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Numerical investigation of blade-tip-vortex dynamics

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A Correction to this article was published on 24 April 2018

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Abstract

Numerical computations on a finite wing are carried out using DLR’s finite-volume solver TAU. The tip-vortex characteristics during static stall and deep dynamic stall are analyzed and compared to particle image velocimetry (PIV) measurements carried out in the side wind facility Göttingen. Computational fluid dynamics (CFD) and experiment are in good agreement, especially for sections close to the blade tip. Too large dissipation within the numerical computations leads to larger vortex size than in the experiment. The dissipation effect increases with larger distances from the wing. The analysis shows that the numerical method is able to capture the complex vortex structures shed from the wing and helps understanding the source of these structures.

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  • 24 April 2018

    The original version of this article unfortunately contained mistakes. Due to typesetting errors several expressions were not displayed correctly.

Abbreviations

c :

Chord length, m

\(C_\text{l}\) :

Sectional lift coefficient

\(C_\text{L}\) :

Global lift coefficient

\(C_\text{D}\) :

Global drag coefficient

\(C_\text{M}\) :

Global pitching moment coefficient

\(C_\text{p}\) :

Local pressure coefficient

f :

Frequency, 1/s

k :

Reduced frequency

M :

Freestream Mach number

Re :

Reynolds number based on c

r :

Radial coordinate, m

S :

Span, m

\(U_\infty\) :

Freestream velocity, m/s

u :

Velocity component along x, m/s

\(u_\theta\) :

Tangential velocity component (swirl velocity), m/s

v :

Velocity component along y, m/s

w :

Velocity component along z, m/s

x :

Cartesian coordinate in streamwise direction, m

y :

Cartesian coordinate in spanwise direction, m

\(y^+\) :

Dimensionless wall distance

z :

Cartesian coordinate perpendicular to x and y, m

\(\alpha\) :

Angle of attack, deg

\(\Gamma\) :

Circulation, m\(^2\)/s

\(\lambda _{2}\) :

\(\lambda _{2}\) vortex criterion

\(\omega _{\text{x}}\) :

Streamwise vorticity, 1/s

\(\uparrow\) :

On the upstroke

\(\downarrow\) :

On the downstroke

0.2:

Circulation at a radius of \(r=0.2\) chord lengths

core:

Vortex core radius

r:

Wing root

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Acknowledgements

The authors gratefully acknowledge the Gauss Centre for Supercomputing e.V. (www.gauss-centre.eu) for funding this project by providing computing time on the GCS Supercomputer SuperMUC at the Leibniz Supercomputing Centre (LRZ, www.lrz.de). Funding of the DLR projects STELAR and FASTrescue is gratefully acknowledged.

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Authors and Affiliations

  1. German Aerospace Center (DLR), Institute of Aerodynamics and Flow Technology, Bunsenstrasse 10, 37073, Göttingen, Germany

    Kurt Kaufmann, C. Christian Wolf, Christoph B. Merz & Anthony D. Gardner

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  1. Kurt Kaufmann
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  2. C. Christian Wolf
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  3. Christoph B. Merz
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  4. Anthony D. Gardner
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Correspondence to Kurt Kaufmann.

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The original version of this article was revised: Due to typesetting errors several expressions were not displayed correctly.

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Kaufmann, K., Wolf, C.C., Merz, C.B. et al. Numerical investigation of blade-tip-vortex dynamics. CEAS Aeronaut J 9, 373–386 (2018). https://doi.org/10.1007/s13272-018-0287-2

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