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Direct Numerical Simulations of a strongly heated jet of water vapor discharging into a low-speed coflow of cold water vapor is fully coupled with a reciprocal Monte-Carlo method to account for radiative heat transfer. The spectral dependency of the radiative properties is modeled using the Correlated-k method. Such a numerical and modeling setup allows for studying accurately the turbulent jet development submitted to radiative heat transfer. Contrary to the previous study by Armengol et al. [International Journal of Heat and Mass Transfer 139 (2019), pp. 456–474], the present conditions show a direct effect of thermal radiation in the jet developed zone located downstream the jet potential core. Results are analyzed to identify the effects of thermal radiation on turbulence properties of the temperature field, and reciprocally. The analysis reveals a complex coupling between the mean temperature field and the mean radiative power as well as between their fluctuations. This is studied in various profiles of average and root-mean-square properties, and completed by considering budgets of enthalpy variance and turbulence spectra., SCOPUS: ar.j, info:eu-repo/semantics/published

The effects of thermal radiation in a heated jet of water vapor are studied with a direct numerical simulation coupled to a Monte-Carlo solver. The adequacy of the numerical setup is first demonstrated in the uncoupled isothermal and heated turbulent plane jets with comparisons to experimental and numerical data. Radiative energy transfer is then accounted for with spectral dependency of the radiative properties described by the Correlated-k (ck) method. Between the direct impact through modification of the temperature field by the additional radiative transfer and the indirect one where the varied flow density changes the turbulent mixing, the present study is able to clearly identify the second one in the jet developed region by considering conditions where effects of thermal radiation are moderate. When using standard jet scaling laws, the different studied cases without radiation and with small-to-moderate radiative heat transfer yield different profiles even when thermal radiation becomes locally negligible. By deriving another scaling law for the decay of the temperature profile, self-similarity is obtained for the different turbulent jets. The results of the study allow for distinguishing whether thermal radiation modifies the nature of heat transfer mechanisms in the jet developed region or not while removing the indirect effects of modified density., SCOPUS: ar.j, info:eu-repo/semantics/published

Modern society will have to meet its energy demands while ensuring low or virtually zero emissions in order to meet future challenges associated to air pollution, climate change and energy storage. Very often, renewable sources cannot be directly employed because of their intermittent nature and because many applications such as transport and other in- dustrial processes require high energy densities. Therefore, novel storage solutions for the energy that renewable sources contribute to produce is necessary and the transformation of this energy into chemical compounds represents the best choice in order to meet the aforementioned demands, which requires novel combustion technologies, such as Moder- ate and Intense Low-oxygen Dilution (MILD) combustion, to be efficient and fuel-flexible. In order to develop such technologies, several studies are being proposed and terabytes of data collected as more and more experiments and high-fidelity simulations are carried out. However, there are two main challenges to this: the huge amount of data available makes it hard for the researcher to distinguish useful from redundant data, with the risk that useful information might stay hidden; the production process of these data-sets re- quires substantial resources as combustion process are multi-physics, multi-scale and thus require high-fidelity computationally-intensive simulations and experiments over a wide range for their operating conditions or input parameters. Digital twins and Artificial Intel- ligence (AI) are shaping the fourth industrial revolution by building data-driven models that make use of machine learning. It makes sense then to extend this approach to combus- tion applications in order to alleviate the two aforementioned issues: the use of machine learning techniques can help automate the process of data interpretation as well as pro- vide a low-dimensional representation of the high-dimensional data produced by either experiments or simulations; they can speed, Doctorat en Sciences de l'ingénieur et technologie, info:eu-repo/semantics/nonPublished

