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Research Papers

Three-Dimensional Aerodynamic Design Optimization of a Turbine Blade by Using an Adjoint Method

[+] Author and Article Information
Jiaqi Luo1

Department of Mechanical and Aerospace Engineering, University of California, Irvine, Irvine, CA 92697-3975jiaqil@uci.edu

Juntao Xiong

Department of Mechanical and Aerospace Engineering, University of California, Irvine, Irvine, CA 92697-3975

Feng Liu

Department of Mechanical and Aerospace Engineering, University of California, Irvine, Irvine, CA 92697-3975fliu@uci.edu

Ivan McBean

 Alstom Power (Switzerland), Baden 5401, Switzerland

1

Visiting Student from Department of Fluid Mechanics, Northwestern Polytechnical University, Xi’an 710072, China.

J. Turbomach 133(1), 011026 (Sep 27, 2010) (11 pages) doi:10.1115/1.4001166 History: Received May 14, 2009; Revised June 26, 2009; Published September 27, 2010; Online September 27, 2010

This paper presents the application of an adjoint method to the aerodynamic design optimization of a turbine blade. With the adjoint method, the complete gradient information needed for optimization can be obtained by solving the governing flow equations and their corresponding adjoint equations only once, regardless of the number of design parameters. The formulations including imposition of appropriate boundary conditions for the adjoint equations of the Euler equations for turbomachinery problems are presented. Two design cases are demonstrated for a turbine cascade that involves a high tip flare, characteristic of steam turbine blading in low-pressure turbines. The results demonstrate that the design optimization method is effective and the redesigned blade yields weaker shock and compression waves in the supersonic region of the flow while satisfying the specified constraint. The relative effects of changing blade profile stagger, modifying the blade profile shape, and changing both stagger and profile shape at the same time are examined and compared. Navier–Stokes calculations are performed to confirm the performance at both the design and off-design conditions of the blade designed by the Euler method.

Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

Configuration of a typical low-pressure turbine stator

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Figure 2

Transformation of annular cascade onto an auxiliary surface

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Figure 3

Rigid rotation of blade section

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Figure 4

Cost function versus design cycle

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Figure 5

Exit flow angle before and after design

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Figure 6

Designed change in stagger angle distribution

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Figure 7

Total pressure, efficiency, and entropy versus design cycle with turning angle constraint

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Figure 8

Turning angle and mass flow rate versus design cycle with turning angle constraint

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Figure 9

Spanwise total pressure distribution

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Figure 10

Spanwise adiabatic efficiency distribution

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Figure 11

Spanwise turning angle distribution

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Figure 12

Spanwise distribution of stagger angle change

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Figure 13

Blade profile at K=17

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Figure 14

Blade isentropic Mach number distribution at K=17

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Figure 15

Mach number contours at K=17

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Figure 16

Mach number contours on blade suction surface

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Figure 17

Pitch-averaged total pressure contours

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Figure 18

Comparisons of total pressure ratio and efficiency of both reference and designed blades

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Figure 19

Variations of adiabatic efficiency gains predicted by the Euler and NS flow calculations

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Figure 20

Total pressure, efficiency, and entropy versus design cycle with mass flow constraint

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Figure 21

Turning angle and mass flow rate versus design cycle with mass flow constraint

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Figure 22

Spanwise distribution of stagger angle change

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