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.

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Fig. 1

Computational domain for DNS; every sixth gridline is shown

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Fig. 2

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

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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)

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Fig. 4

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

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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)

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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

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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

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Fig. 8

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

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Fig. 9

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

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Fig. 10

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

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Fig. 11

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

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Fig. 12

Comparison of k along three wall-normal slices

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Fig. 13

Comparison of Pk along three wall-normal slices

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Fig. 14

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

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Fig. 15

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

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Fig. 16

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




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