Evaluation of high magnification two and three dimensional ...ltces.dem.ist.utl.pt/lxlaser/lxlaser2016/final... · Evaluation of high magnification two and three dimensional particle

18th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 4 – 7, 2016

Evaluation of high magnification two and three dimensional particle image tracking/velocimetry in near wall turbulence

S. Rafati, S. Ghaemi*

Department of Mechanical Engineering, University of Alberta, Canada * Correspondent author: [email protected]

Keywords: Tomographic-PIV, 3D-PTV, Turbulent channel flow

ABSTRACT

Measurement of turbulent statistics in the inner layer of wall flows is of fundamental and applied

importance for development of passive and active flow control systems. Accuracy of two and three

dimensional particle image velocimetry (PIV) and particle tracking velocimetry (PTV) in resolving the

near-wall turbulence statistics of a channel flow is evaluated at Reynolds number of ReH = 6700 (based on

average velocity and channel height H) equivalent to Reτ = 190 (based on friction velocity uτ = 0.0638 m/s

and the half channel height, H / 2). The channel has a rectangular cross-section of W×H = 40×6 mm2 and

wall unit of λ = 16.2 μm. The evaluated 2D techniques include PIV (2D-PIV) with spatial resolution of

3.2+×3.2

+ (digital resolution of 6.25 μm/pix) and long-range microscopic particle tracking velocimetry

(2D-PTV) with spatial resolution of 1.7+×1.7

+ (digital resolution of 2.3 μm/pix). The 3D techniques

include tomographic particle image velocimetry (tomo-PIV) and three-dimensional PTV (3D-PTV) both

carried out at high digital resolution of 7.5 μm/voxel (M = 0.9) and tracer density of 0.015 particles per

pixel. The spatial resolution of the tomo-PIV is 22+×22

+×22

+ (0.36×0.36×0.36 mm

3) and wall-normal

spatial resolution of 3D-PTV is 5.5+ (90 μm). The measurements are compared with channel flow direct

numerical simulation (DNS) of Moser et al. (1999) at Reτ = 180. The 2D-PTV technique shows maximum

uncertainty of 0.06 pix in resolving mean velocity and 0.1 pixel uncertainties in measurement of Reynolds

stresses. The high magnification tomo-PIV shows an uncertainty of 0.2 pix in resolving the mean velocity

while an uncertainty of 0.3-0.7 pixel in measuring peak value of Reynolds stresses. 3D-PTV based on

triangulation of particles demonstrated smaller uncertainty relative to tomo-PIV and 3D-PTV using MART

reconstruction.

1. Introduction

The transport of momentum and heat by turbulent motions increases skin-friction and heat

transfer rate in wall flows. The near-wall turbulence is of particular importance since almost all

the production of turbulent kinetic energy occurs adjacent to the wall at y+ < 90 (Kim et al., 1987).

Development and evaluation of experimental techniques capable of resolving the near-wall flow

is vital in understanding the near wall turbulence and development of flow control strategies.


This is of particular importance since DNS at high Reynolds numbers and non-canonical wall

flows over textured and rough surfaces is still challenging.

The accuracy of PIV in near-wall turbulence may reduce due to several issues including

reflection of the laser light from the wall, small turbulent structures, high velocity gradient, and

low tracer density. The finite spatial-resolution acts as a low-pass filter, systematically

underestimating the small-scale near-wall turbulence and smearing out the spatial gradients

(Westerweel 1993). Several techniques incorporating window offset, grid refinement, window

deformation, and spatially adaptive windows have been developed to improve the accuracy and

robustness of near-wall PIV (Scarano & Riethmuller 2000; Theunissen et al. 2008; Novara et al.

2013). However, even with modern PIV algorithms the uncertainty significantly increases with

reduction of wall-normal distance as the velocity gradient increases (Herpin et al., 2008). Higher

digital resolution can reduce the uncertainties caused by spatial gradients and finite window

size; however, it also causes smaller spatial dynamic range, low number density of tracer

particles, bias error due to non-uniform tracer density, and large particle image size (Cierpka et

al. 2013). As a result, other techniques such as PTV have been sought for near-wall measurement.

The spatial-resolution of PTV is limited by the uncertainty in estimating the center of particle

images, which can be below 0.01 pix for particles of 3 to 15 pix in diameter (Kähler et al., 2012).

The high spatial-resolution of PTV has enabled measurement of the mean velocity gradient in

the linear viscous sublayer (y+< 5) and accurate estimation of wall-shear stress (e.g., Knopp et al.

2013 and Huisman et al., 2013). Although PTV has been evaluated as a robust method for

measurement of near-wall mean velocity, investigation of PTV accuracy in estimation of high-

order turbulence statistics is required.

