For the separated and reattached flows in the converging, diverging and parallel-wall channels at Reh = 19440, 12420 and 15350, respectively. The Reynolds number based on the approach velocity and rib height was Rek  2700. From these measurements, profiles of the mean velocities, turbulent quantities and the various terms in the transport equations for turbulent kinetic energy and Reynolds stresses were also obtained. The flow dynamics in the upper boundary layer in the separated region and the early stages of flow redevelopment were observed to be insensitive to the pressure gradients. In the lower boundary layer, however, the flow dynamics were entirely dominated by the separated shear layer in the separated region as well as the early region of flow redevelopment. The effects of the separated shear layer diminished in the redevelopment region so that the dynamics of the flow were dictated by the pressure gradients. The proper orthogonal decomposition (POD) was applied to educe the dominant large scale structures in the separated and reattached flows. These dominant scales were used to document structural differences between the canonical upstream flow and the flow field within the separated and redeveloping region. The contributions of these dominant structures to the dynamics of the Reynolds normal and shear stresses are also presented and discussed. It was observed that the POD recovers Reynolds shear stress more efficiently than the turbulent kinetic energy. The reconstruction reveals that large scales contribute more to the Reynolds shear stress than the turbulent kinetic energy.