This paper develops the discrete adjoint equations for a turbomachinery Reynolds-averaged Navier–Stokes solver and proposes a framework for fully automatic gradient-based constrained aerodynamic shape optimization in a multistage turbomachinery environment. The systematic approach for the development of the discrete adjoint solver is discussed. Special emphasis is put on the development of the turbomachinery-specific features of the adjoint solver (that is, on the derivation of flow-consistent adjoint inlet and outlet boundary conditions) and, to allow for a concurrent rotor–stator optimization and stage coupling, on the development of an exact adjoint counterpart to the nonreflective, conservative mixing-plane formulation used in the flow solver. The adjoint solver is validated by comparing its sensitivities with finite difference gradients obtained from the flow solver. A sequential-quadratic programming algorithm is used to determine an improved blade shape based on the gradient information provided by the adjoint solution. Optimization within a sequential-quadratic programming framework avoids the time-consuming task to determine the weights of the individual constraints by including the constraints directly into the design problem. The functionality of the proposed optimization method is demonstrated by the redesign of two two-dimensional transonic compressor configurations. The design objective is to maximize the isentropic efficiency while constraining the mass flow rate and the total pressure ratio.


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    Titel :

    Adjoint-Based Constrained Aerodynamic Shape Optimization for Multistage Turbomachines


    Beteiligte:

    Erschienen in:

    Erscheinungsdatum :

    2015-06-08


    Format / Umfang :

    22 pages




    Medientyp :

    Aufsatz (Zeitschrift)


    Format :

    Elektronische Ressource


    Sprache :

    Englisch





    An Adjoint-Based Optimization Method for Multistage Turbomachines

    Nadarajah, S. / Walther, B. | British Library Conference Proceedings | 2013


    Constrained Adjoint-Based Aerodynamic Shape Optimization in a Multistage Turbomachinery Environment

    Walther, B. / Nadarajah, S. / American Institute of Aeronautics and Astronautics | British Library Conference Proceedings | 2012