La simulation numérique représente un outil important pour la conception des systèmes de combustion. La prédiction des flux aux parois joue un rôle déterminant dans le cycle de vie des chambres de combustion, car elle permet de prédire la fatigue thermique des parois. Le transfert de chaleur de la flamme aux parois est entraîné, outre la convection, également par le rayonnement des gaz chauds au sein de la chambre. Pour évaluer les transferts thermiques aux parois il faut donc tenir compte des flux radiatifs. Les pertes thermiques aux parois dépendent de la répartition de la température des gaz qui est, à son tour, fortement modifiée par le rayonnement des gaz brûlés. Afin d’intégrer les contributions convectives et radiatives au flux pariétal dans des simulations numériques, il est nécessaire de résoudre simultanément l'équation de transfert radiatif et les équations régissant l’écoulement réactif. De nos jours, les simulations couplées impliquant combustion et transfert de chaleur radiatif sont de plus en plus utilisées et ciblées. Grâce à l'augmentation de la puissance de calcul, l'utilisation des méthodes de Monte Carlo (MC) dans des simulations 3D instationnaires, telles que les simulations numériques directes (DNS) et les simulations aux grandes échelles (LES), est devenue. Cependant, de telles simulations restent très coûteuses. L’objectif de cette thèse est donc d’investiguer une technique pour améliorer l’efficacité de la méthode MC, basée sur un mécanisme alternatif d’échantillonnage et appelé intégration Quasi-Monte Carlo (QMC). Cette méthode a rarement été utilisée pour la résolution numérique du rayonnement thermique. Dans cette étude, la méthode QMC est appliquée sur plusieurs configurations 3D et comparée à celle de MC. L’amélioration de l’efficacité obtenue par QMC fait de cette méthode un candidat idéal pour des simulations haute-fidélité couplées avec des simulations LES ou DNS. Au cours de cette thèse, la méthode QMC a pu être appliquée à une conf, Doctorat en Sciences de l'ingénieur et technologie, info:eu-repo/semantics/nonPublished

For stationary power sources such as utility boilers, it is useful to dispose of parametric models able to describe their behavior in a wide range of operating conditions, to predict some Quantities of Interest (QOIs) that need to be consistent with experimental observations. The development of predictive simulation tools for large scale systems cannot rely on full-order models, as the latter would lead to prohibitive costs when coupled to sampling techniques in the model parameter space. An alternative approach consists of using a Surrogate Model (SM). As the number of QOIs is often high and many SMs need to be trained, Principal Component Analysis (PCA) can be used to encode the set of QOIs in a much smaller set of scalars, called PCA scores. A SM is then built for each PCA score rather than for each QOI. The advantage of reducing the number of variables is twofold: computational costs are reduced (less SMs need to be trained) and information is preserved (correlation among the original variables).The strategy is applied to a CFD model simulating the Alstom 15 MWth oxy-pilot Boiler Simulation Facility (BSF). In practice, experiments cannot provide full coverage of the pulverized-coal utility boiler due to both practicality and costs. Values of the model’s parameters which guarantee consistency with the experimental data of this test facility for 121 QOIs are found, by training a SM based on the combination of Kriging and PCA, using only 5 latent variables., This project has received funding from the European Union's Horizon 2020 research and innovation program under the Marie Sklodowska-Curie grant agreement no 643134 and was also sponsored by the European Research Council, Starting Grant no 714605. This material is based upon work supported by the Department of Energy, National Nuclear Security Administration, under Award no DE-NA0002375., SCOPUS: ar.j, info:eu-repo/semantics/published

Detailed numerical simulations of detailed combustion systems require substantial computational resources, which limit their use for optimization and uncertainty quantification studies. Starting from a limited number of CFD simulations, a reduced-order model is derived using a few detailed function evaluations.In this work, the combination of Principal Component Analysis (PCA) with Kriging is considered to identify accurate low-order models. PCA is used to identify and separate invariants of the system, the PCA modes, from the coefficients that are instead related to the characteristic operating conditions. Kriging is then used to find a response surface for these coefficients. This leads to a surrogate model that allows to perform parameter exploration with reduced computational cost. Varia- tions of the classical PCA approach, namely Local and Constrained PCA, are also presented.This methodology is demonstrated on 1D and 2D flames produced by OpenSmoke++ and OpenFoam, respectively, for which accurate surrogate models have been developed., This project has received funding from the European Unions Horizon 2020 research and innovation program under the Marie Sklodowska-Curie grant agreement No 643134., SCOPUS: ar.j, info:eu-repo/semantics/published

