Numerical investigation of blade-tip-vortex dynamics

  • Kurt Kaufmann
  • C. Christian Wolf
  • Christoph B. Merz
  • Anthony D. Gardner
Original Paper


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.


Helicopter blade Numerical simulations Blade-tip-vortex Dynamic stall 


List of symbols


Chord length, m


Sectional lift coefficient


Global lift coefficient


Global drag coefficient


Global pitching moment coefficient


Local pressure coefficient


Frequency, 1/s


Reduced frequency


Freestream Mach number


Reynolds number based on c


Radial coordinate, m


Span, m


Freestream velocity, m/s


Velocity component along x, m/s


Tangential velocity component (swirl velocity), m/s


Velocity component along y, m/s


Velocity component along z, m/s


Cartesian coordinate in streamwise direction, m


Cartesian coordinate in spanwise direction, m


Dimensionless wall distance


Cartesian coordinate perpendicular to x and y, m

Greek and other symbols


Angle of attack, deg


Circulation, m\(^2\)/s

\(\lambda _{2}\)

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

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

Streamwise vorticity, 1/s


On the upstroke


On the downstroke



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


Vortex core radius


Wing root



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


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Copyright information

© Deutsches Zentrum für Luft- und Raumfahrt e.V. 2018
corrected publication April 2018

Authors and Affiliations

  1. 1.German Aerospace Center (DLR)Institute of Aerodynamics and Flow TechnologyGöttingenGermany

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