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Research Papers

Improving Pin-Fin Heat Transfer Predictions Using Artificial Neural Networks

[+] Author and Article Information
Jason K. Ostanek

Naval Surface Warfare
Center – Carderock Division,
Energy Conversion R&D,
Philadelphia, PA 19112
e-mail: jason.ostanek@navy.mil

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the JOURNAL OF TURBOMACHINERY. Manuscript received July 8, 2013; final manuscript received July 9, 2013; published online September 27, 2013. Editor: Ronald Bunker.

This material is declared a work of the US Government and is not subject to copyright protection in the United States. Approved for public release; distribution is unlimited.

J. Turbomach 136(5), 051010 (Sep 27, 2013) (9 pages) Paper No: TURBO-13-1142; doi: 10.1115/1.4025217 History: Received July 08, 2013; Revised July 09, 2013

In much of the public literature on pin-fin heat transfer, the Nusselt number is presented as a function of Reynolds number using a power-law correlation. Power-law correlations typically have an accuracy of 20% while the experimental uncertainty of such measurements is typically between 5% and 10%. Additionally, the use of power-law correlations may require many sets of empirical constants to fully characterize heat transfer for different geometrical arrangements. In the present work, artificial neural networks were used to predict heat transfer as a function of streamwise spacing, spanwise spacing, pin-fin height, Reynolds number, and row position. When predicting experimental heat transfer data, the neural network was able to predict 73% of array-averaged heat transfer data to within 10% accuracy while published power-law correlations predicted 48% of the data to within 10% accuracy. Similarly, the neural network predicted 81% of row-averaged data to within 10% accuracy while 52% of the data was predicted to within 10% accuracy using power-law correlations. The present work shows that first-order heat transfer predictions may be simplified by using a single neural network model rather than combining or interpolating between power-law correlations. Furthermore, the neural network may be expanded to include additional pin-fin features of interest such as fillets, duct rotation, pin shape, pin inclination angle, and more making neural networks expandable and adaptable models for predicting pin-fin heat transfer.

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References

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Figures

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Fig. 1

Schematic of a pin-fin array at the trailing edge of a gas turbine airfoil

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Fig. 2

Measured versus predicted array-averaged heat transfer using correlations of (a) Metzger et al. [10] and (b) VanFossen [11]

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Fig. 3

Model of a perceptron, the building block of the artificial neural network

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Fig. 4

Example network for predicting NuD with 3-3-3-1 architecture, where the transfer functions are shown above each layer

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Fig. 5

Effect of activation function on learning rate for a 3-3-3-1 network having (a) logistic-logistic-logistic, (b) logistic-logistic-linear, and (c) hyperbolic tangent-hyperbolic tangent-linear activation functions. Arrow indicates minimum RMSE of combined training/validation data.

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Fig. 6

Effect of network size and training algorithm on predicting array-average heat transfer using (a) BPM, (b) BFGS, and (c) TNC

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Fig. 7

Variation of RMSE and maximum percent error for repeated training attempts using (a) BPM, (b) BFGS, and (c) TNC

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Fig. 8

Effect of network size on the cumulative distribution of prediction error for array-averaged heat transfer

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Fig. 9

Sensitivity of trained networks to changes in (a) ReD, (b) X/D, (c) S/D, (d) H/D using 50% of data in Table 1 for network training

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Fig. 10

Sensitivity of trained networks to changes in (a) ReD, (b) X/D, (c) S/D, (d) H/D using 75% of data in Table 1 for network training

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Fig. 11

Sensitivity of trained networks to changes in (a) ReD, (b) X/D, (c) S/D, (d) H/D using 100% of data in Table 1 for network training

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Fig. 12

Predicted and measured array-averaged NuD for a 4-4-1 network trained using 50% of the available data in Table 1

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Fig. 13

Effect of network size on the cumulative distribution of prediction error for row-averaged heat transfer

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Fig. 14

Predicted and measured row-averaged NuD for a 5-4-1 network trained using 50% of the available data in Table 1

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