This article presents a model to describe the effects of non-equilibrium plasma discharges on gas temperature and species concentration, in the set of equations governing the combustion phenomena. Based on the results reported in the literature, the model is constructed by analysing the channels through which the electric energy is deposited. The two main channels by which the electrons produced during the discharge impact the flow are considered: (1) the excitation and the subsequent relaxation of electronic states of nitrogen molecules which leads to an ultrafast increase of gas temperature and species dissociation within the discharge characteristic time; and (2) the excitation and relaxation of vibrational states of nitrogen molecules which causes a much slower gas heating. The model is fully coupled with multi-dimensional flow balance equations with detailed transport coefficients and detailed combustion chemical kinetic mechanisms. This high level of NRP discharge modelling allows computing high Reynolds flows by means of Direct Numerical Simulations and, therefore, a better understanding of plasma-assisted ignition phenomena in practical configurations. A sequence of discharge pulses in air and methane-air mixture in quiescent and turbulent flow configurations are studied with this model. The results show the minor impact of the vibrational energy on mixture ignition and how the increase of the turbulence spreads this vibrational energy and intermediate combustion species around the discharge zone, minimizing the cumulative effect of multiple pulses. In contrast, the production of O atoms during the discharge has a strong impact on the ignition delays and ignition energies (number of discharge pulses). The results also underscore the impact of the initial turbulent flow Reynolds number and the spatial distribution of turbulent eddies, relative to the discharge channel, on the number of pulses needed to ignite the mixture., SCOPUS: ar.j, info:eu-repo/semantics/published

Three-dimensional (3D) direct numerical simulation and experimental Schlieren results were used to study a non-equilibrium plasma discharge in a lean CH4-air mixture. The impact of gas flow recirculation on the temporal evolution of species and gas temperature in the vicinity of the discharge zone was examined. The results showed that the formation of a fresh gas counterflow with stagnation plane at the center of the discharge and parallel to the electrodes changed the topology of the hot kernel from an initial cylindrical shape to a toroidal one. This phenomenon leads to an increase of the area/volume ratio of the reactive kernel that may result under certain conditions in kernel extinction. Also the importance of considering this 3D gas flow recirculation was revealed to correctly predict the temporal evolution of the hot kernel. Particularly the temperature and species concentrations in the central region of the discharge returned to fresh gas conditions shortly after the end of the pulse in the order of 150 μs. This result is particularly important for ignition by Nanosecond Repetitively Pulsed discharges since the gas conditions at the beginning of each successive pulse depend greatly on the time interval between pulses thus on the pulse frequency., SCOPUS: cp.j, info:eu-repo/semantics/published

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One of the most challenging aspects of turbulent combustion research is the development of reduced-order combustion models which can accurately reproduce the physics of real systems. The identification and utilization of the low dimensional manifolds in these system is paramount to understand and develop robust models which can account for turbulence-chemistry interactions. Recently, principal components analysis (PCA) has been given notable attention in its analysis of reacting systems, and its potential in reducing the number of dimensions with minimum reconstruction error. The present work provides a methodology which has the ability of exploiting the information obtained from PCA. Two formulations of the approach are shown: Manifold Generated from PCA (MG-PCA), based on a global analysis, and Manifold Generated from Local PCA (MG-L-PCA), based on performing the PCA analysis locally. The models are created using the co-variance matrix of a data-set which is representative of the system of interest. The reduced models are then used as a predictive tool for the reacting system of interest by transporting only a subset of the original state-space variables on the computational grid and using the PCA basis to reconstruct the non-transported variables. The present study first looks into the optimal selection of the subset of transported variables and analyzes the effect of this selection on the approximation of the state space and chemical species source terms. Then, a demonstration of various a posteriori cases is presented., SCOPUS: ar.j, info:eu-repo/semantics/published

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Energy generation through combustion of hydrocarbons continues to dominate, as the most common method for energy generation. In the U.S. nearly 84% of the energy consump- tion comes from the combustion of fossil fuels. Because of this demand there is a continued need for improvement, enhancement and understanding of the combustion process. As computational power increases, and our methods for modelling these complex combustion systems improve, combustion modelling has become an important tool in gaining deeper insight and understanding for these complex systems. The constant state of change in computational ability lead to a continual need for new combustion models that can take full advantage of the latest computational resources. To this end, the research presented here encompasses the development of new models, which can be tailored to the available resources, allowing one to increase or decrease the amount of modelling error based on the available computational resources, and desired accuracy. Principal component analysis (PCA) is used to identify the low-dimensional manifolds which exist in turbulent combustion systems. These manifolds are unique in there ability to represent a larger dimensional space with fewer components resulting in a minimal addition of error. PCA is well suited for the problem at hand because of its ability to allow the user to define the amount of error in approximation, depending on the resources at hand. The research presented here looks into various methods which exploit the benefits of PCA in modelling combustion systems, demonstrating several models, and providing new and interesting perspectives for the PCA based approaches to modelling turbulent combustion., Doctorat en Sciences de l'ingénieur, info:eu-repo/semantics/nonPublished

