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Analysis methodology for 3C-PIV data of rotary wing vortices

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3C-PIV data from tip vortices of either fixed-wing or rotating wing experiments are challenging from an analysis point of view. Model motion, vortex wander, spurious vectors, periodic and aperiodic effects, turbulence, and other disturbing effects are all present in the data. In most cases the vortices are not measured perpendicular to their axis as well. Engineers need time-averaged properties from the vortex in the vortex axis system for a proper modelization within simulation codes. This article describes the methods needed to deal with all the mentioned problem areas, including the conditional averaging and rotation into the vortex axis system. The methods are validated by using numerically generated vortex vector fields, and finally applied to experimental data from a hover condition of a model rotor.

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Average value


Blade vortex interaction


HHC aeroacoustic rotor test


Higher harmonic control


Laser doppler velocimetry


Particle image velocimetry

2C, 3C:

Two, three component

a :

speed of sound, m/s

c :

chord, m

C T :

thrust coefficient, T/(ρπΩ2 R 4)

L m :

measurement volume length, m

M H :

hover tip Mach number, Ω R/a

N b :

number of blades

n :

Vatistas swirl shape parameter

r :

radial coordinate, m

r c :

core radius, m

R :

rotor radius, m

t :

time, s

T :

thrust, N

u, v, w :

velocity components, m/s

V :

velocity, m/s

x, y, z :

coordinates, m


angle of attack, deg


vortex inclination angle, deg


circulation, m 2/s

λ2, Q :

flow field operators, (rad/s)2


advance ratio, V/(Ω R)


kinematic viscosity, m 2/s


air density, kg/m 3


solidity, N b c/(π R)


standard deviation


azimuth, Ω t, deg


vorticity, rad/s


rotor rotational frequency, rad/s

b :


S :


s :


v :



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Correspondence to Berend G. van der Wall.

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van der Wall, B., Richard, H. Analysis methodology for 3C-PIV data of rotary wing vortices. Exp Fluids 40, 798–812 (2006). https://doi.org/10.1007/s00348-006-0117-x

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  • Vortex
  • Particle Image Velocimetry
  • Vortex Centre
  • Core Radius
  • Particle Image Velocimetry System