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Fluctuation transfer velocity measurement in a boundary layer around a thin edge plate using

dynamic PIV

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INSTITUTE OF PHYSICS PUBLISHING MEASUREMENT SCIENCE AND TECHNOLOGY

Meas. Sci. Technol. 17 (2006) 13501357 doi:10.1088/0957-0233/17/6/010

Fluctuation transfer velocitymeasurement in a boundary layer arounda thin edge plate using dynamic PIV

N Erkan1, M Ishikawa2 and K Okamoto1

1 Department of Quantum Engineering and Systems Science, University of Tokyo,

7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan2 Department of Mechanical Systems Engineering, University of Ryukyus, 1 Senbaru,

Nishihra-cho, Okinawa 903-0213, Japan

E-mail: erkan@vis.k.u-tokyo.ac.jp

Received 19 September 2005, in final form 23 February 2006Published 2 May 2006Online at stacks.iop.org/MST/17/1350

AbstractThe dynamic (time resolved) PIV (particle imaging velocimetry)measurement technique was applied to high-speed gas flow in a narrowchannel with an obstacle. The boundary layer was visualized with ahigh-speed APX RS camera and an Nd:YLF high repetition double-pulselaser. Nitrogen gas seeded with oil particles using Laskine nozzle flowsthrough a 10 10 mm2 square channel with Reynolds numbers of 11 000and 34 000. Although a sufficient quantity of images was difficult to capturefor the Re = 34 000 flow to visualize the vortex evolution in time for thetime resolved analysis of the boundary layer, large scale structures of

turbulence at the edge of the thin plate are clearly visualized in the temporaldomain. Fluctuation transfer velocities in the boundary layer were measuredemploying the whole field two-point velocity correlation. It is proposed thatdynamic PIV can open a way of measuring the fluctuation transfer velocitiesin the whole flow target area simultaneously for high-speed turbulent flowseven in small scales.

Keywords: two-point velocity correlation, whole field velocity correlation,dynamic (time resolved) PIV, high-speed gas flow, fluctuation transfervelocity

(Some figures in this article are in colour only in the electronic version)

1. Introduction

Statistical analyses, which are implemented for the simulation

or experimental results of turbulent flows, give important

insights into the physics of the turbulence. With the

improvement of the experimental measurement techniquesand

tools, flow measurements have gained great significance in

recent turbulence studies. Dynamic (time resolved) particle

imaging velocimetry (dynamic PIV) with a high-speed camera

and a high repetition laser is typically employed for the

quantitative measurement of transient phenomena. This

system can be expanded to high frequency time resolutions

of 1 kHz, 10 kHz and 20 kHz.

Since previous PIV techniques had insufficient data

acquisition rates, it was difficult to understand the transient

phenomena of high-speed flows. Recent improvements in

imaging technologies have brought about the high temporal

resolution dynamic PIV systems that allow us to acquire

higher time resolved images for analysing the dynamic

information on the flow field. Okamoto (2003) has presented

a detailed explanation about the dynamic PIV and its data

evaluation algorithms. In this studymotivating from thisvirtue

of the dynamic PIV and considering the difficulties using

intrusive measurement techniques such as HW-anemometer

in small scales, the boundary layer formed around an

obstacle in a narrow channel was studied in order to achieve

0957-0233/06/061350+08$30.00 2006 IOP Publishing Ltd Printed in the UK 1350

http://dx.doi.org/10.1088/0957-0233/17/6/010mailto:erkan@vis.k.u-tokyo.ac.jphttp://stacks.iop.org/MST/17/1350http://stacks.iop.org/MST/17/1350mailto:erkan@vis.k.u-tokyo.ac.jphttp://dx.doi.org/10.1088/0957-0233/17/6/010

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Fluctuation transfer velocity measurement in a boundary layer around a thin edge plate using dynamic PIV

Figure 1. Experimental set-up.

the simultaneous whole field fluctuation transfer velocity

measurement makinguseof the two-pointvelocity correlation.

Nitrogen gas as a working fluid seeded with oil particles

flows through a square channel with two different Reynolds

numbers.