The topic of this paper is to propose an extension of the classical one-dimensional Navier- Stokes boundary conditions (1-D-NSCBC) for real gases initially developed by Okong'o and Bellan to a 3-D-NSCBC formulation based on the work of Lodato et al and Coussement et al. All the differences due to the real gas formulation compared to the perfect gas formulation proposed by Coussement et al. are emphasized. A new way of determining the pressure relaxation coefficient is introduced for handling transcritical flows crossing the boundary. The real gas 3-D-NSCBC are then challenged on several test cases :a two-dimensional subsonic vortex convection, a subsonic supercritical bubble convection and a flame vortex interaction. All these test cases are performed by direct numerical simulation of multicomponent flows. It shows the stability of the boundary conditions without creating any numerical artifact., info:eu-repo/semantics/published

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.j, info:eu-repo/semantics/published

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'ingénieur, info:eu-repo/semantics/nonPublished

Control of pollutants and emissions has become a major factor in the design of modern combustion systems. The “Liquid Hydrogen Fueled Aircraft - System Analysis” project funded in 2000 by the European Commission can be seen as such an initiative. Within the framework of this project, the Aachen University of Applied Sciences developed experimentally the “Micromix” hydrogen combustion principle and implemented it successfully in the Honeywell APU GTCP 36-300 gas turbine engine. Lowering the reaction temperature, eliminating hot spots from the reaction zone and keeping the time available for the formation of NOx to a minimum are the prime drivers towards NOx reduction. The “Micromix” hydrogen combustion principle meets those requirements by minimizing the flame temperature working at small equivalence ratios, improving the mixing by means of Jets In Cross-Flow and reducing the residence time in adopting a combustor geometry that provides a very large number of very small diffusion flames. In terms of pollutant emissions, compared to the unconverted APU, an essential reduction in emitted NOx was observed, stressing the potential of this innovative burning principle.The objective of this thesis is to investigate the “Micromix” hydrogen combustion principle with the ultimate goal of an improved prediction during the design process. Due to the complex interrelation of chemical kinetics and flow dynamics, the “Micromixing” was analyzed first. Stereoscopic Particle Image Velocimetry was used to provide insight into the mixing process. A “simplified” set-up, that allowed to investigate the flow characteristics in great detail while retaining the same local characteristics of its “real” counterparts, was considered. The driving vortical structures were identified. To further investigate the physics involved and to extend the experimental results, numerical computations were carried out on the same “simplified” set-up as on a literature test case. In general, a number of ph, Doctorat en Sciences de l'ingénieur, info:eu-repo/semantics/nonPublished

The growing need of mobile power sources with high energy density and the robustness to operate also in the harshest environmental surroundings lead to the idea of downscaling gas turbines to ì-scale. Classified as PowerMEMS devices, a couple of design attempts have emerged in the last decade. One of these attempts was the Belgian “PowerMEMS” design started back in 2003 and aiming towards a ì-scale gas turbine rated at 1 kW of electrical power output.This PhD thesis presents the scientific evaluation and development history of different combustion chamber designs based upon the “PowerMEMS” design parameters. With hydrogen as chosen fuel, the non-premixed diffusive “micromix” concept was selected as combustion principle. Originally designed for full scale gas turbine applications in two different variants, consequently the microcombustor development had to start with the downscaling of these two principles towards ì-scale. Both principles have the advantage to be inherently safe against flashback, due to the non-premixed concept, which is an important issue even in this small scale application when burning hydrogen. By means of water analogy and CFD simulations the hydrogen injection system and the chamber geometry could be validated and optimized. Besides the specific design topics that emerged during the downscaling process of the chosen combustion concepts, the general difficulties of microcombustor design like e.g. high power density, low Reynolds numbers, short residence time, and manufacturing restrictions had to be tackled as well.As full scale experimental test campaigns are still mandatory in the field of combustion research, extensive experimental testing of the different prototypes was performed. All test campaigns were conducted with a newly designed test rig in a combustion lab modified for microcombustion investigations, allowing testing of miniaturized combustors according to full engine requirements with regard to mass flow, inlet temperature, a, Doctorat en Sciences de l'ingénieur, info:eu-repo/semantics/nonPublished

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.j, info:eu-repo/semantics/published

