0
Research Papers: Gas Turbines: Combustion, Fuels, and Emissions

A Numerical Study on the Turbulent Schmidt Numbers in a Jet in Crossflow

[+] Author and Article Information
Elizaveta M. Ivanova

Research Scientist
e-mail: elizaveta.ivanova@dlr.de

Berthold E. Noll

Head of Computer Simulation
e-mail: berthold.noll@dlr.de

Manfred Aigner

Professor Director of Institute
e-mail: manfred.aigner@dlr.de
Institute of Combustion Technology,
German Aerospace Center (DLR),
Stuttgart, 70569Germany

This statement is not meant to imply that the results of LES are independent of the SGS scalar transport model, but a thorough study on this subject is not the focus of the present work.

1Corresponding author.

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received July 14, 2012; final manuscript received August 1, 2012; published online November 30, 2012. Editor: Dilip R. Ballal.

J. Eng. Gas Turbines Power 135(1), 011505 (Nov 30, 2012) (10 pages) Paper No: GTP-12-1277; doi: 10.1115/1.4007374 History: Received July 14, 2012; Revised August 01, 2012

This work presents a numerical study on the turbulent Schmidt numbers in jets in crossflow. This study contains two main parts. In the first part, the problem of the proper choice of the turbulent Schmidt number in the Reynolds-averaged Navier-Stokes (RANS) jet in crossflow mixing simulations is outlined. The results of RANS employing the shear-stress transport (SST) model of Menter and its curvature correction modification and different turbulent Schmidt number values are validated against experimental data. The dependence of the optimal value of the turbulent Schmidt number on the dynamic RANS model is studied. Furthermore, a comparison is made with the large-eddy simulation (LES) results obtained using the wall-adapted local eddy viscosity (WALE) model. The accuracy given by LES is superior in comparison to RANS results. This leads to the second part of the current study, in which the time-averaged mean and fluctuating velocity and scalar fields from LES are used for the evaluation of the turbulent viscosities, turbulent scalar diffusivities, and the turbulent Schmidt numbers in a jet in crossflow configuration. The values obtained from the LES data are compared with those given by the RANS modeling. The deviations are discussed, and the possible ways for the RANS model improvements are outlined.

