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Research Papers

An Efficient Unsteady Adjoint Optimization System for Multistage Turbomachinery

[+] Author and Article Information
Can Ma

Key Laboratory for Thermal Science and Power
Engineering of Ministry of Education,
Tsinghua University,
Beijing 100084, China
e-mail: macan1234@sina.com

Xinrong Su

Assistant Professor
Mem. ASME
Key Laboratory for Thermal Science and Power
Engineering of Ministry of Education,
Tsinghua University,
Beijing 100084, China
e-mail: suxr@mail.tsinghua.edu.cn

Xin Yuan

Professor
Mem. ASME
Key Laboratory for Thermal Science and Power
Engineering of Ministry of Education,
Tsinghua University,
Beijing 100084, China
e-mail: yuanxin@mail.tsinghua.edu.cn

1Corresponding author.

Manuscript received November 13, 2015; final manuscript received June 21, 2016; published online September 8, 2016. Assoc. Editor: Li He.

J. Turbomach 139(1), 011003 (Sep 08, 2016) (12 pages) Paper No: TURBO-15-1258; doi: 10.1115/1.4034185 History: Received November 13, 2015; Revised June 21, 2016

Unsteady blade row interactions play an important role in the performance of multistage turbomachinery. However, most aerodynamic optimizations of multistage turbomachinery are based on mixing-plane steady flow simulations. To take into account the unsteady flow features in the optimization cycle, this paper develops an adjoint-based unsteady aerodynamic optimization system for multistage turbomachinery. To the authors' best knowledge, this is the first work in the literature conducting the unsteady adjoint aerodynamic optimization of multistage turbomachinery. The unsteady flow equations and the discrete adjoint equations are solved using a finite volume code, with the harmonic balance method adopted to reduce the cost of unsteady simulations. The system is applied to the unsteady aerodynamic optimization of a 1.5-stage compressor. Results show the efficiency and capability of the proposed framework for the unsteady aerodynamic optimization of multistage turbomachinery.

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Figures

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Fig. 1

Adjoint phase-lagged boundary condition

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Fig. 2

Adjoint sliding-mesh boundary condition

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Fig. 3

Optimization system flow chart

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Fig. 4

FFD control grid and geometric modification of a compressor airfoil

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Fig. 5

Grid modification after geometric modification of the compressor airfoil

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Fig. 6

Close-up of the NACA 0012 airfoil mesh

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Fig. 7

Gradients of the drag coefficient with respect to the airfoil y-coordinates, time periodic flow over the NACA 0012 airfoil

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Fig. 8

Mesh of the 1.5-stage compressor used in the optimizations and every two points are shown for clarity

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Fig. 9

FFD control grid of the compressor rotor

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Fig. 10

Instantaneous relative Mach number and entropy distributions of the original design, HB, N = 5

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Fig. 11

Relative errors of performance parameters with various number of harmonics

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Fig. 12

History of steady optimization

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Fig. 13

Rotor surface pressure coefficient distributions before and after steady optimization, steady mixing-plane model

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Fig. 14

History of unsteady optimization

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Fig. 15

Instantaneous relative Mach number and entropy distributions after optimization, HB, N = 5: (a) steady optimal and (b) unsteady optimal

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Fig. 16

Rotor surface pressure coefficient distributions before and after optimization, HB, N = 5

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Fig. 17

Mass-averaged entropy variations upstream and downstream the rotor, HB, N = 5: (a) upstream rotor and (b) downstream rotor

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Fig. 18

Performance characteristics of the compressor stage before and after optimization, HB, N = 5

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