Research Papers

Steady/Unsteady Reynolds-Averaged Navier–Stokes and Large Eddy Simulations of a Turbine Blade at High Subsonic Outlet Mach Number

[+] Author and Article Information
Thomas Léonard

SAFRAN – Turbomeca,
Bordes Cedex 1 64511, France

Laurent Y. M. Gicquel, Nicolas Gourdain

Computational Fluid Dynamics Team,
42 Avenue G. Coriolis,
Toulouse Cedex 1 31057, France

Florent Duchaine

Computational Fluid Dynamics Team,
42 Avenue G. Coriolis,
Toulouse Cedex 1 31057, France
e-mail: florent.duchaine@cerfacs.fr

Sensitivity to the exit boundary condition treatment and relative position from the blade trailing edge has been specifically studied. The current results provide the best solution as discussed in a dedicated article under review.

Without points inside the viscous sublayer (i.e., y+ < 1) and without appropriate functions, the k–ω turbulence model cannot be guaranteed to predict the isentropic Mach number.

The spectral analysis relies on a time series of 3 ms obtained for a numerical and experimental probes located at x/cax = 0.933 and pictured in Fig. 16(g). Note that this duration corresponds approximately to 20 cycles of the wake shedding.

Corresponding to a converged simulation for RANS and a temporal integration of 10 ms for LES (note that around 40 ms are needed to pass the transient phase).

1Corresponding author.

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the JOURNAL OF TURBOMACHINERY. Manuscript received October 12, 2010; final manuscript received August 26, 2014; published online October 28, 2014. Assoc. Editor: Beth Wisler.

J. Turbomach 137(4), 041001 (Oct 28, 2014) (10 pages) Paper No: TURBO-10-1188; doi: 10.1115/1.4028493 History: Received October 12, 2010; Revised August 26, 2014

Reynolds-averaged Navier–Stokes (RANS), unsteady RANS (URANS), and large eddy simulation (LES) numerical approaches are clear candidates for the understanding of turbine blade flows. For such blades, the flow unsteady nature appears critical in certain situations and URANS or LES should provide more physical understanding as illustrated here for a laboratory high outlet subsonic Mach blade specifically designed to ease numerical validation. Although RANS offers good estimates of the mean isentropic Mach number and boundary layer thickness, LES and URANS are the only approaches that reproduce the trailing edge flow. URANS predicts the mean trailing edge wake but only LES offers a detailed view of the flow. Indeed, LESs identify flow phenomena in agreement with the experiment, with sound waves emitted from the trailing edge separation point that propagate upstream and interact with the lower blade suction side.

