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Zh. Vychisl. Mat. Mat. Fiz., 2010, Volume 50, Number 9, Pages 1624–1631 (Mi zvmmf4936)  

This article is cited in 5 scientific papers (total in 5 papers)

Effective direct methods in problem of the construction of optimal aerodynamic shapes

A. A. Kraĭko, K. S. P'yankov

Baranov Central Institute for Aircraft Engine Design (TsIAM), Aviamotornaya ul. 2, Moscow, 111116 Russia

Abstract: A direct method for aerodynamic shape optimization based on the use of Bézier spline approximation is proposed. The method is tested as applied to the optimization of the supersonic part of an axisymmetric de Laval nozzle. The optimization results are compared with the exact solution obtained by the control contour method (variational nozzle) and with nozzles constructed using another direct method, namely, local linearization. It is shown that both direct optimization methods can be used on rather coarse grids without degrading the accuracy of the solution. The optimization procedure involves the isoperimetric condition that the surface area of the nozzle is given and fixed, which prevents the use of the control contour method. Optimization with allowance for viscosity is performed using the method. For fairly short maximum possible nozzle lengths in the range of Reynolds numbers under consideration, it is shown that allowance for viscosity does not improve the nozzle shape produced by optimization based on the Euler equations. The role of viscosity is reduced to the determination of an optimal length.

Key words: de Laval nozzle, Bézier spline, direct optimization methods, local linearization method, viscosity.

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English version:
Computational Mathematics and Mathematical Physics, 2010, 50:9, 1546–1552

Bibliographic databases:

UDC: 519.626
Received: 07.07.2009
Revised: 15.03.2010

Citation: A. A. Kraǐko, K. S. P'yankov, “Effective direct methods in problem of the construction of optimal aerodynamic shapes”, Zh. Vychisl. Mat. Mat. Fiz., 50:9 (2010), 1624–1631; Comput. Math. Math. Phys., 50:9 (2010), 1546–1552

Citation in format AMSBIB
\by A.~A.~Kra{\v\i}ko, K.~S.~P'yankov
\paper Effective direct methods in problem of the construction of optimal aerodynamic shapes
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2010
\vol 50
\issue 9
\pages 1624--1631
\jour Comput. Math. Math. Phys.
\yr 2010
\vol 50
\issue 9
\pages 1546--1552

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    This publication is cited in the following articles:
    1. N. P. Isakova, A. A. Kraiko, K. S. P'yankov, “Direct method for the design of optimal three-dimensional aerodynamic shapes”, Comput. Math. Math. Phys., 52:11 (2012), 1520–1525  mathnet  crossref  mathscinet  isi  elib  elib
    2. Bazhenov V.G. Balandin V.V. Grigoryan S.S. Kotov V.L., “Analysis of Models for Calculating the Motion of Solids of Revolution of Minimum Resistance in Soil Media”, Pmm-J. Appl. Math. Mech., 78:1 (2014), 65–76  crossref  mathscinet  isi  scopus
    3. Kraiko A.A. P'yankov K.S., “Contouring Optimal Three-Dimensional Nozzles”, Fluid Dyn., 49:1 (2014), 120–130  crossref  mathscinet  isi  elib  scopus
    4. E. Yu. Linnik, “Chislennyi raschet optimalnoi formy tela vrascheniya pri pronikanii v gruntovye sredy”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 156, no. 2, Izd-vo Kazanskogo un-ta, Kazan, 2014, 95–101  mathnet
    5. Qu X., Zhang R., Liu B., Li H., “An improved TLBO based memetic algorithm for aerodynamic shape optimization”, Eng. Appl. Artif. Intell., 57 (2017), 1–15  crossref  isi  elib  scopus
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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