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Research Papers

Gradient Span Analysis Method: Application to the Multipoint Aerodynamic Shape Optimization of a Turbine Cascade

[+] Author and Article Information
Hadrien Montanelli

NA Group,
Mathematical Institute,
University of Oxford,
Oxford OX26HD, UK
e-mail: montanelli@maths.ox.ac.uk

Marc Montagnac

Research Engineer
Computational Fluid Dynamics Group,
Cerfacs,
42, Avenue G. Coriolis,
Toulouse 31057, CEDEX 1, France
e-mail: marc.montagnac@cerfacs.fr

François Gallard

Research Engineer
IRT Saint Exupéry,
Toulouse 31432, France
e-mail: francois.gallard@irt-saintexupery.com

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF TURBOMACHINERY. Manuscript received October 1, 2014; final manuscript received March 3, 2015; published online March 24, 2015. Assoc. Editor: Graham Pullan.

J. Turbomach 137(9), 091006 (Sep 01, 2015) (8 pages) Paper No: TURBO-14-1260; doi: 10.1115/1.4030016 History: Received October 01, 2014; Revised March 03, 2015; Online March 24, 2015

This paper presents the application of the gradient span analysis (GSA) method to the multipoint optimization of the two-dimensional LS89 turbine distributor. The cost function (total pressure loss) and the constraint (mass flow rate) are computed from the resolution of the Reynolds-averaged Navier–Stokes equations. The penalty method is used to replace the constrained optimization problem with an unconstrained problem. The optimization process is steered by a gradient-based quasi-Newton algorithm. The gradient of the cost function with respect to design variables is obtained with the discrete adjoint method, which ensures an efficient computation time independent of the number of design variables. The GSA method gives a minimal set of operating conditions to insert into the weighted sum model to solve the multipoint optimization problem. The weights associated to these conditions are computed with the utopia point method. The single-point optimization at the nominal condition and the multipoint optimization over a wide range of conditions of the LS89 blade are compared. The comparison shows the strong advantages of the multipoint optimization with the GSA method and utopia-point weighting over the traditional single-point optimization.

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Figures

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Fig. 1

Multiblock structured grid of the LS89 test case

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Fig. 2

CAD model parameters

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Fig. 3

Error on the gradient computed by the discrete adjoint method

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Fig. 4

Evolution of the total pressure loss (square symbol), and correlative evolution of the normalized mass flow rate (circle symbol)

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Fig. 5

Initial blade geometry in a (x, z) plane, and difference Δz of z-coordinates between final and initial shapes (frozen trailing edges not shown)

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Fig. 6

Normalized mass flow rate and total pressure loss with respect to the pressure ratio Π for initial and optimized shapes

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Fig. 7

Evolution of the total pressure loss at the five conditions

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Fig. 8

Evolution of the mass flow rate at the five conditions

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Fig. 9

Initial blade geometry in a (x, z) plane, and difference Δz of z-coordinates between final and initial shapes (frozen trailing edges not shown)

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Fig. 10

Normalized mass flow rate and total pressure loss with respect to the pressure ratio Π for initial and optimized shapes

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Fig. 11

Differences of total pressure losses between initial and optimized shapes, with respect to the pressure ratio Π

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