Tomo-PIV and 3D-PTV have been developed for measurement of 3D spatial structure and the

velocity gradient tensor in turbulent flows (Elsinga et al. 2006; Scarano, 2013). The issue of finite

spatial-resolution is more pronounced in tomo-PIV relative to standard planar PIV since the

minimum size of the interrogation volume (IV) is limited by maximum source density (Ns, image

area covered by particle images) and a minimum of about 10 particles per IV (De Silva et al.,

2012). As a result, the previous tomo-PIV of turbulent wall flows have been limited to relatively

large spatial-resolution as summarized in Table 1. The table also shows that the previous tomo-

PIV experiments have a digital resolution smaller than 28 pix/mm. To the authors’ knowledge,

only Kim et al. (2013) conducted tomo-PIV at a high digital resolution of 4 μm/pix at

magnification of 1.5 using four cameras viewing through a single microscope objective lens. Kim

et al. (2013) measured the average velocity in a droplet on a moving substrate with no

measurement of high order statistics, as the flow was laminar.


Table 1. An overview of modern 3D measurements in turbulent wall flows (turbulent boundary layer (TBL) and channel flow). The spatial resolution of the current tomo-PIV and 3D-PTV measurements are also presented for comparison.

Flow type

Evaluation method

IV size

Digital

resolution

(pix/mm)

Schröder et al. (2008)

TBL

double-frame

correlation

2×2×2 mm3

24.0

Elsinga (2008) TBL double-frame

correlation

1.88×1.88×1.88 mm3

64+×64+×64+

27.0

Schröder et al. (2011) TBL double-frame

correlation

2.75×2.75×2.75 mm3

59.7+×59.7+×59.7+

11.7

Scha ̈fer et al. (2011) channel flow double-frame

correlation

1×1×1 mm3

96

Atkinson et al. (2011) TBL double-frame

correlation

3.2×3.2×3.2 mm3

26.4+×26.4+×26.4+

20

Ghaemi & Scarano, (2011) TBL with

pressure gradient

double-frame

correlation

1.47×1.47×1.47 mm3

48.9+×48.9+×48.9+

21.9

Elsinga & Westerweel

(2012)

TBL after a

tripping device

double-frame

correlation

1.8×1.8×1.8 mm3

15.7

Ghaemi et al. (2012) TBL sliding-average over 3

image pairs

1.53×1.53×1.53 mm3

38+×38+×38+

18.3

Ghaemi & Scarano (2013) TBL sliding-average over 3

image pairs

1.68×0.84×1.68 mm3

43+×22+×43+

19.0

Jodai et al. (2014) TBL double-frame

correlation

1.37×1.37×1.37 mm3

16+×16+×16+

28.0

Schröder et al. (2015) TBL 3D-PTV

shake-the-box method

3.3×3.3×3.3 μm3

1/13+×1/13+×1/13+

33.3

Current experiment channel flow double-frame

correlation

3D-PTV

0.36×0.36×0.36 mm3

22+×22+×22+

15.5×0.09×10 mm3

939+×5.5+×606+

132

132


Three-dimensional measurement with high spatial-resolution can be achieved by tracking the

individual particles (Mass et al. 1993). Kasagi & Nishino (1991), Walpot et al. (2007), and Oliveira

et al. (2013) measured wall turbulence statistics by 3D tracking of large polyamide tracers (200-

250μm). The PTV image sample of Kasagi & Nishino (1991) shows about 0.003 ppp while Walpot

et al. (2007) have detected 150 particles per images (~0.00015 ppp). Mass et al. (1993) also

reported a seeding density of 0.005 ppp. At higher tracer number density, the robustness of 3D-

PTV algorithm is affected by the overlapping particles or crossing trajectories (Novara & Scarano

2013). The seed density and number of valid vectors in 3D-PTV is typically an order of

magnitude less than tomo-PIV (Scarano 2013; Wieneke, 2013), limiting the application of 3D-PTV

in characterization of instantaneous turbulent structures. Kim et al. (2013) compared tomo-PIV

and 3D-PTV based on a common set of 2D images of laminar flow inside a liquid droplet at 0.034

ppp. Their results showed lower noise of tomo-PIV compared to 3D-PTV. The application of

high tracer density images for measurement of turbulent statistics with high spatial-resolution

using 3D-PTV requires further evaluation of the uncertainties.

The current investigation aims at evaluation of planar and volumetric double-frame PIV and

PTV techniques for measurement of turbulent statistics across a channel flow and in particular in

the inner layer (y+ < 100) at Reτ = 190. The investigated measurement techniques include:

2D-PIV, at digital resolution of 6.25 μm/pix, processed using both double-frame correlation

and ensemble of correlation (EC) techniques (Meinhart et al. 2000).

2D-PTV at digital resolution of 2.3 μm/pix (M = 2.9) carried out using long-range

microscope.

Tomo-PIV at digital resolution of 7.5 μm/voxel (M = 0.9).

3D-PTV at the same digital resolution and particle density (0.015 ppp) of the tomo-PIV.

All the methods are evaluated using DNS of turbulent channel flow by Moser et al. (1999) at Reτ

= 180.

