Vérité et amour : une lecture de "La théologique" de Hans Urs von Balthasar

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EXPERIMENTAL AND NUMERICAL INVESTIGATION OF TURBULENT AIR FLOW BEHAVIOUR IN A ROTOR-STATOR CAVITY

International audienceThe present work considers the turbulent air flow inside an annular high speed rotor-stator cavity opened to the atmosphere at the periphery. The interdisk-spacing is sufficiently large so that the boundary layers developed on each disk are separated and the flow belongs to the regime IV of Daily and Nece (1960). In such a system, the solid body rotation of the core predicted by Batchelor in case of infinite disks is not always observed: the flow behavior in the whole interdisk-spacing is governed by the level of the pre-swirl velocity of the fluid which is closely linked to the peripheral geometry (Debuchy et al (2007)). In the first part of the paper, experimental results including mean radial and tangential velocity components, as well as three turbulent correlations, are presented for several peripheral boundary conditions leading to the same value of the pre-swirl ratio. Measurements are performed by hot-wire probes introduced through the stator and connected to a constant temperature anemometer. In the second part, comparisons between experiments and numerical results are provided. The numerical approach is based on one-point statistical modeling using a low Reynolds number second-order full stress transport closure derived from the Launder and Tselepidakis model (1994) and sensitized to rotation effects (Elena and Schiestel 1996). The aim is to find what type of boundary conditions imposed in the RSM provides the best agreement for this set of flow control parameters

Influence of a weak superposed centripetal flow in a rotor-stator system for several pre-swirl ratios

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Analyse des écoulements inter-disques en vue d'optimiser les poussées axiales dans les machines hydrauliques utilisées en station hydro-électrique

The properties of the turbulent flow confined in a cavity delimited by two parallel coaxial disks, one of which is in rotation, are very sensitive to the peripheral geometry of the system. Recent studies have shown that the solid body rotation flow predicted by the theory of Batchelor is not systematically observed when the cavity is isolated, i.e. without superimposed flow. The objective of this thesis is to better understand this phenomenon and extend the study to the case of the cavity with superimposed centripetal inflow. The first part of the work handles with the theoretical aspects of the problem. A first conservation of mass of exchange of fluid is made from stationary solutions of the flow in the boundary layers, developed by von Kármán and Bödewadt. These solutions are coupled with new hypotheses to take account of circulation of flow outside the boundary layers and the rate of pre-swirl velocity. We obtain analytical solutions for the radial distributions of swirl ratio in the central core, of the static pressure on the stationary wall and of total pressure at the mid-high of the cavity, for the both cases with or without superposed radial inflow. The second part is dedicated to the experimental and numerical "tools" needed to validate these theoretical solutions. This chapter includes firstly the description of the experimental setup, techniques of measurements, and the program of case studied in the framework of this thesis. Numerical simulations are performed using the industrial computing code FLUENT. Details regarding the choice of computational domain, grid mesh, boundary conditions and turbulence model used are provided secondly. The validation of theoretical solutions is the subject of the last two chapters, devoted respectively to the cases of isolated cavities and of systems with superposed centripetal radial inflow. The agreement between the experiment, the numerical results and theory is generally very good, what comforts us on choosing the basic assumptions. The analysis of the results leads in particularly to understand the mechanism of apparition of the solid body rotation flow provided by Batchelor. However, the use of models is not universal because it requires adjustment of constants, for which we are trying to identify the most general empirical relationships possible.Les propriétés de l'écoulement turbulent confiné dans une cavité délimitée par deux disques parallèles coaxiaux dont l'un est en rotation sont très sensibles à la géométrie périphérique du système. De récentes études ont montré que l'écoulement en bloc prévu par la théorie de Batchelor n'est pas systématiquement observé lorsque la cavité est isolée, c'est à dire non soumise à un flux forcé. L'objectif de cette thèse est de mieux comprendre ce phénomène et d'étendre le cadre de l'étude au cas d'un écoulement centripète forcé. La première partie du travail aborde l'aspect théorique du problème. Un premier bilan des échanges de fluide dans les couches limites est réalisé à partir des solutions stationnaires de l'écoulement sur un disque, développées par von Kármán et Bödewadt. Ces solutions sont couplées à de nouvelles hypothèses permettant de tenir compte des échanges de flux hors couches limites et du taux de pré-rotation du fluide. Nous obtenons ainsi des solutions analytiques originales pour les distributions radiales du coefficient d'entraînement du fluide dans le noyau central, de la pression statique pariétale et de la pression totale, que la cavité soit isolée ou soumise à un flux radial forcé. La seconde partie est consacrée aux moyens expérimentaux et numériques nécessaires à la validation de ces solutions théoriques. Elle inclut d'abord une description de l'installation expérimentale, des techniques de mesure, et du programme d'essais réalisé dans le cadre de cette thèse. Les simulations numériques sont réalisées à l'aide du code de calcul industriel FLUENT. Les détails concernant le choix du domaine de calcul, le maillage, les conditions aux limites et le modèle de turbulence retenus sont ensuite fournis. La validation des solutions théoriques fait l'objet des deux derniers chapitres, respectivement consacrés aux cas de la cavité isolée et soumise à un écoulement centripète forcé. L'accord obtenu entre l'expérience, les résultats numériques et la théorie est généralement très bon, ce qui nous conforte dans le choix de nos hypothèses. L'analyse des résultats permet en particulier de comprendre le mécanisme d'apparition de l'écoulement en bloc prévu par Batchelor. Toutefois, l'utilisation des modèles n'est pas universelle car elle nécessite l'ajustement de constantes, pour lesquelles nous tentons de dégager des relations empiriques les plus générales, dans la mesure du possible

