Research Papers

Optimization of a U-Bend for Minimal Pressure Loss in Internal Cooling Channels—Part I: Numerical Method

[+] Author and Article Information
Tom Verstraete

e-mail: tom.verstraete@vki.ac.be

Filippo Coletti

e-mail: coletti@vki.ac.be

Tony Arts

e-mail: arts@vki.ac.be
von Karman Institute for Fluid Dynamics,
Turbomachinery and Propulsion Department,
Chaussée de Waterloo 72,
Rhode-Saint-Genèse 1640,Belgium

1Present address: Mechanical Engineering Department, Stanford University, Stanford, CA.

2Present address: Tractable Engineering, Brussels, Belgium.

3Present address: Geosea NV, Zwijndrecht, Belgium.

Contributed by the International Gas Turbine Institute of ASME for publication in the JOURNAL OF TURBOMACHINERY. Manuscript received January 22, 2012; final manuscript received October 25, 2012; published online June 28, 2013. Editor: David Wisler.

J. Turbomach 135(5), 051015 (Jun 28, 2013) (10 pages) Paper No: TURBO-12-1006; doi: 10.1115/1.4023030 History: Received January 22, 2012; Revised October 25, 2012

This two-part paper addresses the design of a U-bend for serpentine internal cooling channels optimized for minimal pressure loss. The total pressure loss for the flow in a U-bend is a critical design parameter, as it augments the pressure required at the inlet of the cooling system, resulting in a lower global efficiency. In this first part of the paper, the design methodology of the cooling channel is presented. The minimization of the total pressure loss is achieved by means of a numerical optimization method that uses a metamodel-assisted differential evolution algorithm in combination with an incompressible Navier–Stokes solver. The profiles of the internal and external side of the bend are parameterized using piece-wise Bezier curves. This allows for a wide variety of shapes, respecting the manufacturability constraints of the design. The pressure loss is computed by the Navier–Stokes solver, which is based on a two-equation turbulence model and is available from the open source software OpenFOAM. The numerical method predicts an improvement of 36% in total pressure drop with respect to a circular U-bend, mainly due to the reduction of the separated flow region along the internal side of the bend. The resulting design is subjected to experimental validation, presented in Part II of the paper.

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Fig. 1

Flow chart of the optimization algorithm

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Fig. 2

Baseline geometry, definition of area in which the shape is allowed to change

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Fig. 3

Parameterization of the outer curve

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Fig. 4

Parameterization of the inner curve

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Fig. 5

Zoom on the grid in the U-bend

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Fig. 6

Artificial neural network (ANN) layout

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Fig. 7

Prediction of mean value and confidence intervals by kriging

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Fig. 8

Optimization result of De Jong F1 test function using an artificial neural network (ANN)

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Fig. 9

Optimization result of De Jong F1 test function using kriging

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Fig. 10

Optimization result using differential evolution without metamodel

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Fig. 11

Optimization result using the artificial neural network

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Fig. 12

Optimization result using kriging

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Fig. 13

Optimal shape of the U-bend

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Fig. 14

D1 parameter versus pressure drop [Pa] for initial database (circle), ANN (square), and kriging (diamond) samples

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Fig. 15

D2 parameter versus pressure drop [Pa] for initial database (circle), ANN (square), and kriging (diamond) samples

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Fig. 16

D3 parameter versus pressure drop [Pa] for initial database (circle), ANN (square), and kriging (diamond) samples

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Fig. 17

y coordinate of the third control point of the third outer curve versus pressure drop [Pa] for initial database (circle), ANN (square), and kriging (diamond) samples



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