2nd UK-JAPAN Bilateral and 1st ERCOFTAC Workshop, Imperial College London
1DIAS,
2School
University of Naples Federico II, Naples (Italy)
for Engineering of Matter, Transport and Energy, Arizona State University,
AZ (USA)
3Los
Alamos National Laboratory, NM (USA)
 Multi-scale generated turbulence may lead to exciting new insights
into turbulence theory as well as important new industrial
applications:
• Turbulence generated by injecting energy over a range of length
scales;
• Uncommon fast turbulence kinetic energy decay, well modeled by a
self-preserving single lengthscale decay model (George and Wang,
POF, 2009);
• About three times higher Reynolds number Reλ than turbulence
generated by classical grids.
 PIV can be a useful tool to obtain a better understanding of the fluid
dynamics of fractal-generated turbulence.
S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge
 Despite of the geometrical complexity, the grid
features are defined by a few parameters:
• Lo an to, i.e. length and thickness of the
largest square;
• RL and Rt, i.e. the scaling factors for the length
and the thickness at each iteration (more
often the thickness ratio tr between the
largest and the smallest scale is considered
as a main parameter).
tr
RL
Rt
σ
Meff [mm]
8.5
0.5
0.490
0.25
15.8
13
0.5
0.425
0.32
15.2
17
0.5
0.389
0.37
14.6
S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge
The grids are tested in a low turbulence level open circuit wind tunnel, with
a 1,524mm long and 152.4mm wide square test section.
The fractal grid is placed at the inlet of the test section, immediately after
the contraction.
S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge
≈50mm
Measurement area
385mm
600mm
The grids are tested in a low turbulence level open circuit wind tunnel, with
a 1,524mm long and 152.4mm wide square test section.
The fractal grid is placed at the inlet of the test section, immediately after
the contraction.
S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge
u 
1  x p 
  
 v  M o t  y p 
Fig. from Raffel et al., Particle Image
Velocimetry – A practical guide, Springer
Ed. (2007)
S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge
• Optical calibration:
• Images of a target with equally spaced dots with diameter of 250μm
and spacing of 1mm are recorded to determine the magnification
map as a function of the physical space coordinates;
• Images of the particle distributions are taken simultaneously by two
cameras in a pre-processing run to determine via disparity map
computation the location of the laser sheet in the physical space to
properly set the local magnification.
• Image acquisition (5000 samples to ensure satisfactorily statistical
convergence)
• Image Processing
• IW: 32 x 32 pixels (0.63 x 0.63 mm  comparable to the laser sheet
thickness) with 75% overlap;
• Multi-pass iterative window deformation with adoption of weighting
windows in cross-correlation to enhance the spatial resolution.
S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge
Mean streamwise velocity for tr=13 and ReM=3.5∙103
U [m/s]
U [m/s]
S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge
U [m/s]
Mean streamwise velocity for tr=13 and ReM=3.5∙103
S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge
u2 [m2/s2]
tr
=13
ReM =3.5∙103
v2 [m2/s2]
S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge
tr
=13
ReM =3.5∙103
u2/ v2
S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge
tr
=13
ReM =3.5∙103
The longitudinal correlation
function changes only slightly
moving downstream,
suggesting that the integral
lengthscale increases with the
streamwise coordinate.
However, the narrow field of
view does not enable to
estimate it with good
confidence.
S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge
x/x*=0.47
tr
=13
ReM =3.5∙103

 

R11r   u1 x  r u1 x 
This is not equivalent to the
longitudinal two-point correlation
function (the velocity component
is always the streamwise one).
S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge
x/x*=0.47
tr
=13
ReM =3.5∙103

 

R22 r   u2 x  r u2 x 
This is not equivalent to the
transverse two-point correlation
function (the velocity component
is always the crosswise one).
S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge
tr
=13
ReM =3.5∙103
x/x*=0.47

 
 2
D11 r   u1 x  r   u1 x 
This is not equivalent to the
longitudinal 2nd order structure
function (the velocity component is
always the streamwise one).
S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge
tr
=13
ReM =3.5∙103
x/x*=0.47