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

References

Kays, W. M., 1994, “Turbulent Prandtl Number—Where Are We?” ASME J. Heat Transfer, 116, pp. 284–295. [CrossRef]
Launder, B. E., 1976, “Heat and Mass Transport,” Turbulence, Topics in Applied Physics, Vol. 12, P.Bradshaw, ed., Springer, Berlin, pp. 232–287.
Reynolds, A. J., 1976, “The Variation of Turbulent Prandtl and Schmidt Numbers in Wakes and Jets,” Int. J. Heat Mass Transfer, 19, pp. 757–764. [CrossRef]
Alvarez, J., Jones, W. P., and Seoud, R., 1993, “Predictions of Momentum and Scalar Fields in a Jet in Cross-Flow Using First and Second Order Turbulence Closures,” Proceedings of the AGARD Conference, Computational and Experiment Assessment of Jets in Cross Flow, Winchester, UK, April 19–22, pp. 1–10.
Ivanova, E., Noll, B., Di Domenico, M., and Aigner, M., 2008, “Improvement and Assessment of RANS Scalar Transport Models for Jets in Crossflow,” Proceedings of the 46th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, January 7–10, Paper No. AIAA-2008-565.
Ivanova, E., Noll, B., Di Domenico, M., and Aigner, M., 2009, “Unsteady Simulations of Flow Field and Scalar Mixing in Transverse Jets,” Proceedings of ASME Turbo Expo 2009: Power for Land, Sea and Air, Orlando, FL, ASME Paper No. GT2009-59147, pp. 101–110. [CrossRef]
Ivanova, E., Noll, B., and Aigner, M., 2011, “Computational Modelling of Turbulent Mixing of a Transverse Jet,” ASME J. Eng. Gas Turbines Power, 133(2), p. 021505. [CrossRef]
Malecki, R. E., Colket, M. B., Rhie, C. M., McKinney, R. G., Ouyang, H., Syed, S. A., and Madabhushi, R. K., 2001, “Application of an Advanced CFD-Based Analysis System to the PW6000 Combustor to Optimize Exit Temperature Distribution—Part 1: Description and Validation of the Analysis Tool,” Proceedings of the ASME Turbo Expo 2001, Paper No. 2001-GT-0062.
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 2010: Power for Land, Sea and Air, Glasgow, UK, June 14–18, ASME Paper No. GT2010-22709, pp. 571–582 [CrossRef].
Jones, W., and Launder, B., 1972, “The Prediction of Laminarization With a Two-Equation Model,” Int. J. Heat Mass Transfer, 15, pp. 301–314. [CrossRef]
He, G., Guo, Y., and Hsu, A. T., 1999, “The Effect of Schmidt Number on Turbulent Scalar Mixing in a Jet-In-Crossflow.” Int. J. Heat Mass Transfer, 42, pp. 3727–3738. [CrossRef]
Menter, F. R., 1994, “Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications,” AIAA J., 32(8), pp. 1598–1605. [CrossRef]
Yuan, L. L., Street, R. L., and Ferziger, J. H., 1999, “Large-Eddy Simulations of a Round Jet in Crossflow,” J. Fluid Mech., 379, pp. 71–104. [CrossRef]
Schlüter, J. U., and Schönfeld, T., 2000, “LES of Jets in Cross Flow and its Application to a Gas Turbine Burner,” Flow, Turbul. Combust., 65, pp. 177–203. [CrossRef]
Majander, P., and Siikonen, T., 2006, “Large-Eddy Simulation of a Round Jet in a Crossflow,” Int. J. Heat Fluid Flow, 27, pp. 402–415. [CrossRef]
Salewski, M., Stankovic, D., and Fuchs, L., 2008, “Mixing in Circular and Non-Circular Jets in Crossflow,” Flow, Turbul. Combust., 80, pp. 255–283. [CrossRef]
Wegner, B., Huai, Y., and Sadiki, A., 2004, “Comparative Study of Turbulent Mixing in Jet in Cross-Flow Configurations Using LES,” Int. J. Heat Fluid Flow, 25, pp. 767–775. [CrossRef]
Jouhaud, J.-C., Gicquel, L. Y. M., and Enaux, B., 2007, “Large-Eddy-Simulation Modeling for Aerothermal Predictions Behind a Jet in Crossflow,” AIAA J., 45(10), pp. 2438–2447. [CrossRef]
Dejoan, A., and Leschziner, M. A., 2005, “Large Eddy Simulation of a Plane Turbulent Wall Jet,” Phys. Fluids, 17, p. 025102. [CrossRef]
Bogey, C., and Bailly, C., 2009, “Turbulence and Energy Budget in a Self-Preserving Round Jet: Direct Evaluation Using Large Eddy Simulation,” J. Fluid Mech., 627, pp. 129–160. [CrossRef]
Dianat, M., Jiang, D., Yang, Z., and McGuirk, J., 2005, “Simulation of Scalar Mixing in Co-Axial Jet Flows Using an LES Method,” Proceedings of GT2005 ASME Turbo Expo 2005: Power for Land, Sea and Air, Reno, NV, June 6–9, ASME Paper No. GT2005-69010, pp. 721–728. [CrossRef]
Lischer, T., Donnert, G., Galleazzo, F., Habisreuther, P., Zarzalis, N., Valdes, R., and Krebs, W., 2008, “Simultaneous Velocity and Concentration Measurements Using Laser-Optical Measurement Methods in Comparison With Reynolds-Averaged Navier-Stokes Models,” Proceedings of the 12th International Symposium on Transport Phenomena and Dynamics of Rotating Machinery, Honolulu, HI, February 17–22, Paper No. ISROMAC12-2008-20112.
Cardenas, C., Suntz, R., Denev, J., and Bockhorn, H., 2007, “Two-Dimensional Estimation of Reynolds-Fluxes and -Stresses in a Jet-In-Crossflow Arrangement by Simultaneous 2D-LIV and PIV,” Appl. Phys. B, 88, pp. 581–591. [CrossRef]
Menter, F. R., 2009, “Review of the Shear-Stress Transport Turbulence Model Experience From an Industrial Perspective,” Int. J. Computat. Fluid Dyn., 23(4), pp. 305–316. [CrossRef]
Hellsten, A., 1997, “Some Improvements in Menter's k-ω SST Turbulence Model,” Proceedings of the 29th AIAA Fluid Dynamics Conference, Albuquerque, NM, June 15–18, Paper No. AIAA-1998-2554.
Wilcox, D. C., 1988, “Reassesssment of the Scale Determining Equation for Advanced Turbulence Models,” AIAA J., 26(11), pp. 1299–1310. [CrossRef]
Esch, T., and Menter, F. R., 2003, “Heat Tranfer Prediction Based on Two-Equation Turbulence Models With Advanced Wall Treatment,” Proceedings of the 4th International Symposium on Turbulence, Heat and Mass Transfer, Antalya, Turkey, October 12–17, K.Hanjalic, Y.Nagano, and M.Tummers, eds., Begell House, Redding, CT.
Nicoud, F., and Ducros, F., 1999, “Subgrid-Scale Stress Modelling Based on the Square of the Velocity Gradient Tensor,” Flow, Turbul. Combust., 62(3), pp. 183–200. [CrossRef]
Ivanova, E., Noll, B., and Aigner, M., 2010, “Unsteady Simulations of Turbulent Mixing in Jet in Crossflow,” Proceedings of the 40th AIAA Fluid Dynamics Conference and Exhibit, Chicago, June 28–July 1, Paper No. AIAA 2010-4724.
Chorin, A., 1968, “Numerical Solution of Navier-Stokes Equations,” Math. Comput., 22(104), p. 745. [CrossRef]
Gerlinger, P., 2005, Numerische Verbrennungssimulation (Numerical Combustion Simulation), Springer, Berlin/Heidelberg (in German).
Patankar, S. V., 1980, Numerical Heat Transfer and Fluid Flow, Series in Computational Methods in Mechanics and Thermal Science, Hemisphere Publishing Corporation, Washington, DC.
Klein, M., Sadiki, A., and Janicka, J., 2003, “A Digital Filter Based Generation of Inflow Data for Spatially Developing Direct Numerical or Large Eddy Simulations,” J. Comput. Phys., 186, pp. 652–665. [CrossRef]
Ivanova, E., 2012, “Numerical Simulations of Turbulent Mixing in Complex Flows,” Institute of Combustion Technology, German Aerospace Center (DLR), Technical Report.

