Modélisation numérique et algébrique des joints labyrinthe des turbines Francis

Il existe plusieurs types de turbines hydrauliques. Selon les conditions d'operation, les geometries sont dierentes, et les technologies aussi. Les joints hydrauliques, objets de cette etude, sont presents seulement dans les turbines de type Francis. Ces turbines sont tres utilisees, partout dans le monde. Le joint hydraulique n'est pas, comme on pourrait l'imaginer, une piece assurant l'etan- cheite. Il s'agit d'un interstice entre la roue de la turbine, en rotation, et le b^ati, statique. Il est necessaire et permet d'eviter le contact entre les deux ensembles. Mais de l'eau passe a travers le joint et ne participe donc pas au processus de conversion d'energie. De plus, les frottements au sein du joint ralentissent la machine. A cause de la fuite et des frottements qu'il provoque, le joint cree une perte de rendement de la turbine. Dans une demarche d'amelioration constante de machines ayant un rendement deja tres eleve, une optimisation de chaque composante, donc des joints hydrauliques, est necessaire. C'est le but de la recherche dans laquelle s'inscrit notre etude : diminuer autant que possible les pertes au sein des joints hydrauliques des turbines Francis. An de bien se rendre compte du probleme, et de comprendre l'existence d'un joint opti- mal, un raisonnement purement analytique, mettant en jeu un ecoulement laminaire dans un joint droit, a d'abord ete mene. Il a permis d'etablir les expressions analytiques des champs de vitesse, de la pression, des pertes et de la longueur optimale en fonction des dierents para- metres du probleme dans ce cas particulier. Dierents essais avec le solveur ANSYS CFX ont ensuite ete menes an de mettre en evidence certains points necessitant une attention parti- culiere lors de la suite de l'etude. Par la suite, un modele numerique de joints labyrinthe a ete valide. Les resultats d'experiences menees dans les annees 1960 chez Dominion Engineering Works, maintenant Andritz Hydro Limitee, ont ete utilises pour cette validation. M^eme si les experiences n'etaient pas toutes utilisables, certaines ont ete reproduites numeriquement. Le modele numerique developpe utilise le modele de turbulence SST, des geometries bidimen- sionnelles axisymetriques, une repartition parabolique du maillage, des parois lisses, et une perte de charge en sortie de joint basee sur la vitesse normale. Les simulations permettent de retrouver les resultats experimentaux avec un ecart moyen de 6.5 % sur les tests consideres. Sur ces m^emes tests, plus de 60% des ecarts entre resultats numeriques et experimentaux sont inferieurs a l'incertitude experimentale. Le modele est donc utilisable pour mener des experiences numeriques dont le resultat sera dele a la realite, sur l'espace de design considere. Un plan d'experiences approprie, remplissant convenablement l'intervalle dans lequel nous nous trouvons, a ete cree en utilisant

Abstract

There are various types of hydraulic turbines. Regarding the operating conditions, geo- metries and technologies dier. Hydraulic seals are only used in Francis turbines, which are widely used. The role of hydraulic seals is not to be waterproof. Their main aim is to prevent contact between the rotating and static parts of the turbine. Although necessary, hydraulic seals create energetic losses : some uid does not ow through the runner (leakage loss) and exerts a torque on the rotor (friction loss). In a context of constant progression towards still more ecient turbines, the optimization of each part of the turbine is necessary. Our study is a part of this research seeking to decrease the losses in turbines as much as possible. In order to understand fully the problem, and to ensure an optimal seal exists, an ana- lytical study has been lead in the rst place. It establishes the analytical expressions of the speeds, pressure, losses and optimal seal length for laminar ows in straight seals. Various tests were then lead with the ANSYS CFX solver in order to highlight aspects which necessi- tate a particular attention. For example, the issues of boundary conditions and dimensionless simulations were adressed. A CFD model has then been validated. The results of the experiences lead in the sixties by Dominion Engineering Works, which later became Andritz Hydro Limited, were used in this process. Even if all the tests were not useable, some of them were reproduced numerically. The CFD model which was used features SST turbulence modeling, 2D axisymmetric geometries, parabolic mesh distributions, smooth walls, and a outlet headloss based on the normal speed. For the various tests which were considered, the average discrepancy between numerical and experimental results is 6.5%. More than 60% of the discrepancies of those simulations are below the empirical uncertainty. That is why this model can be used for numerical experiences : as long as these experiences are in the design space, their result will be coherent with reality. An appropriate space-lling design of experiments was created using the software JMP, from SAS Institute. The numerical results of 34 tests have then been modeled statistically using a quadratic polynomial taking into account interactions between various factors. The response surface obtained this way was compared to experimental results. The average discrepancy was around 7.5%. The response surface is precise enough to get an accurate estimation of the experimental results. As no other experimental data is available, nothing proves that the numerical model, and the statistical model which was obtained thanks to it, will be valid outside the design space which was considered.