2. Experimental setup

2.1. Flow facility

Measurements are carried out in a closed-circuit water tunnel with rectangular cross-section of

40×6 mm2 (W×H). The total length of the rectangular channel is 1200 mm (200H) and the

measurements were carried out 720 mm (120H) downstream of the channel entrance to ensure a

fully developed flow. Figure 1(a) shows the fully transparent test section and downstream

diffuser of the facility. The working fluid is distilled water seeded with silver-coated 2 μm

spherical glass beads with density of 4 g/cm3 (SG02S40 Potters Industries). The Reynolds

number based on the channel height H and the bulk velocity across the channel is ReH = 6700.


The bulk velocity, the maximum velocity, friction velocity, and the wall unit are Ub = 1.12 m/s,

Umax = 1.26 m/s, uτ = 0.064 m/s, and λ = 16.2 μm based on 2D-PTV measurement, respectively.

Table 2. Flow condition at the measurement location based on

2D-PTV measurement.

Parameter

value

λ0 (μm)

16.2

uτ0 (m/s)

0.064

Ub (m/s)

1.121

ReH

6700

Reτ 190

2.2. Planar particle image velocimetry (2D-PIV)

2D-PIV was carried out using a 12-bit CCD camera (Imager Intense, LaVision GmbH) with

1040×1376 pix sensor and pixel area of 6.45×6.45 μm2. The camera was equipped with a Sigma

SLR objective lens with focal length of f = 105 mm at aperture size of f /11. The illumination was

provided by a thin laser sheet of 0.5 mm thickness generated by an Nd:YAG laser (Solo III-15,

New Wave Research). The laser sheet enters the test section from the bottom acrylic wall and

passes though the upper acrylic wall with negligible glare line in the images. Magnification was

set to M = 0.8 with digital resolution of 160 pix/mm and fields-of-view of 8.9×6.7 mm2 in the x

and y directions, respectively. The depth-of-field of the imaging system is estimated 1.3 mm. The

two laser pulses are synchronized with the camera frames using a programmable timing unit

(PTU9, LaVision GmbH) controlled by DaVis 8.2. PIV recordings are obtained in double-frame

mode with laser pulse separation of 63 μs. An ensemble of 10,000 image pairs was recorded.

The signal-to-noise ratio of the images was improved by subtracting the minimum intensity and

image normalization using the ensemble average. The images are processed by both ensemble of

correlation (Meinhart et al. 2000) and double-frame cross correlation. The final window size in

the ensemble of correlation (EC) is 8×8 pix (52×52 μm2 equivalent to 3.2+×3.2+) with 75 percent

overlap. The turbulent intensities are obtained from cross-correlation of the double-frame images

using a multi-pass algorithm with final interrogation windows of 32×32 pix (0.208×0.208 mm2)

with 75 percent overlap conducted in DaVis 8.2 (LaVision, GmbH). The vector fields are post

processed using the universal outlier detection (Westerweel & Scarano, 2005).


2.3. Planar particle tracking velocimetry (2D-PTV)

The 2D-PTV measurement is carried out using the same CCD camera as the PIV equipped with a

long-range microscope (12× zoom lens, Navitar) at a working distance of 86 mm. The

magnification is set to 2.9 with digital image resolution of 440 pix/mm and fields-of-view of

2.4×3.1 mm2 in the x and y directions, respectively. The numerical aperture (NA) is estimated

about 0.05 based on magnification from the Navitar zoom lens performance datasheet (Navitar,

2016). The NA is equivalent to aperture number of f# = 1 / (2×NA) = 10. The depth-of-field (δz)

at high magnification imaging is estimated as 260 μm (Young et al., 1993), which is about half of

the laser sheet thickness. This results in out-of-focus particle images in the 2D-PTV images. The

estimated diameter of in-focus particles is about 8 pix (based on diffraction and geometric

imaging) while the out-of-focus particle image can be as large as 12 pix (Olsen & Adrian, 2000).

An ensemble of 10,000 double-frame image pairs were acquired with a laser pulse separation of

27 μs.

The minimum intensity of the ensemble of images was subtracted from the individual images

followed by image normalization using the average of the image ensemble. In order to overcome

the peak locking effect, a 3×3 pix2 Gaussian smoothing filter was applied to the images (Kähler et

al. 2012). The algorithm initially detects particles based on a preliminary intensity threshold

followed by detection of local maxima (Maas et al. 1993) within a kernel of 12 pixels. The

detected particles are also band-pass filtered within 3-7 pix in diameter. Particle images smaller

than 3 pix in diameter can introduce bias error due to peak locking (Kähler et al. 2012), while

particles larger than 7 pixel are typically out-of-focus or skewed. In addition, the change in the

particle area, the ratio of the major and minor axis, and the peak intensity ratio of the two frames

were limited to 20, 30, and 50 percent, respectively. Peak detection with sub-pixel accuracy is

carried out using a Gaussian fit with kernel of 3×3 pix2. The pairs are detected by searching the

neighborhood in a circle of 5 pix radius after applying an initial shift based on EC analysis

(32×32 pixel window size and 75% overlap). The data is filtered by limiting the magnitude of the

wall-normal velocity component to be smaller than 20% of the streamwise component. The

vectors are averaged in bins with 880×12 pix (2000×28 μm2, 123+×1.7+) in x and y directions,

respectively.

