Research Papers

Direct Numerical Simulation Based Analysis of RANS Predictions of a Low-Pressure Turbine Cascade

[+] Author and Article Information
Christoph Müller-Schindewolffs

Institute of Turbomachinery and Fluid Dynamics,
Leibniz Universität Hannover,
Appelstraße 9,
Hannover 30167, Germany
e-mail: mueller@tfd.uni-hannover.de

Ralf-D. Baier

Aerodynamic Methods,
MTU Aero Engines AG,
Dachauer Straße 665,
Munich 80995, Germany

Joerg R. Seume, Florian Herbst

Institute of Turbomachinery and Fluid Dynamics,
Leibniz Universität Hannover,
Appelstraße 9,
Hannover 30167, Germany

1Corresponding author.

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the JOURNAL OF TURBOMACHINERY. Manuscript received December 13, 2016; final manuscript received January 3, 2017; published online March 21, 2017. Editor: Kenneth Hall.

J. Turbomach 139(8), 081006 (Mar 21, 2017) (11 pages) Paper No: TURBO-16-1319; doi: 10.1115/1.4035834 History: Received December 13, 2016; Revised January 03, 2017

The state-of-the-art design of turbomachinery components is based on Reynolds-averaged Navier–Stokes (RANS) solutions. RANS solvers model the effects of turbulence and boundary layer transition and therefore allow for a rapid prediction of the aerodynamic behavior. The only drawback is that modeling errors are introduced to the solution. Researchers and computational fluid dynamics developers are working on reducing these errors by improved model calibrations which are based on experimental data. These experiments do not typically, however, offer detailed insight into three-dimensional flow fields and the evolution of model quantities in an actual machine. This can be achieved through a direct step-by-step comparison of model quantities between RANS and direct numerical simulation (DNS). In the present work, the experimentally obtained model correlations are recomputed based on DNS of the same turbine profile simulated by RANS. The actual local values are compared to the modeled RANS results, providing information about the source of model deficits. The focus is on the transition process on the blade suction side (SS) and on evaluating the development of turbulent flow structures in the blade's wake. It is shown that the source of disagreement between RANS and DNS can be traced back to three major deficiencies that should be the focus of further model improvements.

Copyright © 2017 by ASME
Your Session has timed out. Please sign back in to continue.