In the literature, spatial two-point velocity measurements

were acquired to provide a statistical description of the large-

scale structures, to define the mean separation between the

high- and low-speed fluid and also to make the initial choice

of the computational domain (Kim et al 1987, Littell and

Eaton 1994). Although two-point velocity correlation has

been documented by Grant et al (1958) and Tritton (1967) for

a two-dimensional turbulent boundary layer, its application to

the experiments has been done as a two-point measurement

using a hot-wire anemometer and results are analysed as two-

point spatial correlation. Recently Li et al (2005) employed

two-point velocity correlation for the analysis of micro-PIV

data in one spatial dimension. The spatio-temporal velocity

correlation analysis was used for measuring the large-scale

structure transfer velocity of a two-dimensional backward-

facing step flow utilizing laser Doppler velocimetry (LDV) by

Furuichi et al (2004).

Dynamic PIV can detect the correlations between the

individual spatial locations in the whole target area of the

flow and the temporal relations between them simultaneously.

From this point of view, full field spatio-temporal velocity

correlations are calculated considering the time delay between

the subsequent correlation peaks. Transfer velocities of

fluctuations, accordingly large-scale transfer velocities, were

measured for the whole flow field in a narrow channel thatdiffers from hot-wire anemometer measurements and that of

the previous measurement methods done before such as LDVs.

2. Experimental set-up

Figures 1 and 2 illustrate the experimental set-up and a

schematic of the test section. A high-speed camera (Photron

APX RS, 1024 1024 @ 3 kHz) and a Nd:YLF double-pulse

laser (New-wave Research Inc. Pegasus-PIV, = 527 nm,

1 mJ @ 10 kHz) were used. A high-speed 10 bit monochrome

C-MOS camera with a 8 GB on board memory was used; 6144

continuous image sequences at 1024 1024 pixels resolution

can be captured in about 2 s with a speed of 3000 frame/s

Figure 2. Enlarged test section.

Table 1. Experimental parameters.

Unit Case 1 Case 2

Re 34 000 11 000Frame rate Frame/s 20 000 20 000Delay1: td1 s 48 48Delay2: td2 s 50 58Interval t s 2 10# of recorded image BMP 20000 20 000Laser repetition rate kHz 10 10

and stored. Even the maximum frame rate can reach to

250 000 frame/s at 128 16 pixels resolution; for practical

use of PIV applications, it can be 10 000 frame/s at 512

512 pixels.

In this experiment, 20 000 8-bit grey-scale bitmap images

at384304pixels were captured anddownloaded to a host PC

via the optical fibre, which has the capability of transferring

data at a theoretical rate of 1 Gbps. Image sequence data

are recorded as raw images in the onboard memory, then

they are converted to the BMP file formats on the PC while

downloading; hence, the downloading time also depends on

the computer configuration. It is reported by Photron thatfor a host PC, which has P4 3.2 GHz CPU, 1GB MEM,

SATA 200GB HDD, 1024 1024 pixels rawsequential image

data can be downloaded via the optical fibre with a speed of

14 frame/s and 19.3 MB/s. If it is preferred to save as AVI

movie file format, this rate increases up to 19 frame/s and

26 MB/s.

The repetitionrateof the doublepulse laser was 10kHz for

each rod. The frequency of this laser is 1 kHz to 10 kHz, and

the energy per pulse is 10 mJ at 1 kHz and 1 mJ at 10 kHz. A

pulse generator for frame straddling synchronizes the camera

and laser beam frequency. The signal-timing chart of the

dynamic PIV system is illustrated in figure 3. The pulse

signal having a frequency of 20 kHz is transmitted to thecamera and the flip-flop device which is connected to the laser.

While the camera is arranged to 20 kHz by this positive edge

signal, the flip-flop device keeps on skipping one pulse and

reduces the pulse frequency to half of the base signals, i.e.

10 kHz, and then the output signal is transmitted to a delay

generator. The delay generator generates two signals with

different delay times; the twin laser rods are controlled by

these signals. For this experiment, the double pulse interval

is arranged as 2 s and 10 s; other experimental parameters

are listed in table 1.

