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Experimental study of secondary vortex structures in a rotor wake

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Abstract

The operation and aerodynamic performance of a helicopter rotor is strongly affected by the structure of its wake, in particular regarding vortex–vortex interactions of hovering rotors. Rotor simulations using modern computational methods have the potential to capture high levels of detail, which recently triggered discussions of secondary vortex braids entangling the primary tip vortices. These structures are highly dependent on the numerical settings and need experimental validation. The current work investigates the wake of a subscale rotor in ground effect by time-resolved and volumetric flow-field measurements using the “Shake-The-Box” technique. Both the Lagrangian tracks of the flow tracers and the derived gradient-based vortex criteria clearly verify the existence of secondary vortices. A post-processing scheme is applied to isolate these vortices in larger data sets. No distinct spatial organization of the structures was observed, but a slightly preferred sense of rotation which agrees to the shear of the wake swirl. The secondary structures were created shortly downstream of the rotor blades, starting at wake ages of approximately \(75^\circ \).

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Fig. 1

Modified from Jain (2018)

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Modified from Martin and Leishman (2002)

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Abbreviations

CFD:

Computational fluid dynamics

DLR:

German Aerospace Center

HFSB:

Helium-filled soap bubbles

LED:

Light-emitting diode

PIV:

Particle image velocimetry

ppc:

Particles per cell

SA-DES:

Spalart–Allmaras Detached Eddy Simulation

STB:

Shake-The-Box

c :

Chord length, \(c={0.061}\hbox { m}\)

\(C_\mathrm{T}\) :

Thrust coeff., \(C_\mathrm{T} = T/(\rho (2\pi Rf)^2 \pi R^2)\)

f :

Rotor frequency, \(f={20.83}\hbox { HZ}\)

H :

Rotor plane height, m

\(k\) :

Norm. turbulent kinetic energy, Eq. (1)

\(k_x, k_y, k_z\) :

Cartesian components of \(k\), Eq. (2)

Q :

Q-criterion, \({1/\mathrm{s}}^2\)

\(Q_{{\text{ neg }}}\) :

Negative secondary vortex criterion, \({1/\mathrm{s}}^2\)

\(Q_{{\text{ pos }}}\) :

Positive secondary vortex criterion, \({1/\mathrm{s}}^2\)

\(Q_{{\text{ tip }}}\) :

Tip vortex criterion, \({1/\mathrm{s}}^2\)

R :

Rotor radius, \(R={0.775}\hbox { m}\)

T :

Rotor thrust, N

u, v, w :

Cartesian velocity components, m/s

\(V_\mathrm{h}\) :

Hover-induced velocity, \(V_\mathrm{h} = \sqrt{T/(2\rho \pi R^2)}\), m/s

\(V_{{\text{ tip }}}\) :

Blade tip velocity, \(V_{{\text{ tip }}}= {101.4}\,\text {m/s}\)

x, y, z :

Cartesian coordinate system, m

\(\varDelta \) :

Difference between two values

\(\rho \) :

Air density, \(\rho ={1.18}\,\hbox {kg/m}^2\)

\(\sigma \) :

Rotor solidity, \(\sigma = 0.05\)

\(\varPsi \) :

Azimuth angle, \(^\circ \)

\(\varPsi _\mathrm{w}\) :

Tip vortex wake age, \(^\circ \)

\(\varvec{\omega }\) :

Vorticity vector, 1/s

\(\nabla \) :

Nabla operator

\(\overline{\;\;}\) :

Time-averaged value

\( ' \) :

Time-varying fluctuation value

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Acknowledgements

The studies were conducted as a part of the DLR project “FAST-Rescue”. The authors would like to thank Markus Krebs, Janos Agocs, Andreas Goerttler, Felix Wienke, and Uwe Dierksheide for their support during the measurements.

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Authors and Affiliations

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

    C. Christian Wolf, Clemens Schwarz, Kurt Kaufmann, Anthony D. Gardner, Johannes Bosbach, Daniel Schanz & Andreas Schröder

  2. LaVision GmbH, Anna-Vandenhoeck-Ring 19, 37081, Göttingen, Germany

    Dirk Michaelis

Authors
  1. C. Christian Wolf
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  2. Clemens Schwarz
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  3. Kurt Kaufmann
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  4. Anthony D. Gardner
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  5. Dirk Michaelis
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  6. Johannes Bosbach
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  7. Daniel Schanz
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  8. Andreas Schröder
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Correspondence to C. Christian Wolf.

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Wolf, C.C., Schwarz, C., Kaufmann, K. et al. Experimental study of secondary vortex structures in a rotor wake. Exp Fluids 60, 175 (2019). https://doi.org/10.1007/s00348-019-2807-1

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  • DOI: https://doi.org/10.1007/s00348-019-2807-1

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