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Research Papers

A Machine Learning Approach for Determining the Turbulent Diffusivity in 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

Thermal/Fluid Science and Engineering,
Sandia National Laboratories,
Livermore, CA 94551

Gonzalo Saez-Mischlich, Julien Bodart

ISAE-SUPAERO,
University of Toulouse,
Toulouse 31400, France

John K. Eaton

Mechanical Engineering Department,
Stanford University,
Stanford, CA 94305

1Corresponding author.

2Currently at Citrine Informatics.

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the JOURNAL OF TURBOMACHINERY. Manuscript received August 22, 2017; final manuscript received September 23, 2017; published online December 6, 2017. Editor: Kenneth Hall.

J. Turbomach 140(2), 021006 (Dec 06, 2017) (8 pages) Paper No: TURBO-17-1132; doi: 10.1115/1.4038275 History: Received August 22, 2017; Revised September 23, 2017

In film cooling flows, it is important to know the temperature distribution resulting from the interaction between a hot main flow and a cooler jet. However, current Reynolds-averaged Navier–Stokes (RANS) models yield poor temperature predictions. A novel approach for RANS modeling of the turbulent heat flux is proposed, in which the simple gradient diffusion hypothesis (GDH) is assumed and a machine learning (ML) algorithm is used to infer an improved turbulent diffusivity field. This approach is implemented using three distinct data sets: two are used to train the model and the third is used for validation. The results show that the proposed method produces significant improvement compared to the common RANS closure, especially in the prediction of film cooling effectiveness.

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Figures

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Fig. 2

Skewed geometry: (a) is from Folkersma [20] and contains a wall-normal plane showing the skewed hole and a spanwise plane showing dimensions and the plenum (the latter image is also valid for the baseline case); (b) shows the mesh used in the RANS simulation at the wall around the injection hole

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Fig. 1

Schematic of the baseline geometry. Figure shows contours of θ¯ at the center spanwise plane as calculated by the LES. The plenum that feeds the jet was in the simulation domain but is not shown.

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Fig. 3

Schematic of the cube geometry with contours of θ¯ as calculated by the DNS at the center spanwise plane

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Fig. 6

Contours of nondimensional turbulent diffusivity field αt/(UD) in the baseline geometry. The figures on the left are a spanwise plane at the center of the channel, z/D=0. The figures on the right show streamwise planes at x/D=2. The plots are blanked in regions in which the dimensionless mean scalar gradient calculated by the RANS or by the LES data sets is smaller than 10−5. Lines show isocontours of αt=0: (a) is the field extracted from the LES using Eq. (2); (b) is the RANS diffusivity calculated via a fixed Prt=0.85; and (c) is the field that the ML algorithm predicts.

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Fig. 4

Example binary decision tree of height 2. To decide on the value of αt for any set of features, the rules are followed starting from the top until a leaf is reached.

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Fig. 5

Mean and standard deviation of the error in the predicted diffusivity field versus the number of trees in the RF. The x-axis is displayed on a log-scale.

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Fig. 7

Mean dimensionless temperature field in the baseline geometry. The left panels show wall-normal planes at the wall (y/D=0), which are equivalent to adiabatic effectiveness. The right panels show streamwise planes at x/D=2. Contour lines are shown at θ¯=0.75,0.5,0.25. (a) has the LES field from Bodart et al. [19], and (b)–(d) contain the mean scalar field calculated using Eq. (4) with different turbulent diffusivity fields.

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Fig. 8

Spanwise-averaged adiabatic effectiveness in the baseline case

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