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.

Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.


Schneider, H., Bauer, H., von Terzi, D., and Rodi, W., 2012, “Coherent Structures in Trailing-Edge Cooling and the Challenge for Turbulent Heat Transfer Modelling,” ASME Paper No. GT2012-69771. [CrossRef]
Martini, P., and Schulz, A., 2004, “Experimental and Numerical Investigation of Trailing Edge Film Cooling by Circular Coolant Wall Jets Ejected From a Slot With Internal Rib Arrays,” ASME J. Turbomach., 126(2), pp. 229–236. [CrossRef]
Martini, P., Schulz, A., Bauer, H.-J., and Whitney, C., 2006, “Detached Eddy Simulation of Film Cooling Performance on the Trailing Edge Cutback of Gas Turbine Airfoils,” ASME J. Turbomach., 128(2), pp. 292–299. [CrossRef]
Holloway, D., Leylek, J., and Buck, F., 2002, “Pressure-Side Bleed Film Cooling: Part 1—Steady Framework for Experimental and Computational Results,” ASME Paper No. GT2002-30471. [CrossRef]
Medic, G., and Durbin, P., 2005, “Unsteady Effects on Trailing Edge Cooling,” ASME J. Heat Transfer, 127(4), pp. 388–392. [CrossRef]
Ravelli, S., and Barigozzi, G., 2013, “Evaluation of RANS Predictions on a Linear Nozzle Vane Cascade With Trailing Edge Cutback Film Cooling,” ASME Paper No. GT2013-94694. [CrossRef]
Schneider, H., von Terzi, D., and Bauer, H.-J., 2010, “Large-Eddy Simulations of Trailing-Edge Cutback Film Cooling at Low Blowing Ratio,” Int. J. Heat Fluid Flow, 31(5), pp. 767–775. [CrossRef]
Tyagi, M., and Acharya, S., 2003, “Large Eddy Simulation of Film Cooling Flow From an Inclined Cylindrical Jet,” ASME J. Turbomach., 125(4), pp. 734–742. [CrossRef]
Martini, P., Schulz, A., Whitney, C., and Lutum, E., 2003, “Experimental and Numerical Investigation of Trailing Edge Film Cooling Downstream of a Slot With Internal Rib Arrays,” Proc. Inst. Mech. Eng., Part A: J. Power Energy, 217(4), pp. 393–401. [CrossRef]
Liu, C., Zhu, H., and Bai, J., 2008, “Effect of Turbulent Prandtl Number on the Computation of Film Cooling Effectiveness,” Int. J. Heat Mass Transfer, 51(25–26), pp. 6208–6218. [CrossRef]
Rossi, R., Philips, D., and Iaccarino, G., 2010, “A Numerical Study of Scalar Dispersion Downstream of a Wall-Mounted Cube Using Direct Simulations and Algebraic Flux Models,” Int. J. Heat Fluid Flow, 31(5), pp. 805–819. [CrossRef]
Xueying, L., Yanmin, Q., Jing, R., and Hongde, J., 2013, “Algebraic Anisotropic Turbulence Modeling of Compound Angled Film Cooling Validated by PIV and PSP Measurements,” ASME Paper No. GT2013-94662. [CrossRef]
Ling, J., Yapa, S., Benson, M., Elkins, C., and Eaton, J., 2013, “3D Velocity and Scalar Field Measurements of an Airfoil Trailing Edge With Slot Film Cooling: The Effect of an Internal Structure in the Slot,” ASME J. Turbomach., 135(3), p. 031018. [CrossRef]
Elkins, C., Markl, M., Pelc, N., and Eaton, J., 2003, “4D Magnetic Resonance Velocimetry for Mean Velocity Measurements in Complex Turbulent Flows,” Exp. Fluids, 34(4), pp. 494–503. [CrossRef]
Benson, M., Elkins, C., and Eaton, J., 2011, “3D Velocity and Scalar Field Diagnostics Using Magnetic Resonance Imaging With Applications in Film-Cooling,” Stanford University, Stanford, CA, Turbulent Flow Report No. 123.
Benson, M., Elkins, C., and Eaton, J., 2011, “Measurements of 3D Velocity and Scalar Field for a Film-Cooled Airfoil Trailing Edge,” Exp Fluids, 51(2), pp. 443–455. [CrossRef]
Papamoschou, D., and Roshko, A., 1988, “The Compressible Turbulent Shear Layer: An Experimental Study,” J. Fluid Mech., 197, pp. 453–477. [CrossRef]
Maqbool, D., and Cadou, C., 2011, Master’s thesis, University of Maryland, College Park, MD.
Barigozzi, G., Armellini, A., Mucignat, C., and Casarsa, L., 2012, “Experimental Investigation of the Effects of Blowing Conditions and Mach Number on the Unsteady Behavior of Coolant Ejection Through a Trailing Edge Cutback,” Int. J. Heat Fluid Flow, 37, pp. 37–50. [CrossRef]
Pelc, N., Sommer, F., Li, K., Brosnan, T., Herfkens, R., and Enzmann, D., 1994, “Quantitative Magnetic Resonance Flow Imaging,” Magn. Reson. Q., 10(3), pp. 125–147. [PubMed]
Elkins, C., Markl, M., Iyengar, A., Wicker, R., and Eaton, J., 2004, “Full-Field Velocity and Temperature Measurements Using Magnetic Resonance Imaging in Turbulent Complex Internal Flows,” Int. J. Heat Fluid Flow, 25(5), pp. 702–710. [CrossRef]
Martini, P., Schulz, A., and Bauer, H.-J., 2006, “Film Cooling Effectiveness and Heat Transfer on the Trailing Edge Cutback of Gas Turbine Airfoils With Various Internal Cooling Designs,” ASME J. Turbomach., 128(1), pp. 196–205. [CrossRef]
Harrison, K., and Bogard, D., 2008, “Comparison of RANS Turbulence Models for Prediction of Film Cooling Performance,” ASME Paper No. GT2008-51423. [CrossRef]
Bradley, A., Najafabadi, H., Karlsson, M., and Wren, J., 2011, “Towards Efficient CFD-Simulations of Engine Like Turbine Guide Vane Film Cooling,” AIAA Paper No. 2011-708. [CrossRef]
Ling, J., Coletti, F., Yapa, S., and Eaton, J., 2013, “Experimentally Informed Optimization of Turbulent Diffusivity for a Discrete Hole Film Cooling Geometry,” Int. J. Heat Fluid Flow, 44, pp. 348–357. [CrossRef]


Grahic Jump Location
Fig. 1

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

Grahic Jump Location
Fig. 2

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

Grahic Jump Location
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.

Grahic Jump Location
Fig. 4

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

Grahic Jump Location
Fig. 5

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

Grahic Jump Location
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.

Grahic Jump Location
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.

Grahic Jump Location
Fig. 8

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

Grahic Jump Location
Fig. 9

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

Grahic Jump Location
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)




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In