TECHNICAL REPORT RDMR-AF-10-03 

NASA/TM-2010-216024

AN ASSESSMENT OF 3-C PIV ANALYSIS

METHODOLOGY FOR HART II

MEASURED DATA

Joon W. Lim 

Aeroflightdynamics Directorate

Aviation Missile Research, Development, 

and Engineering Command

Ames Research Center

 Moffett Field, California

and

Berend G. van der Wall

German Aerospace Center (DLR)

Institute of Flight Systems

Braunschweig, Germany

July 2010

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NASA/TM-2010-216024 

TR-RDMR-AF-10-03

An Assessment of 3-C PIV Analysis Methodology 

for HART II Measured Data 

Joon W. Lim 

Aeroflightdynamics Directorate (AMRDEC) 

US Army Research, Development and Engineering Command 

Ames Research Center, Moffett Field, California 

Berend G. van der Wall 

German Aerospace Center (DLR) 

Institute of Flight Systems 

Braunschweig, Germany 

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July 2010
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NASA/TM-2010-216024 

TR-RDMR-AF-10-03

An Assessment of 3-C PIV Analysis Methodology 

for HART II Measured Data 

 

Joon W. Lim 

Aeroflightdynamics Directorate (AMRDEC) 

US Army Research, Development and Engineering Command 

Ames Research Center, Moffett Field, California 

Berend G. van der Wall 

German Aerospace Center (DLR) 

Institute of Flight Systems 

Braunschweig, Germany 

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National Aeronautics and

Space Administration

Ames Research Center

Moffett Field, CA 94035-1000

July 2010
Acknowledgments 

We acknowledge the support of HART II partners from AFDD, DLR, DNW, NASA, and Onera, 

with special thanks to Casey L. Burley, NASA Langley Research Center and Dr. Chee Tung, Emeritus 

Scientist of AFDD. The authors would like to thank Joelle Zibi, Onera for the Onera results presented in 

this report. We also would like to express our appreciation to Mr. Thomas Maier, Division Chief of 

AFDD, and many special thanks to Mr. Barry Lakinsmith, Deputy Director of AFDD for his strong 

encouragement to complete this report. The authors are indebted to Dr. Gloria K. Yamauchi, NASA 

Ames Research Center for a thorough technical review of this report. 

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1

NOMENCLATURE 

Q 2nd order tensor (shear) of velocity gradient, s-2

rc vortex core radius in the PIV image, m 

R blade radius, m 

U local flow velocity in the horizontal direction, m/sec 

V local flow velocity in the vertical direction, m/sec 

W local flow velocity in the out-of-plane direction, m/sec 

s shaft angle, positive aft, degrees 

v vortex circulation, m2/s

z vorticity in the out-of-plane direction, s-1

2 2

nd order tensor (strain) of velocity gradient, s-2

 elastic torsion, degrees 

 rotor operating speed, radians/sec 

z angular velocity (= z/2), s-1

x, y standard deviations of the vortex centers in the x- or y-direction 

x PIV image rotation in the horizontal axis, degrees 

y PIV image rotation in the vertical axis, degrees 

 rotor azimuth, degrees 

ACRONYMS 

AFDD Aeroflightdynamics Directorate 

BL Baseline 

BVI Blade Vortex Interaction 

CA Conditional Averaging 

DLR Deutsches Zentrum für Luft-und Raumfahrt, German Aerospace Center 

DNW German-Dutch Wind tunnel 

Dpt Data Point 

LLF Large Low-speed Facility 

HART Higher-harmonic control Aeroacoustic Rotor Test 

NASA National Aeronautics and Space Administration 

ONERA Office National d‘Etudes et de Recherches Aerospatiales 

PIV Particle Image Velocimetry 

Pos Position 

SA Simple Averaging 

3-C 3-Component 

ABSTRACT 

Since the completion of the DNW test, HART II partners have put forth significant efforts to derive 

vortex properties from the measured data. These properties include vortex center, rotation angles of the 

vortex axis in the PIV measurement plane, maximum vorticity, core radius, and swirl velocity. 

Differences among the partners‘ results were found for some of these vortex properties, which required 

more efforts to assess the physical significance of the differences. This was because the derived vortex 

properties were an integral of all the sub-processes in the complex PIV data analysis procedure, and more 
2

information was needed to resolve the differences in vortex properties. The objectives of this report are to 

discuss and summarize the parameters and techniques that could contribute to these differences. The 

detailed comparisons in this report have helped establish a strong foundation for a PIV data analysis 

methodology in determining vortex properties. 

INTRODUCTION 

Particle Image Velocimetry (PIV) measurement data can provide a significant amount of 

information about vortex core dynamics in a complex flow field. There have been many reports about the 

PIV data analysis techniques applied to the rotor vortex core properties [1-7], but the techniques have not 

been standardized in the rotorcraft field, which was partially due to the complexity of the inherent, 

rotational flow characteristics. Rotor wakes interact with rotor blades and occasionally with returning 

vortex wakes, which is called Blade-Vortex Interaction (BVI). This BVI phenomenon can be typically 

seen in descending flight. 

One of the difficulties in deriving vortex properties from 3-C PIV measurements is that the plane 

normal to the vortex axis is unknown a priori. Another difficulty is that the convective velocity of a 

vortex is also unknown since it is a sum of a free stream velocity and the velocity induced by other 

vortices. In addition, a vortex is not always rotationally symmetric; often a sheet of trailed vortices is 

found spiraling around a vortex. 

This report describes the efforts of an internationally-joint HART II team for extensive analyses of 

the PIV database that was acquired during a wind tunnel test of the HART II rotor. A brief description of 

the PIV database is also provided, and the techniques for deriving vortex properties such as vortex center, 

rotation angle of the vortex axis, maximum vorticity, core radius, and swirl velocity are followed. 

Differences in resulting vortex properties among the partners are addressed and discussed. Specific 

findings from this study are provided in the conclusions. 

HART II 3-C PIV DATA 

In 2001, an international cooperative test, called the Higher-Harmonic-Control Aeroacoustic Rotor 

Test (HART II) was conducted by the US Army Aeroflightdynamics Directorate (AFDD), Deutsches 

Zentrum für Luft-und Raumfahrt (German Aerospace Center, DLR), Duits-Nederlandse Windtunnel 

(German-Dutch Wind Tunnel, DNW), National Aeronautics and Space Administration (NASA), and the 

Office National d‘Etudes et de Recherches Aerospatiales (Onera) at the large low-speed facility (LLF) of 

the DNW wind tunnel. Primary objectives of the test were to measure rotor wake information extensively 

using 3-component (3-C) PIV, blade surface pressure distributions, blade deformations, and acoustic 

signatures [8-10].

The rotor was a 40% Mach-scaled, hingeless Bo105 main rotor (HART II), and had a precone of 

2.5 degrees at the hub, operating at 1041 rpm. The blade was 2 meters long with -8 degrees twist, and 

consisted of a NACA-23012 airfoil section with a trailing edge tab. The chord length was 0.121 meters. 

The hover tip speed was 218 m/s with a tip Mach number of 0.64. The rotor shaft angle in the test was 5.3 

degrees aft. 

Figure 1 shows the HART II 3-C PIV setup that included three double-pulsed Nd:YAG lasers and 

four digital cameras mounted onto a remote-controlled traverse system. This traverse system was located 

outside of the shear layer in the open jet configuration and moved in the direction of flow. Four cameras 

on the traverse system were used to collect 3-C PIV data. One pair of cameras used 100mm lenses for a 

larger observation area (DNW measurement window) and the other camera pair used 300mm lenses to 

investigate the tip vortex with high spatial resolution (DLR measurement window). 

The PIV measurement plane coordinate system has the positive x-axis to the right direction, the 

positive y-axis up and the positive z-axis out of plane. The rotor hub coordinate system is aligned with the 
3

rotor shaft, such that the positive x is toward the tail boom, the positive y is toward the right wing, and the 

positive z is upward along the shaft. The wind tunnel coordinate system is defined as the inertial frame 

without considering a shaft tilt: the positive x upstream, the positive y to the right (pilot‘s view), and the 

positive z down. 

Figure 2 shows the location and orientation of the PIV measurement planes for the HART II test. 

To avoid interference of the blades with the measurement plane, the reference blade was located 

alternatively at an azimuth of 20° or 70°. In each measurement plane (black line segment), one hundred 

individual PIV images were obtained, and the numerals represent the identification number of each PIV 

measurement position. The measurement planes were oriented at an angle of 149.35o for the advancing 

side and 30.06o

for the retreating side with respect to the positive hub x-axis. 

