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Research Papers: Flows in Complex Systems

Near Wall Modeling for Trailing Edge Slot Film Cooling

[+] Author and Article Information
Julia Ling

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

Riccardo Rossi, John K. Eaton

Mechanical Engineering Department,
Stanford University,
Stanford, CA 94305

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received February 27, 2014; final manuscript received August 21, 2014; published online September 26, 2014. Assoc. Editor: Mark F. Tachie.

J. Fluids Eng 137(2), 021103 (Sep 26, 2014) (10 pages) Paper No: FE-14-1104; doi: 10.1115/1.4028498 History: Received February 27, 2014; Revised August 21, 2014

Trailing edge slot film cooling is a widely used active cooling scheme for turbine blade trailing edges. Current Reynolds-Averaged Navier–Stokes (RANS) models are known to significantly overpredict the adiabatic effectiveness of these configurations. It is shown that this overprediction is due in part to the breakdown of the Reynolds analogy between turbulent shear stress and scalar transport in the near wall region. By examining previously reported direct numerical simulation (DNS) results for a wall-mounted cube in cross flow, it is seen that in a flow with a significantly perturbed outer boundary layer, the turbulent diffusivity is not as strongly damped as the turbulent viscosity in the viscous sublayer and buffer layer of the boundary layer. By removing the Van Driest damping function from the length scale model for the turbulent diffusivity, more accurate turbulent diffusivity predictions are possible. This near wall correction is applied to trailing edge slot film cooling flows and it is demonstrated that the predictive accuracy of the RANS models is significantly enhanced. Detailed comparisons between RANS results and experimental datasets for 15 different cases demonstrate that this correction gives significant improvement to the accuracy of the RANS predictions across a broad range of trailing edge slot film cooling configurations.

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Figures

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Fig. 1

Trailing edge slot film cooling schematic

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Fig. 2

Diagram of near wall vortices acting on scalar concentration c and streamwise velocity u profiles. The small near wall vortex efficiently mixes the streamwise velocity, since that is the region over which the velocity field changes the most sharply. The large outer layer vortex mixes the scalar more effectively, since the concentration profile is not necessarily steepest right next to the wall. Therefore, the governing length scales for the scalar and momentum transport differ in the near wall region when large outer layer vortices scour the wall.

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Fig. 3

Schematic of the wall-mounted cube flow configuration. Locations at which profiles were extracted are shown with solid line segments.

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Fig. 4

Profiles from DNS (solid lines), realizable k–ε RANS (dotted lines), and k–ω SST (dashed lines). Profiles were obtained 5 (blue), 6 (green), 7 (red), and 8 (black) cube heights downstream of the cube center, at a spanwise position 0.75 cube heights off of the centerline.

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Fig. 5

Profiles of Sct and Sct/(1-e-y+/A). These profiles were the result of averaging across the four locations which are represented in Fig. 4.

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Fig. 6

Schematics of six of the trailing edge slot film cooling geometries investigated in this study

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Fig. 7

Contours of coolant concentration 4h downstream of injection. Concentration contours cropped at 5% coolant concentration. Secondary flow vectors (i.e., vectors projected onto a plane perpendicular to the main flow direction) are shown in black. Both the concentration contours and secondary flow vectors are from the experimental data.

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Fig. 8

Schematic of RANS domain. Zoomed-in view of mesh on side of land is shown to depict mesh refinement.

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Fig. 9

Contours of streamwise velocity nondimensionalized by the bulk-averaged main flow velocity for the generic narrow lands case at BR = 1.0 in a plane 0.5h above the breakout surface

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Fig. 10

Error metric evaluation for generic narrow lands airfoil at BR = 1.0. Results for the default turbulent diffusivity formulation shown with dashed line. Results with the Van Driest damping function removed shown with solid line.

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Fig. 11

Contours of adiabatic effectiveness for generic narrow lands case at BR = 1.0

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Fig. 12

Spanwise averaged adiabatic effectiveness. Experimental data shown with circles, RANS results with default Sct = 0.85 shown with dashed lines, RANS results with Sct = 0.45 shown with dashed-dotted lines, and RANS results with Sct = 0.45 and the near wall correction implemented shown with solid lines.

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