2.4 Tomographic particle image velocimetry (tomo-PIV)

The illumination source of the tomo-PIV experiment was provided by an Nd:YAG laser (Solo III-

15, New Wave Research). The laser sheet was collimated and slightly focused to a thickness of 3

mm in the spanwise direction (z). A knife-edge filter with 3 mm width was attached to the

bottom surface of the channel. The imaging system consists of four CCD cameras (Imager ProX,

LaVisison) with 2048×2048 pix sensor and pixel size of 7.4×7.4 μm2. The cameras were equipped


with scheimpflug adapters and f = 105 mm Sigma SLR objectives at an aperture setting of f / 16.

The magnification and digital resolution are M = 0.9 and S = 132 pix/mm, respectively. The

measurement volume is (x, y, z) = 15.5×10×3 mm3 (1971×723×394 voxel). The depth-of-field of

the imaging system is estimated about 2.5 mm, which is slightly smaller than the laser sheet

thickness. This small out-of-focus effect is negligible since the blur image is approximately 7.6

μm (1.03 pix) smaller than the 2 pixel limit proposed by Scarano (2013). The smaller aperture is

desirable here to reduce particle image size and consequently reduce the total area covered by

the particle images. The particle image diameter based on visual inspection of the images range

between 4-7 pixels. The laser and cameras were synchronized using a programmable timing unit

(PTU9, LaVision, GmbH). The solid angle between the two cameras on the left-side of the

channel is 50 degrees while the solid angle of the two right-side cameras is 30 degrees as shown

in Figure 1(b). An ensemble of 1,000 double-frame images with time delay of 72 μs (maximum

displacement of about 13 pix) was recorded.

The initial mapping function is obtained using a pinhole model on a target with 0.3 mm dots

spaced 2 mm apart. The target is traversed in 0.5 mm steps in the depth direction (spanwise

direction of the channel, z). A relatively large image distortion with 1-2 pixel residual root-mean-

square (RMS) in the disparity map was observed. Volume-self-calibration was applied to reduce

the residual RMS of the disparity map to less than 0.05 pixel (Wieneke, 2008). This disparity is

negligible since it is about 1% of mean particle image diameter. The channel flow was seeded

with 2µm silver coated glass beads at a concentration of 90 particles/mm3 with particle number

density of 0.015 particles per pixel (ppp) and source density (Ns) of 0.34.

The minimum of the ensemble of images is subtracted from the individual images followed by

image normalization. The SNR is further improved by subtracting local minimum and intensity

normalization using a local average with kernel of 51 pix. The 3D location of the particles was

reconstructed based on MART algorithm (Herman and Lent 1976) known as “precise

reconstruction” in Davis 8.2. The volumetric cross-correlation is performed using multi-pass

algorithm with final interrogation volume size of 48×48×48 voxel (0.36×0.36×0.36 mm3, 22+

×22+×22+) with 75 percent overlap. The number of particles per IV in the reconstructed images is

about 4-7 particles. The vector fields are post processed using the universal outlier detection

(Westerweel & Scarano, 2005). Davis 8.2 (LaVision, GmbH) is used for image acquisition and

tomo-PIV processing.

2.5 Three-dimensional particle tracking velocimetry (3D-PTV)

The 3D-PTV processing was carried out on the same images acquired for tomo-PIV followed by

the same image preprocessing with the addition of a Gaussian filter to prevent possible peak

locking (Kähler et al., 2012). Two 3D-PTV algorithms were considered. The first method detects


the 3D location of particles based on triangulation (TA) of the particles in 2D images. The process

is carried out in DaVis 8.2.3 (LaVision, GmbH) using the same mapping function obtained for

the tomo-PIV. An ensemble of 4,000 double-frame images was processed using 3D-PTV-TA

algorithm. The second method detects and tracks the particles in the reconstructed 3D intensity

distribution obtained based on the MATR algorithm for tomo-PIV. The 3D particle tracking of

the MART method is conducted using an in-house PTV algorithm developed in MATLAB. The

comparison of the two 3D-PTV methods can separate the effect of calibration and identify the

errors associated with 3D intensity reconstruction (i.e., ghost particles).

The 3D-PTV-MART is carried out in MATLAB based on preliminary detection of local intensity

maxima within a kernel of 12 voxel. The location of the particle peak in x and y directions were

estimated with sub-pixel accuracy using Gaussian fitting in xy plane. The particle peak location

in the z direction is estimated as the average peaks obtained from Gaussian fits in xz and yz

planes. The average velocity field obtained from tomo-PIV is used as an initial estimation to

search for the particle pairs within an elliptical volume with kernel of 5, 3, and 3 voxels in x, y, z,

respectively. The 3D-PTV vectors are averaged in bins with wall normal size of 12 voxel (270 μm,

5.5+). The bins cover full streamwise (15.5 mm) and spanwise extensions (3 mm) of the

measurement volume.