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


Wilcox, D., 1995, Turbulence Modeling for CFD, DCW Industries, La Cañada, CA.
Anderson, J. D., 1995, Computational Fluid Dynamics, McGraw-Hill, New York.
Tennekes, H., and Lumley, J. L., 1972, A First Course in Turbulence, MIT, Cambridge, MA.
Lardeau, S., and Leschziner, M., 2004, “Unsteady Reynolds-Averaged Navier–Stokes Computations of Transitional Wake/Blade Interaction,” AIAA J., 42(8), pp. 1559–1571. [CrossRef]
Ferziger, J. H., and Perić, M., 1997, Computational Methods for Fluid Dynamics, Springer-Verlag, Berlin.
Sagaut, P., 2000, Large Eddy Simulation for Incompressible Flows (Scientific Computation Series), Springer-Verlag, Heidelberg, Germany.
Cebeci, T., and Cousteix, J., 2005, Modeling and Computation of Boundary-Layer Flows, Springer and Horizons, Berlin.
Piomelli, U., 2008, “Wall-Layer Models for Large-Eddy Simulations,” Prog. Aerospace Sci., 44(6), pp. 437–446. [CrossRef]
Sieverding, C., Richard, H., and Desse, J.-M., 2003, “Turbine Blade Trailing Edge Flow Characteristics at High Subsonic Outlet Mach Number,” ASME J. Turbomach., 125(2), pp. 298–309. [CrossRef]
Sieverding, C., Ottolia, D., Bagnera, C., Comadoro, A., Brouckaert, J.-F., and Desse, J.-M., 2004, “Unsteady Turbine Blade Wake Characteristics,” ASME J. Turbomach., 126(4), pp. 551–559. [CrossRef]
Pope, S. B., 2000, Turbulent Flows, Cambridge University Press, Cambridge, UK.
Hirsch, C., 1988, Numerical Computation of Internal and External Flows, Vol. 1, Wiley, New York.
Gourdain, N., Gicquel, L., Montagnac, M., Vermorel, O., Gazaix, M., Staffelbach, G., Garcia, M., Boussuge, J.-F., and Poinsot, T., 2009, “High Performance Parallel Computing of Flows in Complex Geometries: I. Methods,” J. Comput. Sci. Discovery, 2(1), p. 015003. [CrossRef]
Gourdain, N., Gicquel, L., Staffelbach, G., Vermorel, O., Duchaine, F., Boussuge, J.-F., and Poinsot, T., 2009, “High Performance Parallel Computing of Flows in Complex Geometries: II. Applications,” J. Comput. Sci. Discovery, 2(1), p. 015004. [CrossRef]
Shang, T., and Epstein, A., 1997, “Analysis of Hot Streak Effects on Turbine Rotor Heat Load,” ASME J. Turbomach., 119(3), pp. 544–553. [CrossRef]
Cutrone, L., De Palma, P., Pascazio, G., and Napolitano, M., 2005, “Assessment of Laminar-Turbulent Transition Models for Turbomachinery Flow Computations,” ASME Paper No. GT2005-68330. [CrossRef]
Wilcox, D., 1988, “Reassessment of the Scale-Determining Equation for Advanced Turbulence Models,” AIAA J., 26(11), pp. 1299–1310. [CrossRef]
Zheng, X., and Liu, F., 1995, “Staggered Upwind Method for Solving Navier–Stokes and kω Turbulence Model Equations,” AIAA J., 33(6), pp. 991–998. [CrossRef]
Jameson, A., 1991, “Time Dependent Calculations Using Multigrid, With Applications to Unsteady Flows Past Airfoils and Wings,” AIAA Paper No. 91-1596. [CrossRef]
Colin, O., and Rudgyard, M., 2000, “Development of High-Order Taylor-Galerkin Schemes for Unsteady Calculations,” J. Comput. Phys., 162(2), pp. 338–371. [CrossRef]
Smagorinsky, J., 1963, “General Circulation Experiments With the Primitive Equations: 1. The Basic Experiment,” Mon. Weather Rev., 91(3), pp. 99–164. [CrossRef]
Deardorff, J. W., 1970, “A Numerical Study of Three-Dimensional Turbulent Channel Flow at Large Reynolds Numbers,” J. Fluid Mech., 41(2), pp. 453–465. [CrossRef]
Meneveau, C., 1994, “Statistics of Turbulence Subgrid-Scale Stresses: Necessary Conditions and Experimental Tests,” Phys. Fluids, 6(2), pp. 815–833. [CrossRef]
O Neil, J., and Meneveau, C., 1997, “Subgrid-Scale Stresses and Their Modelling in a Turbulent Plane Wake,” J. Fluid Mech., 349, pp. 253–293. [CrossRef]
Launder, B., Reece, G., and Rodi, W., 1975, “Progress in the Development of a Reynolds-Stress Turbulent Closure,” J. Fluid Mech., 68(3), pp. 537–566. [CrossRef]
Ghosal, S., and Moin, P., 1995, “The Basic Equations for the Large Eddy Simulation of Turbulent Flows in Complex Geometry,” J. Comput. Phys., 118(1), pp. 24–37. [CrossRef]
Senoner, J.-M., García, M., Mendez, S., Staffelbach, G., Vermorel, O., and Poinsot, T., 2008, “The Growth of Rounding Errors and the Repetitivity of Large Eddy Simulation on Parallel Machines,” AIAA J., 46(7), pp. 1773–1781. [CrossRef]
Cambier, L., and Veuillot, J.-P., 2008, “Status of the elsA CFD Software for Flow Simulation and Multidisciplinary Applications,” AIAA Paper No. 2008-664. [CrossRef]
Garcia, M., 2009, “Développement et validation du formalisme euler-lagrange dans un solveur parallèle et non-structuré pour la simulation aux grandes échelles,” Ph.D. thesis, Université Paul Sabatier, Toulouse.
Liou, M. S., 1996, “A Sequel to AUSM: AUSM+,” J. Comput. Phys., 129, pp. 364–382. [CrossRef]
Spalart, P. R., Jou, W.-H., Stretlets, M., and Allmaras, S. R., 1997, “Comment on the Feasibility of LES for Wings and on the Hybrid RANS/LES Approach, Advances in DNS/LES,” 1st AFOSR International Conference on DNS/LES, Louisiana Tech University, Ruston, LA.
Deck, S., 2005, “Numerical Simulation of Transonic Buffet Over a Supercritical Airfoil,” AIAA J., 43(7), pp. 1556–1566. [CrossRef]


Grahic Jump Location
Fig. 1

Blade design (a) as experimentally studied by Refs. [9] and [10] and (b) expected flow features and available measurement stations [9,10]

Grahic Jump Location
Fig. 2

Conceptual representation of the turbulent information to be supplied in (a) RANS or URANS and (b) LES in the context of a turbulent isotropic flow

Grahic Jump Location
Fig. 3

Computational domain retained for all RANS, URANS, and LES predictions

Grahic Jump Location
Fig. 4

Typical mesh topology used for RANS, URANS, and LES

Grahic Jump Location
Fig. 5

Norm of the density gradient as obtained by use of (a) RANS, (b) URANS, (c) LES at given instants, and (d) a direct view at the trailing edge flow dynamics as seen in the experiment [9,10]

Grahic Jump Location
Fig. 6

Temporal mean solution as obtained by use of (a) URANS and (b) LES. Note that both results can be directly compared to Fig. 5(a).

Grahic Jump Location
Fig. 7

Mean isentropic Mach distribution along the blade wall predicted numerically and measured in the experiment

Grahic Jump Location
Fig. 8

Mean pressure distribution along the blade trailing edge as predicted numerically and measured in the experiment

Grahic Jump Location
Fig. 9

Temporal evolution of the axial velocity component in the wake of the blade

Grahic Jump Location
Fig. 10

Mesh point distribution for the (a) structured and (b) unstructured meshes

Grahic Jump Location
Fig. 11

Typical snapshot of the density gradient obtained with the block-structured meshes: (a) H1 and (b) H2

Grahic Jump Location
Fig. 12

Typical snapshot of the density gradient obtained with the unstructured meshes: (a) T1, (b) T2, and (c) T3

Grahic Jump Location
Fig. 13

Mean isentropic Mach distribution along the blade wall and as a function of the mesh resolution: (a) structured and (b) unstructured meshes

Grahic Jump Location
Fig. 14

Mean boundary layer profiles as a function of the mesh resolution: (a) and (b) structured and (c) and (d) unstructured meshes. The two sides of the blade are presented: (a) and (c) for the suction side and (b) and (d) for the pressure side.

Grahic Jump Location
Fig. 15

Mean trailing edge pressure profile as a function of the mesh resolution: (a) structured and (b) unstructured meshes

Grahic Jump Location
Fig. 16

Unsteady pressure signal comparisons as issued by structured and unstructured LES at positions along the blade wall



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