Figure 3 shows an individual image for Dpt 995 (position 21), taken by the camera. The upper 

image (0.45m x 0.38m) is the global view taken from the DNW camera with the apparent center of swirl 

motion (vortex center) in the flow field. The close-up view image (0.15m x 0.13m) from the DLR camera 

shows the indicated area of the vortex with a higher resolution. However, the high resolution image does 

not indicate a clear swirl motion. 

The velocities (U, V and W) and the vorticity for image #1 at the position 17 are shown in Fig. 4. 

The vorticity, z was derived using the relation: 

z z

V U 2 (curl ) 

x y

 

 

    

 

k V

 (1) 

where z is the angular velocity and V = (U, V, W). In the figure, the peak vorticity and noise of the 

measurement are easily observed. The noise may result from natural turbulence and unsteadiness of the 

flow field, and the vortex center could be affected by rotor test stand vibration, camera support vibration 

and other unknown resources. 

VORTEX CENTER AND CONDITIONAL AVERAGING 

Averaging a large number of velocity vector fields will reduce the noise inherent in an individual 

image. It is straightforward to overlay all of the individual velocity fields in the PIV images and then to 

average them to a single velocity field. This is called simple averaging (SA) technique and works well 

when the vortex centers are mostly collocated from one image to another. In the test setup, the rotor 

model stand was attached to the tunnel sting. The sting and the camera supports were slightly vibrating at

low frequencies due to elasticity. The test rig vibrations were transferred to the blades, which resulted in 

scattering of the vortex centers between individual PIV images. In addition, natural instabilities of helical 

vortex systems added vortex wandering with the vortex age. This situation makes it necessary to conduct 

a conditional averaging (CA) technique in order to prevent smearing of the vortex which would occur if 

the SA technique is employed. The details of a conditional averaging technique are given in Ref. [11]. 

Figure 5 shows the procedure for conditional averaging of velocity fields, which is briefly given as 

follows: 

1) Specify the sense of rotation of the vortex under investigation, since the vortices in the opposite 

rotation could be in the same image. 

2) Identify the vortex center location in each PIV image using a sub-grid. 

3) Compute the standard deviation of vortex centers for all 100 PIV images. 

4) Within a user-specified Z score (Z ≈ 1.5) select 80-95 individual images (geometric outlier 

removal). Re-compute the mean vortex center position based on selected PIV images. Note that Z 

score is the sample score non-dimensionalized with a standard deviation. 

5) Perform a conditional averaging by collocating selected images with individually computed 

vortex centers. The vortex center of each image does not necessarily lie on a grid point, which 
4

requires re-meshing of the individual images and then interpolating their velocities in the remeshed images. 

A vortex can be defined using a various form of velocity tensors. We consider here four different 

velocity gradient tensors for identification of a vortex: vorticity z, Q criterion, 2 and convolution of 2

[11-12]. The first order tensor, vorticity, is widely used in identifying a vortex. Higher order tensors are 

understood to display a clearer image of a vortex than the lower order tensor. The second order tensors 

include Q criterion, 2 and convolution of 2. The first two definitions are similar to each other, and their 

explicit expressions for the two-dimensional velocity field are given as follows [11, 13-14]: 

2

2 2

2

2

1

2

1

2

1

4

U V V U

x y x y

U V U V V U U V V U Q

x y x y x y x y x y





                     

                 

   



   

         

 

         

 (2) 

Note that vorticity (the first order tensor, z) provides information on the sense of rotation via its sign, but 

the second order tensors (Q and 2) do not provide this information — the sign of their peak values is 

independent of the sense of rotation. The convolution of 2 maps the 2 distribution into a bell-shaped 

normal distribution, S using a normal shape function, F as

   

2

2 2 2

2

1

( , ) ( , ) ( , )

 where ( , ) e

 ( , )

 ( , ) ( , ) (0,0) ( , ) (0,0)

m l

m l

j m i l

j m i l

g r

S i j i l j m F l m

c

F l m

c F l m

r l m x l m x y l m y



 

 

 

   





   

 

 

 (3) 

The newly mapped scalar field, S (convoluted flow field) is computed by superposition of a normal shape 

function, F, over a sub-grid consisting of 2l+1 by 2m+1 grid points. Typically, a value of 7 is used for l

and m, and the grid point (0, 0) denotes the peak location of the shape function, F. The factor c is a scale 

factor to normalize the convoluted flow field. For example, the convoluted flow field will result in a value 

of unity if 2 = 1 everywhere in the sub-grid enclosed by 2l+1 by 2m+1 grid points. The factor g, which is 

a shape factor to F for a bell-shaped distribution, depends on the non-dimensional grid resolution, x or 

y. In this report, g = (x/0.003)2 is used. Note that convolution can be taken with any of the first or 

second order tensors instead of 2 in the above equation. 

The vortex center of an individual velocity field can be identified using various vortex 

identification methods. A weighted mean of velocity gradient tensors is computed for each individual 

image. A weighted mean of vorticity is called the vorticity ―centroid‖, and is defined as 

, , 

, , 

, y

i z i i z i

z i z i

x y

x

 

 

 

   

 

 (4) 

A summation is performed over the sub-grid, which is a small neighboring region of a peak vorticity. 

 

Typically, we define this sub-grid as the regions including the top 10% of the peak vorticity. A vortex 

center using the second-order velocity gradient tensors or a convolution of velocity gradient tensors can 

be computed in a similar manner. 
5

After the vortex center is computed for each of the PIV images, we select 80-95 images for 

averaging in order to remove outliers. This corresponds to a Z score of 1.28-1.96, which was 

recommended by HART II partners based on their collective experience. The vortices with their centers 

being outside of a user-defined Z score are considered geometric outliers. Alternatively, the vortices with 

their peak value of vorticity, Q or 2 outside of the specified threshold are considered strength outliers. 

Considering a normally distributed sample, the standard deviation of vortex center is defined in the 

x- and y-directions as 

2 2

1 1

( ) ( )

, 

i i

x y N N

x x y y

   

 

   

 (5) 

The xi and yi are the vortex center in the x- and y-directions for an individual PIV image, N is the sample 

size and the bar indicates the mean value. A distribution of the sample data can be eccentric in either the 

x- or y-direction. Therefore, a circular standard deviation (i.e.,

2 2    r x y

 

) may not be sufficient to 

standardize the two dimensional, normal distribution. So, we define here a circular Z score for an 

isotropic scaling. 

2 2

, , 

i i

x y

Z X Y x x y x X Y

 

 

 

 

 (6) 

For conditional averaging, each selected PIV image is collocated with its vortex center as shown in Fig. 5, 

and a new vortex center is computed only with the selected 80-95 individual PIV images. The conditional 

averaging is a mandatory process for the analysis of vortex properties in the HART II PIV database [11].

ROTATION OF AVERAGED VELOCITY FIELD 

Tung et al. [15] presented calculations of vortex core velocities using the vortex trajectory method. 

Burley et al. [16] presented two different methods to determine the orientation of the vortex core with 

respect to the PIV measurement plane. Specifically, one method uses the axial flow within the vortex core 

and the other uses the tangential (or spin) velocity within the vortex core to define the orientation. In this 

report, a simple geometry-based vortex trajectory method is used to determine the convective velocity and 

the orientation of vortex core axis. 

In the vortex trajectory method, an averaged velocity field is rotated using a transformation matrix. 

The apparent vortex trajectory is constructed using the vortex centers derived from the averaged measured 

velocity fields, based on the assumption that a vortex trajectory is normal to the vortex core axis or the 

PIV measurement plane. This vortex trajectory method was employed by AFDD using the kinematics of 

Euler rotation by means of a vector dyadic [15]. The method computes Euler rotation angles of the vortex 

axis, taking into account the effect of deformation of the vortex trajectory. Later, an alternative approach 

was used by DLR using the direction cosines computed from the estimated vortex trajectory polynomials 

that were constructed from neighboring PIV measurement plane origins [17].

AFDD Vortex Trajectory Method

For any three adjacent vortex positions P1, P2 and P3, one can fit a circular arc through these points. 