The flow channel has a 10mm 10 mm cross-section and

a length of 1 m. The obstacle made of transparent acrylic resin

has a 45 edge at the tip and a 2 mm width, and is positioned

0.75 m from the downstream flow in the centre of the channel.

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N Erkan et al

Pulse generator

Delay generator

Flip-Flop

Laser 1

Laser 2

20kHz

Camera

10kHz

Delay1: td1

Interval: tDelay2: td2

Frame1 Frame2 Frame1 Frame2 Frame1 Frame2 Frame1

Figure 3. Signal timing chart for a dynamic PIV system.

t=0s (b)(a) t=100 s (c) t=200 s

Figure 4. Images for the acute side (Re= 34 000).

The flow area was illuminated with a laser sheet thickness of

1 mm. Two flow cases were studied with Reynolds numbers

of 34 000 and 11 000. The fluid consists of olive oil particles

suspended in nitrogen gas. The oil particles having a diameter

of about 13 m, which is estimated by Kahleret al (2002),are seeded into the gas through a Laskin nozzle and they are

used as the tracer particles with a volume concentration of less

then 0.1.

3. Methods, results and discussion

The instantaneous velocity vector maps are calculated using

a recursive PIV analysis technique (Scarano 2002). The first

iteration started with an interrogation area of 64 64 pixels

and 50% constant overlap ratio. The calculated displacements

are passed to the next iterations as an initial displacement

to perform the symmetric window shift with respect to the

interrogation locations. It has been shown to reduce the

rms error by Westerweel et al (1997) for the flows with high

turbulence intensity. The same process continues with a 32

32 pixels interrogation size and ends with the size of 16

16 pixels resulting in 8 8 pixels vector grid spacing. The

visualization targetarea wasthe acute side with a measurement

area of 9 7.1 mm2 and a vector grid resolution of 0.19

0.19 mm2.

The time intervals between two consecutive images for

PIV evaluation are 2 s and 10 s for the 34 000 and 11 000

Reynolds number cases, respectively. The time interval

between two consecutive vector maps is 100 s. Figure 4

shows sample images that were recorded at a speed of 20 kHz

and a Reynolds number of 34 000 at the acute side. The

oil particles cannot be identified individually; however, the

pattern motion and dark vortices can be seen clearly. Because

of the centrifugal forces, the particle density decreases at the

core region of the vortices, and this causes those regions to

be seen darker in the raw pictures (figure 4). In spite of thelack of particles in the core region, the particle density in

the 16 16 pixels interrogation area is still enough for valid

vector detection, i.e., greater than ten particles (Raffel et al

1998).

3.1. General measured flow characteristics

Figure 5 displays the time-serial relative velocity vector maps.

Strong velocity fluctuations and vortex structures can be seen

near the boundary in the velocity vector maps. 50% of the

average flow velocity has been subtracted from the streamwise

velocity component, since the transfer velocity of the vortex

is assumed to be 50% of the average velocity. Therefore, theturbulent natureof theflow caneasilybe seen from thevelocity

vector maps. Although the displacement of the vortex in

100s ishalfof animage, the transient ofthe vortexis captured

well. In this experiment, the vortex-emitting frequency from

the edge is as high as several kHz.

In figure 6, the negative vorticity initially appears at the

edge of the obstacle and moves downstream in time sequential

images. The movement of the vortex structure is clearly

visualized in the sequential images even when the vortex is

so fast that it reaches approximately half of the image in just

100 s.

When the fluid reaches the obstacle, it experiences a

volume contraction and, accordingly, a sudden acceleration

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Fluctuation transfer velocity measurement in a boundary layer around a thin edge plate using dynamic PIV

t=0 s t=100 s t=200(c)(b)(a) s

Figure 5. Instantaneous relative velocity vectors for the acute side (Re= 34 000).

t=0 s t=100 s t=200(c)(b)(a) s

Figure 6. Instantaneous vorticity map for the acute side (Re = 34 000).

