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Gradient-based optimum aerodynamic d...

Xie, Lei.

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Gradient-based optimum aerodynamic design using adjoint methods.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Gradient-based optimum aerodynamic design using adjoint methods./
Author:	Xie, Lei.
Description:	128 p.
Notes:	Source: Dissertation Abstracts International, Volume: 63-03, Section: B, page: 1442.
Contained By:	Dissertation Abstracts International63-03B.
Subject:	Engineering, Aerospace. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3047999
ISBN:	0493622837

Gradient-based optimum aerodynamic design using adjoint methods.
Xie, Lei.

Gradient-based optimum aerodynamic design using adjoint methods. - 128 p.

Source: Dissertation Abstracts International, Volume: 63-03, Section: B, page: 1442.

Thesis (Ph.D.)--Virginia Polytechnic Institute and State University, 2002.

Continuous adjoint methods and optimal control theory are applied to a pressure-matching inverse design problem of quasi 1-D nozzle flows. Pontryagin's Minimum Principle is used to derive the adjoint system and the reduced gradient of the cost functional. The properties of adjoint variables at the sonic throat and the shock location are studied, revealing a log-arithmic singularity at the sonic throat and continuity at the shock location. A numerical method, based on the Steger-Warming flux-vector-splitting scheme, is proposed to solve the adjoint equations. This scheme can finely resolve the singularity at the sonic throat. A non-uniform grid, with points clustered near the throat region, can resolve it even better. The analytical solutions to the adjoint equations are also constructed via Green's function approach for the purpose of comparing the numerical results. The pressure-matching inverse design is then conducted for a nozzle parameterized by a single geometric parameter.

ISBN: 0493622837Subjects--Topical Terms:

1018395
Engineering, Aerospace.

Gradient-based optimum aerodynamic design using adjoint methods.
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245 1 0 $a Gradient-based optimum aerodynamic design using adjoint methods.
300 $a 128 p.
500 $a Source: Dissertation Abstracts International, Volume: 63-03, Section: B, page: 1442.
500 $a Chair: Eugene M. Cliff.
502 $a Thesis (Ph.D.)--Virginia Polytechnic Institute and State University, 2002.
520 $a Continuous adjoint methods and optimal control theory are applied to a pressure-matching inverse design problem of quasi 1-D nozzle flows. Pontryagin's Minimum Principle is used to derive the adjoint system and the reduced gradient of the cost functional. The properties of adjoint variables at the sonic throat and the shock location are studied, revealing a log-arithmic singularity at the sonic throat and continuity at the shock location. A numerical method, based on the Steger-Warming flux-vector-splitting scheme, is proposed to solve the adjoint equations. This scheme can finely resolve the singularity at the sonic throat. A non-uniform grid, with points clustered near the throat region, can resolve it even better. The analytical solutions to the adjoint equations are also constructed via Green's function approach for the purpose of comparing the numerical results. The pressure-matching inverse design is then conducted for a nozzle parameterized by a single geometric parameter.
520 $a In the second part, the adjoint methods are applied to the problem of minimizing drag coefficient, at fixed lift coefficient, for 2-D transonic airfoil flows. Reduced gradients of several functionals are derived through application of a Lagrange Multiplier Theorem. The adjoint system is carefully studied including the adjoint characteristic boundary conditions at the far-field boundary. A super-reduced design formulation is also explored by treating the angle of attack as an additional state; super-reduced gradients can be constructed either by solving adjoint equations with non-local boundary conditions or by a direct Lagrange multiplier method. In this way, the constrained optimization reduces to an unconstrained design problem. Numerical methods based on Jameson's finite volume scheme are employed to solve the adjoint equations. The same grid system generated from an efficient hyperbolic grid generator are adopted in both the Euler flow solver and the adjoint solver. Several computational tests on transonic airfoil design are presented to show the reliability and efficiency of adjoint methods in calculating the reduced (super-reduced) gradients.
590 $a School code: 0247.
650 4 $a Engineering, Aerospace. $3 1018395
690 $a 0538
710 2 0 $a Virginia Polytechnic Institute and State University. $3 1017496
773 0 $t Dissertation Abstracts International $g 63-03B.
790 1 0 $a Cliff, Eugene M., $e advisor
790 $a 0247
791 $a Ph.D.
792 $a 2002
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3047999