6th International Symposium on Particle Image Velocimetry
Pasadena, California, USA, September 21-23, 2005
PIV’05 Paper nnnn
PIV Measurements of turbulence statistics and near-wall structure
of fully developed pipe flow at high Reynolds number
J. Takeuchi, S. Satake, N.B. Morley, T. Yokomine, T. Kunugi, M.A. Abdou
Abstract: Fully developed turbulent pipe flow at Re=11300 as well as Re=5300 is measured by PIV using water as
working fluid. Excellent agreement with DNS (Direct Numerical Simulation) by Satake (2000) is achieved by
choosing optimum measurement parameters such as spatial resolution, time separation of two images, and number
of samples. The test section is 6.7m long stainless steel pipe with transparent PIV measurement section attached
seamlessly at the end. The measurement section consists of transparent acrylic circular pipe of 1mm thick and water
jacket with square cross section. The water jacket reduces the image distortion due to the pipe curvature in almost
entire area of the pipe cross section to negligible level except for the region very close to the pipe wall. For turbulent
flow measurement using PIV, the requirement for spatial resolution is very severe in order to resolve the fluctuating
velocity field especially at high Reynolds number. Therefore, higher magnification is chosen at the cost of the size
of measurement area to assure enough spatial resolution. Consequently, the size of the measurement area is half of
the pipe radius and measurement is performed at two regions which are called near-wall region and pipe center. For
image analysis, the iterative multi-step cross-correlation algorithm with spatio-temporal gradient method for subpixel refinement is used. Detail of the algorithm can be found in Scarano (1999) and Sugii (2000). The smallest
interrogation window is 8x16 pixels which corresponds to 249 x 585µm. The near-wall structure is observed from
vector map of fluctuating in-plane velocity components and out-of-plane component of vorticity fluctuation. The
shear layer structure is clearly shown by vorticity fluctuation and ejection and sweep motion is also observed. The
mean velocity profile and statistics are calculated from 4000 samples of vector map by first taking temporal statistics
and then spatial average along streamwise direction and compared with DNS in non-dimensional form using friction
velocity. Since accurate measurement of friction velocity is essential for the comparison with DNS, using pressure
gradient is not appropriate due to the relatively small pressure drop along the pipe. Therefore, curve-fitting method
using near-wall turbulent model developed by McEligot (1984) is applied to calculate friction velocity from the velocity
profile in buffer region.
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Introduction
Fully developed turbulent pipe flow has been studied extensively for engineering purposes for more than a century.
This is also of interest from scientific point of view due to the relative simplicity in geometry. In recent years, there
has been remarkable development in computational capability and Direct Numerical Simulation (DNS) database at
relatively high Reynolds number has been available. At the same time, PIV technique has been successfully applied
to the fully developed turbulent pipe flow at Reynolds number 5,300 and good agreement with DNS (Eggels et al.
1994) has been achieved. Despite the development in numerical simulation at higher Reynolds number flows, PIV
measurement of turbulent statistics comparable to the DNS for such high Reynolds number flow hasn’t been
J. Takeuchi, N.B. Morley, and M.A. Abdou
Mechanical and Aerospace Engineering Dept. University of California, Los Angeles
S.Satake
Department of Applied Electronics, Tokyo University of Science
T. Yokomine
Interdisciplinary Graduate School of Engineering Science, Kyushu University
T. Kunugi
Departiment of Nuclaear Engineering, Kyoto University
Correspondence to:
Junichi Takeuchi, Mechanical and Aerospace Engineering Dept. UCLA, 420 Westwood Plaza, Los Angeles, CA 90095, USA
Email: [email protected]; Phone: +1-310-794-4452 ; Fax : +1-310-825-2599
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PIV’05
available so far. This is partly due to the difficulty in resolving small-scale motion with PIV because this technique
provides average velocity over the interrogation windows. Since the dynamic range of this method is limited by the
size of the CCD camera, higher resolution for small-scale is always accompanied by losing large-scale picture. In
order to compromise between small-scale resolution and large-scale capacity, measurement region is divided into
two regions and measurement is performed separately. The mean velocity and second order turbulence statistics
profile are reconstructed afterwards combining the profile obtained in each region. This allows us to cope with highresolution requirement for high Reynolds number flow and still avoid losing large-scale picture.
