Дисертації: "Low-Mach number flows"

1

Alkishriwi, Nouri. "Large eddy simulation of low mach number flows /." Aachen : Shaker, 2007. http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&doc_number=016487054&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA.

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Detandt, Yves. "Numerical simulation of aerodynamic noise in low Mach number flows." Doctoral thesis, Universite Libre de Bruxelles, 2007. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/210675.

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The evaluation of the noise produced by flows has reached a high level of importance in the past years. The physics surrounding flow-induced noise is quite complex and sensitive to various flow conditions like temperature, shape. Empirical models were built in the past for some special geometries but they cannot be used in a general case for a shape optimization for instance. Experimental aeroacoustic facilities represent the main tool for acoustic analyses of flow fields, but are quite expensive because extreme care must be exercised not to introduce acoustic perturbations in the flow (silent facilities). These tools allow a good analysis of the physical phenomena responsible for noise generation in the flow by a comparison of the noise sources and the flow characteristics (pressure, turbulence,). Nevertheless, the identification and location of noise sources to compare with flow structures requires quite complex methods.The numerical approach complements the experimental one in the sense that the flow characteristics are deeply analyzed where experiments suggest noise production. For the numerical approach, the turbulence modeling is quite important. In the past, some models were appreciated for their good prediction of some aerodynamic parameters as lift and drag for instance. The challenge is now to tune these models for a correct prediction of the noise sources. In the low subsonic range, the flow field is completely decoupled from acoustics, and noise sources can be computed from a purely hydrodynamic simulation before this information is transferred to an acoustical solver which will compute the acoustic field at the listener position. This post processing of the aerodynamic results is not obvious since it can introduce non-physical noise into the solution.This project considers the aspect of noise generation in turbulent jets and especially the noise generated by vortex pairing, as it occurs for instance in jet flows. The axisymmetric version of the flow solver SFELES has been part of this PhD research, and numerical results obtained on the jet are similar to the experimental values. Analyses performed on the numerical results are interesting to go to complete turbulence modeling for aeroacoustics since vortex pairing is one of the basic acoustical processes in vortex dynamics.Currently, a standard static Smagorinski model is used for turbulence modeling. However, this model has well known limitations, and its influence on the noise sources extracted from the flow field is not very clear. For this reason, it is planned to adopt a dynamic procedure in which the subgrid scale model automatically adapts to the flow. We planned also to perform simulations with the variational multiscale approach to better simulate the different interactions between large and unresolved scales. The commercial software ACTRAN distributed by Free Field Technologies is used for the computation of sound propagation inside the acoustic domain. Doctorat en Sciences de l'ingénieur info:eu-repo/semantics/nonPublished

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3

Alkishriwi, Nouri [Verfasser]. "Large Eddy Simulation of Low Mach Number Flows / Nouri Alkishriwi." Aachen : Shaker, 2007. http://d-nb.info/1164341499/34.

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4

Holmberg, Andreas. "Experimental Determination of Aeracoustic Sources in Low Mach Number Internal Flows." Licentiate thesis, KTH, MWL Strömningsakustik, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-26133.

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In this thesis, the in-duct experimental methods for determining aeroacoustic N-ports of in-duct elements are discussed and improved. The scattering matrix determination methods and the related wave decomposition methods are evaluated from measurements in an empty duct carrying a mean flow. The improvements of a new over-determination method for the source part of the N-port is studied using simulations and measurements; in quiescent air as well as measurements of the flow associated noise of a mixer plate, here a triangular plate inserted at an angle in a duct. The new method is shown to improve suppression of random errors while no improvement is achieved for bias errors. Further, the methods are applied in the study of two different aeroacoustic phenomena; one is the effect on the flow associated noise of the triangular plate achieved by varying the bending stiffness. For the most resilient plate tested, it is observed that when the Strouhal number of the flow noise coalesce with the Helmholtz number of a specific eigen-mode of the plate, the noise is drastically dampened. There is also a weaker broad band effect. The other phenomena studied is the amplification and attenuation obtained for sound waves propagating in a T-junction of rectangular ducts. It is found that by adding only 10% of inflow in the side branch relative to that in the main branch, the amplification is heavily increased. By adding another 10% the amplification is again similar to that of no side branch flow. Adding further flow lessens the effects still. QC 20101118 Experimental characterization of aero-acoustic sources

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5

Weng, Chenyang. "Modeling of sound-turbulence interaction in low-Mach-number duct flows." Licentiate thesis, KTH, MWL Strömningsakustik, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-129319.

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When sound waves propagate in a duct in the presence of turbulent flow, tur- bulent mixing can cause extra attenuation of the sound waves in addition to that caused by the viscothermal eects. Experiments show that compared to the vis- cothermal eects, turbulent absorption becomes the dominant contribution to the sound attenuation at suciently low frequencies. The mechanism of this turbulent absorption is attributed to the turbulent stress and the turbulent heat transfer act- ing on the coherent perturbations (including to sound waves) near the duct wall, i.e. sound-turbulence interaction. The purpose of the current investigation is to understand the mechanism of the sound-turbulence interaction in low-Mach-number internal flows by means of theoretical modeling and numerical simulation. The turbulence absorption can be modeled through perturbation turbulent Reynolds stresses and perturbation turbu- lent heat flux in the linearized perturbation equations. In this thesis, the linearized perturbation equations are reviewed, and dierent models for the turbulent absorp- tion of the sound waves are investigated. In addition, a new non-equilibrium model for the perturbation turbulent Reynolds stress is proposed. The proposed model is validated by comparing the computed perturbation fields with experimental data from turbulent pipe flow measurements, and large eddy simulations (LES) of turbu- lent channel flow. Good agreements are observed. Besides the theoretical modeling, LES is also carried out as a numerical investi- gation of the sound-turbulence interaction. Some preliminary results from the LES are presented. Vid ljudutbredning i kanaler med turbulent flöde kan diusion som orsakas av turbulens ge extra dämpning av ljudvågor utöver den som orsakas av viskoter- miska eekter. Experiment visar att vid låga frekvenser ger denna absorption det dominerande bidraget till ljuddämpning. Mekanismen för denna absorption är tur- bulensens inverkan på koherenta störningar, bland annat ljudvågor, dvs ljud - tur- bulensinteraktion. Syftet med denna undersökning är att förstå mekanismen för ljud - turbulensin- teraktion i internströmning vid låga Machtal med hjälp av teoretisk modellering och numeriska simuleringar. Ljudabsorption pga turbulens kan modelleras via mod- ellering av störningar av de turbulenta Reynoldska spänningarna och störningar i den turbulenta värmetransporten i de linjäriserade störningsekvationerna. I denna avhandling går vi igenom de linjäriserade störningsekvationerna, och olika modeller för turbulent absorption av ljudvågor utreds. Dessutom presenteras en ny icke- jämviktsmodell för små störningar av de turbulenta Reynoldska spänningarna. Den föreslagna modellen utvärderas genom att de beräknade störningsfältet jämförs med experimentella data från mätningar i rör med turbulent strömning, samt med Large Eddy Simulations (LES) av turbulent strömning. God överensstämmelse kan visas. Förutom teoretisk modellering, kommer LES också att användas för att numeriskt undersöka ljud - turbulensinteraktion. Några preliminära resultat från LES presen- teras. QC 20130927

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Huval, Danny J. "Heat transfer in variable density, low mach number, stagnating turbulent flows." Diss., Georgia Institute of Technology, 1990. http://hdl.handle.net/1853/12394.

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7

Zucchini, Marco. "Experimental and numerical aeroacoustic investigation of impinging flows at low Mach number." [S.l. : s.n.], 2007. http://nbn-resolving.de/urn:nbn:de:bsz:93-opus-31104.

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8

Weng, Chenyang. "Theoretical and numerical studies of sound propagation in low-Mach-number duct flows." Doctoral thesis, KTH, MWL Marcus Wallenberg Laboratoriet, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-168031.

