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Research Papers

Concurrent Blade Aerodynamic-Aero-elastic Design Optimization Using Adjoint Method

[+] Author and Article Information
L. He

Department of Engineering Science, Osney Laboratory, Oxford University, Parks Road, Oxford OX1 3PJ, UK

D. X. Wang

 Siemens Industrial Turbomachinery Ltd., Ruston House, P.O. Box 1, Waterside South, Lincoln LN5 7FD, UK

J. Turbomach 133(1), 011021 (Sep 23, 2010) (10 pages) doi:10.1115/1.4000544 History: Received July 08, 2009; Revised July 23, 2009; Published September 23, 2010; Online September 23, 2010

Increasing aerothermal and aero-elastic performance requirements and constraints are closely linked in modern blading designs. There is thus a need for more concurrent interaction between the disciplines at earlier stages of a design process. Presented in this paper are the development, validation, and demonstration of the adjoint approach to concurrent blading aerodynamic and aero-elastic design optimizations. A nonlinear harmonic phase solution method is adopted to solve the unsteady Reynolds-averaged Navier–Stokes equations. The flow field response in terms of both the mean aerothermal performance and aero-elastic stability to a geometrical perturbation can be obtained by three “steadylike” flow solutions at three distinctive temporal phases. This unsteady flow solution method is computationally very efficient and provides a convenient and consistent base for formulating the corresponding adjoint equations. The adjoint system for the unsteady flow solver is solved effectively by a relatively simple extension of the method and techniques previously developed for a steady flow adjoint solver. As a result, the sensitivities of both the steady (time-mean) flow loss and the aerodynamic damping/forcing to detailed blade geometry changes can be very efficiently obtained by solving equivalently three steadylike adjoint equations. Several case studies are presented to illustrate the validity and effectiveness of this new concurrent approach.

Copyright © 2011 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Design optimization flow chart

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Figure 2

Pressure coefficient distributions on the blade surface (50% span)

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Figure 3

First harmonic pressure coefficient and phase angle distributions on the blade surface at 50% span

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Figure 4

Changes in aero-elastic and aerodynamic performance parameters with design cycles

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Figure 5

Blade geometry and flow field (mach number) comparison between the original and the two new designs

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Figure 6

Pressure ratio and isentropic efficiency maps

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Figure 7

log-dec variations with interblade phase angle

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Figure 8

Pressure contours on the original blade surfaces

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Figure 9

Pressure contours on the optimized blade surfaces

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Figure 10

Local worksum distributions on the original blade surfaces (“+” destabilizing; “−” stabilizing)

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Figure 11

Local worksum distributions on the optimized blade surfaces (“+” destabilizing; “−” stabilizing)

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Figure 12

Blade geometry comparisons (flutter stability maximization)

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Figure 13

Inlet total pressure distribution

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Figure 14

Changes in aero-elastic performance parameters with design iterations

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Figure 15

Changes in aerodynamic performance parameters with design iterations

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Figure 16

Local worksum distributions on the original blade surfaces (“+” destabilizing; “−” stabilizing)

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Figure 17

Local worksum distributions on the optimized blade surfaces (“+” destabilizing; “−” stabilizing)

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Figure 18

Pressure contours on the original blade surfaces

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Figure 19

Pressure contours on the optimized blade surfaces

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Figure 20

Blade geometry comparisons for forced response minimization

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