An investigation by 2D-2C particle image velocimetry was carried out in the far downstream section (greater than 70 downstream boundary layer thicknesses, δ99 measured in the region of interest) of a nominally zero pressure gradient 0.5m square re-circulating water tunnel seeded with 11μm Potter’s hollow glass spheres. The use of a PCO4000 camera (4008 by 2672 pixel2) in combination with a Nikon Nikkor 200mm f4 IF MF lens and a PK-13 lens extension provides a measurement spatial resolution (in the streamwise-wall normal plane) of between 2 and 25 wall units for momentum Reynolds number between 200 and 2000 respectively. The paper will present characteristic flow quantities with results from the measurements non-dimensionalised by the skin friction velocities that are estimated by the Clauser method

Soria, J.

Wong, C. Y.

An investigation by 2D-2C particle image velocimetry was carried out in the far downstream section (greater than 70 downstream boundary layer thicknesses, δ99 measured in the region of interest) of a nominally zero pressure gradient 0.5m-square re-circulating water tunnel seeded with 11µm Potter’s hollow glass spheres. The use of a PCO4000 camera (4008 by 2672 pixel2) in combination with a Nikon Nikkor 200mm f4 IF MF lens and a PK-13 lens extension provides a measurement spatial resolution (in the streamwise-wall normal plane) of between 2 and 25 wall units for momentum Reynolds number between 200 and 2000 respectively. The paper will present characteristic flow quantities with results from the measurements non-dimensionalised by the skin friction velocities that are estimated by the Clauser method

C. Y. Wong

J. Soria

CiteSeerX

Characterisation of a Low Reynolds Number Turbulent Boundary Layer using PIV

University of Queensland eSpace

16th Australasian Fluid Mechanics Conference 
Crown Plaza, Gold Coast, Australia 
2-7 December 2007 
 
Characterisation of a Low Reynolds Number 
Turbulent Boundary Layer using PIV 
 
C.Y. Wong1 and J. Soria1 
1Laboratory for Turbulence Research in Aerospace and Combustion, Department of Mechanical Engineering 
(LTRAC), Monash University, Melbourne, Victoria 3800, AUSTRALIA 
 
Abstract 
An investigation by 2D-2C particle image velocimetry was 
carried out in the far downstream section (greater than 70 
downstream boundary layer thicknesses, δ99 measured in the 
region of interest) of a nominally zero pressure gradient 0.5m-
square re-circulating water tunnel seeded with 11µm Potter’s 
hollow glass spheres.  The use of a PCO4000 camera (4008 by 
2672 pixel2) in combination with a Nikon Nikkor 200mm f4 IF 
MF lens and a PK-13 lens extension provides a measurement 
spatial resolution (in the streamwise-wall normal plane) of 
between 2 and 25 wall units for momentum Reynolds number 
between 200 and 2000 respectively.  The paper will present 
characteristic flow quantities with results from the measurements 
non-dimensionalised by the skin friction velocities that are 
estimated by the Clauser method. 
 
Introduction  
Recent research into turbulent boundary layers has concentrated 
on characterising and understanding their structure using various 
cutting-edge experimental and numerical techniques [1,2].  This 
work describes the use of an established digital particle image 
velocimetry technique to measure the stream-wise and wall-
normal velocities of a naturally developing nominally zero 
pressure gradient low Reynolds number boundary layer in the 
centre plane of an experimental water tunnel. The results are 
compared with theory and with results from single-point 
measurements. Normalised velocity data (+) are based on friction 
velocity (uτ) calculated by the Clauser method. The aim of the 
paper is to characterise the LTRAC water tunnel and to examine 
the limitation of the DPIV technique in various regions of the 
boundary layer. 
 
Experimental Details 
This section describes the experimental water tunnel and the 
particle image velocimetry technique used in the experiments. 
 
Experimental Facility 
The experiments were conducted in the LTRAC water tunnel that 
has a 500mm-square cross-section with a test-section length of 
5.5m.  Further details of the tunnel are described in Kostas [5].  
The tunnel, shown in figure 1, is a closed circuit facility and the 
flow is driven by a 55kW Western Electric motor coupled to a 
Goulds pump system.  The freestream flow velocity can be 
adjusted in increments of 1mm/s.  The maximum theoretical 
freestream velocity of this system is 775mm/s.  However, the 
maximum velocity used in the present experiments is limited to 
540mm/s to ensure uniformity of the freestream in the presence 
of a free surface.  The turbulence intensity at the inlet plane was 
reported to be less than 1% [5] while the freestream turbulence 
intensity in the region of interest is measured to be just under 5%. 
 