(a)

(b)

Fig. 1 (a) The planar PIV consists of the camera on the left side of the channel. The long-range

microscopic PTV is carried out using the right-side camera equipped with Navitar zoom lens.

The side wall of the channel are glass while the top and bottom walls are from acrylic. The laser

illuminates a wall-normal streamwise plane from the bottom of the channel. (b) The setup of the

tomo-PIV showing four cameras imaging a streamwise/wall-normal field-of-view. The angle

between the right-side cameras is 50º while the angle between the left-side cameras is 30º.


3. Optimization of 3D-PTV-TA

Two input parameters of 3D-PTV-TA include an intensity threshold (I) for particle detection and

a triangulation error (e). These parameters need to be optimized to maximize the accuracy of

particle peak detection while collecting enough number of particles for statistical convergence.

The accuracy of the 3D-PTV-TA is evaluated using second order turbulent statistics <u2>, <v2>,

and <w2> in comparison with the DNS data in Figure 2 (a), (b), and (c), respectively.

Triangulation error smaller than e = 1 did not result in statistical convergence. The 3D-PTV-TA

data with triangulation error of e = 1 pixel (at intensity threshold of I = 30) has the smallest noise

level relative to the two other cases. Increase of the intensity threshold to I = 50 results in an

increase of noise level in the outer layer and loss of the near-wall peak for <u2>. Increase of

triangulation error to e = 2 pix has a large effect on the measurement noise. The observed noise at

the channel centerline (y+=180) by increase of e from 1 to 2 pix is equivalent to 0.6, 0.3, and 1 pix

for <u2>, <v2>, and <w2>, respectively. The results show that PTV parameters of e = 1 pix and I =

30 counts resulted in relative overlap of <u2> and <v2> with the DNS data across the channel.

However, <w2> is still overestimated by about 0.5 pix.

(a) (b) (c)

Fig. 2 The effect of intensity threshold (I) and triangulation error (e) on the accuracy of 3D-PTV-

TA in evaluation of second order turbulent statistics. The dashed lines represent the DNS data of

Moser et al. (1999) at Reτ =180.


4. Mean velocity profile

A comparison of the measured mean velocity using all the applied techniques within y+ < 35 is

shown in Figure 3(a). The 2D-PIV data is obtained using the ensemble of correlation (EC)

method. 2D-PIV deviates relative to DNS within 12 < y+ < 35 where there is a large change of

velocity gradient in the buffer layer. The maximum deviation in this range is about 0.7uτ

(equivalent to 0.5 pix). The bias error in PIV (based on EC) is associated with broadening of the

correlation peaks in the buffer layer due to asymmetric distribution of the turbulent fluctuations

(Kähler et al. 2006). The analytical analysis of Kähler et al. (2006) showed overestimation of EC

with respect to the most probable value of the distribution. The first valid data point of 2D-PIV is

at y+ = 0.9 (~ 2 pix). The deviation of 2D-PIV at y+ = 3.5 is about 0.3uτ (9% relative error) while it

increases to a maximum of 0.6uτ (0.4 pixel and 5% relative error) at y+ = 21. Kähler et al. (2012)

applied single-pixel EC with digital resolution of 11.1 pix/mm in a turbulent boundary layer and

observed up to 50% uncertainty within the viscous sublayer (y+ ≤ 5).

The first data point of 2D-PTV is observed at y+ = 1.6 with negligible deviation with respect to

y+=u+. A slight deviation is observed at 12 <y+ ≤ 18 where there is a large change in velocity

gradient. The maximum error of 2D-PTV is about 0.25uτ (equivalent to 0.2 pixel) observed at y+ =

13. The 2D-PIV and 2D-PTV have sufficient spatial resolution (at least two data points) within y+

< 5 for estimation of the velocity gradient within the linear viscous sublayer, and consequently

estimation of the friction velocity.

The bias error of tomo-PIV decreases with increase of wall-normal distance. The maximum

deviation is about 2uτ (equivalent to 1.2 pix) at y+ = 6 while the next data point at y+ = 12 has 5%

deviation (equivalent to 0.4 pix). Atkinson et al. (2011) associated the overestimation with poor

spatial resolution and large near-wall velocity gradient. 3D-PTV based on MART overlaps with

DNS at y+ = 3 (0.04 pix deviation) while there is about 0.9 pix underestimation at y+ = 8. The 3D-

PTV based on TR shows more accurate results relative to the MART method with maximum

uncertainty of about 0.8uτ (0.5 pix) at y+ = 3. The number of detected particle pairs limited the

spatial resolution of 3D-PTV (bin size), in particular close to the wall. However, rhe spatial

resolution of the 3D-PTV techniques (12 pix in wall-normal) is four times larger than that of the

tomo-PIV (48 pix IV with 75% overlap). The 3D-PTV-TR is more accurate in comparison to 3D-

PTV-MART and tomo-PIV. Therefore, the uncertainty of tomo-PIV and 3D-PTV-MART might

originate from the reconstruction errors and formation ghost particles (Elsinga et al. 2010).