The Navier-Stokes Charateristic Boundary Conditions (NSCBC) is a very efficient numerical strategy to treat boundary conditions in fully compressible solvers. The present work is an extension the 3D-NSCBC method proposed by Yoo et al. and Lodato et al. in order to account for multi-component reactive flows with detailed chemistry and complex transport. A new approach is proposed for the outflow boundary conditions which enables clean exit of non-normal flows, and the specific treatment of all kinds of edges and corners is carefully addressed. The proposed methodology is successfully validated on various challenging multi-component reactive flow configurations., SCOPUS: ar.j, info:eu-repo/semantics/published

The problems of oil resources and CO2 emissions becoming increasingly alarming, the search for alternatives to fossil fuels is an important concern of our society. Even though hydrogen has been recognized as a promising fuel, implementing a global hydrogen-based economy is at present a non-feasible approach unless a suitable storage medium could be found. To bypass such difficulties, the use of ammonia in a modified spark ignition engine has been suggested. Since hydrogen must still be produced to obtain ammonia in large amount, it can be seen as a H2 vector. The successful application of ammonia as an alternative transportation fuel should be based on a detailed understanding of its combustion characteristics. The main objective of this thesis is thus the study of the ammonia combustion reaction in several conditions of pressure and temperature. First of all, a low pressure ammonia flames structure study allows a more fundamental investigation of the ammonia consumption and products formation pathways. The elaboration of a kinetic mechanism able to reproduce the experimentally observed phenomena is the main objective of this first part. Then, the kinetic of ammonia under atmospheric pressure is investigated thanks to an ammonia laminar burning velocity study. Because of its low value, the laminar flame speed of ammonia in air is to date still unknown and in that way this part makes a significant contribution in the field of ammonia combustion research. This part allows also to validate the kinetic mechanism at atmospheric pressure. Finally, the combustion of ammonia in a spark ignition engine is experimentally investigated. The effects of the compression ratio, the spark timing and the equivalence ratio on the exhaust gases composition and the engine performances are analyzed. Such a study has never been performed for ammonia to the best of our knowledge., (CHIM 3) -- UCL, 2011

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This study quantifies the mixing resulting of a pulsed jet injected in a jet in crossflow configuration. By large eddy simulation computations, it also helps to under- stand the physical phenomena involved in the formation of the pulsed jet in crossflow. The boundary conditions of the jet inlet were implemented via an NSCBC coupled with a Fourier series development. The signal used to pulse the jet inlet was a square or a sine wave. A new way of charac- terizing the mixing is introduced with the goal of easily in- terpreting and quantifying the complicated mixing process involved in pulsed jet in crossflow flow fields. Different flow configurations, pulsed and non-pulsed were computed and compared. This comparison no only allows to characterize the mixing but also to point out some properties of those mix- ing curves., Article numéro art. no. 2010-0561, info:eu-repo/semantics/published

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/nonPublished

This thesis presents the author's contribution to the design and implementation of COOLFluiD,an object oriented software platform for the high performance simulation of multi-physics phenomena on unstructured grids. In this context, the final goal has been to provide a reliable tool for handling high speed aerothermodynamic applications. To this end, we introduce a number of design techniques that have been developed in order to provide the framework with flexibilityand reusability, allowing developers to easily integrate new functionalities such as arbitrary mesh-based data structures, numerical algorithms (space discretizations, time stepping schemes, linear system solvers, ),and physical models. Furthermore, we describe the parallel algorithms that we have implemented in order to efficiently read/write generic computational meshes involving millions of degrees of freedom and partition them in a scalable way: benchmarks on HPC clusters with up to 512 processors show their effective suitability for large scale computing. Several systems of partial differential equations, characterizing flows in conditions of thermal and chemical equilibrium (with fixed and variable elemental fractions)and, particularly, nonequilibrium (multi-temperature models) have been integrated in the framework. In order to simulate such flows, we have developed two state-of-the-art flow solvers: 1- a parallel implicit 2D/3D steady and unsteady cell-centered Finite Volume (FV) solver for arbitrary systems of PDE's on hybrid unstructured meshes; 2- a parallel implicit 2D/3D steady vertex-centered Residual Distribution (RD) solver for arbitrary systems of PDE's on meshes with simplex elements (triangles and tetrahedra). The FV~code has been extended to handle all the available physical models, in regimes ranging from incompressible to hypersonic. As far as the RD code is concerned, the strictly conservative variant of the RD method, Doctorat en Sciences de l'ingénieur, info:eu-repo/semantics/nonPublished

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