These vortex positions are the vortex centers derived from the averaged velocity fields. In Fig. 6, the 

normal vector (B3) is defined as the unit vector parallel to the vector connecting the two positions (P1 and 

P3), crossing at the position P2. This normal vector and the in-plane vector connecting the positions P1

and P2 (

PP1 2

) form the vortex trajectory plane, and the cross product of these two vectors gives the 
6

vertical vector (B2) at the position P2. Again, the cross product of the vertical vector and the normal 

vector at the position P2 gives a bi-normal vector (B1). Thus, the rotated PIV plane, which is normal to the 

vortex trajectory, contains the bi-normal vector in the x direction (B1) and the vertical vector in the y 

direction (B2). The mathematical expressions for these three vectors are described in terms of the 

positions, P1, P2 and P3 as: 

1 3 1 2

3 2 3 1 2 3

1 3 1 2

, , 

P P P P

PP PP

B B B B B B     

 (7) 

Note that determination of the normal vector (B3) may introduce a large error if the position P2 is not the 

mid-point of a circular arc connecting the three vortex positions (P1, P2, P3).

Rotation angles can be found from kinematics of Euler rotation. A transformation matrix of an 

unrotated PIV image to a rotated one is determined from Euler rotation sequence. The rotation angles are 

computed using a transformation matrix in the following dyadic relation: 

, , 1,2,3 where BA BA BA

i xyz j xyz j xyz i j i j ij

T A i j B A  B T A T B A       

 (8) 

where A and B are the unit vectors in the unrotated and rotated planes, respectively. The rotation tensor 

BA Txyz

is a transformation matrix (dyadic tensor) containing all three rotation angles in nature with a rotation 

sequence about the z-, y-, and then x-axes. To eliminate unnecessary z-rotation in the rotated PIV image, 

one could take the inverse z transformation such that 

1

BA BA BA

xy xyz z

T T T    (9) 

The rotation angle about the z-axis is computed using 

BA T

xyz

 by the relation, 

1

12 11 tan ( / ).  z

T T 

Thus, the 

transformation matrix having a rotation about the y-axis and then the x-axis, is given by 

0

BA

xy

cy sy

sx sy cx sx cy

cx sy sx cx cy



 

  

 

 



 

   

T

 (10)

The finite rotation angles (horizontal and vertical) are computed by 

 

1 1 23

13

33

tan , sin x y

T

T

T

 

 

 

      

 (11) 

This method requires three vortex measurement positions to compute the associated vectors. When 

actual measurement is not made at three points along the vortex trajectory, there is not enough 

information to compute the vortex trajectory. In such cases, the vortex positions could be estimated using 

the available PIV measurement plane positions, ignoring deformation of the vortex trajectories. 

 

DLR Vortex Trajectory Method

This method estimates the vortex trajectory by constructing polynomials based on PIV 

measurement plane positions, based on the assumed vortex centers as the origin of the PIV measurement 

plane [17]. The direction cosines are computed from the estimated vortex trajectory polynomials in the 
7

wind tunnel coordinate system, and the corresponding direction cosine angles are inversely computed by 

the following relations: 

1 1

, ,

tan , and tan hub hub

x hub y hub

hub hub

y x

x z

 

 

     

           

 (12) 

These angles are transformed back into the PIV measurement plane coordinate system, where the sense of 

rotation is defined as follows: 

o

, ,

o

, ,

, advancing side + 30 , advancing side

, 

 , retreating side - 30 , retreating side

x hub y hub

x y

x hub y hub

 

 

 

 

 

   

   

   

 (13) 

Note that these angles are direction cosine angles and can be converted into Euler angles using a 

coordinate transformation matrix. 

The AFDD and DLR vortex trajectory methods provide a good estimate for rotation angles of a 

PIV image, and quantitative comparison will be given in a later section. There are the cases having the 

unbalanced (non-concentric) contours of the cross flow field surrounding the vortex center, which may 

require an additional adjustment in the rotation of the velocity field. In such cases, we incrementally 

rotate the unbalanced cross flow field until it becomes concentric. When the cross flow field is concentric 

around the vortex center, the vorticity field also becomes concentric under the ideal situation [11]. In 

reality, interactions with shear layers, turbulence or other unsteady behaviors will make the contours to be 

non-concentric. 

COMPUTATION OF GRADIENTS 

All flow field tensors such as vorticity, Q and 2, are based on the gradients of the velocity field, i.e. 

∂V/∂x, ∂U/∂y, ∂V/∂y and ∂U/∂x. Various numerical schemes are available to compute these gradients. 

The most commonly accepted scheme is the 2nd-order-accurate central difference scheme in one 

dimension. More accurate schemes are available, such as the 3rd-order-accurate Richardson extrapolation. 

These schemes are given as follows: 

1, 1, 2

,

2, 1, 1, 2, 3

,

central difference: ( )

2 

8 8

Richardson extrapolation: ( )

12 

i j i j

i j

i j i j i j i j

i j

V V V

O x

x x

V V V V V

O x

x x

 

   

 

  

 

    

  

 

 (14) 

An alternative numerical scheme is to include two-dimensional dependency of the velocity fields in 

the PIV measurement planes. Reference [18] provides a derivation based on circulation around a point of 

interest. The vorticity is expressed using Stokes‘ theorem as follows: 

, ij

, ,

 where z

i j i j

ij

ij

ij

V U d d

x y A



  

       

    γ S V l (15) 
8

where Aij is the area enclosed by the grid points, (i-1,j-1), (i+1,j-1), (i+1,j+1), and (i-1,j+1) around the 

point of interest. This integration takes into account the velocity data from eight surrounding grid points. 

For equally spaced grid points around the point (i,j), the gradients ∂V/∂x and ∂U/∂y are: 

1, 1 1, 1, 1 1, 1 1, 1, 1

,

1, 1 , 1 1, 1 1, 1 , 1 1, 1

,

2 2

8 

2 2

8 

i j i j i j i j i j i j

i j

i j i j i j i j i j i j

i j

V V V V V V V

x x

U U U U U U U

y y

         

         

     



 

     



 

 (16) 

Note that U and V are the velocities in the x- and y-directions, respectively. This approach is 

equivalent to applying the central difference scheme to a smoothed 3x3 kernel velocity field, and the 

uncertainty in the vorticity estimate with this approach is therefore expected to decrease. Other gradients 

such as shear strain can be computed in a similar fashion. It is noted that the robustness of this approach 

over the central difference or Richardson‘s extrapolation is described in Ref. [18].

VATISTAS MODEL 

Tip vortices often interact with other flow structures including shear layers, turbulence and vortices 

shed from other blades. A characterization of a vortex core model can be made with a curve-fit to a swirl 

(tangential) velocity profile of a vortex [11, 19]. A simple model is the Rankine vortex, which models the 

core as a solid body. The Oseen-Lamb model is expressed in terms of the exponential decay function as a 

simplified solution of the Navier-Stokes equation [20]: 

2

1

 where 

2

v

c c

e r V

r r



 



 

   

  

 (17) 

Γv is the vortex circulation, and rcis the vortex core radius. The coefficient α depends on the kinematic 

viscosity and vortex age, which can be set as 1.25643 [19]. A more general mathematical expression for a 

swirl velocity profile is given by Vatistas et al. [21] as 

2 1/ 2 (1 )

v

n n

c

V

r





 



 



 (18) 

At the vortex core radius (ρ = 1), the maximum swirl velocity should satisfy the relation, 

1/

,max 2

2

v n

c

V

r





 

 

 (19) 

Therefore, the total circulation Γ∞ of a potential vortex is determined such that 

1/

,max 2 2 n

c v r V

       

 (20) 

Note that the Scully core model, which is widely used in the rotorcraft field, is identical to the Vatistas 

model with n = 1. The Rankine vortex model is obtained as n → ∞, and the Lamb-Oseen model is closely 

approximated when n = 2 [19]. 
9

RESULTS AND DISCUSSION 

The PIV analysis results collected from HART II partners were presented by the DLR [22]. Sample 

comparisons of the derived vortex core properties for the baseline case are presented in Fig. 7. Vortex 

positions, rotation angles, peak vorticity, core radius and peak swirl velocity are shown. Comparisons are 

made in the longitudinal cutting plane of y/R = 0.7 on the advancing side. Small-to-large differences 

among the partners‘ results were found, and assessing the physical significance of these differences was 

difficult. In fact, the findings were not sufficient to resolve the differences. This report will discuss and 

summarize the parameters and techniques which could contribute to these differences. 

