0
Research Papers

Numerical Benchmark of Nonconventional RANS Turbulence Models for Film and Effusion Cooling

[+] Author and Article Information
Cosimo Bianchini

e-mail: cosimo.bianchini@htc.de.unifi.it

Bruno Facchini

Energy Engineering Department “S.Stecco,” University of Florence,
via di S. Marta 3,
50139 Florence, Italy

1Corresponding author.

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the Journal of Turbomachinery. Manuscript received August 20, 2012; final manuscript received August 22, 2012; published online June 10, 2013. Assoc. Editor: David Wisler.

J. Turbomach 135(4), 041026 (Jun 10, 2013) (11 pages) Paper No: TURBO-12-1176; doi: 10.1115/1.4007614 History: Received August 20, 2012; Revised August 22, 2012

Over the course of the years, several turbulence models specifically developed to improve the predicting capabilities of conventional two-equations Reynolds-averaged Navier–Stokes (RANS) models have been proposed. They have, however, been mainly tested against experiments only comparing with standard isotropic models, in single hole configuration and for very low blowing ratio. A systematic benchmark of the various nonconventional models exploring a wider range of application is hence missing. This paper performs a comparison of three recently proposed models over three different test cases of increasing computational complexity. The chosen test matrix covers a wide range of blowing ratios (0.5–3.0) including both single row and multi-row cases for which experimental data of reference are available. In particular the well-known test by Sinha et al. (1991, “Film-Cooling Effectiveness Downstream of a Single Row of Holes with Variable Density Ratio,” J. Turbomach., 113, pp. 442–449) at BR = 0.5 is used in conjunction with two in-house carried out experiments: a single row film-cooling test at BR = 1.5 and a 15 rows test plate designed to study the interaction between slot and effusion cooling at BR = 3.0. The first two considered models are based on a tensorial definition of the eddy viscosity in which the stream-span position is augmented to overcome the main drawback connected with standard isotropic turbulence models that is the lower lateral spreading of the jet downwards the injection. An anisotropic factor to multiply the off diagonal position is indeed calculated from an algebraic expression of the turbulent Reynolds number developed by Bergeles et al. (1978, “The Turbulent Jet in a Cross Stream at Low Injection Rates: A Three-Dimensional Numerical Treatment,” Numer. Heat Transfer, 1, pp. 217–242) from DNS statistics over a flat plate. This correction could be potentially implemented in the framework of any eddy viscosity model. It was chosen to compare the predictions of such modification applied to two among the most common two-equation turbulence models for film-cooling tests, namely the two-layer (TL) model and the k–ω shear stress transport (SST), firstly proposed and tested in the past respectively by Azzi and Lakeal (2002, “Perspectives in Modeling Film Cooling of Turbine Blades by Transcending Conventional Two-Equation Turbulence Models,” J. Turbomach., 124, pp. 472–484) and Cottin et al. (2011, “Modeling of the Heat Flux For Multi-Hole Cooling Applications,” Proceedings of the ASME Turbo Expo, Paper No. GT2011-46330). The third model, proposed by Holloway et al. (2005, “Computational Study of Jet-in-Crossflow and Film Cooling Using a New Unsteady-Based Turbulence Model,” Proceedings of the ASME Turbo Expo, Paper No. GT2005-68155), involves the unsteady solution of the flow and thermal field to include the short-time response of the stress tensor to rapid strain rates. This model takes advantage of the solution of an additional transport equation for the local effective total stress to trace the strain rate history. The results are presented in terms of adiabatic effectiveness distribution over the plate as well as spanwise averaged profiles.

FIGURES IN THIS ARTICLE
<>
Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.