Wilcox, D. C. , 1988, “ Reassessment of the Scale-Determining Equation for Advanced Turbulence Models,” AIAA J., 26(11), pp. 1299–1309. [CrossRef]
Menter, F. , 1994, “ Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications,” AIAA J., 32(8), pp. 1598–1605. [CrossRef]
Langtry, R. B. , and Menter, F. R. , 2009, “ Correlation-Based Transition Modeling for Unstructured Parallelized Computational Fluid Dynamics Codes,” AIAA J., 47(12), pp. 2894–2906. [CrossRef]
Kožulović, D. , Röber, T. , and Nürnberger, D. , 2007, “ Application of a Multimode Transition Model to Turbomachinery Flows,” 7th European Turbomachinery Conference, Athens, Greece, Mar. 5–9.
Denton, J. D. , 2010, “ Some Limitations of Turbomachinery CFD,” ASME Paper No. GT2010-22540.
Bode, C. , Aufderheide, T. , Kožulović, D. , and Friedrichs, J. , 2014, “ The Effects of Turbulence Length Scale on Turbulence and Transition Prediction in Turbomachinery Flows,” ASME Paper No. GT2014-27026.
Herbst, F. , Fiala, A. , and Seume, J. R. , 2014, “ Modeling Vortex Generating Jet-Induced Transition in Low-Pressure Turbines,” ASME J. Turbomach., 136(7), p. 071005. [CrossRef]
Drechsel, B. , Müller, C. , Herbst, F. , and Seume, J. , 2015, “ Influence of Turbulent Flow Characteristics and Coherent Vortices on the Pressure Recovery of Annular Diffusers—Part B: Scale-Resolving Simulations,” ASME Paper No. GT2015-42477.
Ludewig, T. , Mack, M. , Niehuis, R. , and Franke, M. , 2011, “ Optimization of the Blowing Ratio for a Low Pressure Turbine Cascade With Active Flow Control,” 9th European Turbomachinery Conference (ETC), Istanbul, Turkey, Mar. 21–25, Paper No. 131.
Scillitoe, A. , Tucker, P. , and Adami, P. , 2015, “ Evaluation of RANS and ZDES Methods for the Prediction of Three-Dimensional Separation in Axial Flow Compressors,” ASME Paper No. GT2015-43975.
Sandberg, R. , Pichler, R. , Chen, L. , Johnstone, R. , and Michelassi, V. , 2014, “ Compressible Direct Numerical Simulation of Low-Pressure Turbines—Part I: Methodology,” ASME Paper No. GT2014-25685.
Breuer, M. , 2002, Direkte Numerische Simulation und Large-Eddy Simulation turbulenter Strömungen auf Hochleistungsrechnern, Habilitationsschrift, Universität Erlangen, Erlangen, Germany.
Witherden, F. , Farrington, A. , and Vincent, P. , 2014, “ PyFR: An Open Source Framework for Solving Advection-Diffusion Type Problems on Streaming Architectures Using Flux Reconstruction Approach,” Comput. Phys. Commun., 185(11), pp. 3028–3040. [CrossRef]
OpenCFD (ESI Group), 2015, “ OpenFOAM: The Open Source CFD Toolbox,” OpenCFD Ltd., Berkshire, UK, accessed Feb. 2, 2017, http://www.openfoam.com/
Vuorinen, V. , Larmi, M. , Schlatter, P. , and Boersma, B. , 2012, “ A Low-Dissipative, Scale-Selective Discretization Scheme for Navier-Stokes Equations,” Comput. Fluids, 70, pp. 195–205. [CrossRef]
Vuorinen, V. , Keskinen, J.-P. , Duwig, C. , and Boersma, B. , 2014, “ On the Implementation of Low-Dissipative Runge-Kutte Projection Methods for Time Dependent Flows Using OpenFOAM,” Comput. Fluids, 93, pp. 153–163. [CrossRef]
Hillewaert, K. , Wiart, C. , Verheylewegen, G. , and Arts, T. , 2014, “ Assessment of a High-Order Discontinuous Galerkin Method for the Direct Numerical Simulation of Transition at Low-Reynolds Number in the T106C High-Lift Low Pressure Turbine Cascade,” ASME Paper No. GT2014-26739.
Koschichow, D. , Fröhlich, J. , Kirik, I. , and Niehuis, R. , 2014, “ DNS of the Flow Near Endwall in a Linear Low Pressure Turbine Cascade With Periodically Passing Wakes,” ASME Paper No. GT2014-25071.
Breuer, M. , Peller, N. , Rapp, C. , and Manhart, M. , 2009, “ Flow Over Periodic Hills: Numerical and Experimental Study in a Wide Range of Reynolds Numbers,” Comput. Fluids, 38(2), pp. 433–457. [CrossRef]
Michelassi, V. , Chen, L. , Pichler, R. , and Sandberg, R. , 2014, “ Compressible Direct Numerical Simulation of Low-Pressure Turbines—Part II: Effect of Inflow Disturbances,” ASME Paper No. GT2014-25689.
Michelassi, V. , Chen, L. , Pichler, R. , Sandberg, R. , and Bhaskaran, R. , 2015, “ High-Fidelity Simulations of Low-Pressure Turbines: Effect of Flow Coefficient and Reduced Frequency on Losses,” ASME Paper No. GT2015-43429.
