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Research Papers: Gas Turbines: Turbomachinery

Optimal Turbulent Schmidt Number for RANS Modeling of Trailing Edge Slot Film Cooling

[+] Author and Article Information
Julia Ling

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

Christopher J. Elkins, John K. Eaton

Department of Mechanical Engineering,
Stanford University,
Stanford, CA 94305

Contributed by the Turbomachinery Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received October 8, 2014; final manuscript received October 13, 2014; published online December 30, 2014. Editor: David Wisler.

J. Eng. Gas Turbines Power 137(7), 072605 (Jul 01, 2015) (8 pages) Paper No: GTP-14-1572; doi: 10.1115/1.4029206 History: Received October 08, 2014; Revised October 13, 2014; Online December 30, 2014

It has been previously demonstrated that Reynolds-averaged Navier–Stokes (RANS) simulations do not accurately capture the mixing between the coolant flow and the main flow in trailing edge slot film cooling configurations. Most RANS simulations use a fixed turbulent Schmidt number of either 0.7 or 0.85 to determine the turbulent scalar flux, based on the values for canonical flows. This paper explores the extent to which RANS predictions can be improved by modifying the value of the turbulent Schmidt number. Experimental mean 3D velocity and coolant concentration data obtained using magnetic resonance imaging techniques are used to evaluate the accuracy of RANS simulations. A range of turbulent Schmidt numbers from 0.05 to 1.05 is evaluated and the optimal turbulent Schmidt number for each case is determined using an integral error metric which accounts for the difference between RANS and experiment throughout a three-dimensional region of interest (ROI). The resulting concentration distribution is compared in detail with the experimentally measured coolant concentration distribution to reveal where the fixed turbulent Schmidt number assumption fails. It is shown that the commonly used turbulent Schmidt number of 0.85 overpredicts the surface effectiveness in all cases, particularly when the k-omega shear stress transport (SST) model is employed, and that a lower value of the turbulent Schmidt number can improve predictions.

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Figures

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Fig. 1

Schematic of the test section. Region over which experimental MRC measurements were obtained is indicated by the dashed box.

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Fig. 2

Schematics of the baseline (top) and island (bottom) airfoils. All dimensions are in mm.

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Fig. 3

Contours of surface effectiveness (%). (a) Baseline, BR = 0.7, (b) baseline, BR = 1.0, (c) baseline, BR = 1.3, and (d) island, BR = 1.3.

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Fig. 4

Spanwise averaged surface effectiveness. Results from Holloway et al. [4] and Martini et al. [22] shown for comparison.

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Fig. 5

Computational domain for RANS simulations. Zoomed-in box shows section of mesh in the breakout region.

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Fig. 6

Contours of streamwise velocity 0.5 h above the breakout surface in a plane parallel to the breakout surface. Units of (m/s). Solid regions of airfoil shown in white. (a) Experiment, (b) RANS RKE, and (c) RANS k-omega SST.

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Fig. 7

Contours of turbulent viscosity normalized by molecular viscosity. Solid regions of airfoil shown in white. (a) RANS RKE, plane 0.5 h above breakout. (b) RANS k-omega SST, plane 0.5 h above breakout; (c) RANS RKE, symmetry plane; and (d) RANS k-omega SST, symmetry plane.

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Fig. 8

Diagram of the ROIs for evaluating the integral error metric. ROI-1 shown outlined in black. ROI-2 outlined in white.

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Fig. 9

Integral error metric as a function of turbulent Schmidt number, evaluated over both ROIs. (a) ROI-1 and (b) ROI-2.

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Fig. 10

Contours of coolant concentration for (a) experiment, surface effectiveness; (b) experiment, centerplane; (c) RKE, surface effectiveness (Sct = 0.25); (d) RKE, centerplane (Sct = 0.25); (e) k-omega SST, surface effectiveness (Sct = 0.05); (f) k-omega SST, centerplane (Sct = 0.05)

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