References

Goldstein, R. J., 1971, “Film Cooling,” Adv. Heat Transfer, 7, pp. 321–379. [CrossRef]
Crabb, D., Durao, D. F. G., and Whitelaw, J. H., 1981, “A Round Jet Normal to a Crossflow,” ASME J. Fluids Eng, 103, pp. 142–153. [CrossRef]
Galeazzo, F. C. C., Donnert, G., Habisreuther, P., Zarzalis, N., Valdes, R. J., and Krebs, W., 2010, “Measurement and Simulation of Turbulent Mixing in a Jet in Crossflow,” Proceedings of the ASME Turbo Expo, Glasgow, UK, June 14–18, ASME Paper No. GT2010-22709. [CrossRef]
Schluter, J. U., and Schonfeld, T., 2001, “LES of Jets in Cross Flow and Its Application to a Gas Turbine Burner,” Flow, Turbul. Combust., 65(2), pp. 177–203. [CrossRef]
Mendez, S., and Nicoud, F., 2008, “An Adiabatic Homogeneous Model for the Flow Around a Multi-Perforated Plate,” AIAA J., 10(46), pp. 2623–2633. [CrossRef]
Hoda, A., and Acharya, S., 2000, “Predictions of a Film Coolant Jet in Crossflow With Different Turbulence Models,” ASME J. Turbomach., 122, pp. 558–569. [CrossRef]
Harrison, K. L. and Bogard, D. G., 2008, “Comparison of RANS Turbulence Models for Prediction of Film Cooling Performance,” Proceedings of the ASME Turbo Expo, Berlin, June 9–13, ASME Paper No. GT2008-51423. [CrossRef]
Bacci, A., and Facchini, B., 2007, “Turbulence Modeling for the Numerical Simulation of Film and Effusion Cooling Flows,” Proceedings of the ASME Turbo Expo, Montreal, Canada, May 14–17, ASME Paper No. GT2007-27182. [CrossRef]
Holloway, D. S., Walters, D. K., and Leylek, J. H., 2005, “Computational Study of Jet-In-Crossflow and Film Cooling Using a New Unsteady-Based Turbulence Model,” Proceedings of the ASME Turbo Expo, Reno, NV, June 6–9, ASME Paper No. GT2005-68155. [CrossRef]
Bergeles, G., Gosman, G., and Launder, A. D., 1978, “The Turbulent Jet in a Cross Stream at Low Injection Rates: A Three-Dimensional Numerical Treatment,” Numer. Heat Transfer, 1, pp. 217–242. [CrossRef]
Azzi, A., and Lakehal, D., 2002, “Perspectives in Modeling Film Cooling of Turbine Blades by Transcending Conventional Two-Equation Turbulence Models,” ASME J. Turbomach., 124, pp. 472–484. [CrossRef]
Mangani, L., and Andreini, A., 2008, “Application of an Object-Oriented CFD Code to Heat Transfer Analysis,” Proceedings of the ASME Turbo Expo, Berlin, June 9–13, ASME Paper No. GT2008-51118. [CrossRef]
Andreini, A., Bianchini, C., Ceccherini, A., Facchini, B., Mangani, L., Cinque, G., and Colantuoni, S., 2009, “Investigation of Circular and Shaped Effusion Cooling Arrays for Combustor Liner Application—Part 2: Numerical Analysis,” Proceedings of the ASME Turbo Expo, Orlando, FL, June 8–12, ASME Paper No. GT2009-60038. [CrossRef]
Boust, B., Lalizel, G., Bianchini, C., Ceccherini, A., Cinque, G., and Colantuoni, S., 2009, “Dual Investigations on the Improvement of Effusion Cooling by Shaped Holes,” Proceedings of the 7th World Conference on Experimental Heat Transfer, Fluid Mechanics and Thermodynamics, Krakow, Poland, June 28–July 3.
Andreini, A., Bianchini, C., Facchini, B., Mangani, L., and Maritano, M., 2010, “Heat Transfer Performances of Fan Shaped Film Cooling Holes: Part II—Numerical Analysis,” Proceedings of the ASME Turbo Expo, Glasgow, UK, June 14–18, ASME Paper No. GT2010-22809. [CrossRef]
Cottin, G., Laroche, E., Savary, N., and Millan, P., 2011, “Modeling of the Heat Flux for Multi-Hole Cooling Applications,” Proceedings of the ASME Turbo Expo, Vancouver, Canada, June 6–10, ASME Paper No. GT2011-46330. [CrossRef]
Li, X., Ren, J., and Jiang, H., 2011, “Algebraic Anisotropic Eddy-Viscosity Modeling Application to the Turbulent Film Cooling Flows,” Proceedings of the ASME Turbo Expo, Vancouver, Canada, June 6–10, ASME Paper No. GT2011-45791. [CrossRef]
Walters, D. K., 2000, “Development of Novel Turbulence Modeling Techniques for Turbomachinery Applications,” Ph.D. thesis, Clemson University, Clemson, SC.
L'Ecuyer, M. R., and Soechting, F. O., 1985, “A Model for Correlating Flat Plate Film-Cooling Effectiveness for Rows of Round Holes,” AGARD-CP-390.
Weller, H. G., Tabor, G., Jasak, H., and Fureby, C., 1998, “A Tensorial Approach to Computational Continuum Mechanics Using Object-Oriented Techniques,” Comput. Phys., 12(6), pp. 620–631. [CrossRef]
Patankar, S. V., 1980, Numerical Heat Transfer and Fluid Flow, Taylor & Francis, New York.
Jasak, H., 1996, “Error Analysis and Estimation for the Finite Volume Method With Applications to Fluid Flows,” Ph.D. thesis, Imperial College of Science, Technology and Medicine, London.
Andreini, A., Bianchini, C., Facchini, B., and Mangani, L., 2007, “Development and Validation of a C++ Object Oriented CFD Code for Heat Transfer Analysis,” Proceedings of the ASME-JSME 2007 Thermal Engineering and Summer Heat Transfer Conference, Vancouver, Canada, July 8–12.
Azzi, A., and Jubran, B. A., 2003, “Numerical Modeling of Film Cooling From Short Length Stream-Wise Injection Holes,” Heat Mass Transfer, 39, pp. 345–353. [CrossRef]
Lakehal, D., Theodoris, G. S., and Rodi, W., 1998, “Computation of Film Cooling of a Flat Plate by Lateral Injection From a Row of Holes,” Int. J. Heat Fluid Flow, 19, pp. 418–430. [CrossRef]
Kaszeta, R. W., and Simon, T. W., 2000, “Measurement of Eddy Diffusivity of Momentum in Film Cooling Flows With Streamwise Injection,” ASME J. Turbomach., 122, pp. 178–183. [CrossRef]
Lakehal, D., 2002, “Near-Wall Modeling of Turbulent Convective Heat Transport in Film Cooling of Turbine Blades With the Aid of Direct Numerical Simulation Data,” ASME J. Turbomach., 124, pp. 485–498. [CrossRef]
Kim, J., Moin, P., and Moser, R., 1987, “Turbulence Statistics in Fully Developed Channel Flow at Low Reynolds Number,” J. Fluid Mech., 177, pp. 133–166. [CrossRef]
Lakehal, D., Theodoris, G. S., and Rodi, W., 2001, “Three-Dimensional Flow and Heat Transfer Calculations of Film Cooling at the Leading Edge of a Symmetrical Turbine Blade Model,” Int. J. Heat Fluid Flow, 22, pp. 113–122. [CrossRef]
Lien, F. S., 1992, “Computational Modeling of 3-D Flow in Complex Ducts and Passages,” Ph.D. thesis, University of Manchester, Institute of Science and Technology, Manchester, UK.
Sinha, A. K., Bogard, D. G., and Crawford, M. E., 1991, “Film-Cooling Effectiveness Downstream of a Single Row of Holes With Variable Density Ratio,” ASME J. Turbomach., 113, pp. 442–449. [CrossRef]
Andreopoulos, J., 1983, “Measurements in a Jet-Pipe Flow Issuing Perpendicularly into a Cross Stream,” ASME J. Fluids Eng., 26, pp. 493–500. [CrossRef]
Bonanni, L., Facchini, B., Tarchi, L., Maritano, M., and Traverso, S., 2010, “Heat Transfer Performance of Fan-Shaped Film Cooling Holes: Part I—Experimental Analysis,” Proceedinigs of the ASME Turbo Expo, Glasgow, UK, June 14–18, ASME Paper No. GT2010-22808. [CrossRef]
Andreini, A., Caciolli, G., Facchini, B., Tarchi, L., Coutandin, D., Peschiulli, A., and Taddei, S., 2012, “Density Ratio Effects on the Cooling Performances of a Combustor Liner Cooled by a Combined Slot/Effusion System,” Proceedings of the ASME Turbo Expo, Copenhagen, June 11–15, ASME Paper No. GT2012-68263.