Wheeler, A. , Sandberg, R. , Sandham, N. , Pichler, R. , Michelassi, V. , and Laskowski, G. , 2015, “ Direct Numerical Simulation of a High Pressure Turbine Vane,” ASME Paper No. GT2015-43133.
Entlesberger, R.-G. , Martinstetter, M. , and Staudacher, W. , 2005, “ Untersuchungen am Turbinengitter T161 zur Bestimmung der Profildruckverteilung und der Gittercharakteristik,” Institutsbericht LRT-WE12-05/12, Universität der Bundeswehr München, Neubiberg, Germany.
Franke, M. , Kügeler, E. , and Nürnberger, D. , 2005, “ Das DLR-Verfahren TRACE: Moderne Simulationstechniken für Turbomaschinenströmungen,” DGLR-Jahrbuch, Deutscher Luft- und Raumfahrtkongress, Friedrichshafen, Germany, Sept. 26–29.
Kügeler, E. , Nürnberger, D. , Weber, E. , and Engel, K. , 2008, “ Influence of Blade Fillets on the Performance of a 15 Stage Gas Turbine Compressor,” ASME Paper No. GT2008-50748.
Marciniak, V. , Kügler, E. , and Franke, M. , 2010, “ Predicting Transition on Low-Pressure Turbine Profiles,” V European Conference on Computational Fluid Dynamics ( ECCOMAS CFD), Lisbon, Portugal, June 14–17.
Fiala, A. , and Kügeler, E. , 2011, “ Roughness Modeling For Turbomachinery,” ASME Paper No. GT2011-45424.
Marciniak, V. , Weber, A. , and Kügler, E. , 2014, “ Modelling Transition for the Design of Modern Axial Turbomachines,” 6th European Conference on Computational Fluid Dynamics (ECFD), Barcelona, Spain, July 20–25.
Müller, C. , and Herbst, F. , 2014, “ Modelling of Crossflow-Induced Transition Based on Local Variables,” 6th European Conference on Computational Fluid Dynamics (ECFD), Barcelona, Spain, July 20–25.
Müller, C. , Herbst, F. , Fiala, A. , Zscherp, C. , Kügeler, E. , and Seume, J. , 2015, “ Parameter Study for an Improved Prediction of Wake-Induced Transition in Low-Pressure Turbines,” 11th International Gas Turbine Congress (IGTC), Tokyo, Nov. 15–20, Paper No. IGTC2015-0043.
Kato, M. , and Launder, B. E. , 1993, “ The Modelling of Turbulent Flow Around Stationary and Vibrating Square Cylinders,” 9th Symposium on Turbulent Shear Flows, Kyoto, Japan, Aug. 16–18, Vol. 1, pp. 10.4.1–10.4.6.
Coleman, G. , and Sandberg, R. , 2010, “ A Primer on Direct Numerical Simulations of Turbulence—Methods, Procedures and Guidelines,” Technical Report No. AFM-09/01a.
Pope, S. , 2011, Turbulent Flows, Cambridge University Press, Cambridge, UK.
Choi, H. , and Moin, P. , 1994, “ Effects of the Computational Time Step on Numerical Solutions of Turbulent Flow,” J. Comput. Phys., 113(1), pp. 1–4. [CrossRef]
Martinstetter, M. , Niehuis, R. , and Franke, M. , 2010, “ Passive Boundary Layer Control on a Highly Loaded Low Pressure Turbine Cascade,” ASME Paper No. GT2010-22739.
Lumley, J. , and Newman, G. , 1977, “ The Return to Isotropy of Homogeneous Turbulence,” J. Fluid Mech., 82(8), pp. 161–178. [CrossRef]
Martinstetter, M. , 2010, “ Experimentelle Untersuchungen zur Aerodynamik hoch belasteter Niederdruckturbinen-Beschaufelung,” Ph.D. dissertation, Universität der Bundeswehr München, Neubiberg, Germany.
Monkewitz, P. A. , and Huerre, P. , 1982, “ Influence of the Velocity Ratio on the Spatial Instability of Mixing Layers,” Phys. Fluids, 27(7), pp. 1137–1143. [CrossRef]
Yang, Z. , and Voke, P. R. , 2001, “ Large-Eddy Simulation of Boundary-Layer Separation and Transition at a Change of Surface Curvature,” J. Fluid Mech., 439, pp. 305–333. [CrossRef]
Abu-Ghannam, B. J. , and Shaw, R. , 1980, “ Natural Transition of Boundary Layers: The Effects of Turbulence, Pressure Gradient, and Flow History,” J. Mech. Eng. Sci., 22(5), pp. 213–228. [CrossRef]
Menter, F. , Langtry, R. , Likki, S. R. , Suzen, Y. , Huang, P. , and Völker, S. , 2004, “ A Correlation-Based Transition Model Using Local Variables—Part 1: Model Formulation,” ASME J. Turbomach, 128(3), pp. 413–422.
Langtry, R. B. , 2006, “ A Correlation-Based Transition Model Using Local Variables for Unstructured Parallelized CFD Codes,” Ph.D. dissertation, Institut für Thermische Strömungsmaschinen und Maschinenlaboratorium, Universität Stuttgart, Stuttgart, Germany.
Menter, F. , Smirnov, P. , Liu, T. , and Avancha, R. , 2015, “ A One-Equation Local Correlation-Based Transition Model,” Flow Turbul. Combust., 95(4), pp. 583–619. [CrossRef]