Figure 3(b) shows semi-log representation of mean velocity versus wall-normal distance

normalized using inner variables. The law of the wall (y+ = u+) and the logarithmic law (u+ =

1/0.39 ln y+ + 5.4) are also shown for comparison. All the measurement techniques except tomo-

PIV and 3D-PIV-TR have captured the viscous sublayer.


(a) (b)

Fig. 3 (a) Mean velocity profile in near-wall region and (b) semi-logarithmic plot of mean

velocity. Both plots normalized using inner scaling (uτ0 and λ0) obtained from 2D-PTV. The solid

line in Figure (a) shows linear fit on 2D-PTV data within y+<3.

5. Reynolds stresses

The streamwise Reynolds stress <u2> normalized using the reference friction velocity uτ0

(obtained from 2D-PTV) is shown in Figure 4(a). The x-axis of the plot shows wall-normal

coordinate up to y+=180 which overlaps with the middle of the channel. The correlation-based

techniques (2D-PIV and tomo-PIV) are not able to resolve the near-wall peak of <u2> and the

values increases with decrease of y+. This is associated with poor spatial resolution and overlap

of interrogation windows/volumes with the mirrored particle images. The peak of <u2> is

located at about y+ = 15 based on DNS which translates to 34 pix away from the wall in the 2C-

PIV experiment and 30 pix away from the wall in the tomo-PIV experiment. The 2D-PTV could

capture the <u2> peak value an uncertainty of about 0.1 pix. 2D-PTV slightly overestimates <u2>

in comparison with DNS data in the outer layer and the mid-section of the channel (y+ > 60). This

overestimation is about 8% (equivalent to 0.1 pix) and is associated with measurement noise and

small difference in the Reynold number since the inner scaling is expected to overlap the data in

the inner layer. The 3D-PTV-TR overestimated the peak value by 3% (equivalent to 0.3 pix) while

3D-PTV-MART overestimates it by 20% (equivalent to 0.7 pix).

The wall-normal Reynolds stress <v2> normalized by the reference friction velocity uτ0 is shown

in Figure 4(b). The tomo-PIV and 3D-PTV-MART both have significantly overestimated <v2>

across the channel. The uncertainty is about 0.25u2τ0 (equivalent to 0.3 pix) and 0.45u2τ0


(equivalent to 0.4 pix) at y+ = 50 for tomo-PIV and 3D-PTV-MART, respectively. The noise is

associated with 3D reconstruction errors while the lower noise of tomo-PIV is due to the low

pass filtering effect of large interrogation volumes. The 3D-PTV-TR estimates the peak value

with uncertainty of 0.08 pix. The 2D-PIV and 2D-PTV measure the <v2> peak with 1% and 2%

percent error equivalent to 0.05 and 0.08 pix, respectively.

Figure 4(c) shows the normalized Reynolds shear stress <uv> across the channel. All

measurement techniques underestimate <uv> in the peak region (y+<70). The underestimation of

shear stress is due to the measurement noise which reduces the correlation of the u and v

components. Peak locking has been considered as a possible source of noise reducing the u and v

correlation signal (Christensen, 2004) and also the accuracy peak detection in PTV.

The out-of-plane component <w2> measured by the volumetric systems in comparison with the

DNS data is shown in Figure 4(d). The tomo-PIV has not captured the peak value showing an

overestimation of about 0.7 pix at y+ ≈ 30 which reduces to 0.6 pix and stays constant till the

channel centerline. The 3D-PTV results based on MART and TR shows the same trend as the

DNS profile while the values are overestimated by 0.5 and 0.7 pix, respectively. The 3D-PTV-TR

has the most accurate measurement and captures the peak location at y+ = 21 with 20%

discrepancy with respect to the DNS. The uncertainty of the techniques in measurement of mean

velocity and Reynolds stress is summarized in Table 3 in terms of pixels.

Table 3. Unceratinty of the evaulated techniques in pixel in comaprison with DNS. NA stand for “not

available”.

2D-PIV (EC)

2D-PTV

Tomo-PIV

3D-PTV-TR

3D-PTV-MART

<U> at y+ = 3

0.12

0.05

NA

0.5

0.04

<U> at y+ ≈ 20

0.38 0.06 0.2 0.02 0.12

<u2> peak value

at y+=15

NA 0.1 0.6 0.4 0.7

<v2> peak value

at y+=50

0.04 0.08 0.3 0.1 0.4

<w2> peak value

at y+=35

NA NA 0.7 0.5 0.7

<uv> peak value

at y+=30

0.17 0.28 0.2 0.3 0.2


(a) (b)

(c) (d)

Fig. 4 Normalized <u2>, <v2>, <uv>, and <w2> across half-channel in comparison with DNS of

Moser et al. (1999).

