This paper proposes a framework for fully automatic gradient-based constrained aerodynamic shape optimization in a multirow turbomachinery environment. The concept of adjoint-based gradient calculation is discussed and the development of the discrete adjoint equations for a turbomachinery Reynolds-averaged Navier–Stokes (RANS) solver, particularly the derivation of flow-consistent adjoint boundary conditions as well as the implementation of a discrete adjoint mixing-plane formulation, are described in detail. A parallelized, automatic grid perturbation scheme utilizing radial basis functions (RBFs), which is accurate and robust as well as able to handle highly resolved complex multiblock turbomachinery grid configurations, is developed and employed to calculate the gradient from the adjoint solution. The adjoint solver is validated by comparing its sensitivities with finite-difference gradients obtained from the flow solver. A sequential quadratic programming (SQP) algorithm is then utilized to determine an improved blade shape based on the gradient information from the objective functional and the constraints. The developed optimization method is used to redesign a single-stage transonic flow compressor in both inviscid and viscous flow. The design objective is to maximize the isentropic efficiency while constraining the mass flow rate and the total pressure ratio.
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August 2015
Research-Article
Optimum Shape Design for Multirow Turbomachinery Configurations Using a Discrete Adjoint Approach and an Efficient Radial Basis Function Deformation Scheme for Complex Multiblock Grids
Benjamin Walther,
Benjamin Walther
Department of Mechanical Engineering,
e-mail: benjamin.walther@mail.mcgill.ca
McGill University
,Montreal, QC H3A 0C3
, Canada
e-mail: benjamin.walther@mail.mcgill.ca
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Siva Nadarajah
Siva Nadarajah
Department of Mechanical Engineering,
e-mail: siva.nadarajah@mcgill.ca
McGill University
,Montreal, QC H3A 0C3
, Canada
e-mail: siva.nadarajah@mcgill.ca
Search for other works by this author on:
Benjamin Walther
Department of Mechanical Engineering,
e-mail: benjamin.walther@mail.mcgill.ca
McGill University
,Montreal, QC H3A 0C3
, Canada
e-mail: benjamin.walther@mail.mcgill.ca
Siva Nadarajah
Department of Mechanical Engineering,
e-mail: siva.nadarajah@mcgill.ca
McGill University
,Montreal, QC H3A 0C3
, Canada
e-mail: siva.nadarajah@mcgill.ca
Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the JOURNAL OF TURBOMACHINERY. Manuscript received December 9, 2014; final manuscript received December 11, 2014; published online January 28, 2015. Editor: Kenneth C. Hall.
J. Turbomach. Aug 2015, 137(8): 081006 (20 pages)
Published Online: August 1, 2015
Article history
Received:
December 9, 2014
Revision Received:
December 11, 2014
Online:
January 28, 2015
Citation
Walther, B., and Nadarajah, S. (August 1, 2015). "Optimum Shape Design for Multirow Turbomachinery Configurations Using a Discrete Adjoint Approach and an Efficient Radial Basis Function Deformation Scheme for Complex Multiblock Grids." ASME. J. Turbomach. August 2015; 137(8): 081006. https://doi.org/10.1115/1.4029550
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