Figure 7. For the 34 000 Reynolds number case, the time averagedvelocity vector map and velocity magnitude contour map.Spatio-temporal average of the streamwise velocity is 42.3 m s1.Spatio-temporal average of cross-streamwise velocity is 1.3 m s1.

is observed. Figure 7 shows the distribution of the averaged

velocity for the 34 000 Reynolds number case. Although

the flow velocity in the uniform channel is 34 m s1, it

reaches an average of42.3 m s1 on the acute site of theobstacle. In regions close to the obstacle wall, an expected

decrease in mean flow velocity is also observed, as in figure 7,

because of the mean flow energy loss to the turbulent kinetic

energy, which then immediately generates small-scale viscous

dissipations. This event can also be observed in the Reynolds

stress distribution and turbulent kinetic energy distributions in

figure 9.

The Reynolds stress is negative in regions close to the

edge tip. Therefore, the contribution of the Reynolds stress to

the TKE production can be observed by an increase in TKE

around the same spatial locations in figure 9(a).

Averaged flow parameters are listed in table 2 for the two

different flow cases.

Figure 8. For the 11 000 Reynolds number case, the time averagedvelocity vector map and velocity magnitude contour map.Spatio-temporal average of the streamwise velocity is13.7 m s1.Spatio-temporal average of cross-streamwise velocity is 0.4 m s1.

Table 2. Averaged flow properties.

Reynolds (34000) Reynolds (11000)

Average U 42.3 m s1 13.7 m s1

Average V 1.3 m s1

0.4 m s1

Average TKE 16.2 m2 s2 2.6 m2 s2

3.2. Method of two-point velocity correlation and fluctuation

transfer velocity measurement

A measure of the degree of correlation between the two

velocities at different spatial locations changes with respect

to time. At the different spatial locations, which are located

on the downstream path of the vortices, relatively huge and

sudden velocity fluctuations are created. These velocity

fluctuations, which are located inside the vortex structure,

must have quantitative relationships with each other. While

the vortex continues downstream, it can be expected to create

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N Erkan et al

Figure 9. (a) Time averaged turbulent kinetic energy (TKE) distribution in (m2 s2) and (b) Reynolds stress distribution in (m2 s2). TheReynolds number is 34 000.

Figure 10. Sampling points for correlation calculations at the acuteside of the flow channel (TKE contour map), Re= 34 000.

fluctuations. However, the magnitudes of these fluctuations

may not necessarily be the same because of the vortex

stretching mechanism and the loss of energy. The fluctuation

creation on the vortex path occurs with a time delay between

two different spatial positions. This time delay (also inversely

proportional to the vortex transfer velocity) increases as thedistance between thesetwopositions increases. Unfortunately,

since the measure of the degree of correlation will decrease as

the distance increases, it might not be easy to detect the peak

correlation value with a time delay between the two different

downstream locations.

The measure of the degree of correlation between the two

velocity fluctuations is defined as a function of space and timedelay:

C(x,y,)k =

u(xk, yk,t)u(x,y,t+ ) dt

u(xk, yk, t)2 dt

u(x,y,t+ )2 dt

.

(1)

In equation (1), C(x,y,)k is the correlation value, which is

a function ofx, y and time delay . krepresents the reference

point index and u(x,y,t) is the downstream component of

the fluctuation velocity. Figures 10 and 11 illustrate some

chosen sampling points for the calculation of the correlationvalues. While calculating the correlation value, infinite

integral intervals were taken as [0, 0.2] s, which corresponds

to 2000 time resolved velocity vector maps. With the delay

time of the reference point fixed as zero, the value of was

changed in the interval of [2, 2] ms with an increment of

0.1 ms, and the correlations were calculated at every discrete

value; then the same procedure was applied to all points inthe flow field. The correlation values versus time delay at the

points P1 and P2 are plotted in figures 12 and 13, respectively,

Figure 11. Sampling points for correlation calculations at the acuteside of the flow channel (TKE contour map), Re = 11 000.