On the Flow Behavior in Rotor-Stator System with Superposed Flow

The flow between a rotor and a stator at high Reynolds number and small Ekman number is divided into three domains, two boundary layers adjacent to the discs separated by a central core. In the present work, a simple theoretical approach provides analytical solutions for the radial distribution of the core swirl ratio valid for a rotor-stator system with a superposed radial inflow rate. At first, the flow in the rotor boundary layer is assumed to behave as expressed by Owen and Rogers (1989) in the case of a turbulent flow on a rotating single disc. On the stator side, a necessary compensation flow rate must take place according to the conservation of mass. It is found that this compensation flow rate cannot be estimated with a good accuracy using the hypotheses of a stationary disc in a rotating fluid by Owen and Rogers (1989). Thus, two innovative weighting functions are tested, leading to new analytical laws relating the core swirl ratio K to the coefficient of flow rate Cqr introduced by Poncet et al. (2005). The adequacy between the theoretical solutions and numerous results of the literature is clearly improved and the discussion allows a better understanding of the flow behavior

Analyse des écoulements inter-disques en vue d'optimiser les poussées axiales dans les machines hydrauliques utilisées en station hydro-électrique

Les propriétés de l'écoulement turbulent confiné dans une cavité délimitée par deux disques parallèles coaxiaux dont l'un est en rotation sont très sensibles à la géométrie périphérique du système. De récentes études ont montré que l'écoulement en bloc prévu par la théorie de Batchelor n'est pas systématiquement observé lorsque la cavité est isolée, c'est à dire non soumise à un flux forcé. L'objectif de cette thèse est de mieux comprendre ce phénomène et d'étendre le cadre de l'étude au cas d'un écoulement centripète forcé. La première partie du travail aborde l'aspect théorique du problème. Un premier bilan des échanges de fluide dans les couches limites est réalisé à partir des solutions stationnaires de l'écoulement sur un disque, développées par von Kármán et Bödewadt. Ces solutions sont couplées à de nouvelles hypothèses permettant de tenir compte des échanges de flux hors couches limites et du taux de pré-rotation du fluide. Nous obtenons ainsi des solutions analytiques originales pour les distributions radiales du coefficient d'entraînement du fluide dans le noyau central, de la pression statique pariétale et de la pression totale, que la cavité soit isolée ou soumise à un flux radial forcé. La seconde partie est consacrée aux moyens expérimentaux et numériques nécessaires à la validation de ces solutions théoriques. Elle inclut d'abord une description de l'installation expérimentale, des techniques de mesure, et du programme d'essais réalisé dans le cadre de cette thèse. Les simulations numériques sont réalisées à l'aide du code de calcul industriel FLUENT. Les détails concernant le choix du domaine de calcul, le maillage, les conditions aux limites et le modèle de turbulence retenus sont ensuite fournis. La validation des solutions théoriques fait l'objet des deux derniers chapitres, respectivement consacrés aux cas de la cavité isolée et soumise à un écoulement centripète forcé. L'accord obtenu entre l'expérience, les résultats numériques et la théorie est généralement très bon, ce qui nous conforte dans le choix de nos hypothèses. L'analyse des résultats permet en particulier de comprendre le mécanisme d'apparition de l'écoulement en bloc prévu par Batchelor. Toutefois, l'utilisation des modèles n'est pas universelle car elle nécessite l'ajustement de constantes, pour lesquelles nous tentons de dégager des relations empiriques les plus générales, dans la mesure du possible.The properties of the turbulent flow confined in a cavity delimited by two parallel coaxial disks, one of which is in rotation, are very sensitive to the peripheral geometry of the system. Recent studies have shown that the solid body rotation flow predicted by the theory of Batchelor is not systematically observed when the cavity is isolated, i.e. without superimposed flow. The objective of this thesis is to better understand this phenomenon and extend the study to the case of the cavity with superimposed centripetal inflow. The first part of the work handles with the theoretical aspects of the problem. A first conservation of mass of exchange of fluid is made from stationary solutions of the flow in the boundary layers, developed by von Kármán and Bödewadt. These solutions are coupled with new hypotheses to take account of circulation of flow outside the boundary layers and the rate of pre-swirl velocity. We obtain analytical solutions for the radial distributions of swirl ratio in the central core, of the static pressure on the stationary wall and of total pressure at the mid-high of the cavity, for the both cases with or without superposed radial inflow. The second part is dedicated to the experimental and numerical "tools" needed to validate these theoretical solutions. This chapter includes firstly the description of the experimental setup, techniques of measurements, and the program of case studied in the framework of this thesis. Numerical simulations are performed using the industrial computing code FLUENT. Details regarding the choice of computational domain, grid mesh, boundary conditions and turbulence model used are provided secondly. The validation of theoretical solutions is the subject of the last two chapters, devoted respectively to the cases of isolated cavities and of systems with superposed centripetal radial inflow. The agreement between the experiment, the numerical results and theory is generally very good, what comforts us on choosing the basic assumptions. The analysis of the results leads in particularly to understand the mechanism of apparition of the solid body rotation flow provided by Batchelor. However, the use of models is not universal because it requires adjustment of constants, for which we are trying to identify the most general empirical relationships possible.PARIS-Arts et Métiers (751132303) / SudocSudocFranceF