Discussion about the simple averaging technique [11, 13] is not included in this report since HART 

II partners have agreed that conditional averaging is required for HART II PIV analysis. The HART II 

partners have also agreed to use the PIV measured data in 24 pixels x 24 pixels (interrogation window 

size with 50% overlap) due to more availability of the data in the HART II database. In this report, only 

the data from the DLR measurement window will be presented. The cameras for a close-up view (DLR 

window) had a resolution of 1280 x 1024 pixels, the exposure time of an individual PIV image was about 

120 s, and the time delay between the two PIV images was mainly 17 s.

Conditional Averaging

At each PIV measurement position, one hundred individual images are available. A young vortex, 

which sheds from the preceding blade at an azimuth of 135.6o (refer to Fig. 2a), quickly reaches position 

17 (Dpt 1003) at a wake age of 25.3o, and is accompanied by a strong shear layer generated along the 

blade trailing edge. For a lightly loaded rotor, the vorticity strength of a shear layer has a similar 

magnitude to the tip vortex as in this case. For a highly loaded rotor as seen on the retreating side or in 

hover, the vorticity strength of a shear layer becomes less significant compared to the tip vortex. 

After passing the position 17, the young vortex continuously travels downstream. When it reaches 

the first quadrant of the rotor disk, the vortex is already grown to a fully-developed vortex and encounters 

significant blade-vortex interactions (BVI) with following blades, which is a typical phenomenon in 

descending flight. A good example of a fully grown vortex is the one at position 22 (Dpt 998), which is at 

a wake age of 425.3o. Figure 8 shows typical (unrotated) vorticity maps for positions 17 and 22. The 

vorticity was non-dimensionalzed with the rotor operating speed. A fully grown vortex at the position 22 

displays its strength more diffused than a young vortex at the position 17. 

The vortex centers of one hundred individual images are plotted in Fig. 9 for position 17 (Dpt 1003) 

of the baseline case. AFDD used a centroid for the center identification while DLR used convolution of 

2. The centroid method displays individual vortex centers largely collocated with some scatter, while the 

convolution of 2 method results in much less scatter. 

Figure 10 compares conditionally averaged vortex centers for position 17 (Dpt 1003). The vortex 

centers computed using a centroid (AFDD), Q criterion (Onera), and 2 and convolution of 2 (DLR) are 

almost collocated, with difference of 0.02-0.04% R (0.36-0.61% c). A tabulated comparison of the vortex 

properties for position 17 is given in Table 1a, which includes the maximum vorticity, vortex centers and 

their standard deviation. Note that 1% of the blade radius is equivalent to 16.5% of the blade chord 

length. 

Differences in vortex properties among various methods are given in Table 1b. The reference value 

was taken from the centroid result. The differences of maximum vorticities fall within 7% of the rotor 

speed. The vortex centers that were derived using a centroid, Q criterion and 2 show good agreement, but 

the vortex center from convolution of 2 is different from the other methods by about 0.3-0.5% of the 

chord. 

The vorticity maps, computed using a centroid, Q criterion, 2 and convolution of 2, are shown in 

Fig. 11, exhibiting a strong shear layer. This shear layer, resulting from airfoil thickness, includes the 

effects of the boundary layer (mainly in the cross-flow component) as well as the radial circulation 
10 

distribution (vorticity). The vorticity and shear layer contours of the four methods appear almost identical 

to each other, except for the value of the maximum vorticity. Figure 12 shows the same comparison but 

with the first- and second-order velocity gradient tensors, and demonstrates that the level of difficulty in 

visual identification of vortex center significantly reduces with the second-order tensors. Note that the 

coordinate system of the contour using Q criterion was rearranged at the vortex center. Although all the 

second order tensors (Q criterion, 2 and convolution of 2) display a cleaner image of the vortex core 

than the first-order tensor, the accuracy in the vortex center location does not depend on the order of the 

tensor — at least within this example — as seen in Table 1. 

 The conditionally averaged vortex centers at position 22 are compared in Table 2. The centroid 

results are used as a reference. The vortex center using Q criterion differs largely by 2.0-3.3% of the 

chord. Considering vortex core radius to be 4-15% of the chord for a typical rotor tip vortex, this 

difference is not trivial. 

Number of Individual PIV Images

When inspecting each individual PIV images, some images were found to be too diffused or blurry. 

In most cases, these images were identified outliers. A typical characteristic of these outlier images is that 

the vortex core image is diffused and the vortex center is away from the mean vortex center. Figure 9 

shows the vortex centers of all 100 individual images using the centroid and the convolution of 2. Outlier 

images were eliminated in conditional averaging (geometric outlier removal). Selecting good images from 

the population of 100 images is controlled by a Z score of the normally distributed vortex centers. 

Choosing the images with a 95% confidence level corresponds to a Z score of 1.96, and HART II partners 

agreed to use about 80-95 images, corresponding to Z = 1.28-1.96. 

Table 3 shows a relationship between a Z score and the number of the PIV images selected. As 

expected, the maximum vorticity rapidly decreases when more images are included for averaging. The 

corresponding vorticity maps are shown for position 17 in Fig. 13. The vortex contours are almost 

unchanged with a variation of Z scores, but the peak vorticity values (hot spot) are moderately changed. 

With 39 images (Z=0.5), the peak vorticity increases by 16% from the vorticity with 89 images. 

In addition to this geometric-position-based elimination of outliers, one can alternatively consider 

dealing with vortex strength (strength outlier removal) by analyzing the peak vorticity, peak Q, peak 2 or 

the peak value of the convolution with any of those inside a vortex core. For example, one can eliminate 

the images having unusually lower vortex strength by defining a threshold (or Z score) below the mean. 

The reasoning is that blade-vortex-interaction noise is dominated by the strongest interactions and a 

proper averaging should thus retain the strongest vortices for analysis of their properties. The number of 

the images eliminated by this method is similar to the number with the geometric outlier removal, and 

thus the number of remaining images with the strength outlier removal is typically in the range of 80-95. 

However, in cases where the vortex of interest is close to another one having the opposite sense of 

rotation (dual vortices), the number of images may drop down significantly, and an automatic procedure 

for robust identification of the images requires more complicated sub-processes. 

Sub-grid in Vortex Center Identification

A vorticity field typically displays a hot spot where a strong vortex lies, and so it is not difficult to 

visually identify a vortex center. An automatic identification of a vortex center using a computer program, 

though more consistent and objective, is not as straightforward as a visual identification. It is more 

difficult to identify a vortex center containing some noise and a shear layer. Figure 14 shows a 

perspective view of the vorticity map of image #3 at position 17. A sharp peak of a vortex is accompanied 

by a series of moderate peaks from a shear layer. 

The PIV measurement data are provided on a grid, and the scalar values (first and second order 

tensors) are computed on the grid to identify a vortex center. The physical vortex center, however, is not 
11 

confined to any resolution represented by this grid, and can be anywhere between the grid points. For this 

reason, re-meshing of the grid points by interpolation is required. 

A vortex center in the vorticity map is determined by first computing the vortex strength (z, 2, Q 

or convolution of 2) on the grid and then searching for the maximum vortex strength to determine the 

vortex center. A sub-grid is a small neighboring region surrounding peak vorticities, and the neighboring 

region is defined by a specified threshold in terms of the maximum vortex strength. Figure 14 shows subgrids with the top 10% and 40% of the vorticity peak, and the latter case (top 40%) displays two sub-grids 

which would result in a large shift of the vortex center. 

Figure 15 shows the vortex centers of image #3 at position 17 with sub-grids defined using the top 

10% to 50% of the peak vorticity. Note that the grid resolution in the PIV data was 1.25% of the chord (= 

0.0756% R) in both the x- and y-directions. The sub-grid with the top 50% results in a vortex center 

shifted 15% chord away from the vortex center computed with the top 10%. As observed, the sub-grid 

size is sensitive in determining a vortex center. The question remains about what sub-grid size is adequate 

for determining the vortex center. We recommend using the top 10% of the maximum strength of a 

vortex (z, 2, Q or convolution of 2) for a sub-grid definition. Note that this sub-grid is used only for 

identifying the vortex centers in each individual image. 

Figure 16 shows the perspective and top views of 2 and convolution of 2 of image #3 at position 

17 (Dpt 1003). As compared to the vorticity using a centroid method in Fig. 14, the perspective view of 2

(Fig. 16a) seems slightly cleaner. But, the views of the convolution of 2 display less noisy even when 

compared with the same 2nd-order tensor, 2. 