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Анотація:

When sound waves propagate in a duct in the presence of turbulent flow, turbulent mixing can cause attenuation of the sound waves extra to that caused by the viscothermal effects. Experiments show that compared to the viscothermal effects, this turbulent absorption becomes the dominant contribution to the sound attenuation at sufficiently low frequencies. The mechanism of this turbulent absorption is attributed to the turbulent stress and the turbulent heat transfer acting on the coherent perturbations (including the sound waves) near the duct wall, i.e. sound-turbulence interaction. The purpose of the current investigation is to understand the mechanism of the sound-turbulence interaction in low-Mach-number internal flows by theoretical modeling and numerical simulations. The turbulence absorption can be modeled through perturbation turbulent Reynolds stresses and perturbation turbulent heat flux in the linearized perturbation equations. In this thesis, the linearized perturbation equations are reviewed, and different models for the turbulent absorption of the sound waves are investigated. A new non–equilibrium model for the perturbation turbulent Reynolds stress is also proposed. The proposed model is validated by comparing with experimental data from the literature, and with the data from Direct Numerical Simulations (DNS) of pulsating turbulent channel flow. Good agreement is observed. QC 20150526

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9

Avila, Matías. "Nonlinear subgrid finite element models for low Mach number flows coupled with radiative heat transfer." Doctoral thesis, Universitat Politècnica de Catalunya, 2012. http://hdl.handle.net/10803/285809.

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The general description of a fluid flow involves the solution of the compressible Navier-Stokes equations, a very complex problem whose mathematical structure is not well understood. It is widely accepted that these equations provide an accurate description of any problem in fluid mechanics which may present many different nonlinear physical mechanisms. Depending on the physics of the problem under consideration, different simplified models neglecting some physical mechanisms can be derived from asymptotic analysis. On the other hand, radiative heat transfer can strongly interact with convection in high temperature flows, and neglecting its effects may have significant consequences in the overall predictions. Problems as fire scenarios emphasized the need for an evaluation of the effect of radiative heat transfer. This work is directed to strongly thermally coupled low Mach number flows with radiative heat transfer. The complexity of these mathematical problem makes their numerical solution very difficult. Despite the important difference in the treatment of the incompressibility, the low Mach number equations present the same mathematical structure as the incompressible Navier-Stokes equations, in the sense that the mechanical pressure is determined from the mass conservation constraint. Consequently the same type of numerical instabilities can be found, namely, the problem of compatibility conditions between the velocity and pressure finite element spaces, and the instabilities due to convection dominated flows. These instabilities can be avoided by the use of stabilization techniques. Many stabilization techniques used nowadays are based on the variational multiscale method, in which a decomposition of the approximating space into a coarse scale resolvable part and a fine scale subgrid part is performed. The modeling of the subgrid scale and its influence leads to a modified coarse scale problem providing stability. The quality of the final approximation (accuracy, efficiency) depends on the particular model. The extension of these techniques to nonlinear and coupled problems is presented. The distinctive features of our approach are to consider the subscales as transient and to keep the scale splitting in all the nonlinear terms appearing in the finite element equations and in the subgrid scale model. The first ingredient permits to obtain an improved time discretization scheme(higher accuracy, better stability). The second ingredient permits to prove global conservation properties, being also responsible of the higher accuracy of the method. This ingredient is intimately related to the problem of thermal turbulence modeling from a strictly numerical point of view. The capability for the simulation of turbulent flows is a measure of the ability of modeling the effect of the subgrid flow structures over the coarser ones. The performance of the model in predicting the behavior of turbulent flows is demonstrated. The radiation transport equation has been also approximated within the variational multiscale framework, the design and analysis of stabilized finite element methods is presented. La descripción general del movimiento de un flujo implica la solución de las ecuaciones de Navier-Stokes compresibles, un problema de muy compleja estructura matemática. Estas ecuaciones proporcinan una descripción detallada de cualquier problema en mecánica de fluidos, que puede presentar distintos mecanismos no lineales que interactúan entre si. En función de la física del problema que se esté considerando, pueden derivarse modelos simplificados de las ecuaciones de Navier-Stokes mediante analisis dimensional, que ignoran algunos fenómenos físicos. Por otro lado, la transferencia de calor por radiación puede interactuar con el movimiento de un fluido, e ignorar sus efectos puede tener consecuencias importantes en las predicciones del flujo. Problemas donde hay fuego implican la evaluacion del efecto del calor por radiación. El presente trabajo está dirigido a flujos a bajo número de Mach térmicamente acoplados, donde el calor por radiación afecta al flujo. Debido a la complejidad del problema matemático, la solución numérica es muy complicada. A pesar de las diferencia en el tratamiento de la incompresibilidad, las ecuaciones de flujo a bajo número de Mach poseen una estructura matemática similar a la de flujo incompresible, en el sentido que la presión mecánica se determina a partir de la ecuación de conservación de la masa. En consecuencia poseen el mismo tipo de inestabilidades numéricas, que son el problema de condiciones de compatibilidad entre los espacios de elementos finitos de velocidad y presión, y las inestabilidades debidas a flujos con convección dominante. Estas inestabilidades pueden evitarse mediante técnicas de estabilización numérica. Muchos métodos de estabilización utilizados hoy día se basan en el método de multiscalas variacionales, donde el espacio funcional de la solucion se divide en un espacio discreto y resolubre y un espacio infinito de subscalas. El modelado de las subescalas y su influencia modifican el problema discreto proporcionando estabilidad. La calidad de la aproximación numérica final (precisión, eficiencia) depende del modelo particular de subescalas. En este trabajo se extienden estas técnicas de estabilización a problemas no lineales y acoplados. Las características que distinguen a nuestra aproximación son considerar las subsecalas como transitorias y mantener la división de escalas en todos los términos no lineales que aparecen en las ecuaciones de elementros finitos y en las del modelo de subescalas. La primera característica permite obtener mayor precisión y mejor estabilidad en la solución, la segunda característica permite obtener esquemas donde las propiedades se conservan globalmente, y mayor precisión del método. El hecho de mantener la división de escalas en todos los términos no lineales está intimamemte relacionado con el modelado de turbulencia en flujos térmicamente acoplados desde un punto de vista estrictamente numérico. La capacidad de simulación de flujo turbulento es una medida de la habilidad de modelar el efecto de las estructuras de escala fina sobre las estructuras de escala gruesa. Se muestra en esta tesis el desempeño del método para de predecir flujo turbulento. La ecuación de transporte de radiación también se aproxima numéricamente en el marco de multiscala variacional. El diseño y análisis de este método se presenta en detalle en esta tesis

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10

Kierkegaard, Axel. "Numerical investigations of generation and propagation of sound waves in low mach number internal flows /." Stockholm : Department of Aeronautical and Vehicle Engineering, Royal Institute of Technology, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-9388.

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11

Miczek, Fabian [Verfasser], Friedrich [Akademischer Betreuer] Röpke, and Björn [Akademischer Betreuer] Garbrecht. "Simulation of low Mach number astrophysical flows / Fabian Miczek. Gutachter: Friedrich Röpke ; Björn Garbrecht. Betreuer: Friedrich Röpke." München : Universitätsbibliothek der TU München, 2013. http://d-nb.info/1034951963/34.

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12

Kraushaar, Matthias. "Application of the compressible and low-mach number approaches to large-eddy simulation of turbulent flows in aero-engines." Thesis, Toulouse, INPT, 2011. http://www.theses.fr/2011INPT0114/document.

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Анотація:

La Simulation aux Grandes Echelles (SGE) est de plus en plus utilisée dans les processus de développement et la conception des réacteurs aéronautiques industriels. L'une des raisons pour ce besoin résulte dans la capacité de la SGE à fournir des informations instantanées d'un écoulement turbulent augmentant la quantité des prédictions de la composition des gaz d'échappement. Ce manuscrit de thèse aborde deux sujets récurrents de la SGE. D'une part, les schémas numériques pour la SGE nécessitent certaines propriétés, notamment une précision élevée avec une diffusivité faible pour ne pas nuire aux modèles de turbulence. Afin de répondre à ce pré requis, une famille de schémas d'intégration temporelle d'ordre élevée est proposée, permettant de modifier la diffusion numérique du schéma. D'autre part, la SGE étant intrinsèquement instationnaire, elle est très consommatrice en temps CPU. De plus, une géométrie complexe prend beaucoup de temps de simulation même avec les super calculateurs d'aujourd'hui. Dans le cas particulier d'intérêt et souvent rencontré dans les applications industrielles, l'approche bas-Mach est constitue une alternative intéressante permettant de réduire le coût et le temps de retour d'une simulation LES. L'impact et la comparaison des formalismes compressible et incompressible sont toutefois rarement quantifiés, ce qui est proposé dans ce travail pour une configuration représentative d'un brûleur swirlé industriel mesuré au CORIA Large-Eddy Simulation (LES) becomes a more and more demanded tool to improve the design of aero-engines. The main reason for this request stems from the constraints imposed on the next generation low-emission engines at the industrial development level and the ability for LES to provide information on the instantaneous turbulent flow field which greatly contributes to improving the prediction of mixing and combustion thereby offering an improved prediction of the exhaust emission. The work presented in this thesis discusses two recurring issues of LES. For one, numerical schemes for LES require certain properties, i.e. low-diffusion schemes of high order of accuracy so as not to interfere with the turbulence models. To meet this purpose in the context of fully unstructured solvers, a new family of high-order time-integration schemes is proposed. With this class of schemes, the diffusion implied by the numerical scheme become adjustable and built-in. Second, since fully unsteady by nature, LES is very consuming in terms of CPU time. Even with today's supercomputers complex problems require long simulation times. Due to the low flow velocities often occurring in industrial applications, the use of a low-Mach number solver seems suitable and can lead to large reductions in CPU time if comparable to fully compressible solvers. The impact of the incompressibility assumption and the different nature of the numerical algorithms are rarely discussed. To partly answer the question, detailed comparisons are proposed for an experimental swirled configuration representative of a real burner that is simulated by LES using a fully explicit compressible solver and an incompressible solution developed at CORIA