 
 
 
 
 
 
 
 
 
Figure 1.  Schematic diagram of the horizontal closed-circuit water tunnel 
(adapted from Kostas 2002). 
 
DPIV Technique 
Digital Particle Image Velocimetry was used in all the 
experiments.  A comprehensive background of the technique can 
be found in [7]. In summary, the technique involves the recording 
of particles in the field of interest by 2 singly-exposed images.  
Illumination of the particles by a monochromatic light source 
over a known time (Δt) within each recording sensor allows the 
spatial position of the particle images to be recorded.  Knowledge 
of the spatial displacement of a group of particles within a given 
interrogation window (IW) over a known time internal allows the 
average velocity component to be calculated.  In the present 
experiment, the flow was seeded with 11mm hollow glass 
spheres (Sg=1.1) and illumination of a 1mm thick laser sheet was 
provided by a pulsed Nd:YAG laser (Newwave) at a wavelength 
of 532nm.  The particle images were recorded by a PCO.4000 
camera with a spatial resolution of 4008 by 2672 pixels2 and 
positioned perpendicular to the region of interest illuminated by 
the lightsheet.  A Nikon Nikkor 200mm f/4.0 MF lens with a 
PK13 extension coupled to the camera enabled a fixed length-to-
pixel conversion of 13.9µm/px.  Since this magnification was 
fixed with varying Reynolds number, the typical size of 
measurement volumes (l+x, l+y, l+z) varied as follows. Increasing 
Reθ increased the relative size of the interrogation volume, thus 
reducing spatial resolution of the PIV system. 
 
  Reθ = 209  (0.9, 0.9, 2.2);  Reθ = 1988  (24, 24, 58). 
 
Standard multi-grid cross-correlation algorithm was employed to 
process each set of PIV image pair.  The experiments were 
optimized for an interrogation window size of 32×32 px2 and 
50% overlap between each IW.  For each experimental condition, 
standard vector validation algorithms were used to process 420 
image pairs to obtain a total of 166 by 247 vectors per image 
pair. 
 
A summary of the boundary layer conditions is found in Table 1. 
 
 
726
Reθ δ99 
(mm) 
δ1 (mm) 
displacement 
δ2 or θ 
(mm) 
momentum 
H12 
(δ1/δ2) 
uτ 
(mm/s) 
U∞ 
(mm/s) 
209 49.15 9.76 5.48 1.78 2.05 34.97 
373 46.16 7.08 4.38 1.62 4.11 75.46 
491 41.85 5.84 3.77 1.55 6.11 115.52 
599 39.90 5.11 3.40 1.50 7.86 152.39 
626 20.49 2.39 1.74 1.37 14.85 300.97 
740 31.50 4.13 2.79 1.48 11.45 229.93 
1088 29.31 3.42 2.37 1.44 18.39 382.98 
1101 22.19 3.03 2.05 1.48 22.00 464.25 
1190 19.41 2.76 1.87 1.48 25.16 538.43 
1988 17.36 1.98 1.51 1.32 37.59 862.06 
 
Table 1.  Summary of boundary layer conditions.   
 
Results 
Effect of Spatial Resolution 
In order to assess the effect of measurement volume on the 
experimental results, the flow case for Reθ=1100 was fixed for 
two different spatial resolutions: 13.0µm/px and 17.8µm/px.  
These results are compared with the experimental hot-wire data 
of Murlis, Tsai and Bradshaw (1982) taken at Reθ=1100, and 
empirical equations for turbulent boundary layer flows.  
Referring to Figure 2, the U+ velocities of the 13.9µm/px case 
follows the trend of the theoretical curves  down to y+~20 
(~0.8mm).  This result is expected since the velocity gradient 
within the 17.8µm/px measurement volume is much steeper than 
the 13.0µm/px case.  
10
0
10
1
10
2
10
3
10
4
y
+
(=yu
!
/")
0
5
10
15
20
25
U
+
(=
U
/u
!
)
13.9µm/px
17.8µm/px
U
+
=y
+
U
+
=2.5 ln(y
+
-4.7) + 5
U
+
=2.5 ln(y
+
) + 5
10
0
10
1
10
2
10
3
y
+
0
1
2
3
u
' rm
s
/u
!
Present (PIV)
Murlis et al. 1982 (Hot-Wire)
 