Conditional Averaging Using a Subset of the PIV Database

The PIV data analysis is an integral of all the sub-level processes in conditional averaging with the 

various numerical differentiation schemes for computing velocity gradients, which affect the first- and 

second-order tensor data. Establishing thresholds for removing outliers is another sub-level process 

followed by applying various vortex center identification methods. The differences between HART II 

partners‘ results (Fig. 7) originated from each of the sub-level processes. Due to the large size of the PIV 

database, data analysis became very complex and quantifying these differences at each sub-process level 

became challenging. To help this situation, we attempted a conditional averaging with a subset of the 

data, so that a few PIV images were used instead of all 100 images. 

For this exercise, two PIV positions were selected in the longitudinal plane of y/R = 0.7 on the 

advancing side: position 17 (Dpt 1003) and position 22 (Dpt 998). Two individual images were used for 

position 17 and three images for position 22. Conditionally averaged results with these images are 

compared for the two positions 17 and 22. 

a) Case 1: Pos 17 (Dpt 1003) 

Figure 17 shows the first 16 individual PIV images at position 17 of the baseline. Among these 16 

images, images #1 and #3 are selected for this exercise. Figure 18 shows a comparison of vortex 

properties for image #1 as calculated by the HART II partners. The figure shows a strong vortex (hot 

spot), accompanied by a moderately strong shear layer. The maximum vorticity is much higher than the 

conditionally averaged value using all the images (see Table 1). The label,  ̳A‘ in the contour stands for 

AFDD,  ̳D‘ for DLR, and  ̳O‘ for Onera. In a large window (left image), vortex centers are collocated 

almost to each other, and so this image is enlarged by roughly 25 times (right image). Note that one grid 

spacing in this enlarged image is equal to 1.25% of the chord (= 0.0756% R), and 1% of the radius (% R) 

equals to 16.5% of the chord. The maximum vorticity difference (max) between different methods is 

small, and the difference in the circular vortex center (rv =

2 2

v v

   x y

) is 0.06% R (= 0.99% c), as 

shown in Table 4a. 
12 

A similar comparison was made for image #3 in Fig. 19 and Table 4b. This image appears slightly 

fuzzy. Computed vortex properties, such as vorticity as well as vortex center, are almost identical to each 

other when using the centroid and Q criterion methods. The vorticity by the convolution of 2 is also 

similar to the values by other methods, but its vortex center shifts to the x-direction by about 0.08% R (= 

1.36% c). 

Finally, both images were used for conditional averaging. The vortex properties with images #1 and 

#3 are compared in Fig. 20 and Table 4c-4d. The vorticity by the convolution of 2 is 10% higher than the 

value using a centroid or Q criterion. The vortex center by the convolution of 2 differs from the centroid 

method result by 0.03% R (= 0.50% c). 

b) Case 2: Pos 22 (Dpt 998) 

Figure 21 shows first 16 individual images at position 22 of the baseline. Images #2, #3 and #8 are 

used for conditional averaging. The images #2 and #3 show a clear hot spot and the image #8 seems 

slightly fuzzy. The vortex at this position is fully grown, its vortex strength diffused, and the flow field 

seems relatively noisy. 

 Vortex properties are derived using conditional averaging by the centroid and convolution of 2

methods shown in Fig. 22 and Table 5. The peak vorticity at the position 22 is substantially less than the 

peak at the position 17. The circular vortex center is different by 0.054% R (= 0.89% c) between the two 

methods. Note that a fuzziness of the vortex image in this figure is seen typically from older vortices. 

Rotation Angles for an Averaged Image

The PIV measurement plane is not generally normal to the vortex trajectory due to pre-setting the 

orientation of the measurement plane prior to the test. Since an accurate analysis of the vortex core can be 

made only in the vortex axis, the rotation angles from the measurement plane to the vortex axis should be 

accurately identified. In this study, these rotation angles were defined in terms of Euler angles with a 

sequence of the y-x rotation, or direction cosine angles. Ideally, the resulting vortex image will be normal 

to the vortex trajectory after rotation. 

As a general hypothesis, every vortex in an individual PIV image is assumed to have the same 

inclination of the vortex axis with respect to the measurement plane, though the vortex axis orientation 

may vary in each individual image. During the PIV analysis exercise among the HART II partners, the 

discussion evolved whether individual images should be rotated prior to conditional averaging or not, and 

the conclusion was that this would introduce additional complication and uncertainties without having 

significant benefits. After the rotation of the velocity field, the meshes in the rotated image are no longer 

orthogonal and thus data interpolation on the rotated grid of the individual images becomes more 

complicated. In addition, the analysis of rotation angles for each individual is repeated over the number of 

individual images. Reference [11] showed, using hover data, that averaging of individual rotation angles 

was in agreement within one degree tolerance despite a standard deviation of about four degrees, and this 

difference is considered negligible. Therefore, the conditionally averaged velocity field will be used in the 

present work. 

Figure 23 shows the contours of vorticity () and cross flow (Vzv/R) before and after rotation. 

Note that the cross flow velocity was filtered out by the velocity at the vortex center. The conditionally 

averaged image was generated using a centroid method with images #2, #3 and #8 at position 22. The 

rotation angles were found to 6.3o and -34.3o, respectively, in the x- and y-axes of the PIV measurement 

plane. The peak vorticity of the unrotated image was 24.40, and that of the rotated image was 24.41. 

Small differences are observed in both peak values and the contour patterns, which forces to preclude 

using the vorticity map for judging the quality of rotation angles. On the contrary, the cross flow velocity 

field shows a relatively good quality of concentric contour after rotation. Therefore, the cross-flow 

velocity field is considered a primary indicator for an identification of rotation angles in this report. 

Though the resulting image is a projection of the measured data at a view angle parallel to the vortex axis, 
13 

it is assumed that the flow field may not be significantly different within the volume covered by the zcoordinate of the image after rotation. The projection can be also assumed as being measured in the plane 

normal to the vortex axis, and thus an analysis of vortex properties may be allowed within this projected 

data field. 

Figure 24 compares two rotation angles (horizontal and vertical), at position 22, derived using the 

centroid (AFDD) and the convolution of 2 (DLR). Larger differences in the rotation angles between the 

two methods are found from image #8. This result is expected since image #8 is fuzzy compared with the 

other two images and so more difficult to accurately identify the vortex properties. The rotation angles 

after being conditionally averaged (ca) are shown in the figure. Interestingly the difference of the rotation 

angles from the averaged image is less than that from the single image #8, and a similar example is found 

in Ref. [11]. In Table 6, the difference in the rotation angles between the two methods is about 3o or less 

with a conditional average, but the difference increases to 6o

to 12o when the rotation angles are compared 

between individual images. Derived rotation angles using all 100 images (see Fig. 7), are given in Table 7 

for positions 17 and 22. Note that after rotation into the vortex axis system, the resulting grid is no longer 

orthogonal and skewed instead. Care must be taken when derivatives such as ∂V/∂x are computed, since 

the data must be properly interpolated. 

Swirl Velocity

An accurately rotated vorticity or velocity field in the PIV image displays a concentric contour 

around the vortex center, provided that the vortex is rotationally symmetric. This concentric contour can 

be distorted due to interactions with other vortices, shear layers, or turbulence. From the rotated, averaged 

velocity field, a swirl velocity can be reconstructed in two steps. First, tangential velocities are collected 

from the cutting axes — the straight lines in the radial direction from a vortex core. The direction of the 

cutting axes can be to the right, up, left, down and in between, and this process generates multiple 

tangential velocity profiles. Secondly, by taking an algebraic averaging of these velocity profiles, the 

desired tangential velocity profile is obtained. 

As an alternative approach, all individual images can be separately analyzed instead of a single 

averaged image. Collecting individual velocity profiles provides a tangential velocity ―cloud‖, from 

which an averaged tangential velocity profile can be computed. The outlier removal methodology can be 

applied to reduce the bandwidth of the cloud before averaging (DLR approach). 

Figure 25 shows the vorticity map and tangential velocities of the conditionally averaged image at 

position 17 using the centroid method. Images #1 and #3 were used for averaging. The cutting axis 

azimuths are shown on the vorticity map as an example, and the associated tangential (swirl) velocity 

profiles are also presented. The cloud in the tangential velocity profiles represents all the tangential 

velocities possible from the averaged image at this position 17, and the tangential velocities show a large 

scatter which is likely due to a shear layer. Figure 26 shows a similar plot for position 22, where 

averaging was performed with images #2, #3 and #8. 