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13

Klein, Benedikt [Verfasser], Martin [Akademischer Betreuer] Oberlack, and Johannes [Akademischer Betreuer] Janicka. "A high-order Discontinuous Galerkin solver for incompressible and low-Mach number flows / Benedikt Klein. Betreuer: Martin Oberlack ; Johannes Janicka." Darmstadt : Universitäts- und Landesbibliothek Darmstadt, 2015. http://d-nb.info/1112044507/34.

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14

Schmidt, Steffen Joachim [Verfasser], Nikolaus A. [Akademischer Betreuer] [Gutachter] Adams, and Terwisga Tom J. C. [Gutachter] van. "A low Mach number consistent compressible approach for simulation of cavitating flows / Steffen Joachim Schmidt ; Gutachter: Tom J. C. van Terwisga, Nikolaus A. Adams ; Betreuer: Nikolaus A. Adams." München : Universitätsbibliothek der TU München, 2015. http://d-nb.info/1121206689/34.

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15

Calegari, Priscila Cardoso. "Simulação computacional de escoamentos reativos com baixo número Mach aplicando técnicas de refinamento adaptativo de malhas." Universidade de São Paulo, 2012. http://www.teses.usp.br/teses/disponiveis/45/45132/tde-21082012-051927/.

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O foco principal do presente trabalho é estender uma metodologia numérica embasada no uso de uma técnica de refinamento adaptativo de malha (AMR - Adaptive Mesh Refinement) e no uso de esquemas temporais multipasso implícitos-explícitos (IMEX) a aplicações envolvendo escoamentos reativos com baixo número de Mach. Originalmente desenvolvida para escoamentos incompressíveis, a formulação euleriana daquela metodologia emprega as equações de Navier-Stokes como modelo matemático para descrever a dinâmica do escoamento e o Método da Projeção, baseado no divergente nulo da velocidade do escoamento, para tratar o acoplamento pressão-velocidade presente na formulação com variáveis primitivas. Tal formulação euleriana original é estendida para acomodar novas equações agregadas ao modelo matemático da fase contínua: conservação de massa, fração de mistura (para representar as concentrações de combustível e oxidante), e energia. Além disso, uma equação termodinâmica de estado é integrada ao modelo matemático estendido e é empregada juntamente com a equação de conservação de massa para produzir uma nova restrição (não nula desta vez) ao divergente do campo de velocidade. Assume-se que o escoamento ocorre a baixo número de Mach (hipótese principal). O Método de Diferença Finita é empregado na discretização espacial das variáveis eulerianas de estado, empregando-se uma malha AMR. As vantagens e dificuldades desta extensão são cuidadosamente investigadas e reportadas. Pela importância, do ponto de vista de aplicações práticas, alguns estudos numéricos preliminares envolvendo escoamentos incompressíveis turbulentos com sprays são realizados (as gotículas compõem a fase dispersa). Num primeiro momento, apenas sprays com gotículas inertes são considerados. Embora ainda apenas iniciais, tais estudos já se mostram importantes pois identificam com clareza, em primeira instância, algumas das dificuldades inerentes a serem enfrentadas ao se tratar dentro desta nova metodologia um conjunto relativamente grande de gotículas lagrangianas. No caso de escoamentos incompressíveis turbulentos com sprays, a integração temporal se dá com métodos IMEX para a fase contínua e com o Método de Euler Modificado para a fase dispersa. A turbulência, em todos os casos que a envolvem, é tratada pelo modelo de Simulação das Grandes Escalas (LES - Large Eddy Simulation). As simulações computacionais se dão em um domínio tridimensional, um parelelepípedo, e empregam uma extensão (resultante do presente trabalho) do código AMR3D, um programa de computador sequencial implementado em Fortran90, oriundo de uma colaboração de longa data entre o IME-USP e o MFLab/FEMEC-UFU (Laboratório de Dinâmica de Fluidos da Universidade Federal de Uberlândia). O processamento foi efetuado no LabMAP (Laboratório da Matemática Aplicada do IME-USP). It is the main goal of the present work to extend a numerical methodology based on both the use of an adaptive mesh refinement technique (AMR) and the use of a multistep, implicit-explicit time-step strategy (IMEX) to applications involving low Mach number reactive flows. Originally developed for incompressible flows, the Eulerian formulation of that methodology employs the Navier-Stokes equations to model the flow dynamics and the Projection Method, based on the vanishing divergence of the velocity field, to tackle the pressure-velocity coupling present when using primitive variables. That Eulerian formulation is extended by adding a new set of equations to the original mathematical model, describing the various properties of the continuous phase: mass conservation, mixture fraction (to represent concentrations of fuel and oxidizer) and energy. Also, a thermodynamic equation of state is included into the extended mathematical model which is employed, along with the equation for the conservation of mass, to derive a new restriction (this time, different from zero) to the divergence of the velocity field. It is assumed that one is dealing with a low Mach number flow (the main hipothesis). The discretization in space employs the Finite Difference Method for the Eulerian variables on a AMR mesh. Advantages and difficulties of such an extension of the previous methodology are carefully investigated and reported. For its importance in the real-world applications, few preliminary numerical studies involving incompressible turbulent flows with sprays are performed (the droplets form what it is called the dispersed phase). Only sprays formed by inert droplets are considered. Even though initial yet, such studies are most important because they clearly identify, first hand, certain difficulties in handling relatively large sets of Lagrangian droplets in the context of this new AMR methodology. In the context of turbulent incompressible flows with sprays, the overall time-step scheme is given by IMEX methods for the continuous phase and by the Improved Euler Method for the dispersed phase. In all the cases in which it is considered, turbulence is modeled by the Large Eddy Simulation (LES) model. The computational simulations are held in a tridimensional domain given by a paralellepiped and all of them employ the extention (resulting of the present work) of the AMR3D code, a sequencial computer program implemented in Fortran90, whose origin is the collaborative work between IMEUSP and MFLab/FEMEC-UFU (Fluid Dynamics Laboratory, Federal University of Uberlândia). Computations were performed at LabMAP (Applied Mathematics Laboratory at IME-USP).

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16

Courtin, Victor. "Extensions of some approximate Riemann Solvers for the computation of mixed incompressible-compressible flows." Electronic Thesis or Diss., université Paris-Saclay, 2024. http://www.theses.fr/2024UPASM041.