The experimental facility is designed to measure the turbulent flow and heat transfer characteristics of electrolyte
aqueous solution (Water-KOH solution in particular) under the magnetic field to investigate the effect of MHD force
on the low conductivity molten salt simulant flow. The use of molten salt coolants, in particular fluorine-lithiumberyllium or FLiBe, has attractive features for liquid wall and liquid breeder blanket designs in fusion reactors. The
low electrical conductivity of such salts reduces the pressure drop associated with magneto-hydrodynamic forces to
a nearly negligible level when compared to high conductivity liquid metals. But there are still many issues related to
fluid mechanics and heat transfer in a blanket design using FLiBe. In particular, FLiBe is high Prandtl number fluid
meaning low thermal diffusivity and/or high kinematic viscosity. Heat transfer to the high Prandtl number fluid, in
general, the thermal boundary layer is much thinner than viscous boundary layer and sometimes lies even in the
viscous sub-layer so the heat tends to confined in the thin layer next to the heating surface. In order to apply high
Prandtl number fluid to high heat flux device, turbulence has to play an important role to spread heat into bulk fluid.
Therefore the flow properties have to be carefully chosen based on the reliable data. To understand the underlying
science and phenomena of fluid mechanics and heat transfer of FLiBe, a series of experiments as part of the USJapan Jupiter-II collaboration are in progress. A fluid flow facility utilizing water and water-based electrolytes as
simulant for generic high Prandtl number, electrically conducting fluids like FLiBe has been constructed at UCLA.
The approach involves flow field measurement and heat transfer experiments using these FLiBe simulant fluids
along with modeling and analysis of fundamental phenomena of turbulence and heat transfer. Since this is
preliminary stage of this project, it is important to establish a good reference data in order to ensure the quality of
the data. Therefore water is used as working fluid flow measurement is conducted using PIV technique.
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Experimental setup
Schematic diagram of the pipe flow apparatus is shown in Fig. 1. The fluid flow is introduced into the horizontal
pipe test section by electromagnetic pump and passes through the heat exchanger, flow meter and honeycomb before
it entered the test section. Flow rate is controlled by variable frequency power controller. A throttle valve in the
main loop and a bypass line are also equipped to help flow rate control. Flow rate is measured by Karman vortex
type flow meter and monitored to achieve constant flow rate. Temperature of the fluid is monitored at both the inlet
and the outlet and the inlet temperature is maintained to be constant.
Fig. 1 Schematic view of the experimental apparatus
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The test section is a smooth circular pipe made of SUS304 with 90mm in inner diameter and 6.7m in length which is
74 times of the pipe diameter. This length is sufficient to obtain a fully developed turbulent flow. In order to
visualize the flow field, measurement section made of 1mm thick transparent acrylic pipe is attached seamlessly to
the end of the stainless steel pipe. Since circular pipe is used, the image inside of the pipe is distorted by pipe
curvature and the difference in index of refraction between air, fluid and acrylic. To minimize and compensate the
distortion, acrylic pipe with very thin wall is used and square water jacket filled with the same fluid as in the main
flow is attached to the test section. This eliminates the optical distortion to negligible level except for the region very
close to the wall. The cross section view of the water jacket and PIV optics is shown in Fig. 2.
Flow field is measured by Dantec FlowMap 2000 PIV system. It consists of flow visualization by laser
illumination of seeding particles, CCD camera, laser/camera synchronization system, and analysis software. PIV
laser sheet is supplied by Newwave mini Nd:YAG laser. Its intensity is 50mJ per pulse and its repetition rate is
15Hz double pulsed. The laser sheet passes horizontally the half plane of the pipe and illuminates the seeding
particles flowing with the water flow. The flow is seeded with polyamide particles with relative density of 1.02.
Diameter of the particles is 5µm. The particles are small enough to follow the flow and their specific gravity is close
enough to 1.0 to neglect the particle sedimentation due to the gravity force. The number density of the seeding
particles is adjusted so that the particle images have several particles in the 16x8 pixel interrogation window.