Grahic Jump Location
Fig. 1

Computational domain for DNS; every sixth gridline is shown

Grahic Jump Location
Fig. 2

Turbulent spectra of the inflow boundary condition (see Fig. 1)

Grahic Jump Location
Fig. 3

Left: Dot—Reference level of turbulence in RANS and lines—spanwise distribution of the level of turbulence and divergence in DNS and right: color-coded invariant charts; order: top—inlet, middle—midsection, and bottom—outlet (see Fig. 1)

Grahic Jump Location
Fig. 4

Turbulent spectra at x/lAx = 0.96 and y/lAx = 0.032 at various spanwise positions (see Fig. 1)

Grahic Jump Location
Fig. 5

Comparison of averaged quantities between RANS and DNS at Re = 70,000 and Re = 90,000; left and middle: profile pressure distribution; right: pressure loss coefficient downstream of the cascade at x/lAx = 1.4 (solid) and at x/lAx = 1.34 (dashed)

Grahic Jump Location
Fig. 6

Turbulent spectrum at x/lAx = 0.87 close to the maximum amplification of the KH instability; peak frequency of fKH = 17,600 Hz is marked, which corresponds to ω* = 0.227

Grahic Jump Location
Fig. 7

Interaction of freestream turbulence and Kelvin–Helmholtz instabilities in boundary layer; dot indicates position of probe use in Fig. 6; isosurface: Λ2 = 3e+8; and color: velocity magnitude

Grahic Jump Location
Fig. 8

Streamwise evolution of k inside the wake at x/lAx = 1.1, 1.25, and 1.4

Grahic Jump Location
Fig. 9

Reynolds-stresses along the profile wake at x/lAx = 1.4; top—τ11 and bottom—τ12

Grahic Jump Location
Fig. 10

Left: RANS-modeled k and right: k derived from resolved perturbation in DNS

Grahic Jump Location
Fig. 11

Left: RANS-modeled k; isoline indicates γeff = 0.9; right: k derived from resolved turbulent fluctuations in DNS; zoom with adjusted colormap

Grahic Jump Location
Fig. 12

Comparison of k along three wall-normal slices

Grahic Jump Location
Fig. 13

Comparison of Pk along three wall-normal slices

Grahic Jump Location
Fig. 14

Acceleration parameter λθ. Left—RANS; right—DNS; lines indicate slices from Fig. 15.

Grahic Jump Location
Fig. 15

Comparing ReV (continuous line) with Reθc · 2.193 (dashed dotted line) to estimate the start of transition; long dashed line measures Fθt

Grahic Jump Location
Fig. 16

Left—Acceleration parameter λθ; right—momentum thickness θ; solid—locally obtained; dashed—integrated



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