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Research Papers

Applying Machine Learnt Explicit Algebraic Stress and Scalar Flux Models to a Fundamental Trailing Edge Slot

[+] Author and Article Information
R. D. Sandberg

Department of Mechanical Engineering,
University of Melbourne,
Parkville 3010, VIC, Australia
e-mail: richard.sandberg@unimelb.edu.au

R. Tan, J. Weatheritt, A. Ooi, A. Haghiri

Department of Mechanical Engineering,
University of Melbourne,
Parkville 3010, VIC, Australia

V. Michelassi

Baker Hughes, a GE Company,
Florence 50127, Italy
e-mail: vittorio.michelassi@bhge.com

G. Laskowski

General Electric Aviation,
Lynn, MA 01905
e-mail: laskowsk@ge.com

1Corresponding author.

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the JOURNAL OF TURBOMACHINERY. Manuscript received August 15, 2018; final manuscript received August 21, 2018; published online September 28, 2018. Editor: Kenneth Hall.

J. Turbomach 140(10), 101008 (Sep 28, 2018) (11 pages) Paper No: TURBO-18-1202; doi: 10.1115/1.4041268 History: Received August 15, 2018; Revised August 21, 2018

Machine learning was applied to large-eddy simulation (LES) data to develop nonlinear turbulence stress and heat flux closures with increased prediction accuracy for trailing-edge cooling slot cases. The LES data were generated for a thick and a thin trailing-edge slot and shown to agree well with experimental data, thus providing suitable training data for model development. A gene expression programming (GEP) based algorithm was used to symbolically regress novel nonlinear explicit algebraic stress models and heat-flux closures based on either the gradient diffusion or the generalized gradient diffusion approaches. Steady Reynolds-averaged Navier–Stokes (RANS) calculations were then conducted with the new explicit algebraic stress models. The best overall agreement with LES data was found when selecting the near wall region, where high levels of anisotropy exist, as training region, and using the mean squared error of the anisotropy tensor as cost function. For the thin lip geometry, the adiabatic wall effectiveness was predicted in good agreement with the LES and experimental data when combining the GEP-trained model with the standard eddy-diffusivity model. Crucially, the same model combination also produced significant improvement in the predictive accuracy of adiabatic wall effectiveness for different blowing ratios (BRs), despite not having seen those in the training process. For the thick lip case, the match with reference values deteriorated due to the presence of large-scale, relative to slot height, vortex shedding. A GEP-trained scalar flux model, in conjunction with a trained RANS model, was found to significantly improve the prediction of the adiabatic wall effectiveness.

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Figures

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Fig. 1

(a) Computational domain (not to scale) and (b) LES blocks

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Fig. 4

Thermal diffusivity obtained from LES using Eq. (11)

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Fig. 6

Alignment of strain and anisotropy tensor using baseline kω-SST model: (a) t/s = 1.14 and (b) t/s = 0.126

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Fig. 5

Thermal diffusivity obtained using GGDH, Eq. (12)

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Fig. 2

Instantaneous temperature fields obtained from LES and unsteady RANS using the baseline kω-SST model, dashed lines denote time-averaged temperature at Tslot + 2 K and Tfs – 2 K. (a) Instantaneous LES temperature field for t/s = 1.14. (b) Instantaneous LES temperature field for t/s = 0.126. (c) Instantaneous URANS temperature field for t/s = 1.14. (d) Instantaneous URANS temperature field for t/s = 0.126.

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Fig. 3

Comparison of ηwall obtained from LES, experiments [1] and baseline RANS for different t/s

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Fig. 7

Training regions for RANS (top) and heat flux (bottom) models

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Fig. 8

Alignment of strain and anisotropy tensor using different trained nonlinear RANS models for t/s = 1.14 case. Note that arrows are pointing toward the areas of highest interest (close to the lower wall) where significant improvement in the alignment is observed compared to Fig. 6.

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Fig. 9

Rxx (a) and Rxy (b) from trained models compared with baseline RANS and LES profiles at x/s = 30 for t/s = 1.14

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Fig. 10

Rxx (left) and Rxy (right) from trained models compared with baseline RANS and LES profiles at x/s = 30 for t/s = 0.126 at different blowing ratios: (a) BR = 1.26, (b) BR = 1.07, and (c) BR = 0.86

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Fig. 11

Comparison of streamwise heat flux obtained from different flux models for case t/s = 1.14: (a) LES streamwise heat flux, (b) HF.1 streamwise heat flux, (c) HF.2 GGDH streamwise heat flux, and (d) HF.3 GGDH streamwise heat flux.

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Fig. 12

Comparison of wall-normal heat flux obtained from different flux models for case t/s = 1.14: (a) LES wall-normal heat flux, (b) HF.1 wall-normal heat flux, (c) HF.2 GGDH wall-normal heat flux, and (d) HF.3 GGDH wall-normal heat flux.

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Fig. 13

Comparison of ηwall for different RANS models for t/s = 0.126 at different blowing ratios: (a) BR = 1.26, (b) BR = 1.07, and (c) BR = 0.86.

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Fig. 14

Comparison of ηwall for different RANS and heat flux models for t/s = 1.14

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