Numerical investigation of blade-tip-vortex dynamics

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

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.

Keywords

Helicopter blade Numerical simulations Blade-tip-vortex Dynamic stall 

Abbreviation

List of symbols

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

Greek and other symbols

\(\alpha\)

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

Subscripts

0.2

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

core

Vortex core radius

r

Wing root

Notes

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.

References

  1. 1.
    Richez, F., Ortun, B.: Numerical investigation of the flow separation on a helicopter rotor in dynamic stall configuration. In: 42nd European rotorcraft forum. Lille, France (2016)Google Scholar
  2. 2.
    Widnall, S.: Helicopter noise due to Blade–Vortex interaction. J. Acoust. Soc. Am. 50(1B), 354–365 (1971).  https://doi.org/10.1121/1.1912640 CrossRefGoogle Scholar
  3. 3.
    Yu, Y.H.: Rotor Blade–Vortex interaction noise. Progress Aerosp. Sci. 36(2), 97–115 (2000).  https://doi.org/10.1016/S0376-0421(99)00012-3 CrossRefGoogle Scholar
  4. 4.
    McCroskey, W.J., McAlister, K.W., Carr, L.W., Pucci, S.L., Lambert, O., Indergrand, R.F.: Dynamic stall on advanced airfoil sections. J. Am. Helicopter Soc. 26(3), 40–50 (1981).  https://doi.org/10.4050/JAHS.26.40 CrossRefGoogle Scholar
  5. 5.
    Carr, L.W.: Progress in analysis and prediction of dynamic stall. J. Aircr. 25(1), 6–17 (1988).  https://doi.org/10.2514/3.45534 MathSciNetCrossRefGoogle Scholar
  6. 6.
    Ramaprian, B.R., Zheng, Y.: Near field of the tip Vortex behind an oscillating rectangular wing. AIAA J. 36(7), 1263–1269 (1998).  https://doi.org/10.2514/2.508 CrossRefGoogle Scholar
  7. 7.
    Chang, J.W., Park, S.O.: Measurements in the tip Vortex roll-up region of an oscillating wing. AIAA J. 38(6), 1092–1095 (2000).  https://doi.org/10.2514/2.1072 CrossRefGoogle Scholar
  8. 8.
    Birch, D., Lee, T.: Tip Vortex behind a wing undergoing deep-stall oscillation. AIAA J. 43(10), 2081–2092 (2005).  https://doi.org/10.2514/1.13139 CrossRefGoogle Scholar
  9. 9.
    Birch, D., Lee, T.: Investigation of the near-field tip Vortex behind an oscillating wing. J. Fluid Mech. 544, 201–241 (2005).  https://doi.org/10.1017/S0022112005006804 CrossRefMATHGoogle Scholar
  10. 10.
    Mohamed, K., Nadarajah, S., Paraschivoiu, M.: Detached-Eddy Simulation of a wing tip Vortex at dynamic stall conditions. J. Aircr. 46(4), 1302–1313 (2009).  https://doi.org/10.2514/1.40685 CrossRefGoogle Scholar
  11. 11.
    Richez, F., Le Pape, A., Costes, M.: Zonal detached-Eddy simulation of separated flow around a finite-span wing. AIAA J. 53(11), 3157–3166 (2015).  https://doi.org/10.2514/1.J053636 CrossRefGoogle Scholar
  12. 12.
    Costes, M., Richez, F., Le Pape, A., Gavériaux, R.: Numerical investigation of three-dimensional effects during dynamic stall. Aerosp. Sci. Technol. (2015).  https://doi.org/10.1016/j.ast.2015.09.025
  13. 13.
    Kaufmann, K., Costes, M., Richez, F., Gardner, A. D., & Le Pape, A., “Numerical Investigation of Three-Dimensional Static and Dynamic Stall on a Finite Wing. J. Am. Helicopter Soc. (2015).  https://doi.org/10.4050/JAHS.60.032004
  14. 14.
    Merz, C.B., Wolf, C.C., Richter, K., Kaufmann, K., Raffel, M.: Experimental investigation of dynamic stall on a pitching rotor blade tip. In: New results in numerical and experimental fluid mechanics X, notes on numerical fluid mechanics and multidisciplinary design 132, 339–348 (2016).  https://doi.org/10.1007/978-3-319-27279-5_30
  15. 15.
    Merz, C.B., Wolf, C.C., Richter, K., Kaufmann, K., Mielke, A., Raffel, M.: Spanwise differences in static and dynamic stall on a pitching rotor blade tip model. J. Am. Helicopter Soc. 62(1), 1–11 (2017).  https://doi.org/10.4050/JAHS.62.012002 CrossRefGoogle Scholar
  16. 16.
    Wolf, C.C., Merz, C.B., Richter, K., Raffel, M.: Tip-Vortex dynamics of a pitching rotor blade tip model. AIAA J. 54(10), 2947–2960 (2016).  https://doi.org/10.2514/1.J054656 CrossRefGoogle Scholar
  17. 17.
    Schneider, O. van der Wall, B. G. & Pengel, K.: HART II blade motion measured by stereo pattern recognition (SPR). In: 59th American helicopter society forum, Phoenix, USA, May 6–8, (2003)Google Scholar
  18. 18.
    Kaufmann, K., Merz, C.B., Gardner, A. D.: Dynamic stall simulations on a pitching finite wing. J. Aircr. (2017).  https://doi.org/10.2514/1.C034020 (accepted for publication)
  19. 19.
    Menter, F.R.: Zonal two equation k-\(\omega\) turbulence models for aerodynamic flows, AIAA Paper 93-2906. In: 23rd AIAA fluid dynamics, plasma dynamics and lasers conference, Orlando, USA, July 6–9, (1993).  https://doi.org/10.2514/6.1993-2906
  20. 20.
    Richter, K., Le Pape, A., Knopp, T., Costes, M., Gleize, V., Gardner, A.D.: Improved two-dimensional dynamic stall prediction with structured and hybrid numerical methods. J. Am. Helicopter Soc. 56(4), 1–12 (2011).  https://doi.org/10.4050/JAHS.56.042007 CrossRefGoogle Scholar
  21. 21.
    Goerttler, A., Braukmann, J.N., Schwermer, T., Gardner, A.D., & Raffel, M.: Tip-Vortex investigation on a rotating and pitching rotor blade. In: 43rd European rotorcraft forum, Milan, Italy, September 12–15 (2017)Google Scholar
  22. 22.
    Jeong, J., Hussain, F.: On the identification of a Vortex. J. Fluid Mech. 285, 69–94 (1995).  https://doi.org/10.1017/S0022112095000462 MathSciNetCrossRefMATHGoogle Scholar
  23. 23.
    Löwe, J., Probst, A., Knopp, T., Kessler, R.: Low-dissipation low-dispersion second-order scheme for unstructured finite volume flow solvers. AIAA J. 54(10), 2961–2971 (2016)CrossRefGoogle Scholar

Copyright information

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

Authors and Affiliations

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

Personalised recommendations