Dantec 80C42 DoubleImage700 progressive scan interline CCD is used to capture the particle images. The
resolution of the camera is 768x484 pixels. The camera is placed 1.0m above the test section and zoom lens and
close-up lens are attached. With this optical configuration, the error caused by out-of-plane motion is significantly
reduced. The time interval between two frames is optimized depending on the flow condition and 6ms is chosen for
Re=11300, 10ms for Re=5300. The laser firing and the image capturing are synchronized by the control unit
equipped in Dantec system. The control box stores the images at 3.75Hz and transfer them to the computer after the
acquisition. Fig. 3 shows the timimg of the pulsed laser and camera exposure.
For PIV analysis, Dantec FlowManager ver.3.70 equipped with adaptive correlation is used. The adaptive
correlation is based on the cross-correlation technique and is equipped with discrete window offset, iterative
multigrid method, and the spatio-temporal gradient sub-pixel analysis as a built-in feature. This method improves
the dynamic range of the PIV, which is essential to the multi-scale flow measurement. Combined with the iterative
approach, local median validation method is applied to remove spurious vectors. The spatio-temporal gradient
method has the advantage over the conventional three-point gaussian curve fitting method especially the
displacement of the particles are relatively small and achieves the accuracy of 0.01 pixels at most even with small
interrogation window.
Fig. 2 Optical configuration of the experiment
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Fig. 3 Synchronization of timing of laser and camera
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Result
Mean Velocity Profile
The mean velocity profiles at Re=11,300 and Re=5,300 are shown in Fig. 4 and Fig. 5. In order to obtain higher
magnification, the flow field is divided into two measurement regions, which are near wall region and center region,
and separate measurement is performed at the same flow condition. The two curves at the different regions are
combined when they are plotted. The average is taken over 5,000 instantaneous flow velocities for each region and
11,210 vectors (190 in radial direction and 59 in streamwise direction) are obtained in each region with 50% overlap
of the interrogation window. The distance between each vector is 0.127mm in radial direction and 0.292mm in
streamwise direction.
Fig. 4 Mean velocity distribution at Re=11300
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Fig. 5 Mean velocity distribution at Re=5300
In Fig. 4 and Fig. 5, the mean velocity profile is converted into wall coordinates, to obtain the universal velocity
profile independent of Reynolds number, defined by:
u + = u / uτ
y + = yuτ /ν
where y is distance from the wall, uτ is friction velocity and ν is kinematic viscosity of the liquid. The definition of
friction velocity is given by
uτ =
τw
ρ
where τw is wall shear stress and ρ is density. The experimental data is plotted along with the DNS (Direct
Numerical Simulation) data by Satake (2000). Since universal velocity profile is very sensitive to the determination
of friction velocity, accurate determination of the friction velocity is essential. The rough estimation of the wall
shear stress is initially given by Blasius’ law
Cf =
1
2
τw
= 0.079 Re −0.25 .
2
ρU
In order to obtain accurate friction velocity from rough estimation and given velocity profile, curve-fitting method
developed by McEligot (1984) is successfully applied. Agreement between experimental result and DNS is excellent
in both cases.
Since the image very close to the wall is skewed by the curvature of the pipe and elongated in radial direction
even though the water jacket reduces the distortion, there is still difficulty in velocity measurement near the wall.
For Re=11,300, the velocity profile in viscous sub-layer is not resolved because the viscous sub-layer is very thin
and lies within the region where the distortion is significant. Whereas the velocity profile for in the viscous sub-layer
for Re=5,300 is resolved well and agrees well with linear profile u+=y+ obtain by theoretical analysis. The universal
velocity profile has logarithmic distribution in the region y+>30 and commonly accepted equation of this profile is
u + = 2.5ln y + + 5.5 .
The experimental result for Re=11,300 agrees very well with the universal profile although it varies from the
empirical equation for Re=5,300. This discrepancy with the “law of the wall” for low Reynolds number case is
discussed by Eggels et al. (1994).
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Turbulent Intensities
The rms (root-mean-square) values of the fluctuation component of the velocities normalized by friction velocity,
which are called turbulent intensity, are shown in Fig. 6 and Fig. 7 for Re=11,300 and Re=5,300, respectively. Both
streamwise component (urms) and radial component (vrms) of the turbulent intensities are compared with DNS and
good agreement is obtained except for the near wall region where fluctuation must go to zero by theory. In the near
wall region, the discrepancy is especially large for vrms because the image is distorted in radial direction and this
cause PIV to detect the displacement of the particle larger than the actual displacement.