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Dans cette thèse, on s'intéresse à la simulation d'écoulements compressibles à l'aide de méthodes numériques implicites de type solveurs de Riemann, telles que la méthode de Roe ou le schéma HLLC. L'objectif est de développer des extensions faible nombre de Mach afin de préserver la précision des solutions discrètes dans la limite bas Mach. Ce type d'écoulement est souvent rencontré dans la simulation de configurations industrielles, caractérisées par la présence de zones plus ou moins étendues à faible vitesse.On se focalise sur la composante hyperbolique des équations de Navier-Stokes, qui constitue le cœur du problème d'analyse numérique abordé dans cette thèse, les équations d'Euler. On y expose une analyse approfondie et détaillée retraçant un sujet de recherche vieux de plusieurs décennies, qui présente encore d'importants défis, même pour ce modèle académique. La littérature recense un grand nombre d'extensions possibles pour le schéma de Roe, qui sont généralement faciles à implémenter. Ces extensions consistent à modifier certains termes de la dissipation numérique, en amplifiant ou diminuant leur contribution dans la limite faible nombre de Mach (on parle de « rescaling » de la dissipation numérique). Elles permettent par ailleurs d'obtenir une solution discrète compressible approchant la solution analytique issue de la théorie du potentiel pour le problème incompressible, sans pour autant introduire une détérioration des résultats dans le régime compressible. La capture des ondes de choc pour les écoulements transsoniques et supersoniques reste quasiment inchangée. Cependant, il existe plusieurs études suggérant de faire preuve de vigilance quant au choix de la formulation de ce type de correction. Il est connu de la littérature que des pertes de stabilité numérique sont généralement observées, ainsi que des risques d'apparition de problèmes de découplage vitesse-pression, détériorant fortement la précision globale de la solution discrète dans les faibles vitesses.Ces travaux se fondent sur deux corrections très différentes du schéma de Roe, issues de la littérature scientifique, et qui présentent des propriétés discrètes distinctes. La première approche, proposée par C.-C. Rossow, amplifie les sauts de pression en introduisant une vitesse artificielle du son, tandis que la seconde, développée par F. Rieper, vise à uniquement atténuer les sauts de vitesse. Ces deux approches illustrent deux stratégies majeures fréquemment utilisées dans les extensions à faible nombre de Mach. Nous commençons tout d'abord par l'analyse asymptotique discrète de l'approche proposée par C.-C. Rossow non publiée dans la littérature, en abordant également la formulation de la condition de stabilité au sens de von Neumann. On montre que cette correction évite l'écueil du découplage vitesse-pression. Ensuite, nous présentons une méthode numérique, visant à construire des phases implicites exactes nécessaires à l'intégration temporelle, en utilisant la différentiation algorithmique et un solveur direct. Ces techniques nous permettent de contourner la contrainte très stricte de stabilité sur le pas de temps, et d'obtenir des solutions discrètes en quelques centaines d'itérations, et ce même pour des écoulements à très faible nombre de Mach. La généralisation de ces travaux au schéma HLLC se fait ensuite en poursuivant l'analyse de la structure d'onde faite par M. Pelanti. Ces travaux révèlent une profonde similarité entre les dissipations numériques de ces méthodes. En particulier, nous dérivons un formalisme commun entre ces deux schémas, afin de simplifier les analyses, et la transposition d'une correction d'un solveur de Riemann approché à l'autre, au sens d'une relation très claire entre les deux méthodes. Cette analyse nous permet en particulier de dériver le schéma HLLC-Rossow, mais également d'expliciter l'expression de la matrice de viscosité du schéma HLLC, qui exhibe une ressemblance intéressante avec celle du schéma Roe In this thesis, we focus on the simulation of compressible flows using implicit Godunov-type methods, such as the Roe method or the HLLC scheme. The objective is to develop low Mach number extensions that preserve the accuracy of discrete solutions in the low Mach number limit. This type of flow is frequently encountered in the simulation of industrial configurations, which are often characterized by the presence of more or less extensive low-speed areas.We focus on the hyperbolic component of the Navier-Stokes equations, which form the core of the numerical analysis problem addressed in this thesis, the Euler equations. We present an in-depth and detailed analysis of research topic that has been the subject of investigations for decades, and which continues to present significant challenges, even for this academic model. A review of the literature reveals a large number of possible extensions to the Roe scheme, which are generally easy to implement. These involve modifying specific terms of the numerical dissipation, either by amplifying or by diminishing their contribution in the low Mach number limit (also known as a rescaling of the numerical dissipation). They also enable us to obtain a discrete compressible solution that approaches the analytical solution derived from potential theory for the incompressible problem, without introducing any deterioration in the results in the compressible regime. The capture of shock waves for transonic and supersonic flows remains almost unaltered. However, there are a number of studies suggesting that care should be taken in the choice of formulation for this type of correction. It is well documented in the literature that losses in numerical stability are generally observed, as well as the risk of velocity-pressure decoupling problems appearing, which can significantly deteriorate the overall accuracy of the discrete solution for low-speed flows.This work is based on two very different corrections of the Roe scheme, taken from the scientific literature, and highlighting distinct discrete properties. The first approach, proposed by C.-C. Rossow, amplifies pressure jumps by introducing an artificial speed of sound, whereas the second approach, developed by F. Rieper, aims to attenuate velocity jumps exclusively. These two approaches illustrate two major strategies frequently used in low-Mach extensions. We begin with a discrete asymptotic analysis of the approach proposed by C.-C. Rossow, which has not been published in the literature, including the formulation of the von Neumann stability condition. It is demonstrated that this correction avoids the issue of pressure- velocity decoupling. Next, we present a numerical method for constructing the exact implicit phases required for time integration, using algorithmic differentiation and a direct solver. These techniques enable us to bypass the very strict stability constraint on the time step, thereby facilitating the acquisition of discrete solutions within a few hundred iterations, even for very low Mach number flows. The generalization of this work to the HLLC scheme is then made by continuing the wave structure analysis carried out by M. Pelanti. This work demonstrates a significant similarity between the numerical dissipations of these methods. In particular, a common formalism between these two schemes is derived, with the aim of simplifying the analyses, and transposing of a correction from one approximate Riemann solver to the other, in the sense of a very clear relationship between the two methods. In particular, this analysis enables us to derive the HLLC-Rossow scheme, but also to clarify the expression of the viscosity matrix of the HLLC scheme, which exhibits an interesting resemblance to that of the Roe scheme

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17

Chauveheid, Daniel. "Ecoulements multi-matériaux et multi-physiques : solveur volumes finis eulérien co-localisé avec capture d’interfaces, analyse et simulations." Thesis, Cachan, Ecole normale supérieure, 2012. http://www.theses.fr/2012DENS0032/document.

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Ce travail de thèse porte sur l'extension et l'analyse d'un solveur volumes finis eulérien, co-localisé avec capture d'interfaces pour la simulation des écoulements multi-matériaux non miscibles. Les extensions proposées s'inscrivent dans la volonté d'élaborer un outil de simulation multi-physiques. Dans le cadre de ce mémoire, le caractère multi-physiques recouvre les champs que nous allons détailler. Nous traitons le cas des écoulements radiatifs modélisés par un système à deux températures qui couple les phénomènes purement hydrodynamiques aux phénomènes radiatifs. Nous proposons un solveur permettant la prise en compte des effets de tension superficielle à l'interface entre deux fluides. Nous développons un solveur implicite permettant la simulation précise d'écoulements faisant intervenir de faibles nombres de Mach par le biais d'une méthode de renormalisation de la diffusion numérique. Enfin, les effets tri-dimensionnels sont considérés ainsi que la possibilité d'étendre le schéma de base aux écoulements à un nombre quelconque de matériaux. A chaque étape, les solveurs développés sont validés sur des cas-tests This work is devoted to the extension of a eulerian cell-centered finite volume scheme with interfaces capturing for the simulation of multimaterial fluid flows. Our purpose is to develop a simulation tool which could be able to handle multi-physics problems in the following sense. We address the case of radiating flows, modeled by a two temperature system of equations where the hydrodynamics are coupled to radiation transport. We address a numerical scheme for taking surface tension forces into account. An implicit scheme is proposed to handle low Mach number fluid flows by means of a renormalization of the numerical diffusion. Eventually, the scheme is extended to three-dimensional flows and to multimaterial flows, that is with an arbitrary number of materials. At each step, numerical simulations validate our schemes

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18

Dupuy, Dorian. "Analyse et modélisation de l'interaction entre thermique et turbulence dans les récepteurs solaires à haute température." Thesis, Perpignan, 2018. http://www.theses.fr/2018PERP0038/document.