5. Conclusion

The uncertainty of 2D-PIV, 2D-PTV, tomo-PIV, and 3D-PTV in measurement of channel flow

turbulent statistics at Reτ = 190 is evaluated using channel flow DNS of Moser et al. (1999). 2D-

PIV is processed using both double-frame correlation and ensemble of correlation (EC)

techniques (Meinhart et al. 2000). 2D-PTV is carried out at digital resolution of 2.3 μm/pix (M =

2.9) using a long-range microscope. The tomo-PIV and 3D-PTV are carried out at a high digital

resolution of 7.5 μm/voxel (M = 0.9) and particle density of 0.015 ppp). The 2D-PTV technique


shows maximum uncertainty of 0.06 pix in resolving mean velocity and 0.1 pixel uncertainties in

measurement of Reynolds stresses. The high magnification tomo-PIV shows an uncertainty of 0.2

pix in resolving the mean velocity while an uncertainty of 0.3-0.7 pixel in estimating peak value

of Reynolds stresses. 3D-PTV based on triangulation of particles demonstrated smaller

uncertainty relative to tomo-PIV and 3D-PTV using MART reconstruction.

6. Acknowledgement

This work has been supported by the Natural Sciences and Engineering Research Council of

Canada (NSERC RGPIN 1512 GHAEMI). The authors thank Dr. David Nobes for providing the

tomo-PIV equipment.

7. References

Atkinson, C., Coudert, S., Foucaut, J.-M., Stanislas, M., & Soria, J. (2011). The accuracy of

tomographic particle image velocimetry for measurements of a turbulent boundary layer.

Exp. Fluids, 50(4), 1031–1056.

Christensen, K. T. (2004). The influence of peak-locking errors on turbulence statistics computed

from PIV ensembles. Exp. Fluids, 36(3), 484–497.

Cierpka, C., Lütke, B., & Kähler, C. C. J. (2013). Higher order multi-frame particle tracking

velocimetry. Exp. Fluids, 54(5), 1533.

De Silva, C. M., Baidya, R., Khashehchi, M., & Marusic, I. (2012). Assessment of tomographic PIV

in wall-bounded turbulence using direct numerical simulation data. Exp. Fluids, 52(2), 425–

440.

Elsinga, G. (2008). Tomographic particle image velocimetry and its application to turbulent

boundary layers, PhD thesis, Delft University of Technology.

Elsinga, G. E., Scarano, F., Wieneke, B., & van Oudheusden, B. W. (2006). Tomographic particle

image velocimetry. Exp. Fluids, 41(6), 933–947.

Elsinga, G. E., & Westerweel, J. (2012). Tomographic-PIV measurement of the flow around a

zigzag boundary layer trip. Exp. Fluids, 52(4), 865–876.

Elsinga, G. E., Westerweel, J., Scarano, F., & Novara, M. (2010). On the velocity of ghost particles

and the bias errors in Tomographic-PIV. Exp. Fluids, 50(4), 825–838.

Ghaemi, S., Ragni, D., & Scarano, F. (2012). PIV-based pressure fluctuations in the turbulent

boundary layer. Exp. Fluids, 53(6), 1823–1840.

Ghaemi, S., & Scarano, F. (2011). Counter-hairpin vortices in the turbulent wake of a sharp

trailing edge. J. Fluid Mech., 689, 317–356.


Ghaemi, S., & Scarano, F. (2013). Turbulent structure of high-amplitude pressure peaks within

the turbulent boundary layer. J. Fluid Mech., 735, 381–426.

Herman, G. T., & Lent, A. (1976). Iterative Reconstruction Algorithms. Computer Biological

Medision, 6(3), 273–294.

Herpin, S., Wong, C. Y., Stanislas, M., & Soria, J. (2008). Stereoscopic PIV measurements of a

turbulent boundary layer with a large spatial dynamic range. Exp. Fluids, 45(4), 745–763.

Huisman, S. G., Scharnowski, S., Cierpka, C., Kähler, C. J., Lohse, D., & Sun, C. (2013).

Logarithmic Boundary Layers in Strong Taylor-Couette Turbulence. Physical Review Letters,

110(26), 264501.

Jodai, Y., Westerweel, J., & Elsinga, G. (2014). Time-resolved Tomographic-PIV measurement in

the near-wall region of a turbulent boundary layer. In International Symposium on

Application of Laser Techniques to Fluid Mechanics (Vol. 17th).

Kähler, C. J., Scharnowski, S., & Cierpka, C. (2012). On the uncertainty of digital PIV and PTV

near walls. Exp. Fluids, 52(6), 1641–1656.

Kähler, C. J., Scholz, U., & Ortmanns, J. (2006). Wall-shear-stress and near-wall turbulence

measurements up to single pixel resolution by means of long-distance micro-PIV. Exp. Fluids,

41(2), 327–341.

Kasagi, N., & Nishino, K. (1991). Probing turbulence with three-dimensional particle-tracking

velocimetry. Experimental Thermal and Fluid Science, 4(5), 601–612.

Kim, H., Westerweel, J., & Elsinga, G. E. (2013). Comparison of Tomo-PIV and 3D-PTV for

microfluidic flows. Measurement Science and Technology, 24(2), 024007.

Kim, J., Moin, P., & Moser, R. (1987). Turbulence statistics in fully developed channel flow at low

Reynolds number. J. Fluid Mech., 177(-1), 133.