Figure 2. Effect of spatial resolution on the U+ (Top) and u′rms (Bottom) 
terms at Reθ=1100.  
In the u′+=u′rms/uτ graph, a good collapse with less than 3% 
difference from Murlis et al’s data in the region 15<y+<60 is 
observed.  Interestingly, datapoints greater than y+=60 
consistently over-estimate the hot-wire (lx+=15) data of Murlis et  
al. (1982) from 5% at y+=60 to 30% at y+=1070. This may be 
attributed to the higher freestream turbulence intensity (~5%) for 
the present data compared with Murlis’ data at 3.28%.  Finally, 
the inability of the PIV system to resolve scales less than y+=20 
results in an over-estimation of the u′+ data in these regions.     
 
Mean and RMS results 
In figures 3 to 5, the data in the graphs are averaged across all 
streamwise locations and are found to be closely self-similar at 
each x+ location. For the sake of clarity, discrete data points are 
represented by fitting spline-fits through them. Interpretation of 
the results is based on the model proposed by Adrian et al. 2000. 
 
The following empirical equations were used to model the 
various regions of the flow in the y-axis from the wall: 
 
++
= yU  
    (1) 
5
4.0
1
ln
4.0
1
U
0
+!
"
#
$
%
&
+'= +++ yy  
             (2) 
( ) 5ln
4.0
1
U += ++ y  
   (3) 
 
These equations are shown alongside the present experimental 
data in Figure 3.  It is noted that the case at Reθ=209 follows 
equation (1) fairly well down to y+=1.  On the other hand, the 
experimental data seem to be under-resolved for higher Reθ 
numbers in the region of severe velocity gradients (y+<30).  This 
is the result of using a fixed measurement volume to measure in a 
boundary layer thickness decreasing with increasing Reθ.  Note 
also that the point of departure from the empirical equation 
coincides with the non-dimensional size of the measurement 
volume. 
 
10
-1
10
0
10
1
10
2
10
3
10
4
y
+
0
5
10
15
20
25
30
35
40
45
U
+
209
373
491
599
740
626
1088
1101
1190
1988
Eqn-1
Eqn-2
Eqn-3
 
Figure 3. U+ versus y+ for Reθ from 209 to 1988.  Empirical solutions 
represented by Eqn-1, -2 and -3 are overlaid on the graph and share the 
same axes as Re=209.  U+ origins of all other graphs are incrementally 
shifted by +2 units.  
 
Interestingly, most of the data for Reθ<600 in the range 10<y
+<30 
do not seem to follow the graph defined by equation 2.  Equation 
727
2 consistently overestimates the experimental data.  This anomaly 
is not likely due to insufficient spatial resolution for cases 
Reθ<600. In general, data in the logarithmic region agree well 
with the empirical equation (Eqn 3).    
 
Figure 4 shows the graphs for the normalised u-fluctuation (u’+) 
component against the wall normal distance.  The data are 
compared with Direct Numerical Simulation (DNS) of Spalart 
(1988).  In general, the DNS data steadily increase to a peak of 
about 2.5 by y+=15, as reported in the literature (Murlis et al., 
1982; Spalart, 1988; Ching et. al, 1995).  This location coincides 
with production events in the buffer layer. Also noteworthy is an 
inflexion point at around y+=2.  After the peak value of u’+, a 
steady decrease occurs.  This decrease is characterized by 3 
inflexion points that vary with position depending on Reθ.  This 
suggests that, unlike the mean velocities, the fluctuating 
components of u beyond the viscous regime cannot be 
appropriately scaled by inner units.  
 
In general, the experimental data exhibit similar peak and 
inflexion point characteristics as the DNS data.  However, data 
less than y+<10 consistently overestimate the DNS data. This is 
likely due to inadequate spatial resolution of the measurement 
volume.  Despite this inadequacy, the location of the peak u-
fluctuations occur at y+~20, albeit at slightly higher values (2.6 < 
u’+ <2.9).  Interestingly, the DNS u’+ peak values increase with 
increasing Reθ.  In contrast, the experimental u’
+ data do not 
provide a clear trend.  Some data collapse are observed in the 
post-buffer region (30<y+>100) and show no discernable trend 
compared with the trend of increasing y+ with increasing Reθ in 
that region.  However, beyond y+=100, there is a clear trend, for a 
given u’+, that the y+ increases with increasing Reθ. The 
experimental data also show similar inflexion points similar to 
the DNS data post-peak.  Inflexion points near to y+~100 
coincide with the location of hairpin heads and VITA (variable- 
interval time-averaging) events.  However, the free-stream u’+ 
results do not converge to zero as in the DNS data.  Data collapse 
for y+>30 is likewise also not observed in the experimental data.     
10
-1
10
0
10
1
10
2
10
3
10
4
y
+
0
2
4
6
8
10
12
14
u
'+
209
373
491
599
740
626
1088
1101
1190
1988
300 -DNS
670 -DNS
1410 - DNS
 
