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Research Papers

Constrained Adjoint-Based Aerodynamic Shape Optimization of a Single-Stage Transonic Compressor

[+] Author and Article Information
Benjamin Walther

e-mail: benjamin.walther@mail.mcgill.ca

Siva Nadarajah

e-mail: siva.nadarajah@mcgill.ca
Department of Mechanical Engineering,
McGill University,
Montreal, Quebec, H3A 2S6, Canada

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the Journal of Turbomachinery. Manuscript received June 28, 2012; final manuscript received August 7, 2012; published online November 2, 2012. Editor: David Wisler.

J. Turbomach 135(2), 021017 (Nov 02, 2012) (10 pages) Paper No: TURBO-12-1086; doi: 10.1115/1.4007502 History: Received June 28, 2012; Revised August 07, 2012

This paper develops a discrete adjoint formulation for the constrained aerodynamic shape optimization in a multistage turbomachinery environment. The adjoint approach for viscous internal flow problems and the corresponding adjoint boundary conditions are discussed. To allow for a concurrent rotor/stator optimization, a nonreflective adjoint mixing-plane formulation is proposed. A sequential-quadratic programming algorithm is utilized to determine an improved airfoil shape based on the objective function gradient provided by the adjoint solution. The functionality of the proposed optimization method is demonstrated by the redesign of a midspan section of a single-stage transonic compressor. The objective is to maximize the isentropic efficiency while constraining the mass flow rate and the total pressure ratio.

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Figures

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Fig. 1

Schematic mixing-plane interface

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Fig. 2

Computational grid for the investigated section (55% span) of Darmstadt Rotor No. 1

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Fig. 3

Relative Mach number contours of the baseline design of Darmstadt Rotor No. 1

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Fig. 4

The ψ1contours, objective function: entropy generation rate without constraints

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Fig. 5

Gradient for the rotor (left) and stator (right) baseline; unconstrained optimization

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Fig. 6

Shape modification of rotor and stator; unconstrained optimization

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Fig. 7

Relative Mach number contours optimized design (left), and difference in entropy field (right) δs=s0-sopt; unconstrained optimization

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Fig. 8

Normalized objective function and isentropic efficiency (left), and change in mass flow rate and total pressure ratio (right); unconstrained optimization

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Fig. 10

Relative Mach number contours optimized design (left), and difference in entropy field (right) δs=s0-sopt; constrained optimization I

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Fig. 11

Relative Mach number contours optimized design (left), and difference in entropy field (right), δs=s0-sopt; constrained optimization II

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Fig. 12

Normalized objective function and isentropic efficiency (left), and change in mass flow rate and total pressure ratio (right); constrained optimization

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Fig. 9

Shape modification rotor and stator; constrained optimization

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