To determine a tangential velocity profile, an appropriate method for choosing cutting axis is 

needed, and it would take into account the least noisy flow field where the influence of other neighboring 

vortices or shear layers is minimized. Practically, a perfectly concentric flow field around the vortex core 

is not feasible and the judgment about the quality of the vortical flow field is also subject to a researcher‘s 

experience. A common approach for determining the cutting axis (horizontal, vertical, in between, or a 

combination of these choices) is to choose the axes manually in the region where a cleaner vorticity field 

is observed. For example, the optimum cutting axis is selected as the azimuths of 90o and 180o for the 

positions 17 and 22 as in Figs. 25 and 26, respectively. 

The corresponding tabulated data of vortex core radii and tangential velocities are given in Table 8. 

When the four horizontal and vertical axes (0o, 90o, 180o and 270o) are selected, the mean vortex core 

radii are 5.3% chord for the position 17 and 10.7% chord for the position 22. The use of the optimum 

cutting axis at 90o and 180o enables to substantially reduce the vortex core radius compared with the use 

of the four axes — for a young vortex (position 17) by 40% to 3.2% chord, but for an older vortex 
14 

(position 22) it unexpectedly increases the core radius by 7%. The peak tangential velocities with the 

optimum cutting axes increase by less than 8% for both positions 17 and 22. 

Figure 27 is an example of the curve-fit results using a Vatistas model for positions 17 and 22, and 

the selected cutting axes are 90o and 180o for both positions. For position 17, the core radius was 3.2% 

chord (= 0.20 %R) with the peak swirl velocity 2.9% of the rotor tip speed. The Vatistas exponent of 

n=0.60 was best-fit to the tangential velocity. For position 22, the core radius was 11.4% chord (= 0.69% 

R) with the peak swirl velocity 2.58% of the tip speed. The Vatistas exponent was slightly increased to 

n=0.70. Note that the Vatistas exponent may depend on the choice of the cutting axes. This exponent n 

can be considered as a shape factor for the tangential velocity profile. Since the number of data points 

within the peak velocity is relatively scarce, Vatistas exponent n may not be highly accurate. 

CONCLUSIONS 

Despite the past experiences of HART II partners who have dealt with PIV data analyses for years, 

the complexity of the PIV analysis procedures became readily apparent in the large HART II database. 

Comparisons of the partners‘ results typically led to unresolved questions and ambiguity. As a result, the 

partners focused on a much smaller sample of the database. Although the use of a subset of the PIV 

database may not be sufficient to establish comprehensive guidelines for establishing a PIV data 

processing methodology, the effort in this report certainly offers some insights on the PIV data analysis 

techniques, and helps establish a strong foundation for an analysis methodology. The following are of the 

main findings from this study: 

1) Vortex center identification method – Four methods were used for comparison. The methods 

were: centroid (AFDD, DLR), Q criterion (ONERA, AFDD, DLR), 2 (DLR, AFDD) and convolution of 

2 (DLR). Although the contours of all the second order velocity gradient tensors (Q criterion, 2 and 

convolution of 2) displayed a strong hot spot surrounded with a cleaner flow field compared to the firstorder tensor (vorticity), the accuracy of the computed vortex center location was not affected by the order 

of the tensor. The difference of the vortex center locations among the partners was 1.5 - 1.7% of the chord 

for position 17, and 2.0 - 3.3% for position 22. 

2) Number of individual PIV images – Although the vortex contour was almost unchanged with a 

variation of the number of images, the peak vorticity value (hot spot) was moderately sensitive. The peak 

vorticity for position 17 increased by 16% with 38 images (Z=0.5) compared to the value with 89 images 

(Z=1.5). 

3) Sub-grid in vortex center identification – The sub-grid with the top 50% of the peak vorticity 

showed the vortex center shift by 15% of the chord from the reference value computed with the top 10%. 

The sub-grid size was important in determining a vortex center, and the top 10% of the maximum 

vorticity for a sub-grid definition was recommended. 

4) Conditional averaging with a subset of the PIV database – Since a subset of the PIV images 

significantly reduced the problem size, it was possible that each PIV analysis technique was closely 

examined and accordingly the differences between HART II partners‘ results were better understood. 

5) Rotation angles - The difference of the rotation angles between the averaged images computed 

using the centroid and convolution of 2 was less than 3o for position 22, but the differences between 

individual images were interestingly larger (6o to 12o).

6) Swirl velocity – The optimum cutting axis for extracting swirl (tangential) velocities was 90o

and 180o azimuths for the cases analyzed, which reduced substantially the vortex core radius for a young 

vortex (position 17) by 40% to 3.2% chord when compared to using four cutting axes (0o, 90o, 180o and 

270o). A Vatistas model gave good estimates for swirl velocity profiles. 
15 

REFERENCES 

1. Raffel, M., Seelhorst, U., and Willert, C., ―Vortical Flow Structure at a Helicopter Model Rotor 

Measured by LDV and PIV,‖ The Aeronautical Journal of the Royal Aeronautical Society, Vol. 

102, No. 1012, 1998, pp. 221-227. 

2. McAlister, K. W., Tung, C., and Heineck, J. T., ―Forced Diffusion of Trailing Vorticity from a 

Hovering Rotor,‖ American Helicopter Society 57th Annual Forum Proceedings, Washington, D. 

C., May 9-11, 2001. 

3. Heineck, J. T., Yamauchi, G. K., Wadcock, A. J., Lourenco, L., and Abrego, A., ―Application of 

Three-Component PIV to a Hovering Rotor Wake,‖ American Helicopter Society 56th Annual 

Forum Proceedings, Virginia Beach, VA, May 2-4, 2000. 

4. Richard, H., and Raffel, M., ―Rotor Wake Measurements: Full-Scale and Model Tests‖, American 

Helicopter Society 58th Annual Forum Proceedings, Montreal, Canada, May 25-27, 2002. 

5. Ramasamy, M., and Leishman, J. G., ―A Multi-Region Vortex Model for Transitional Rotor Blade 

Tip Vortices,‖ Journal of the American Helicopter Society, Vol. 51, No. 1, 2006, pp. 92-103. 

6. Yamauchi, G. K., Burley, C. L., Mercker, E., Pengel, K., and JanakiRam, R., ―Flow Measurements 

of an Isolated Model Tilt Rotor,‖ American Helicopter Society 55th Annual Forum Proceedings, 

Montreal, Canada, May 25-27, 1999. 

7. Raffel, M., Richard, H., Schneider, G., Klinge, F., Ehrenfried, K., Pengel, K., and Feenstra, G., 

―Recording and Evaluation Methods of PIV Investigations on a Helicopter Rotor Model‖, 11th

International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, July 8-

11, 2002. 

8. Yu, Y. H., Tung, C., van der Wall, B. G., Pausder, J., Burley, C. L., Brooks, T. F., Beaumier, P., 

Delrieux, Y., Mercker, E., and Pengel, K., ―The HART II Test: Rotor Wake and Aeroacoustics with 

Higher-Harmonic Control Inputs,‖ American Helicopter Society 58th Annual Forum Proceedings, 

Montreal, Canada, May 25-27, 2002. 

9. van der Wall, B. G., Burley, C. L., Yu, Y. H., Pengel, K., and Beaumier, P., ―The HART II Test - 

Measurement of Helicopter Rotor Wakes,‖ Aerospace Science and Technology, Vol. 8, No. 4, 

2004, pp. 273-284. 

10. Lim, J. W., Tung, C., Yu, Y. H., Burley, C. L., Brooks, T. F., Boyd, D., van der Wall, B. G., 

Schneider, O., Richard, H., Raffel, M., Beaumier, P., Delrieux, Y., Pengel, K., and Mercker, E., 

―HART II: Prediction of Blade-Vortex Interaction Loading,‖ 29th European Rotorcraft Forum 

Proceedings, Friedrichshafen, Germany, September 16-18, 2003. 

11. van der Wall, B. G., and Richard, H., ―Analysis Methodology for 3C PIV Data of Rotary Wing 

Vortices,‖ Experiments in Fluids, Vol. 40, No. 5, 2006, pp. 798-812. 