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Dans les centrales solaires à tour, le flux solaire est concentré vers un récepteur solaire où son énergie est transférée à un fluide caloporteur. L'écoulement au sein du récepteur solaire est turbulent, fortement anisotherme et à bas nombre de Mach. L'optimisation du récepteur solaire exige une meilleure compréhension et modélisation de l'interaction entre la température et la turbulence. Cette thèse cherche à y contribuer selon deux approches. Tout d'abord, on étudie les échanges énergétiques entre les différentes parties de l'énergie totale. On propose pour cela une nouvelle représentation des échanges énergétiques, fondée sur la moyenne de Reynolds. Cette représentation permet la caractérisation, à partir de simulations numériques directes d'un canal plan bipériodique anisotherme, de l'effet du gradient de température sur les échanges énergétiques associées à l'énergie cinétique turbulente dans les domaines spatial et spectral. Ensuite, on étudie la simulation des grandes échelles des équations de bas nombre de Mach. En utilisant les résultats de simulations numériques directes, on identifie les termes sous-mailles spécifiques à modéliser lorsque l'on utilise le filtre classique, non pondéré, et lorsque l'on utilise le filtre de Favre, pondéré par la masse volumique. Dans les deux cas, on évalue a priori la performance de différents modèles sous-mailles. La pertinence des modèles est vérifiée a posteriori par la réalisation de simulation des grandes échelles In solar power towers, the solar flux is concentrated towards a solar receiver, wherethrough its energy is transferred to a heat transfer fluid. The flow in the solar receiver is turbulent, strongly anisothermal and at low Mach number. The optimisation of the solar receiver requires a better understanding and modelling of the interaction between temperature and turbulence. In this thesis, this is investigated following two approaches. First, we study the energy exchanges between the different parts of total energy. To this end, a new representation of the energy exchanges, based on the Reynolds averaging, is established. The representation allows the characterisation, from direct numerical simulations of a strongly anisothermal channel flow, of the effect of the temperature gradient on the energy exchanges associated with turbulence kinetic energy in the spatial and spectral domains. Second, we study the large-eddy simulation of the low Mach number equations. Using the results of direct numerical simulations, we identify the specific subgrid terms to model when the unweighted classical filter is used and when the density-weighted Favre filter is used. In both cases, the performance of different subgrid-scale models is assessed a priori. The relevance of the subgrid-scale models is then verified a posteriori by carrying out large-eddy simulations

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19

Malandain, Mathias. "Simulations massivement parallèles des écoulements turbulents à faible nombre de Mach." Phd thesis, INSA de Rouen, 2013. http://tel.archives-ouvertes.fr/tel-00834845.

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L'objectif de cette thèse est l'accélération des solveurs de Gradient Conjugué avec déflation utilisés pour la résolution de l'équation de Poisson pour la pression, dans le cas de la simulation d'écoulements à faible nombre de Mach sur des maillages non structurés. Une méthode de redémarrage basée sur une estimation de l'effet des erreurs numériques a été mise en œuvre et validée. Par la suite, une méthode à trois niveaux de maillage a été créée, et deux techniques ont dû être développées pour réduire le nombre d'itérations sur les niveaux grossiers : l'une permet la création de solutions initiales grâce à une méthode de projection adaptée, l'autre consiste en une adaptation du critère de convergence sur les niveaux grossiers. Les résultats numériques sur des simulations massivement parallèles montrent entre autres une réduction considérable du temps de calcul global. D'autres pistes de recherche sont introduites, notamment concernant l'équilibrage dynamiques de charge de calcul.

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20

Haddad, Adel. "Modèles numériques à faibles nombres de Mach pour l'étude d'écoulements en convection naturelle et mixte." Thesis, Aix-Marseille 1, 2011. http://www.theses.fr/2011AIX10154.

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Le modèle numérique que nous avons développé au cours de cette thèse présente deux caractéristiques principales : un modèle dilatable pour l'eau et la prise en compte de domaines ouverts. Les difficultés associées au premier aspect concernent l'adaptation de la loi d'état de l’eau au modèle dilatable sous l’approximation à faibles nombres de Mach, tandis que celles associées au second sont relatives à la mise en œuvre de conditions aux limites numériques de sortie compatibles avec l'algorithme de projection utilisé. Les résultats de simulations d'écoulement de convection mixte en canal horizontal chauffé par le bas ont été confrontés à celles utilisant l'approximation de Boussinesq et aux expériences The 3D numerical model which we developed in this thesis presents two main features: a Low-Mach-Number approximation for water along with an open boundary condition formulation. Indeed, the difficulties related to the former point stand in a computationally efficient adaptation of the water equation of state in the framework of Low Mach number approximation, whereas the difficulties related to the latter concern the introduction of Open Boundary Conditions in the projection algorithm used. We have computed a mixed convection flow in a horizontal channel uniformly heated from below and compared the results obtained with both the Boussinesq approximation and experimental results

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21

Birken, Philipp [Verfasser]. "Numerical Simulation of Flows at Low Mach Numbers with Heat Sources / Philipp Birken." Aachen : Shaker, 2006. http://d-nb.info/117052916X/34.

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22

Nana, Cyril. "Simulation du bruit d'écoulements anisothermes par méthodes hybrides pour de faibles nombres de Mach." Phd thesis, Université de Poitiers, 2012. http://tel.archives-ouvertes.fr/tel-00741298.

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Cette étude porte sur le calcul numérique du champ acoustique rayonné par des écoulements subsoniques turbulents présentant des inhomogénéités de température. Des méthodes hybrides sont développées grâce à un développement de Janzen-Rayleigh des équations de Navier-Stokes. L'écoulement est résolu par un calcul quasi incompressible puis les perturbations acoustiques sont propagées selon deux méthodes : les équations d'Euler linéarisées (EEL) et l'approximation à faible nombre de Mach perturbée (PLMNA). Les méthodes sont validées sur des cas simples puis appliquées à une couche de mélange isotherme et anisotherme en développement spatial.

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23

Parasiliti, Rantone Giuseppe. "Physical, mathematical and numerical modelling of a gas flow in pipeline networks with low Mach number expansion." Electronic Thesis or Diss., Sorbonne université, 2023. http://www.theses.fr/2023SORUS547.

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Cette étude porte sur les écoulements de gaz à faible vitesse dans des réseaux de tuyaux, en se concentrant sur un régime caractérisé par un faible nombre de Mach. Nous utilisons un modèle unidimensionnel obtenu en moyennant les équations de Navier-Stokes pour un fluide compressible sur la section d'une conduite. Notre approche utilise le développement asymptotique à faible nombre de Mach pour décrire les effets compressibles de manière plus précise, contrairement à l'approximation classique de Boussinesq qui en est un cas limite lorsque l'élévation de température est assez faible. Nous utilisons un schéma numérique fondé sur la méthode des caractéristiques et la méthode de projection pour traiter ce modèle à faible Mach. Nous présentons des résultats numériques pour une configuration appelée "thermosiphon". Cette configuration consiste en une boucle fermée constituée de deux tuyaux horizontaux adiabatiques et de deux tuyaux verticaux avec des températures de paroi prescrites, qui entraînent l'écoulement. L'algorithme développé permet de prendre en compte des distributions de Dirac, qui peuvent apparaître en terme source dans le modèle pour représenter les coins de la géométrie. La méthode proposée est également adaptée au modèle pour des conditions aux limites de type périodique en plus des conditions de type Dirichlet. Nous incorporons dans notre algorithme le traitement des distributions de Dirac en tant que dérivées du terme de gravité discontinu aux coins et des conditions périodiques. Afin d'établir une référence pour le problème du thermosiphon, nous fournissons une solution exacte mais semi-implicite d'un écoulement laminaire en régime permanent. Cette solution sert de référence pour valider la méthode proposée. Nous proposons également des lois qui régissent les jonctions entre plusieurs conduites et présentons des résultats numériques pour des configurations de conduites plus complexes. Nous nous intéressons en particulier à l'échelle à trois barreaux, une configuration fermée composée de tuyaux horizontaux adiabatiques et de tuyaux verticaux dont les parois sont soumises à des températures imposées afin d'induire un gradient de température qui alimente l'écoulement. qui corresponds à une extension du thermosiphon. À partir de celle-ci, plusieurs configurations générales peuvent être dérivées. Nous développons un algorithme pour garantir des conditions de transmission adéquates aux jonctions, en fournissant autant que possible des solutions stationnaires semi-analytiques pour valider nos résultats numériques. Cette étude contribue à une meilleure compréhension des principes qui régissent les écoulements de gaz à faible nombre de Mach en utilisant des techniques numériques avancées et en les comparant à des références établies This project aims to develop a model for low Mach flow in pipelines and an industrial code implementing it. The model can describe low mach regimes while avoiding blunt approximations, improving over legacy approaches like Boussinesq; as a result, our program is more accurate. In order to build our model and program, we investigate gas flow at low velocities in a network of pipes. We consider a one-dimensional system of equations obtained by averaging the Navier-Stokes equations for a compressible fluid over the pipe section. In contrast to the classical Boussinesq approximation, we employ the Low Mach Expansion to describe asymptotically compressible effects, aiming for a more accurate solution capable of characterizing flows with significant temperature variations. We first apply the model we obtained thus far to a well-known configuration of pipes called the "thermosyphon.". This setup consists of a loop of two horizontal adiabatic pipes and two vertical pipes with prescribed wall temperatures, resulting in a temperature gradient that drives the flow. The application of the model to this configuration gives us an exact but semi-implicit solution under laminar and steady-state conditions. This solution serves as a benchmark against which we validate our numerical results. By comparing our computed values with the quasi-exact solution, we demonstrate the accuracy and reliability of our approach. To implement the low Mach averaged model, we use a numerical method based on the characteristics method and the projection technique. We incorporate in our algorithm the treatment of periodic conditions and Dirac distributions as derivatives of the discontinuous gravity term at the corners. To generalize the model to more complex configurations of pipes, we propose laws that govern the junctions between multiple pipes. We study the "three-rung ladder," a closed configuration consisting of horizontal adiabatic pipes and vertical ones with imposed wall temperatures to induce a temperature-driven flow. %From this setup, more complex pipeline configurations can be derived. To tackle the challenges junctions pose in this context, we implemented an algorithm in the program capable of ensuring proper transmission conditions. Whenever feasible, we provide quasi-exact solutions under laminar and steady-state conditions to validate our numerical results further. Overall, this study investigates further low Mach number gas flows, employing advanced numerical techniques and validating our findings against established benchmarks