Figures

Grahic Jump Location
Fig. 1

Anisotropic factor near wall profile

Grahic Jump Location
Fig. 2

Sketch of the adopted computational domain

Grahic Jump Location
Fig. 3

Maps of adiabatic effectiveness (all maps but LES and WHLU are mirrored against hole symmetry line)

Grahic Jump Location
Fig. 4

Near hole flow and thermal field details

Grahic Jump Location
Fig. 5

Spanwise distribution of adiabatic effectiveness

Grahic Jump Location
Fig. 6

Centerline and spanwise averaged adiabatic effectiveness

Grahic Jump Location
Fig. 7

Sketch of computational domain and boundary conditions

Grahic Jump Location
Fig. 8

Maps of adiabatic effectiveness

Grahic Jump Location
Fig. 9

Spanwise distribution of adiabatic effectiveness

Grahic Jump Location
Fig. 10

Spanwise-averaged adiabatic effectiveness

Grahic Jump Location
Fig. 11

Sketch of computational domain and boundary conditions

Grahic Jump Location
Fig. 12

Maps of adiabatic effectiveness

Grahic Jump Location
Fig. 13

Velocity profile on the symmetry plane (TL simulation)

Grahic Jump Location
Fig. 14

Mid-line adiabatic effectiveness

Tables

Errata

Discussions

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