12. Jeong, J., and Hussain, F., ―On the Identification of a Vortex,‖ Journal of Fluid Mechanics, Vol. 

285, 1995, pp. 69-94. 
16 

13. van der Wall, B. G., and Burley, C. L., ―2nd HHC Aeroacoustics Rotor test (HART II) - Part II: 

Representative Results,‖ Institute Report IB 111-2005/03, German Aerospace Center (DLR), 

Braunschweig, Germany, February 2005. 

14. Bailly, J., Delrieux, Y., and Beaumier, P., ―HART-II: Experimental Analysis and Validation of 

ONERA Methodology for the Prediction of Blade-Vortex Interaction,‖ 30th European Rotorcraft 

Forum Proceedings, Marseilles, France, September 14-16, 2004. 

15. Tung, C., and Lim, J. W., ―Analysis of Rotor Vortex Wake Structure Using 3-C PIV 

Measurements,‖ Vortex Dominated Flows, Chapter 13, edited by Blackmore, Krause, and Tung, 

World Scientific, Hackensack, NJ, 2005. 

16. Burley, C. L., Brooks, T. F., van der Wall, B. G., Richard, H., Raffel, M., Beaumier, P., Delrieux, 

Y., Lim, J. W., Yu, Y. H., and Tung, C., ―Rotor Wake Vortex Definition Using 3C-PIV 

Measurements – Corrected for Vortex Orientation,‖ AIAA 2003-3175, 9th AIAA/CEAS 

Aeroacoustics Conference Proceedings, Hilton Head, SC, May 12-14 2003. 

17. Hoffmann, F., and van der Wall, B. G., ―The Vortex Trajectory Method Applied to HART II PIV 

Data,‖ Institute Report IB 111-2005/34, German Aerospace Center (DLR), Braunschweig, 

Germany, August 2005. 

18. Raffel, M., Willert, C., Werely, and S., Kompenhans, J., Particle Image Velocimetry – A Practical 

Guide, 2

nd edition, Springer Berlin, Heidelberg, New York, 2007. 

19. Leishman, J. G., Principles of Helicopter Aerodynamics, Cambridge University Press, Cambridge, 

United Kingdom, 2000. 

20. Lamb, H., Hydrodynamics, Cambridge University Press, Cambridge, United Kingdom, 1932. 

21. Vatistas, G. H., Kozel, V., and Mih, W. C., ―A Simpler Model for Concentrated Vortices,‖ 

Experiments in Fluids, Vol. 11, No. 1, 1991, pp. 73-76. 

22. van der Wall, B. G., ―Comparison of 3C PIV Data Analysis, BL Case,‖ US/German MoU on 

Helicopter Aeromechanics 55th meeting, Braunschweig, Germany, October 17-18, 2005. 
17 

Table 1. Vortex properties of the PIV image at position 17 

 a) Conditionally averaged properties 

centroid a Q criterion o 2

a

conv 2 

d

max

max/ 33.1 30.8 32.7 31.5 2.3

xv/R (%) 0.41 0.43 0.40 0.44 0.04

yv/R (%) 0.52 0.52 0.52 0.54 0.02

x/R (%) 0.60 --

*

0.61 0.13 0.48

v/R (%) 0.29 --

*

0.30 0.11 0.19

 b) Difference in the averaged property, referenced from a centroid 

centroid a Q criterion o 2

a

conv 2 

d

max/ (%) --

r

-6.9 -1.2 -4.8

xv/c (%) --

r

0.26 -0.15 0.46

yv/c (%) --

r

-0.03 -0.18 0.28

a provided by AFDD, o provided by Onera, d provided by DLR, r

reference data, 

* no data provided 

Table 2. Vortex properties of the PIV image at position 22 

 a) Conditionally averaged properties 

centroid a Q criterion o 2

a

conv 2 

d

max

max/ 24.8 25.6 24.9 25.2 0.8

xv/R (%) -0.08 0.04 -0.08 -0.13 0.17

yv/R (%) 0.03 -0.17 0.04 0.01 0.21

x/R (%) 0.76 --

*

0.76 0.57 0.19

v/R (%) 0.46 --

*

0.46 0.41 0.05

 b) Difference in the averaged property, referenced from a centroid 

centroid a Q criterion o 2

a

conv 2 

d

max/ (%) --

r

1.6 0.4 1.6

xv/c (%) --

r

1.98 0.0 -0.83

yv/c (%) --

r

-3.31 0.17 -0.33

a provided by AFDD, o provided by Onera, d provided by DLR, r

reference data, 

* no data provided 
18 

Table 3. Z score, the number of images and the maximum vorticity for the PIV image at position 17 

when the centroid method is employed 

Z score # of images max/ (

Z=1.5

)/

Z=1.5

0.5 38 38.3 15.7%

0.7 62 36.5 10.3%

1.5 89 33.1 --

r

5.0 99 31.7 -4.2%

r

reference data 

Table 4. Vortex properties derived with the individual PIV images #1 and #3 at position 17

 a) Image #1 

centroid a Q criterion o

conv 2 

d max

max/ 51.9 52.6 52.6 0.7

xv/R (%) 0.31 0.35 0.29 0.06

yv/R (%) 0.52 0.52 0.53 0.01

 b) Image #3 

centroid a Q criterion o

conv 2 

d max

max/ 34.1 34.1 34.1 0.0

xv/R (%) 0.35 0.35 0.43 0.08

yv/R (%) 0.75 0.75 0.73 0.02

c) Conditional averaging with images #1 and #3 

centroid a Q criterion o

conv 2 

d max

max/ 43.3 43.4 47.7 4.4

xv/R (%) 0.33 --

*

0.36 0.03

yv/R (%) 0.64 --

*

0.64 0.0

d) Difference in conditionally averaged property with images #1 and #3, referenced from the 

results of a centroid 

centroid a Q criterion o

conv 2 

d

max/ (%) --

r

0.2 10.2

xv/c (%) --

r

--

*

0.50

yv/c (%) --

r

--

*

0.0

a provided by AFDD, o provided by Onera, d provided by DLR, r

reference data, 

* no data provided, 
19 

Table 5. Vortex properties derived with the individual PIV images #2, #3 and #8 at position 22

 a) Conditional averaging 

centroid a

conv 2 

d max

max/ 24.4 23.3 1.1

xv/R (%) -0.29 -0.34 0.05

yv/R (%) 0.35 0.37 0.02

 b) Difference in conditionally averaged property, referenced from a centroid 

centroid a

conv 2 

d

max/ (%) --

r

4.5

xv/c (%) --

r

0.83

yv/c (%) --

r

0.33

a provided by AFDD, d provided by DLR, r

reference data 

Table 6. Rotation angles computed with the individual PIV images #2, #3 and #8 at position 22

 a) Image-to-image (i2i) difference 

centroid a

conv 2 

d

x,i2i 7.7o

12.3o

y,i2i 6.2o

5.2o

 b) Conditional average (ca) 

centroid a

conv 2 

d max

x,ca 6.3o

8.3o2.0o

y,ca -34.3o

-31.4o2.9o

a provided by AFDD, d provided by DLR 
20 

Table 7. Rotation angles computed from the conditionally averaged image with all 100 PIV images at 

positions 17 and 22 

 

 a) Pos 17 

centroid a Q criterion o

conv 2 

d

x,ca -0.7o

1.6o4.3o

y,ca -19.4o

-25.7o-19.2o

 b) Pos 22 

centroid a Q criterion o

conv 2 

d

x,ca 2.2o

-1.4o12.4o

y,ca -33.9o

-20.6o-22.6o

a provided by AFDD, o provided by Onera, d provided by DLR 

Table 8. Vortex core radii and tangential velocities at positions 17 and 22, averaged (centroid) with a few 

selected images 

Pos 17 Pos 22

cutting axis rc /c (%) v,max/R (%) rc /c (%) v,max/R (%)

0

o

4.8 2.4 10.4 2.1

90o2.8 3.0 12.4 2.6

180o3.6 2.9 10.4 2.6

270o10.1 2.6 9.8 2.5

mean

(0o,90o,180o,270o)

5.3 2.7 10.7 2.4

optimum mean

(90o, 180o)

3.2 2.9 11.4 2.6
21 

a) Reference blade at 70 degrees

b) Reference blade at 20 degrees

Figure 2. Schematic diagram for PIV 

measurement planes

Figure 1. HART rotor and 3-C PIV test setup
22 

Figure 3. Raw image from two different cameras for the

baseline case, position 21.
23 

Figure 4. Single PIV image of 3-C velocity and vorticity map (image #1) for position 17 (Dpt 