An Analytical Modeling of the Central Core Flow in a Rotor-Stator System With Several Preswirl Conditions

International audienceAuthor(s): Roger Debuchy IUT de Béthune, Laboratoire de Mécanique de Lille UMR 8107, PRES Université Nord de France, 1230 Rue de l'université BP 819, 62408 Béthune Cedex, France Fadi Abdel Nour and Gérard Bois Arts et Métiers ParisTech, Laboratoire de Mécanique de Lille UMR 8107, PRES Université Nord de France, 8, Boulevard Louis XIV, 59046 Lille Cedex, France In the most part of an enclosed rotor-stator system with separated boundary layers, the flow structure is characterized by a central core rotating as a solid body with a constant core-swirl ratio. This behavior is not always observed in an isolated rotor-stator cavity, i.e., without any centripetal or centrifugal throughflow, opened to the atmosphere at the periphery: Recent works have brought to evidence an increasing level of the core-swirl ratio from the periphery to the axis, as in the case of a rotor-stator with superposed centripetal flow. The present work is based on an asymptotical approach in order to provide a better understanding of this process. Assuming that the boundary layers behave as on a single rotating disk in a stationary fluid on the rotor side, and on a stationary disk in a rotating fluid on the stator side, new analytical relations are obtained for the core-swirl ratio, the static pressure on the stator, and also the total pressure at midheight of the cavity. An experimental study is performed: Detailed measurements provide data for several values of the significant dimensionless parameters: 1.14<=10−6×Re<=1.96, 0.05<=G<=0.10, and 0.07<=104×Ek<=2.65. The analysis of the results shows a good agreement between the theoretical solution and the experimental results. The analytical model can be used to provide a better understanding of the flow features. In addition, radial distributions of both core-swirl ratio, dimensionless static pressure on the stator, as well as dimensionless total pressure at midheight of the cavity, which are of interest to the designers, can be computed with an acceptable accuracy knowing the levels of the preswirl coefficient Kp and the solid body rotation swirl coefficient KB

Influence of Peripheral Opening on the Central Core Flow Behaviour in a Rotor-Stator System

International audienceThis work relates to an experimental, theoretical and numerical study of a turbulent flow with separated boundary layers between a rotating disc (rotor) and a stationary one (stator) without any superposed radial flow. The originality of this study is that the pre-swirl ratio at the periphery of the cavity (Kp) is lower than the core swirl ratio (KB) corresponding to the solid body rotation, as predicted by Batchelor in the case of infinite discs: this is what the authors call a rotor-stator system with low pre-swirl ratio. Under these conditions, recent works have shown that the core swirl ratio (K) is a decreasing function of the radius, at least in the peripheral region. This behaviour has rather been observed in the cavities with superposed centripetal radial flow. In the present paper, this flow property is explained starting from an asymptotic approach which leads to step-by-step analytical computation method of the radial distribution of the core swirl ratio (K) and of the static pressure on the stator side p*. The validation of the theory is based both on experimental and numerical results. The experimental tests are carried out in a rotor-stator cavity for different values of the pre-swirl ratio, which is done by geometrical changes of the periphery of the system. The experimental data mostly include the velocity measurements and the turbulent correlations by hot-wire anemometry in interstice between the discs, as well as the static pressure measurements on the stator side. Comparisons with predictions from the CFD code Fluent are also provided. The numerical simulations are performed using the two-equation k – ω SST turbulence model, assuming a 2D-axisymmetric steady flow, in a domain corresponding to the inter-disks spacing and the peripheral outer region of the cavity. Computed and experimental values are in good agreement with the theoretical results