 
 2
D22 r   u2 x  r   u2 x 
This is not equivalent to the
transverse 2nd order structure
function (the velocity component is
always the crosswise one).
S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge
Space filling square fractal grids are characterized by an unusually fast
decay: is it governed by an exponential law or a power law?
tr =13
u
2
e
ReM =11.5∙103

 xB 
C
B=0.526
C=0.262
R2=0.91
S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge
u
2
 x  B 
C
B=-0.481
C=-3.90
R2=0.91
ReM =3.5∙103
tr
B
C
R2
8.5
-0.075
0.281
0.89
13
-0.074
0.244
0.90
17
-0.127
0.261
0.85
Exponential decay
u
ReM =11.5∙103
tr
B
C
R2
8.5
0.596
0.265
0.90
13
0.526
0.262
0.91
17
0.523
0.269
0.90
S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge
2
e

 xB 
C
ReM =3.5∙103
tr
B
C
R2
8.5
-0.956
-5.50
0.91
13
-0.962
-6.24
0.91
17
-0.991
-6.15
0.91
Power-law decay
u
ReM =11.5∙103
tr
B
C
R2
8.5
-0.410
-3.55
0.92
13
-0.481
-3.90
0.91
17
-0.484
-3.88
0.87
S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge
2
 x  B 
C
ReM =11.5∙103
u2  e
S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge

 xB 
C
ReM
=11.5∙103
u
2
S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge
 x  B 
C

It is not possible to conclude if the decay law is exponential or
a power law by visual inspection or using the correlation
factor of the fitting law;

More confidence in specifying the decay law can be obtained
by increasing the measurement area in the streamwise
direction;

Even if the decay was not exponential, it is still governed by a
power law with an unusually high exponent!
S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge

W.K. George (Physics of Fluids, 1992) showed that single length
scale power law solutions of the spectral equations for the
decay of isotropic turbulence is possible;

W.K. George and H. Wang (Physics of Fluids, 2009) proposed a
viscous solution (exponential decay) and an inviscid one
(power law decay);

An important feature is that the turbulent statistics collapse
if normalized with respect u2 and λT.
S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge
tr = 13
S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge
X = 385 mm


DIRECT METHOD:
INDIRECT METHOD:
S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge
T 
T 
u
2
 u 
 
 x 
2
u2
 R11

x 2
2

DIRECT METHOD:
T 
u
2
 u 
 
 x 
2
 Very simple and straightforward application;
The noise effects are amplified by the derivative operator;
The data need to be filtered: the choice of the filter
intensity is critical.
S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge

INDIRECT METHOD:
T 
u2
 2 R11

x 2
The peak of the two-point correlation
is fitted with a parabolic function:
2

r
2
R11 r   u 1  2
 2T
S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge




INDIRECT METHOD:
T 
u2
 2 R11

x 2
The peak of the two-point correlation
is fitted with a parabolic function:
2

r
2
R11 r   u 1  2
 2T
S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge




INDIRECT METHOD:
T 
u2
 2 R11

x 2
According to Adrian and Westerweel
(2011):


~
E R11r   R11r    2 , r  d I
S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge

INDIRECT METHOD:
T 
u2
 2 R11

x 2
According to Adrian and Westerweel
(2011):


~
E R11r   R11r    2 , r  d I
At least the first 3 measurement points
have to be excluded in the fitting, since
we are using interrogation windows
with 75% overlap.
S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge

INDIRECT METHOD:
T 
u2
 2 R11

x 2
 A least square fitting may lead to a more accurate estimate of both
the Taylor lengthscale and the turbulent fluctuations;
 A Signal to Noise criterion can be introduced by considering the ratio
of the estimate peak of the two-point correlation, and the one
obtained by best fitting of the peak.
u2
u2
SNR  ~
 2
2

R11 0  u
S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge
2
2
u
u
SNR  ~
 2
2

R11 0  u
S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge
Direct method
tr =13
Indirect method
ReM =3.5∙103
S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge
tr =13 ReM =3.5∙103
S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge
tr =13
ReM =11.5∙103


DIRECT METHOD:

  3 S
INDIRECT METHOD:
2
11
 S
2
22
  15
 12 S
2
12
u2
T2
 One can use the Taylor lengthscale estimated with the indirect method.

ENERGY BALANCE:
1 q 2
  U
2 x
 One can use the relations of the power law and exponential decay.
S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge
tr =13
ReM =3.5∙103
S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge
 PIV performances are assessed for measurements in nearly
isotropic and homogeneous low-intensity turbulence; the results
are in close agreement with the literature;
 PIV complements pointwise measurement techniques by its
capability of detecting inhomogeneity and anisotropy;
 The results confirm the presence of a single lengthscale decay; it is
not possible to conclude on the nature of the decay;
 Fitting of the peak of the two-point correlation enables a more
accurate estimate of the Taylor length scale and of the dissipation;
 Three dimensional measurements (Tomo-PIV) are planned to get a
better understanding of the underlying dynamics (QR pdf,
dissipation, etc.).
S. Discetti, I.B. Ziskin, R.J. Adrian, K. Prestridge
This research was supported in part by Contract
79419-001-09, Los Alamos National Laboratory.