Figures

Grahic Jump Location
Fig. 2

Computational grid for LES calculations. (a) x/d = 0 and x/d = 15 planes. (b) z/d = 0 plane.

Grahic Jump Location
Fig. 1

Flow configuration, computational domain, and coordinate system

Grahic Jump Location
Fig. 4

Turbulent kinetic energy k and Reynolds shear stress u'xu'y¯. z/d = 0. LES and two RANS turbulence models in comparison with experimental data.

Grahic Jump Location
Fig. 3

Components of the mean velocity vector U¯x and U¯y. z/d = 0. LES and two RANS turbulence models in comparison with experimental data.

Grahic Jump Location
Fig. 5

RMS of the x- and y-velocity fluctuations. z/d = 0. LES and two RANS turbulence models in comparison with experimental data.

Grahic Jump Location
Fig. 6

Mean transported passive scalar, different y/d planes. LES and two RANS turbulence models (σt = 1.0) in comparison with experimental data. (a) Experimental data, y/d = 7. (b) WALE LES, y/d = 7. (c) SST, y/d = 7. (d) SST curv. corr., y/d = 7. (e) Experimental data, y/d = 5. (f) WALE LES, y/d = 5. (g) SST, y/d = 5. (h) SST curv. corr., y/d = 5.

Grahic Jump Location
Fig. 7

Transported passive scalar. LES and two RANS turbulence models at σt = 1.0 in comparison with experimental data.

Grahic Jump Location
Fig. 8

Turbulent scalar flux in x-direction. z/d = 0. LES and two RANS turbulence models at σt = 1.0 in comparison with experimental data.

Grahic Jump Location
Fig. 9

Transported passive scalar. z/d = 0. Different turbulent Schmidt numbers σt.

Grahic Jump Location
Fig. 10

Dimensionless turbulent viscosity νt/ν evaluated from LES data in two different ways. y/d = 7, z/d = 0. The raw and the smoothed curves.

Grahic Jump Location
Fig. 11

Dimensionless turbulent viscosity νt/ν evaluated from LES data and resulting from RANS modeling. y/d = 7, z/d = 0.

Grahic Jump Location
Fig. 12

Dimensionless turbulent scalar diffusivity αt/α evaluated from LES data in different ways. y/d = 7, z/d = 0.

Grahic Jump Location
Fig. 13

Dimensionless turbulent scalar diffusivity αt/α evaluated from LES data and resulting from RANS modeling at different σt

Grahic Jump Location
Fig. 14

Turbulent Schmidt number σt evaluated from LES data

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