Knopp, T., Schanz, D., Schröder, A., Dumitra, M., Cierpka, C., Hain, R., & Kähler, C. J. (2013).

Experimental Investigation of the Log-Law for an Adverse Pressure Gradient Turbulent

Boundary Layer Flow at Re θ = 10000. Flow, Turbulence and Combustion, 92(1-2), 451–471.

Maas, H. G., Gruen, a, & Papantoniou, D. (1993). Particle tracking velocimetry in 3-dimensional

flows. 1. Photogrammetric determination of partacle coordinates. Exp. Fluids, 15(2), 133–146.

Meinhart, C. D., Wereley, S. T., & Santiago, J. G. (2000). A PIV Algorithm for Estimating Time-

Averaged Velocity Fields. Journal of Fluids Engineering, 122(2), 285.

Moser, R. D., Kim, J., & Mansour, N. N. (1999). Direct numerical simulation of turbulent channel

flow up to Reτ=590. Phys. Fluids, 11(4), 943.

Navitar. (2016). 12X Zoom Performance Specifications, Navitar. Retrieved January 16, 2016.


Novara, M., & Scarano, F. (2013). A particle-tracking approach for accurate material derivative

measurements with tomographic PIV This article is part of the Topical Collection on

Application of Laser Techniques to Fluid Mechanics 2012. Exp. Fluids, 54(8).

Oliveira, J. L. G., van der Geld, C. W. M., & Kuerten, J. G. M. (2013). Lagrangian and Eulerian

Statistics of Pipe Flows Measured with 3D-PTV at Moderate and High Reynolds Numbers.

Flow, Turbulence and Combustion, 91(1), 105–137.

Scarano, F. (2013). Tomographic PIV: principles and practice. Measurement Science and

Technology, 24(1), 012001.

Scarano, F., & Riethmuller, M. L. (2000). Advances in iterative multigrid PIV image processing.

Exp. Fluids, 29(7), S051–S060.

Scha ̈fer, L., Dierksheide, U., Klaas, M., & Schro ̈der, W. (2011). Investigation of dissipation

elements in a fully developed turbulent channel flow by tomographic particle-image

velocimetry. Phys. Fluids, 23(3), 035106.

Scharnowski, S., Hain, R., & Kähler, C. J. (2011). Reynolds stress estimation up to single-pixel

resolution using PIV-measurements. Exp. Fluids, 52(4), 985–1002.

Schröder, A., Geisler, R., Elsinga, G. E., Scarano, F., & Dierksheide, U. (2008). Investigation of a

turbulent spot and a tripped turbulent boundary layer flow using time-resolved tomographic

PIV. Exp. Fluids, 44(2), 305–316.

Schröder, A., Geisler, R., Staack, K. É. A. A., Elsinga, G. E., Scarano, F., Wieneke, B., ... &

Westerweel, J. (2011). Eulerian and Lagrangian views of a turbulent boundary layer flow

using time-resolved tomographic PIV. Exp. Fluids, 50(4), 1071-1091.

Schröder, A., Schanz, D., Michaelis, D., Cierpka, C., Scharnowski, S., & Kähler, C. J. (2015).

Advances of PIV and 4D-PTV ”Shake-The-Box” for Turbulent Flow Analysis –the Flow over

Periodic Hills. Flow, Turbulence and Combustion, 95(2-3), 193–209.

Stanislas, M., Perret, L., & Foucaut, J.-M. (2008). Vortical structures in the turbulent boundary

layer: a possible route to a universal representation. J. Fluid Mech., 602, 327–382.

Theunissen, R., Scarano, F., & Riethmuller, M. L. (2008). On improvement of PIV image

interrogation near stationary interfaces. Exp. Fluids, 45(4), 557–572.

Walpot, R. J. E., van der Geld, C. W. M., & Kuerten, J. G. M. (2007). Determination of the

coefficients of Langevin models for inhomogeneous turbulent flows by three-dimensional

particle tracking velocimetry and direct numerical simulation. Phys. Fluids, 19(4), 045102.

Westerweel, J. (1993). Digital particle image velocimetry: theory and application. PhD thesis,

Delft University of Technology.

Westerweel, J., & Scarano, F. (2005). Universal outlier detection for PIV data. Experiments in

Fluids, 39(6), 1096-1100.


Wieneke, B. (2008). Volume self-calibration for 3D particle image velocimetry. Exp. Fluids, 45(4),

549–556.

Wieneke, B. (2013). Iterative reconstruction of volumetric particle distribution. Measurement

Science and Technology.

Young, I., Zagers, R., Vliet, L. J. van, Mullikin, J., Boddeke, F., & Netten, H. (1993). Depth-of-

focus in microscopy. In Proc. of the 8th Scandinavian Conference on Image Analysis. Tromso,

Norway.

Documents

Evaluation of high magnification two and three dimensional ...ltces.dem.ist.utl.pt/lxlaser/lxlaser2016/final... · Evaluation of high magnification two and three dimensional particle