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24

Ekaterinaris, John A. "Steady and unsteady internal flow computations via the solution of the compressible navier stokes equations for low mach numbers." Diss., Georgia Institute of Technology, 1987. http://hdl.handle.net/1853/12366.

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25

Sinibaldi, Edoardo. "Implicit preconditioned numerical schemes for the simulation of three-dimensional barotropic flows." Doctoral thesis, Scuola Normale Superiore, 2006. http://hdl.handle.net/11384/85704.

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A numerical method for simulating three-dimensional, generic barotropic flows on unstructured grids is developed. Space and time discretizations are separately considered. A finite volume compressible approach, based on a suitable Roe numerical flux function, is proposed and the accuracy of the resulting semi-discrete formulation for nearly-incompressible flows is ensured by ad hoc preconditioning. Moreover, a linearized implicit time-advancing technique is proposed, only relying on the algebraic properties of the Roe flux function and therefore applicable to a variety of problems. This implicit strategy is extended so as to incorporate the aforementioned preconditioning. The considered numerical ingredients are firstly defined in a one-dimensional context; after validation, they are extended to three-dimensional non-rotating as well as rotating frames. Finally, the resulting numerical method is validated by considering complex industrial flows, namely the water flow around a hydrofoil (for which specific experimental data are available) and the water flow around a rotating turbo-pump inducer. By starting from a particular industrial problem (namely the numerical simulation of propellant flows around an axial inducer belonging to the feed turbo-pump system of a liquid propellant rocket engine), a numerical method which can be applied to generic barotropic flows is defined. Along the way, a constructive procedure for solving the 1D Riemann problem associated with a generic convex barotropic state law is proposed. This solution, also exploited for defining a Godunov numerical flux suitable for incorporation into finite volume schemes, is systematically used in order to define exact benchmarks for the quantitative validation of the proposed one-dimensional numerical methods.

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26

Gokpi, Kossivi. "Modélisation et Simulation des Ecoulements Compressibles par la Méthode des Eléments Finis Galerkin Discontinus." Thesis, Pau, 2013. http://www.theses.fr/2013PAUU3005/document.

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L’objectif de ce travail de thèse est de proposer la Méthodes des éléments finis de Galerkin discontinus (DGFEM) à la discrétisation des équations compressibles de Navier-Stokes. Plusieurs challenges font l’objet de ce travail. Le premier aspect a consisté à montrer l’ordre de convergence optimal de la méthode DGFEM en utilisant les polynômes d’interpolation d’ordre élevé. Le deuxième aspect concerne l’implémentation de méthodes de ‘‘shock-catpuring’’ comme les limiteurs de pentes et les méthodes de viscosité artificielle pour supprimer les oscillations numériques engendrées par l’ordre élevé (lorsque des polynômes d’interpolation de degré p>0 sont utilisés) dans les écoulements transsoniques et supersoniques. Ensuite nous avons implémenté des estimateurs d’erreur a posteriori et des procédures d ’adaptation de maillages qui permettent d’augmenter la précision de la solution et la vitesse de convergence afin d’obtenir un gain de temps considérable. Finalement, nous avons montré la capacité de la méthode DG à donner des résultats corrects à faibles nombres de Mach. Lorsque le nombre de Mach est petit pour les écoulements compressibles à la limite de l’incompressible, la solution souffre généralement de convergence et de précision. Pour pallier ce problème généralement on procède au préconditionnement qui modifie les équations d’Euler. Dans notre cas, les équations ne sont pas modifiées. Dans ce travail, nous montrons la précision et la robustesse de méthode DG proposée avec un schéma en temps implicite de second ordre et des conditions de bords adéquats The aim of this thesis is to deal with compressible Navier-Stokes flows discretized by Discontinuous Galerkin Finite Elements Methods. Several aspects has been considered. One is to show the optimal convergence of the DGFEM method when using high order polynomial. Second is to design shock-capturing methods such as slope limiters and artificial viscosity to suppress numerical oscillation occurring when p>0 schemes are used. Third aspect is to design an a posteriori error estimator for adaptive mesh refinement in order to optimize the mesh in the computational domain. And finally, we want to show the accuracy and the robustness of the DG method implemented when we reach very low mach numbers. Usually when simulating compressible flows at very low mach numbers at the limit of incompressible flows, there occurs many kind of problems such as accuracy and convergence of the solution. To be able to run low Mach number problems, there exists solution like preconditioning. This method usually modifies the Euler. Here the Euler equations are not modified and with a robust time scheme and good boundary conditions imposed one can have efficient and accurate results

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27

Delmas, Simon. "Simulation numérique directe d'un jet en écoulement transverse à bas nombre de Mach en vue de l'amélioration du refroidissement par effusion des chambres de combustion aéronautiques." Thesis, Pau, 2015. http://www.theses.fr/2015PAUU3035/document.

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Dans cette thèse on s'intéresse aux jets en écoulement transverse dans une configuration générique de celle du refroidissement par effusion de chambres de combustion aéronautiques. L'amélioration des modèles de paroi avec transfert de masse passe par une meilleure connaissance de l'interaction entre les jets et l’écoulement principal. Nous avons donc réalisé la simulation numérique directe d'un jet issu d'un perçage incliné avec ou sans giration, pour des écoulements isothermes, turbulents et à bas nombre de Mach, dans un contexte compressible. Pour cela nous avons travaillé avec la bibliothèque AeroSol d'éléments finis continus et discontinus sur maillage hybride. En particulier nous nous sommes intéressés à la stabilité des flux numériques pour le compressible instationnaire associés à la méthode de Galerkin discontinue lorsque le nombre de Mach tend vers zéro. Nous avons pu mettre en évidence des comportements instables lors de l'utilisation de discrétisation temporelle explicite que nous avons corrigés en proposant un nouveau flux. Dans un deuxième temps, nous avons effectué les développements nécessaires à la réalisation des calculs. Nous nous sommes en particulier intéressés à la génération d'un champ de vitesse turbulent synthétique par la méthode SEM (Synthetic Eddy Method) que nous avons implantée dans AeroSol et validée. Grâce aux outils de post-traitement développés, nous avons conduit l'analyse de nos résultats. Dans le cas sans giration, les comparaisons avec les résultats expérimentaux et les résultats de simulations RANS que nous avons obtenus en parallèle sur la configuration du banc d'essai MAVERIC sont encourageants. La structure moyenne d'ensemble du jet est notamment correctement reproduite. En ce qui concerne la cas avec giration, le comportement attendu de déflexion successive du jet dans les deux plans caractéristiques (plan d'injection et plan de l'écoulement transverse) est bien reproduit et illustre tout le potentiel prévisionnel de la librairie de calcul que nous avons contribué à développer In this work we are interested in jet in crossflow in a generic configuration to the one used in effusion cooling for combustion chambers. Improved wall models with mass transfer requires a better knowledge of the interaction between the jets and the main flow. We therefore carried out the direct numerical simulation of a jet issuing from an inclined hole with or without gyration, for isothermal turbulent flow at low Mach number, in a compressible context. To achieved this, we worked with the continuous and discontinuous finite element library : AeroSol on hybrid grid. In particular we studied the stability of numerical flux for the unsteady compressible flow associated with discontinuous Galerkin method when the Mach number tends to zero. We were able to demonstrate unstable behavior when using explicit time discretization and we corrected them by providing a new flux. In a second time, we have performed the necessary development to achieve the calculations. We have been especially interested in the generation of a synthetic turbulent velocity field using the SEM method (Synthetic Eddy Method) that we have implemented in aerosol and validate. Thanks to the developed post-processing tools, we have conducted an analysis of our results. In the case without gyration, comparisons with experimental results and the results of RANS simulations we obtained on the Maveric test-bench configuration are encouraging. The mean flow of the jet is correctly reproduced. In the case with gyration, the expected behavior of successive deflection of the jet in both planes (injection plane and transverse plane of the flow) is reproduced and shows all the potential of the AeroSol library we helped to develop