Figure 12. Correlation value (C(x,y,)0) for reference point P0(6.56, 2.44) with P1 (6.75, 2.63).

Figure 13. Correlation value (C(x,y,)0) for reference point P0

(6.56, 2.44) with P2 (6.0, 2.44).

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Fluctuation transfer velocity measurement in a boundary layer around a thin edge plate using dynamic PIV

(a) (b)

(c) (d)

Figure 14. (a), (c) Spatial distribution of peak correlation values, (b), (d) time delay (in s) distributions of peak correlation values forreference point P0. (a) and (b) have a Reynolds number of 34000. (c) and (d) have a Reynolds number of 11000.

for the reference point P0. Since the points P0 and P1 are closeto each other, the peak correlation value occurs at zero delayand values near zero have a higher correlation value.

As the distance between the correlated points increases,the correlation value decreases and the peak position shifts.In the delay time interval of [2, 2] ms, the correlationvalue between two points takes a highest value at a particulardelay. As could be expected, while a vortex structure moves

downstream, correlation values can also take negative values.It is assumed that if the two points are affected by the samevortex in the same manner, in other words, the same signof fluctuation velocity is given to them, these two points arecorrelated, i.e., they are located on the same side of the vortex

at the different times. Therefore, the maximum correlationbetween two points is defined as the peak value of the two-point velocity correlation in the time domain.

Since the temporal dimension contains discrete values,Gaussian three-point curve fitting was applied to capture the

fractional estimate of time delay values. The maximumpositive correlation occurrence time is taken as a centralpoint; then the other two neighbouring delay points, whichalso correspond to the positive correlation value, are fitted tothe Gaussian curve.

3.3. Results and discussions

The above calculation procedure was implemented for allpoints shown in figure 10 at Reynolds numbers of 34 000 and

11 000. Correlations and time delay spatial distributions were

plotted in figures 14 and 15 for two different reference points.

Since all the points have similar characteristics, some results

andcomments for various pointsare discussed in the following

paragraphs, although all of the graphs are not provided to

preserve space.

Correlation values are much higher for points closer to

the reference point, as seen in figures 14 and 15(a) and (c).

While moving away from the reference point along the cross-

streamwise (y-axis) direction, correlation values decrease

rapidly to small values, especially outside the boundary layer.

On the other hand, while moving away from the reference

point in the streamwise direction, correlation values decrease

slowly relative to the cross-streamwise direction. This result

suggests that in the boundary layer, that is, along the path of

the vortices, fluctuating velocities have stronger correlations

with each other than in the cross-streamwise direction.

Figures 14 and 15(b)and(d) depict time delay distribution

contour maps, where reference point locations are marked by

a black circle. To the right of the reference point, the delay is

negative, and to the left, the delay is positive. This indicates

that fluctuating events on the right-hand side occur earlier

than the reference point, and fluctuating events on the left-

hand side occur after the reference point. Since the 34000

Reynolds number is higher than the 11000 case, the time delay

area, which has a value of nearly zero around the reference

point, is wider for the 34 000 case, as predicted. This implies

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N Erkan et al

(a) (b)

(c) (d)

Figure 15. (a), (c) Spatial distribution of peak correlation values, (b), (d) time delay (in s) distributions of peak correlation values forreference point P1. (a) and (b) have a Reynolds number of 34000. (c) and (d) have a Reynolds number of 11 000.

(a) (b)

Figure 16. Positiontime graphs of fluctuation transfers. Reynolds number of 11 000.

that time resolution (100 s) is not enough to measure thefluctuation transfer velocity with a reasonable accuracy for the

Reynolds number 34 000 case. Therefore, in the following

paragraphs, discussions mainly focus on the case of Re =

11 000.

Using the time delay maps, time delay versus x-axis

graphs (streamwise axes) are plotted in figure 16 for the

Reynolds numbers of 11 000 at all chosen reference points.

The inverse of the slope of the delay curve, which is

obtained by linear curve fitting in figure 16, gives the average

transfer velocity of the fluctuations at this point due to

equation (2):

x =1

utr. (2)

The time delay data contain noisy information, as can be seenin figures 14 and 15, which also spreads to the time delay

curves plotted in figure 16.

