Geodesic
Shape Optimization of Labyrinth Seals
International Journal of Applied Mathematics and Computer Science, Tome 10 (2000) no. 2, pp. 381-404.

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In this work, we determine the optimal shape of a labyrinth seal in a hydraulic Francis turbine. The numerical approximation of the optimal shape is obtained using shape optimization techniques. The flow is governed by Navier-Stokes equations. We first prove the existence of an optimal domain, and later we present the computation of the shape gradient which allows us to approximate numerically the optimal domain.
Keywords: shape optimization, hydraulic turbine, Navier-Stokes equations, finite element method
Mots-clés : optymalizacja, metoda elementów skończonych 
@article{IJAMCS_2000_10_2_a10,
     author = {Aboulaich, R. and Azelmat, K. and Baranger, J. and Souissi, A.},
     title = {Shape {Optimization} of {Labyrinth} {Seals}},
     journal = {International Journal of Applied Mathematics and Computer Science},
     pages = {381--404},
     publisher = {mathdoc},
     volume = {10},
     number = {2},
     year = {2000},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IJAMCS_2000_10_2_a10/}
}
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Aboulaich, R.; Azelmat, K.; Baranger, J.; Souissi, A. Shape Optimization of Labyrinth Seals. International Journal of Applied Mathematics and Computer Science, Tome 10 (2000) no. 2, pp. 381-404. http://geodesic.mathdoc.fr/item/IJAMCS_2000_10_2_a10/