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28

Khalighi, Yaser Moin Parviz Lele Sanjiva K. Wang Meng. "Computational aeroacoustics of complex flows at low Mach number." 2010. http://purl.stanford.edu/gj871wv3443.

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29

Nigro, Alessandra, Maria Laura Luchi, Bartolo Carmine De, and Francesco Bassi. "Discontinuous Galerkin Methods for inviscid low Mach number flows." Thesis, 2014. http://hdl.handle.net/10955/366.

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Dottorato di ricerca in Ingegneria Meccanica, XX Ciclo, a.a. 2007 In this work we present two preconditioning techniques for inviscid low Mach number flows. The space discretization used is a high-order Discontinuous Galerkin finite element method. The time discretizations analyzed are explicit and implicit schemes. The convective physical flux is replaced by a flux difference splitting scheme. Computations were performed on triangular and quadrangular grids to analyze the influence of the spatial discretization. For the preconditioning of the explicit Euler equations we propose to apply the fully preconditioning approach: a formulation that modifies both the instationary term of the governing equations and the dissipative term of the numerical flux function. For the preconditioning of the implicit Euler equations we propose to apply the flux preconditioning approach: a formulation that modifies only the dissipative term of the numerical flux function. Both these formulations permit to overcome the stiffness of the governing equations and the loss of accuracy of the solution that arise when the Mach number tends to zero. Finally, we present a splitting technique, a proper manipulation of the flow variables that permits to minimize the cancellation error that occurs as an accumulation effect of round-off errors as the Mach number tends to zero. Università della Calabria

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30

Hadjiconstantinou, Nicolas G., and Alejandro L. Garcia. "Statistical Error in Particle Simulations of Low Mach Number Flows." 2002. http://hdl.handle.net/1721.1/4017.

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We present predictions for the statistical error due to finite sampling in the presence of thermal fluctuations in molecular simulation algorithms. Expressions for the fluid velocity, density and temperature are derived using equilibrium statistical mechanics. The results show that the number of samples needed to adequately resolve the flow-field scales as the inverse square of the Mach number. The theoretical results are verified for a dilute gas using direct Monte Carlo simulations. The agreement between theory and simulation verifies that the use of equilibrium theory is justified. Singapore-MIT Alliance (SMA)

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31

URBANO, ANNAFEDERICA. "Analysis of Heat Transfer Characteristics of Supercritical Fuels in Rocket Cooling Systems by a Space Marching Numerical Technique." Doctoral thesis, 2012. http://hdl.handle.net/11573/918521.

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Methane and Liquefied Natural Gas (LNG) have been recently considered both for launch and for in-space applications because of several advantages they present if compared with other commonly used fuels. In particular, several studies are dedicated at the use of methane in liquid rocket engines with turbopumb fed systems. In this framework, the present study focuses on the use of methane or LNG as coolant in regenerative cooling systems. The study has two main purposes. The first is to understand what are the differences between using pure methane or LNG in a cooling system. The second purpose is to investigate on the heat transfer deterioration which is a thermodynamic phenomenon that could affect methane or LNG in cooling channels. The idea is to fulfill these objectives by numerical studies. The test cases that have to be analyzed are straight channels with circular cross section, a length of the order of the meter and a diameter of the order of the millimeter. The Reynolds number is of the order of 10^5 − 10^6 , which implies that the flow is turbulent. The coolant enters the channels with a supercritical pressure (∼10 MPa) and a subcritical temperature (∼ 110 K), which correspond to a very low compressibility. As a consequence, the inlet Mach number are very low (∼ 0.01). High heat fluxes up to 10 MW/m^2 are enforced along the channel. The temperature variations along the channel cause a change in all the thermophysical properties that strongly nfluence the coolant behavior. Thermophysical properties of real fluids and mixtures of real fluids are used to carry out the present investigations. An equation of state based on the Helmholtz free energy is used for the thermodynamic properties. Transport property models are based on the extended corresponding states approach used in combination with accurate models for the transport properties of each considered species. A numerical code is developed pecifically to deal with the test cases of interest. It is based on parabolized Navier Stokes equations which can be solved with a space marching approach. The numerical model, used together with the selected thermophysical models, is validated against experimental data. Finally the developed code is used to obtain the desired results. First a comparison between LNG and pure methane behavior is carried out which permits to emphasize their different properties. In particular, the influence of the LNG composition on the coolant flow is analyzed. Subsequently, study of the deterioration of the heat transfer is addressed both with methane and LNG. Parametric studies permit to understand what are the main parameters involved in the phenomenon and how it can be handled.

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32

Zang, Yi-Chong, and 曾臆璁. "Numerical Investigation of Low-Mach-Number Flows on the Tetrahedral/Prismatic Meshes." Thesis, 2008. http://ndltd.ncl.edu.tw/handle/10223416758535838990.

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碩士 國立成功大學 航空太空工程學系碩博士班 96 For the low-mach-number flows, a lot of experimental and theoretical results have been presented, but the theoretical computation is still worthwhile to study. According to the Rossow’s pressure correction concept, a numerical solution proceduce is created to investigate the low-mach-number flow behavior in this paper. First the unstructured tetrahedral and prismatic meshes are generated in the flow domain. Then the above-mentioned numerical approach is used to solve the three-dimensional Euler/Navier-Stokes equations. This approach includes four-step Runge-kutta time-integration scheme, revised form of Roe’s flux-difference-splitting method in terms of Mach number and Jacobi / Gauss-Seidel / Modified Gauss-Seidel interation methods with/without relaxation factor for solving the Rossow’s pressure correction equation. In the present calculations, the operations by using one core and duo cores/quad cores with parallel computations are processed. To evaluate this numerical method, the inviscid flow around sphere and passing through the converging-diverging nozzle with circular cross-section are investigated first. For the different Mach numbers, the computed pressure coefficient and velocity distributions on the surface of sphere are compared with those from the potential flow theory. Also, the history of convergence and computing time are studied. About the nozzle flow, the pressure and velocity distributions along the nozzle axis are presented. Comparing with those from the one-dimensional isentropic flow the present method is evaluated. Secondly, the computation of viscous pipe flow is processed. From the comparison betwteen the resent results and the analytical solution, the accuracy of current numercail approach for solving the laminar flow is confirmed. Keywords: unstructured tetrahedral/prismatic meshes, pressure correction equation, low-mach-number flow, parallel computation

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33

PINNA, fabio calogero. "Numerical study of stability of flows from low to high Mach number." Doctoral thesis, 2012. http://hdl.handle.net/11573/918810.