Defining the fluctuation transfer velocities for not just a

few points, but for all discrete points in the boundary layer

and its close neighbourhood regions, would provide moreinformation about the behaviour of large-scale structures in

a two-dimensional flow environment. Two-point velocity

correlation was applied, and the fluctuation transfer velocity

distribution was obtained in the flow area and depicted in

figure 17 as a two-dimensional contour map. Figure 18

represents the normalized fluctuation transfer velocitydistribution. All fluctuation transfer velocities are divided by

the time averaged local bulk flow velocities at every location.

Since turbulent kinetic energy production mainly occurs in

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Fluctuation transfer velocity measurement in a boundary layer around a thin edge plate using dynamic PIV

Figure 17. Fluctuation transfer velocity distribution in (m s1).(Re= 11 000).

Figure 18. Normalized fluctuation transfer velocity distribution.Normalized by local average velocities. (utr(x,y)/Uav(x,y))(Re= 11 000).

boundary layers, the margins of the boundary layer were

defined roughly, as shown in figures 17 and 18. The green

regions in coloured maps andthe brighter regions in grey-scale

maps correspond to approximately half of the average flow

velocity in theboundarylayer. That resultis in good agreementwith those from Furuichi etal (2004) and Hijikata etal (1991).

After some particular distance towards the downstream region,

the fluctuation transfer velocities reach values close to those

of the average flow velocity. This can be attributed to typical

vortex behaviour: vortices initially have small drift velocities,

but their drift velocities gradually increase and approach those

of the bulk flow velocity.

As for the accuracy, some possible sources of error (e.g.,

out-of-plane motion, optical aberrations and inhomogeneous

illumination) that are considered to be of minor importance,

the velocity field measurement has several per cent relative

errors normally. Average detected particle displacements

are 3.6 pixels and 5.8 pixels for the Reynolds numbers of34 000 and 11 000 cases, respectively. With a correlation

peak centroid estimate error of 0.1 pixels, then the full-scale

error in the velocity measurements is 3% and 2% for the

cases of Re = 34 000 and Re = 11 000. Because of the

high accelerations, instantaneous velocity measurements may

have higher error. Spread of this error to the fluctuation

transfer velocities decreases due to the averaging process.

Additionally, the linear curve fitting contributes the relative

error of around0.5% to the fluctuation transfer velocities for

Re = 11 000.

If figure 8 is compared with figure 18, it can be seen

that when the average flow velocity is higher, the fluctuation

transfer velocity decreases to smaller values in the boundary

layer region. In the near wall region, the average flow velocity

takes on smaller values whereas the fluctuation transfer

velocity takes on higher values. Because of the reflections

from the surface, velocity measurements in this region contain

higher errors. Therefore an assessment of this situation is

avoided. Accurate velocity measurement in the near wall

region is the next challenge.

4. Conclusions

Dynamic PIV was applied to high-speed gas flow in a narrow

channel to measure the fluctuation transfer velocities. The

velocity distributions were obtained with 0.19 0.19 mm2

spatial resolution every 0.1 ms, i.e., 10 kHz, which is almost

equivalent to HWA. Spatial and temporal relations of the

fluctuating velocities were measured using the time dependent

multi-point velocity correlation. It was shown that high

speed dynamic PIV could discover the fine structures of the

fluctuating velocity near the edge region.

