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dc.contributor.authorXie, Leien_US
dc.date.accessioned2014-03-14T20:10:53Z
dc.date.available2014-03-14T20:10:53Z
dc.date.issued2002-04-12en_US
dc.identifier.otheretd-04262002-101328en_US
dc.identifier.urihttp://hdl.handle.net/10919/27306
dc.description.abstractContinuous 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 logarithmic 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. 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.en_US
dc.publisherVirginia Techen_US
dc.relation.haspartetd.pdfen_US
dc.rightsI hereby certify that, if appropriate, I have obtained and attached hereto a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to Virginia Tech or its agents the non-exclusive license to archive and make accessible, under the conditions specified below, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report.en_US
dc.subjectOptimum aerodynamic designen_US
dc.subjectBoundary conditionsen_US
dc.subjectAdjoint methoden_US
dc.subjectTransonic airfoil designen_US
dc.titleGradient-Based Optimum Aerodynamic Design Using Adjoint Methodsen_US
dc.typeDissertationen_US
dc.contributor.departmentAerospace and Ocean Engineeringen_US
dc.description.degreePh. D.en_US
thesis.degree.namePh. D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen_US
thesis.degree.disciplineAerospace and Ocean Engineeringen_US
dc.contributor.committeechairCliff, Eugene M.en_US
dc.contributor.committeememberMason, William H.en_US
dc.contributor.committeememberGrossman, Bernard M.en_US
dc.contributor.committeememberBorggaard, Jeffrey T.en_US
dc.contributor.committeememberDevenport, William J.en_US
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-04262002-101328/en_US
dc.date.sdate2002-04-26en_US
dc.date.rdate2003-05-02
dc.date.adate2002-05-02en_US


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