Geodesic
Maximization of the lift/drag ratio of airfoils with a turbulent boundary layer: Sharp estimates, approximation, and numerical solutions
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 3, pp. 578-592 
A. M. Elizarov; A. N. Kalimullina. Maximization of the lift/drag ratio of airfoils with a turbulent boundary layer: Sharp estimates, approximation, and numerical solutions. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 3, pp. 578-592. http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_3_a15/
@article{ZVMMF_2009_49_3_a15,
     author = {A. M. Elizarov and A. N. Kalimullina},
     title = {Maximization of the lift/drag ratio of airfoils with a turbulent boundary layer: {Sharp} estimates, approximation, and numerical solutions},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {578--592},
     year = {2009},
     volume = {49},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_3_a15/}
}
TY  - JOUR
AU  - A. M. Elizarov
AU  - A. N. Kalimullina
TI  - Maximization of the lift/drag ratio of airfoils with a turbulent boundary layer: Sharp estimates, approximation, and numerical solutions
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2009
SP  - 578
EP  - 592
VL  - 49
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_3_a15/
LA  - ru
ID  - ZVMMF_2009_49_3_a15
ER  - 
%0 Journal Article
%A A. M. Elizarov
%A A. N. Kalimullina
%T Maximization of the lift/drag ratio of airfoils with a turbulent boundary layer: Sharp estimates, approximation, and numerical solutions
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2009
%P 578-592
%V 49
%N 3
%U http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_3_a15/
%G ru
%F ZVMMF_2009_49_3_a15

Voir la notice de l'article provenant de la source Math-Net.Ru

The lift/drag ratio of an airfoil placed in an incompressible attached flow is maximized taking into account the viscosity in the boundary-layer approximation. An exact solution is constructed. The situation when the resulting solutions are not in the admissible class of univalent flows is discussed. A procedure is proposed for determining physically feasible airfoils (with a univalent flow region) with a high lift/drag ratio. For this purpose, a class of airfoils is constructed that are determined by a twoparameter function approximating the found exact solution to the variational problem. For this class, the ranges of free parameters leading to physically feasible flows are found. The results are verified by computing a turbulent boundary layer using Eppler's method, and airfoils with a high lift/drag ratio in an attached flow are detected.

[1] Elizarov A. M., “Tochnye resheniya nekotorykh zadach aerodinamicheskoi optimizatsii”, Modeli mekhan. sploshnoi sredy. Obzornye dokl. i lektsii XVII sessii Mezhdunar. shkoly po modelyam mekhan. sploshnoi sredy (Kazan, 4–10 iyulya 2004 goda), Tr. Matem. tsentra im. N. I. Lobachevskogo, 22, Izd-vo Kazanskogo matem. ob-va, Kazan, 2004, 13–54

[2] Elizarov A. M., Ilinskii N. B., Potashev A. B., Obratnye kraevye zadachi aerogidrodinamiki: teoriya i metody proektirovaniya i optimizatsii formy krylovykh profilei, Fizmatlit, M., 1994 | MR | Zbl

[3] Haslinger J., Neittaanmaki P., Finite element approximation for optimal shape design: theory and application, John Wiley and Sons Ltd., New York, 1988 | MR | Zbl

[4] Pironneau O., Optimal shape design for elliptic systems, Springer Lect. Notes in Comput. Phys., Springer, New York, 1984 | MR | Zbl

[5] Sirazetdinov T. K., Optimizatsiya sistem s raspredelennymi parametrami, Nauka, M., 1977 | MR

[6] Elizarov A. M., Ilinskii N. B., Potashev A. B., Stepanov G. Yu., Osnovnye metody, rezultaty, prilozheniya i nereshennye problemy teorii obratnykh kraevykh zadach aerogidrodinamiki, Tr. Matem. tsentra im. N. I. Lobachevskogo, 10, DAS, Kazan, 2001 | MR | Zbl

[7] Aksentev L. A., Ilinskii N. B., Nuzhin M. T. i dr., “Teoriya obratnykh kraevykh zadach dlya analiticheskikh funktsii i ee prilozheniya”, Itogi nauki i tekhn. Matem. analiz, 18, VINITI, M., 1980, 67–124 | MR

[8] Loitsyanskii L. G., Mekhanika zhidkosti i gaza, Nauka, M., 1987 | MR

[9] Stepanov G. Yu., Gidrodinamika reshetok turbomashin, Fizmatgiz, M., 1962

[10] Shlikhting G., Teoriya pogranichnogo sloya, Nauka, M., 1974

[11] Bam-Zelikovich G. M., “Raschet otryva pogranichnogo sloya”, Izv. AN SSSR. Otd. tekhn. nauk, 1954, no. 12, 68–85

[12] Elizarov A. M., Il'inskiy N. B., Potashev A. V., Mathematical methods of airfoils design. Inverse boundary-value problems of aerohydrodynamics, Wiley-VCH, Berlin, 1997 | MR

[13] Ilinskii A. H., Ilinskii H. B., Polyakov D. V. i dr., Utochnenie kriteriya otryva turbulentnogo pogranichnogo sloya s ispolzovaniem empiricheskikh dannykh, Preprint No 98-2, Kazan, 1998, 62 pp.

[14] Elizarov A. M., “Nekotorye ekstremalnye zadachi teorii kryla”, Izv. vuzov. Matematika, 1988, no. 10, 71–74 | MR

[15] Fokin D. A., “Maksimizatsiya aerodinamicheskogo kachestva krylovykh profilei s turbulentnym pogranichnym sloem”, Izv. RAN. Mekhan. zhidkosti i gaza, 1998, no. 3, 177–184 | Zbl

[16] Elizarov A. M., Fëdorov E. V., “Reshenie variatsionnykh obratnykh kraevykh zadach aerogidrodinamiki metodami chislennoi optimizatsii”, Zh. prikl. mekhan. i tekhn. fiz., 1993, no. 2, 73–80 | MR

[17] Liebeck R. H., A class of airfoils designed for high lift in incompressible flow, AIAA Paper. no 86, 1973

[18] Elizarov A. M., Fokin D. A., “Upper estimates of airfoil aerodynamic characteristics for a viscous incompressible flow”, Z. Angew. Math. und Mech., 79:11 (1999), 757–762 | 3.0.CO;2-V class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI | MR | Zbl

[19] Ilinskii A. H., Potashev A. B., “Reshenie obratnoi kraevoi zadachi aerogidrodinamiki s uchetom pogranichnogo sloya”, Izv. AN SSSR. Mekhanika zhidkosti i gaza, 1989, no. 4, 28–32

[20] Eppler R., Airfoil design and data, Springer, Berlin, 1990