1003) with an age of 25.3o.
24 

Figure 5. Conditional averaging procedure

vortex trajectory plane

vortex 

trajectory x,i z k,

y j ,

unrotated

rotated plane

(normal)  x

 y

P1

P2

P3

Figure 6. Re-orientation of the PIV measurement plane for the vortex trajectory method.
25 

Vortex Horizontal Position, BL, y/R=0.7

-30

-20

-10

0

10

20

-1.0 -0.5 0.0 0.5 1.0

xw t/R

x0 / c (%)

DLR

AFDD

ONERA

Vortex Vertical Position, BL, y/R=0.7

-10

0

10

20

30

40

-1.0 -0.5 0.0 0.5 1.0

xw t/R

y0 / c (%)

DLR

AFDD

ONERA

Horizontal Angle, BL, y/R=0.7

-20

-10

0

10

20

30

-1.0 -0.5 0.0 0.5 1.0

xw t/R

x (deg)

DLR

AFDD

ONERA

Vertical Angle, BL, y/R=0.7

-40

-30

-20

-10

0

10

-1.0 -0.5 0.0 0.5 1.0

xw t/R

y (deg)

DLR

AFDD

ONERA

Peak Vorticity, BL, y/R=0.7

0

10

20

30

40

50

60

-1.0 -0.5 0.0 0.5 1.0

xw t/R

 z / 

DLR

AFDD

ONERA

Vortex Core Radius, BL, y/R=0.7

0

2

4

6

8

10

12

14

16

-1.0 -0.5 0.0 0.5 1.0

xw t/R

rc / c (%)

DLR

AFDD

ONERA

Maximum Swirl Velocity, BL, y/R=0.7

0

2

4

6

8

10

-1.0 -0.5 0.0 0.5 1.0

xw t/R

V,max / R (% )

DLR

AFDD

ONERA

Figure 7. Comparison of vortex properties among HART II partners‘ results in the 

longitudinal plane of y/R=0.7 on the advancing side (baseline, positions 17-23)
26 

Figure 8. Conditionally averaged vorticity maps (unrotated) for positions 17 (Dpt 1003, wake age 

of 25.3o) and 22 (Dpt 998, wake age of 425.3o).
27 

Comparison of Means

Dpt 1003, Pos 17

0.00

0.25

0.50

0.75

1.00

0.00 0.25 0.50 0.75 1.00

X [%R]

Y [%R]

AFDD, centroid

DLR, conv lamb2

ONERA, Q criterion

Figure 10. A comparison of the mean vortex center derived using centroid, Q criterion and 

convolution of 2 for position 17 (Dpt 1003).

AFDD, Centroid

Dpt 1003, Pos 17

-4

-2

0

2

4

-4 -2 0 2 4

X [%R]

Y [%R]

100 images

mean

DLR, Conv of Lamb2

Dpt 1003, Pos 17

-4

-2

0

2

4

-4 -2 0 2 4

X [%R]

Y [%R]

100 images

mean

a) centroid b) convolution of 2

Figure 9. Vortex center distribution of all 100 individual images for position 17 (Dpt 1003).
28 

Figure 11. Comparison of conditionally averaged vorticity () using various center 

identification methods for position 17 (Dpt 1003).

AFDD, 2 DLR, conv 2

AFDD, centroid ONERA, Q criterion
29 

Figure 12. Comparison of conditionally averaged velocity gradient tensors - centroid, Q criterion, 

2, and convolution of 2 - using various center identification methods for position 17 (Dpt 

1003).

AFDD, 2

AFDD, centroid ONERA, Q criterion

DLR, conv 2
30 

Figure 13. Effect of Z scores or standard deviation of vortex center on the conditionally averaged 

vorticity for position 17 (Dpt 1003): standard deviations of 0.5, 0.7, 1.5, and 5.0.

SD = 0.5

SD = 1.5

SD = 0.7

SD = 5.0
31 

Figure 14. A perspective view of the vorticity map and the locations of its sub-grids in the 

PIV image #3 for position 17 (Dpt 1003) in the baseline case.

peaks top 10% of the peak
32 

 a) Centroid b) Q criterion

Figure 15. Vortex centers with a variation of the sub-grid size for the PIV image #3 for position 

17 (Dpt 1003).

Sub-grid Effect on Vortex Center (Centroid)

Dpt 1003, Pos 17, Image #3

10%

20%

30%

40%

50%

Conv(2)

0.0

0.2

0.4

0.6

0.8

1.0

-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6

xPIV (%R)

yPIV (%R)

Centroid

Sub-grid Effect on Vortex Center (Q)

Dpt 1003, Pos 17, Image #3

10%

20%

30%

40%

50%

Conv(2)

0.0

0.2

0.4

0.6

0.8

1.0

-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6

xPIV (%R)

yPIV (%R)

Q criterion
33 

Figure 16. Perspective and top views of 2 and convolution of 2 in the PIV image #3 

for position 17 (Dpt 1003) in the baseline case.

b) Top view of 2 d) Top view of convolution of 2

a) Perspective view of 2 c) Perspective view of convolution of 2
34 

Figure 17. The first 16 individual PIV images at position 17 (Dpt 1003) in the baseline case.

1 2

3 4

6

7 8

5

10

11

9

12

14

16

13

15
35 

Figure 18. Individual Image #1: position 17 (Dpt 1003).

Figure 19. Individual Image #3: position 17 (Dpt 1003).
36 

Figure 20.Conditional averaging with images #1 and #3: position 17 (Dpt 1003).

Figure 21. The first 16 individual PIV images: position 22 (Dpt 998).
37 

Figure 22. Conditional averaging with images #2, #3 and #8: position 22 (Dpt 998).

Figure 23. The vorticity () and cross flow (vz/R) averaged with images #2, #3 and #8 for

position 22 (Dpt 998) before and after the rotation.
38 

Figure 24. A comparison of the centroid and convolution of 2 rotation results for each individual 

image, #2, #3 and #8 and its averaged image for position 22 (Dpt 998). The label, ―ca‖ is the

conditionally averaged image.

a) Vorticity b) Swirl velocity

Figure 25. Cutting axes in the vorticity map and the associated tangential velocities at 0o, 90o, 180oand 

270ofor position 17 (Dpt 1003).

0

5

10

15

20

2 3 8 c a

Image number

Rotation Angle, x

centroid

conv of lamb2

-50

-40

-30

-20

-10

0

2 3 8 c a

Image number

Rotation Angle, y
39 

a) Vorticity b) Swirl velocity

Figure 26. Cutting axes in the vorticity map and the associated tangential velocities at 0o, 90o, 180o

and 270ofor position 22 (Dpt 998).

a) Position 17 b) Position 22

Figure 27. Swirl velocities using a Vatistas model of the prototyped images for positions 17 and 22.
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1.AGENCY USE ONLY 2. REPORT DATE

 July 2010

3. REPORT TYPE AND DATES COVERED

 Technical Report

4. TITLE AND SUBTITLE

An Assessment of 3-C PIV Analysis Methodology for HART II 

Measured Data

5. FUNDING NUMBERS

 

6. AUTHOR(S)

Joon W. Lim and Berend G. van der Wall 

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

Commander, U.S. Army Research, Development, and 

 Engineering Command

ATTN: RDMR-AF

Redstone Arsenal, AL 35898

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 11. SUPPLEMENTARY NOTES

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lim@merlin.arc.nasa.gov

12a. DISTRIBUTION / AVAILABILITY STATEMENT

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13. ABSTRACT (Maximum 200 Words)

 Since the completion of the DNW test, HART II partners have put forth significant efforts to derive vortex 

properties from the measured data. These properties include vortex center, rotation angles of the vortex axis in 

the PIV measurement plane, maximum vorticity, core radius , and swirl velocity. Differences among the 

partners’ results were found for some of these vortex properties, which required more effort to assess the 

physical significance of the differences. This was because the derived vortex properties were an integral of all 

the sub-processes in the complex PIV data analysis procedure, and more information was needed to resolve the 

differences in vortex properties. The objectives of this report are to discuss and summarize the parameters and 

techniques that could contribute to these differences. The detailed comparisons in this report have helped 

establish a strong foundation for a PIV data analysis methodology in determining vortex properties.

14. SUBJECT TERMS

HART II, Particle Image Velocimetry (PIV), vortex center, conditional averaging, 

vortex trajectory method, swirl velocity, vorticity, vortex core radius, centroid, Q 

criterion, lambda 2, convolution of lambda 2

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