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Interest in the study of stability lies in the strong link with the laminar-to-turbulent transition with several implications in the design of new vehicles in the aerospace community. If on one side aeronautics would like to predict and control transition to limit drag, boost efficiency and reduce the fuel consumption on the other hand, space design faces reentry problem where an accurate transition prediction could lead to a better sizing of the thermal protection system, thus enhancing the overall performance of the spacecraft. Nevertheless one has to keep in mind that transition can occur because of several causes, which make the link between stability and transition not as direct as one would it like to be. On an engineering point of view the use of the eN method has been selected as our preferred way of estimating the onset of transition. Despite the great amount of software available to study stability of incompressible flows and, to a lesser extent, low supersonic flows, there is a restricted number of codes dealing specifically with hypersonic flows. The objective of this work is then to write a consistent toolkit to be able to study stability of flows at different regimes, from low to high Mach numbers. The VESTA toolkit (VKI Extensible Stability and Transition Analysis toolkit) gathers a number of codes for different regimes which are based on Chebyshev pseudo-spectral methods. It compares well against literature for the incompressible and compressible flows while hypersonic cases are more difficult to test, because of the narrower body of literature treating them. Nevertheless some comparisons allow us to estimate a reasonable good matching with existing results. The incompressible study was not limited to the reproduction of standard cases and techniques but included also an original expansion of the $\tau$-method capable of treating boundary layer flows. Results have been verified against the ones obtained by other methods even if its complexity makes the $\tau$-method an unideal candidate for the development of the compressible solver. The compressible linear stability solver is able to cope with both subsonic and supersonic regime and it has been used to verify and expand the current database of neutral stability curves at different Mach, by plotting results for adiabatic flows with different free stream static temperatures. The compressible solver served as a base for the implementation of the specialized hypersonic code. For this case, when temperature is high enough, air molecules start dissociating and chemical reactions happen between the different species. For this reason air should be considered as a mixture of gases. In the present work this effect is taken into account by means of the Local Thermodynamic Equilibrium (LTE) assumption. A deep investigation has been carried on the effect of free stream temperature and pressure. It turned out that in the investigated range, pressure plays a minor role, while temperature results to be the driving parameter, even more at lower Reynolds numbers. It has been observed that the critical Reynolds number decreases when temperature increases. As the free stream temperature increase the neutral stability curves show also a larger instability area. Another important aspect of hypersonic flows is the strong shock in front of the body. Its influence on the boundary layer has been modeled as a boundary condition for the calorically perfect gas (CPG) and LTE solver. Nevertheless the latter implementations is new and only simple verifications against a calorically perfect gas was possible. It is already known in literature that the shock stabilizes the flow at low wave numbers. Our computations on chemically reacting flows found out that LTE tends to stabilize it even more, with growth rates as low as three times the respective one for CPG. Future works will take advantage of the modularity of the VESTA toolkit to add other stability feature like Parabolized Stability Equations and BiGlobal stability. On the numerical side some work will be devoted to the implementation of more general and faster algorithm retaining the same level of accuracy of the present solvers. On a different level the results found in this work could be readily used together with an eN code for the prediction of transition for flight condition and ground testing while the software will be used as the founding brick of an Uncertainty Quantification for transition prediction.

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Klein, Benedikt. "A high-order Discontinuous Galerkin solver for incompressible and low-Mach number flows." Phd thesis, 2015. https://tuprints.ulb.tu-darmstadt.de/5143/1/Dissertation-Klein-2015.pdf.

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In this work, we present a high-order Discontinuous Galerkin Method (DGM) for simulating incompressible and variable density flows at low-Mach numbers. For steady cases, we apply the SIMPLE algorithm to solve the non-linear system in a segregated manner. For unsteady cases, the solver is implicit in time using backward differentiation formulae and the SIMPLE algorithm is applied to solve the non-linear system in each time step. The proposed method is implemented in the in-house software library BoSSS. The solver is extensively tested with respect to temporal and spatial convergence rates, performance and stability by simulating various test cases. In the first part of this work, we describe the discretization and algorithm for incompressible flows. Using a mixed-order formulation for the spatial discretization, we obtain convergence rates of k+1 for velocity and k for pressure for various test cases, where k and k-1 are the orders of the approximation polynomials for velocity and pressure, respectively. Applying pressure stabilization for the equal-order formulation, the convergence rates are approximately the same, while the absolute error is smaller. By simulating the Orr-Sommerfeld problem we investigate the stability of the proposed method. The solver is validated by studying the two- and three-dimensional flow past a square cylinder. Main parts of this work concerning the solver and numerical results for incompressible flows have been published before by the author of this thesis in [KLEIN, B., KUMMER, F., OBERLACK, M. (2013): A SIMPLE based discontinuous Galerkin solver for steady incompressible flows. Journal of Computational Physics 237, 235–250] and [KLEIN, B., KUMMER, F., KEIL, M., OBERLACK, M. (2015): An extension of the SIMPLE based discontinuous Galerkin solver to unsteady incompressible flows. International Journal for Numerical Methods in Fluids 77, 10, 571–589]. In the second part of this work, the solver is extended to variable density flows at low-Mach numbers. An intermediate step in the development of the solver for low-Mach number flows is a method for simulating multiphase flows with a smooth interface approach and without surface tension. The solver for low-Mach number flows is based on the low-Mach number equations, which are an approximation of the compressible Navier-Stokes equations in the limit of zero Mach number. To the best of the author's knowledge, it is the first time that the DGM is applied to the low-Mach number equations. For spatial discretization the mixed-order formulation is applied. Various test cases confirm the high accuracy of the method also for multiphase flows and low-Mach number flows.

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35

Yang, Ming-Jung, and 楊銘榮. "Towards Simple Implicit Preconditioning Riemann Solvers for the Simulation of the Low Mach number Flows." Thesis, 2016. http://ndltd.ncl.edu.tw/handle/96313237209310800704.

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碩士 淡江大學 航空太空工程學系碩士班 104 Here, a scalar matrix-free implicit type preconditioning hybrid AUSMD(R) solver for multi-phase flows is developed. The numerical stability problem caused by the multi-scale speed of sound due to uncertain dissipation terms in the current schemes which can be resolved by rescaling the eigenvalues of the Euler type system equations to enhance computational convergence. This paper presents implicit pre-conditioning approaches which indicate similarly accurate results obtained with the fully implicit and Runge-Kutta explicit schemes. The current used homogeneous two-phase mixture model with the assumption of kinematics and thermodynamics equilibriums. The thermodynamics behaviors of liquid phase, vapor phase and their phase transitional process are described by a temperature dependent hybrid equation of state which includes a mass-fraction averaged formula of water-vapor saturation process. The current work shows that the scalar matrix free implicit schemes are capable of improving the computational efficiency over its explicit counterpart. Several benchmark tests are used for numerical validations.

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36

Zucchini, Marco [Verfasser]. "Experimental and numerical aeroacoustic investigation of impinging flows at low Mach number / vorgelegt von Marco Zucchini." 2007. http://d-nb.info/984953256/34.

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37

Hassanaly, Malik. "Large eddy simulations (LES) of boundary layer flashback in wall-bounded flows." Thesis, 2014. http://hdl.handle.net/2152/28248.

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In the design of high-hydrogen content gas turbines for power generation, flashback of the turbulent flame by propagation through the low velocity boundary layers in the premixing region is an operationally dangerous event. The high reactivity of hydrogen combined with enhanced flammability lim- its (compared to natural gas) promotes flame propagation along low-speed boundary layers adjoining the combustion walls. This work focuses on the simulation of boundary layer flashback using large-eddy simulations (LES). A canonical channel configuration is studied to assess the capabilities of LES and determine the modeling requirements for boundary layer flashback simulations. To extend this work to complex geometries, a new reactive low-Mach number solver has been written in an unstructured code. text

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MINGZONG-WANG and 王銘宗. "Solving Low-Mach Number Euler Flow with Local Preconditioning Technique." Thesis, 2001. http://ndltd.ncl.edu.tw/handle/96576713678298720065.

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碩士 國立成功大學 機械工程學系 89 The aim of this paper is using local preconditioning methods to solve nearly incompressible flow problems with numerical algorithms that were designed for compressible flow。First，we calculate the flux jacobin of primitive variables in 3D Euler equations in the Cartesian coordinate system，then multiply a preconditioner ，and transfer matrices after preconditioning。Final，we obtain the flux jacobin matrix of conservative variables 。The aim of the local preconditioning is changing numerical modes of Euler equations，and overcome the large disparity of the acoustic wave speed ，and the convected waves at the fluid speed 。The preconditioning that are applied here not only accelerate the convergence to a steady state but also change steady-state solution。 In numerical methods，we use cell-centered finite volume upwind method，and the inviscid flux vector is computed by Roe’s flux difference splitting 。In order to raise the level of the space difference scheme，we use Frink cell reconstruction schemes。The four-stage Runge-Kutta scheme is used to achieve the time integration。To accelerate the convergence，local time stepping and residual smoothing are utilized。Finally，we can endvince that the conservative Euler equation after preconditioning have better pressure contours diagrams。

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