In the core region where the fluctuations are rather small, the PIV result varies from the DNS and gives larger.
This is obvious for Re=5,300 where the fluctuation is smaller. This result suggests that resolving fluctuating
component is very difficult and is sensitive to the measurement error. One of the possible sources of the error is socalled peak-locking effect due to the small particle images. The other may be large measurement error due to the
small number of particles in each interrogation window. These are largely due to the small (16x8) interrogation
window because it is difficult to have large particle images such as 4 pixels for each image and also enough number
particles in each interrogation window.
Fig. 6 Turbulent intensities at Re=11300
Fig. 7 Turbulent intensities at Re=5300
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Reynolds stress
The Reynolds shear stress distribution is shown in Fig. 8 and Fig. 9 for Re=11,300 and Re=5,300, respectively.
Although there are still some fluctuation in the profile seen in both Re=11,300 and Re=5,300, the agreement
between the experimental result and DNS is very good. The fluctuation implies that the convergence of the statistics
may not be perfect or there may be some large spurious vectors presented due to the mismatch in the particle pair.
The total shear stress of the fully developed statistically steady flow in the pipe must be linear and shown by the
straight line of gradient 1. This is because the gradient of the total shear stress must balance the pressure gradient
along the axis. In the near wall region, the viscous stress plays dominant role and Reynolds stress goes to zero with
r/R close to one. On the other hand, the Reynolds stress plays dominant role and viscous stress is small in the core
region. The region where the Reynolds stress has peak value corresponds to the region where the turbulence is
generated (Tennekes and Lumley, 1972).
Fig. 8 Reynolds stress distribution at Re=11,300
Fig. 9 Reynolds stress distribution at Re=5,300
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Turbulence structure
Turbulence structure is observed from vector map of the instantaneous fluctuation velocity. Both the PIV
measurement and DNS show similar structure in near wall region. Vorticity contours show clearly the near wall
shear layer structure and ejection and sweep motions.
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Conclusion
Flow measurement using PIV to study fully developed turbulent pipe flow. Flow condition of the experiment is
Reynolds number 5,300 and 11,300 based on the bulk mean velocity and pipe diameter. Turbulent structure, mean
flow property and turbulent statistics obtained by the experiment are compared with the DNS data by Satake et al.
(2000) and the experimental results agree well with DNS and empirical correlation.
The mean flow profile shows very good agreement with DNS and the measurement error is less than 2% of the
mean centerline velocity. Since the resolution of the small-scale motion is not the concern for the measurement of
mean flow field, the smoothing over the interrogation window, which is the biggest issue when PIV is applied to the
turbulent flow measurement, does not have considerable effect on mean flow measurement. On the other hand, the
small-scale resolution affects the measurement of the fluctuation component of the velocity and then turbulent
intensities and Reynolds stress. To obtain enough resolution, the measurement region is divided into two regions and
separate measurements are performed. This approach leads us to reconstruct turbulent statistics profiles very
successfully. Consequently, the turbulent intensities and Reynolds stress profile agree well with DNS, which means
that the fluctuation of the turbulent flow is well resolved by PIV in this experiment.
For the comparison with DNS, determination of the wall shear stress is also essential. Innovative approach to
deduce wall shear stress developed by McEligot (1984) is successfully applied and the velocity profiles in the wall
coordinate match with DNS perfectly. Although the turbulent statistics profiles agree very well with DNS, there are
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still discrepancies existing in the near wall region due to the image distortion by the curvature of the pipe. Despite
the effort to minimize this effect, the distortion cannot be eliminated. This is significant for radial component of the
velocity.
Since this experimental work is designated to clarify the flow and heat transfer characteristics of the molten salt
simulant fluid under the magnetic field, this work is a preliminary experiment to obtain a benchmark data for the
facility. In the next stage of the project, flow and heat transfer measurement using electrolyte aqueous (KOH-water)
solution with the magnetic field will be performed. This experiment provides us with the good reference data to
ensure the quality of the next stage.
Acknowledgement
The authors wish to acknowledge support by the US DOE Grant No.DE-FG03-86ER52123, and by the Japanese
Ministry of Education, Culture, Sports, Science and Technology (MEXT) via the Jupiter-II Collaboration.
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