Figure 4. u′+ versus y+ for Reθ from 209 to 1988.  DNS solutions [from 8] 
for selected Reθ are also overlaid on the same graph. Each graph is offset 
by +1 unit from the previous graph in the vertical axis. 
 
Figure 5 shows the normalized v-component fluctuations (v’+) as 
a function of wall normal distance.  Comparable DNS data from 
Spalart (1988) are also shown in the figure.  The experimental 
data largely follow the trend of the DNS graphs for regions where 
spatial resolution is not an issue as illustrated in Figure 2.    Due 
to characteristic fluctuations in the water tunnel, the value of v’+ 
for each case does not decrease to zero compared with the DNS 
data.  Peaks of v’+ are broader than u’+ and these v’+ peaks 
appear to shift to higher locations of y+ with increasing Reθ. 
Interestingly, the upturn in v’+ value after the first peak coincides 
with the maximum rate of decrease in u’+.  In contrast, DNS data 
approach to zero in the free-stream.  Again, normalization by 
inner variables fails to collapse data in the wake region.    
10
-1
10
0
10
1
10
2
10
3
10
4
y
+
0
2
4
6
8
10
12
14
v
'+
209
373
491
599
740
626
1088
1101
1190
1988
300 -DNS
670 -DNS
1410 - DNS
 
Figure 5. v′+ versus y+ for Reθ from 209 to 1988.  DNS solutions by [8] 
are also overlaid on the same graph. Each graph is offset by +1 unit from 
the previous graph in the vertical axis. 
 
Conclusions 
Particle Image Velocimetry experiments were conducted in a 
mid-tunnel region downstream of a water tunnel for a Reynolds 
number ranging from 209 to 1988. Characteristic u and v velocity 
distributions in the wall-normal direction were measured and 
compared with DNS data of similar Reynolds number range.  In 
general, experimental data nearer the wall (i.e. below y+=30) 
were found to be sensitive to the size of the interrogation volume 
and over-estimates the expected magnitudes of velocities.  The 
general shape of the experimental data graphs closely matches 
the DNS data in the regions where spatial resolution is not an 
issue.  Increases in magnitudes of u’ and v’ towards the end of 
the logarithmic layer may be due to inherent fluctuations present 
in the water tunnel warranting further investigation.   
 
Acknowledgments 
CYW acknowledges the post-doctoral fellowship provided by an 
ARC discovery grant DP0663499. 
 
References 
 
[1] Adrian, R. J., Particle-Imaging Techniques for Experimental Fluid 
Mechanics, Ann. Rev. Fluid Mech., 23, 1991, 261-304. 
[2] Adrian, R.J., Meinhart, C.D., Tomkins, C.D., Vortex organization in 
the outer region of the turbulent boundary layer,  J. Fluid Mech., 
422, 2000, 1-54. 
[3] Ching C. Y., Djenidi L., Antonia R. A., Low-Reynolds-number effects in 
a turbulent boundary layer, Exp. Fluids, 19, 1995, 61-68. 
[4] Clauser, F. H., Turbulent boundary layer, In Advances in Applied 
Mechanics, 4, 1954, 1-51. 
[5] Kostas J.,An experimental investigation of the structure of a 
turbulent backward facing step flow. PhD Thesis, Laboratory for 
Turbulence Research in Aerospace Combustion, Department of 
Mechanical Engineering, Monash University Melbourne, 2002. 
[6] Murlis, J., Tsai, H.M., Bradshaw, P., The structure of turbulent boundary 
layers at low Reynolds numbers, J .Fluid Mech., 122, 1982, 13-56. 
[7] Raffel, M., Willert, C., Kompenhans, J., Particle Image Velocimetry – A 
Practical Guide Germany, Springer-Verlag, 1998.  
[8] Spalart, P. R., Direct numerical simulation of a turbulent boundary layer 
up to Rθ=1410, J. Fluid Mech., 187, 1988, 61-98.
 
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Characterisation of a Low Reynolds Number Turbulent Boundary Layer using PIV

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