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Research Papers

Physical Interpretation of Machine Learning Models Applied to Film Cooling Flows

[+] Author and Article Information
Pedro M. Milani

Mechanical Engineering Department,
Stanford University,
Stanford, CA 94305
e-mail: pmmilani@stanford.edu

Julia Ling

Principal Scientist,
Citrine Informatics,
Redwood City, CA 94063

John K. Eaton

Mechanical Engineering Department,
Stanford University,
Stanford, CA 94305

1Corresponding author.

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the JOURNAL OF TURBOMACHINERY. Manuscript received August 16, 2018; final manuscript received August 22, 2018; published online October 17, 2018. Editor: Kenneth Hall.

J. Turbomach 141(1), 011004 (Oct 17, 2018) (10 pages) Paper No: TURBO-18-1209; doi: 10.1115/1.4041291 History: Received August 16, 2018; Revised August 22, 2018

Current turbulent heat flux models fail to predict accurate temperature distributions in film cooling flows. The present paper focuses on a machine learning (ML) approach to this problem, in which the gradient diffusion hypothesis (GDH) is used in conjunction with a data-driven prediction for the turbulent diffusivity field αt. An overview of the model is presented, followed by validation against two film cooling datasets. Despite insufficiencies, the model shows some improvement in the near-injection region. The present work also attempts to interpret the complex ML decision process, by analyzing the model features and determining their importance. These results show that the model is heavily reliant of distance to the wall d and eddy viscosity νt, while other features display localized prominence.

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References

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Figures

Grahic Jump Location
Fig. 1

Center spanwise plane showing contours of θ¯ calculated by the RANS simulation with Prt = 0.85 in (a) the baseline case and (b) the FPG case. BR = 1 and DR = 1 for both cases.

Grahic Jump Location
Fig. 2

Schematic showing the film cooling hole in the Skewed case, adapted from Folkersma and Bodart [24]. The first image shows the top view, and the second shows the side view. Lengths are nondimensionalized by the hole diameter.

Grahic Jump Location
Fig. 3

Center spanwise plane of the Cube geometry, with contours of θ¯ taken from the DNS

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Fig. 4

Mean scalar field in the Baseline geometry. The left panels show wall-normal planes at the wall (Y/D = 0), equivalent to adiabatic effectiveness. The right panels show streamwise planes at X/D = 2 and X/D = 5, respectively. Contour lines are shown at θ¯=0.75, 0.5, 0.25. (a) has the LES field, (b)–(d) contain the mean scalar field calculated using different turbulent diffusivity fields.

Grahic Jump Location
Fig. 5

Line plots of θ¯ in the Baseline geometry. (a) shows wall-normal variation at Z/D = 0 and X/D = 2; (b) shows streamwise variation at Z/D = 0 and Y/D = 0. The top-right corner of plot (b) shows a zoomed-in version of itself close to injection.

Grahic Jump Location
Fig. 6

Mean scalar field in the FPG case. The left panels show wall-normal planes at a near-wall location (Y/D = 0.15). The right panels show streamwise planes at X/D = 2 and X/D = 5, respectively. Contour lines are shown at θ¯=0.75, 0.5, 0.25. (a) has the MRC field from Coletti et al. [23], (b) and (c) contain the mean scalar field calculated using different turbulent diffusivity fields.

Grahic Jump Location
Fig. 7

Line plots of θ¯ in the FPG geometry. (a) shows wall-normal variation at the centerline of the X/D = 2 position; (b) shows streamwise variation at the centerline of Y/D = 0.15 position (near-wall centerline adiabatic effectiveness). The top-right corner of plot (b) shows a zoomed-in version of itself close to injection.

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Fig. 8

Feature importance for each model feature in the training set. Error bars indicate the standard deviation between the 1000 trees in the forest.

Grahic Jump Location
Fig. 9

Contour plots showing the pointwise feature usage of selected features in the Baseline case. These are streamwise planes at X/D = 2 and the contour lines show levels of θ¯=0.75, 0.5, 0.25 in the LES field. The figure is blanked in cells where the gradient of the mean scalar field is negligible. Color plots are available in the online version.

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