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Recent developments in background oriented Schlieren methods for rotor blade tip vortex measurements

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Abstract

The compressible blade tip vortex of rotary wings has been the subject of numerous investigations and its importance for the understanding of the helicopter flow field has been clearly emphasised. Due to its great impact on the dynamics of the flow field, the investigation of the tip vortex is directly linked to issues of flow control and aeroacoustic optimisation. However, among velocity field data, additional core density information on the blade tip vortex is desirable with a view to vortex modelling. In this work we describe an airborne background oriented Schlieren system for full-scale helicopter flight tests as well as the first results of the tomographic reconstruction of the compressible vortex core. We report the measurements of both a 0.4 Mach-scaled rotor model of the MBB BO 105 and the corresponding full-scale helicopter in hover flight condition. The tomographic reconstruction of the data allows us to estimate the density and the radius for the viscous core.

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Abbreviations

a :

distance, vortex–background (m)

c :

blade chord length (m)

C T :

thrust coefficient

f :

focal length (mm)

f # :

f-stop

G :

Gladstone–Dale constant (m3/kg)

I :

intensity (a.u.)

k x,y :

spatial frequencies (1/m)

m :

magnification

Ma :

blade tip Mach number

n :

index of refraction

p ∞ :

pressure, ambient conditions (Pa)

r :

radial coordinate (m)

r c :

core radius (m)

R :

rotor radius (m)

Re :

Reynolds number

snr:

signal-to-noise ratio

T :

thrust (N)

x,y,z :

Cartesian coordinates (m)

γ:

deflection angle (°)

Γ∞ :

circulation (m2/s)

δx :

apparent image shift in x (mm)

Δx :

deviation of x

ζ:

non-dimensional quantity, \(\zeta = \Gamma_\infty\rho_\infty/8\pi^2\gamma p_\infty r_{\rm c}^2\)

Θ:

projection angle (°)

κ:

specific heat ratio

ρ:

density (kg/m3)

ρ∞ :

density, ambient conditions (kg/m3)

σ:

rotor solidity, σ = 4c/πR

\({\fancyscript{F}}\) :

Fourier transform

\({\fancyscript{R}}\) :

Radon transform

ACF:

Autocorrelation function

BTV:

Blade tip vortex

BVI:

Blade–vortex interaction

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Acknowledgments

The authors very much appreciated the cooperation with the DLR flight department at Braunschweig and we would like to mention in particular the test pilot U. Göhmann.

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Authors and Affiliations

  1. German Aerospace Centre (DLR), Institute for Aerodynamics and Flow Technology, Göttingen, Germany

    Kolja Kindler & Markus Raffel

  2. Institute of Turbomachinery and Fluid Dynamics (TFD), Technical University of Hannover, Hannover, Germany

    Erik Goldhahn

  3. French–German Research Institute of Saint-Louis (ISL), Saint-Louis, France

    Friedrich Leopold

Authors
  1. Kolja Kindler
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  2. Erik Goldhahn
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  3. Friedrich Leopold
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  4. Markus Raffel
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Corresponding author

Correspondence to Kolja Kindler.

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Kindler, K., Goldhahn, E., Leopold, F. et al. Recent developments in background oriented Schlieren methods for rotor blade tip vortex measurements. Exp Fluids 43, 233–240 (2007). https://doi.org/10.1007/s00348-007-0328-9

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  • DOI: https://doi.org/10.1007/s00348-007-0328-9

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