References

Furuichi N, Hachiga T and Kumada M 2004 An experimentalinvestigation of a large-scale structure of a two-dimensionalbackward-facing step by using advanced multi-point LDVExp. Fluids 36 27481

Grant H L 1958 The large eddies of turbulent motion J. FluidMech. 4 14990

Hijikata K, Mimatsu J and Inoue J 1991 A study of a wall pressurestructure in a backward step flow by a holographic/velocity-pressure cross-correlation visualization ASME-FEDExp. Numer. Flow Vis. 128 618

Kim J, Moin P and Moser R 1987 Turbulence statistics in fullydeveloped channel flow at low Reynolds numberJ. Fluid Mech.177 13366

Kahler C J, Sammler B and Kompenhans J 2002 Generation andcontrol of tracer particles for optical flow investigations in airExp. Fluids 33 73642

Li H, Ewoldt R and Olsen G M 2005 Turbulent and transitionalvelocity measurements in a rectangular microchannel usingmicroscopic particle image velocimetry Exp. Thermal FluidSci. 29 43566

Littell H S and Eaton K 1994 Turbulence characteristics of theboundary layer on a rotating disk J. Fluid Mech. 266 175207

Maeda M, Kawaguchi T and Hishida K 2000 Novel interferometricmeasurement of size and velocity distributions of sphericalparticles in fluids flowsMeas. Sci. Technol.11 L138

Okamoto K 2003 Dynamic PIV: a strong tool to resolve theunsteady phenomena Particle Image Velocimetry: RecentImprovements (Proc. EuroPIV 2 Workshop (Zaragoza, Spain)ed M Stanislas, J Westerweel and J Kompenhans (Berlin:

Springer)Park S, Cho H, Yoon I and Min K 2002 Measurement of droplet size

distribution of gasoline direct injection spray by dropletgenerator and planar image technique Meas. Sci. Technol.13 85964

Raffel M, Willert C and Kompenhans J 1998 Particle ImageVelocimetry A Practical Guide (Berlin: Springer)

Scarano F 2002 Iterative image deformation methods in PIV Meas.Sci. Technol 13 R119

Taitel Y, Barnea D and Dukler A E 1980 Modeling flow patterntransitions for upward gas-liquid flow in vertical tube AIChE J.26 34554

Tritton D J 1967 Some new correlation measurements in a turbulentboundary layerJ. Fluid Mech. 28 43962

Westerweel J, Dabiri D and Gharib M 1997 The effect of a discretewindow offset on the accuracy of cross-correlation analysis ofdigital PIV recordings Exp. Fluids 23 208

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http://dx.doi.org/10.1007/s00348-003-0718-6http://dx.doi.org/10.1007/s00348-003-0718-6http://dx.doi.org/10.1017/S0022112058000379http://dx.doi.org/10.1017/S0022112058000379http://dx.doi.org/10.1017/S0022112087000892http://dx.doi.org/10.1017/S0022112087000892http://dx.doi.org/10.1016/j.expthermflusci.2004.06.001http://dx.doi.org/10.1016/j.expthermflusci.2004.06.001http://dx.doi.org/10.1016/j.expthermflusci.2004.06.001http://dx.doi.org/10.1088/0957-0233/11/12/101http://dx.doi.org/10.1088/0957-0233/11/12/101http://dx.doi.org/10.1088/0957-0233/11/12/101http://dx.doi.org/10.1088/0957-0233/11/12/101http://dx.doi.org/10.1088/0957-0233/13/6/305http://dx.doi.org/10.1088/0957-0233/13/6/305http://dx.doi.org/10.1088/0957-0233/13/1/201http://dx.doi.org/10.1088/0957-0233/13/1/201http://dx.doi.org/10.1002/aic.690260304http://dx.doi.org/10.1002/aic.690260304http://dx.doi.org/10.1017/S0022112067002216http://dx.doi.org/10.1017/S0022112067002216http://dx.doi.org/10.1007/s003480050082http://dx.doi.org/10.1007/s003480050082http://dx.doi.org/10.1007/s003480050082http://dx.doi.org/10.1017/S0022112067002216http://dx.doi.org/10.1002/aic.690260304http://dx.doi.org/10.1088/0957-0233/13/1/201http://dx.doi.org/10.1088/0957-0233/13/6/305http://dx.doi.org/10.1088/0957-0233/11/12/101http://dx.doi.org/10.1016/j.expthermflusci.2004.06.001http://dx.doi.org/10.1017/S0022112087000892http://dx.doi.org/10.1017/S0022112058000379http://dx.doi.org/10.1007/s00348-003-0718-6